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2026 AMC8 #2 · Algebra · ★★
In the array shown below, three 3s are surrounded by 2s, which are in turn surrounded by a border of 1s. What is the sum of the numbers in the array?
在下面的数组中，三个数字 3 被数字 2 包围，而这些 2 又被一圈 1 包围。该数组中所有数字之和是多少？

正确答案：C · 分值：1

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2026 AMC8 #3 · Geometry · ★★
Haruki has 24 centimeters of wire. He cuts the wire and bends it into the following shapes, one at a time: - A regular hexagon with side length 5 cm - A square of area 36 cm² - A right triangle whose legs are 6 and 8 cm long
Which of the shapes can Haruki make?
Haruki 有 24 厘米长的铁丝。他剪断铁丝并把它弯成以下形状，一次做一个： - 边长为 5 cm 的正六边形 - 面积为 36 cm² 的正方形 - 两条直角边分别为 6 cm 和 8 cm 的直角三角形
Haruki 能做出哪些形状？

正确答案：D · 分值：1

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2026 AMC8 #4 · Algebra · ★
Brynn's savings decreased by 20% in July, then increased by 50% in August. Brynn's savings are now what percent of the original amount?
Brynn 的存款在七月减少了 20%，然后在八月增加了 50%。现在她的存款是原始金额的百分之多少？

正确答案：E · 分值：1

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2026 AMC8 #5 · Algebra · ★
Casey went on a road trip that covered 100 miles, stopping only for a lunch break along the way. The trip took 3 hours in total and her average speed while driving was 40 miles per hour. In minutes, how long was the lunch break?
Casey 进行了一次总路程为 100 英里的公路旅行，途中只停了一次吃午饭。整个旅程耗时 3 小时，她开车时的平均速度为每小时 40 英里。请问她的午餐休息了多长时间（以分钟计）？

正确答案：B · 分值：1

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2026 AMC8 #6 · Geometry · ★★
Peter lives near a rectangular field that is filled with blackberry bushes. The field is 10 meters long and 8 meters wide, and Peter can reach any blackberries that are within 1 meter of an edge of the field. The portion of the field he can reach is shaded in the figure below. What fraction of the area of the field can Peter reach?
Peter 住在一块长方形黑莓地附近。这块地长 10 米，宽 8 米。他能够采摘到距离地块边缘 1 米范围内的所有黑莓。下图中阴影部分表示他能到达的区域。他能到达的区域占整块地面积的几分之几？

正确答案：E · 分值：1

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2026 AMC8 #7 · Algebra · ★★
Mika would like to estimate how far she can ride a new model of electric bike on a fully charged battery. She completed two trips totaling 40 miles. The first trip used 1/2 of the total battery power, while the second trip used 3/10 of the total battery power. How many miles can this electric bike go on a fully charged battery?
Mika 想估算她新买的电动自行车充满电后最多能骑行多远。她完成了两次行程，总共骑行了 40 英里。第一次行程消耗了总电量的 1/2，第二次行程消耗了总电量的 3/10。这辆电动自行车充满电后最多能骑行多少英里？

正确答案：C · 分值：1

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2026 AMC8 #8 · Number Theory · ★★
A poll asked a number of people if they liked solving mathematics problems. Exactly 74% answered "yes." What is the fewest possible number of people who could have been asked the question?
一项民意调查询问若干人是否喜欢解数学题。恰好有 74% 的人回答“是”。最少可能有多少人接受了这项调查？

正确答案：D · 分值：1

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2026 AMC8 #10 · Counting, Probability & Statistics · ★★
Five runners completed the grueling Xmarathon: Luke, Melina, Nico, Olympia, and Pedro.Nico finished 11 minutes behind Pedro.Olympia finished 2 minutes ahead of Melina, but 3 minutes behind Pedro.Olympia finished 6 minutes ahead of Luke. Which runner finished fourth?
五名选手完成了艰苦的 X 马拉松比赛：Luke、Melina、Nico、Olympia 和 Pedro。已知：Nico 比 Pedro 晚了 11 分钟；Olympia 比 Melina 早 2 分钟，但比 Pedro 晚 3 分钟；Olympia 比 Luke 早 6 分钟。 谁是第四名？

正确答案：A · 分值：1

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2026 AMC8 #11 · Geometry · ★★★
Squares of side length 1, 1, 2, 3, and 5 are arranged to form the rectangle shown below. A curve is drawn by inscribing a quarter circle in each square and joining the quarter circles in order, from shortest to longest. What is the length of the curve?
边长分别为 1、1、2、3 和 5 的正方形被排列成如下所示的矩形。在每个正方形内画一个四分之一圆，并按从小到大的顺序将这些四分之一圆连接起来形成一条曲线。这条曲线的长度是多少？

正确答案：B · 分值：1

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2026 AMC8 #12 · Algebra · ★★★
In the figure below, each circle will be filled with a digit from 1 to 6. Each digit must appear exactly once. The sum of the digits in neighboring circles is shown in the box between them. What digit must be placed in the top circle?
下图中的每个圆圈需填入 1 到 6 中的一个数字，且每个数字恰好使用一次。相邻两个圆圈中的数字之和标在它们之间的方框中。顶部圆圈中必须填入哪个数字？

正确答案：D · 分值：1

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2026 AMC8 #13 · Geometry · ★★★
The figure below shows a tiling of 1×1 unit squares. Each row of unit squares is shifted horizontally by half a unit relative to the row above it. A shaded square is drawn on top of the tiling. Each vertex of the shaded square is a vertex of one of the unit squares. In square units, what is the area of the shaded square?
下图展示了一种由 1×1 单位正方形组成的铺砖图案。每一行相对于上一行水平偏移半个单位。图中还有一个覆盖在铺砖上的阴影正方形，其每个顶点都是某个单位正方形的顶点。这个阴影正方形的面积是多少（单位：平方单位）？

正确答案：A · 分值：1

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2026 AMC8 #14 · Algebra · ★★★
Jami picked three equally spaced integer numbers on the number line. The sum of the first and the second numbers is 40, while the sum of the second and third numbers is 60. What is the sum of all three numbers?
Jami 在数轴上选取了三个等间距的整数。第一个数与第二个数之和为 40，第二个数与第三个数之和为 60。这三个数的总和是多少？

正确答案：B · 分值：1

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2026 AMC8 #15 · Geometry · ★★★
Elijah has a large collection of identical wooden cubes which are white on 4 faces and gray on 2 faces that share an edge. He glues some cubes together face-to-face. The figure below shows 2 cubes being glued together, leaving 3 gray faces visible. What is the fewest number of cubes that he could glue together to ensure that no gray faces are visible, no matter how he rotates the figure?
Elijah 有很多相同的木制小立方体，每个立方体有 4 个白色面和 2 个灰色面，且这两个灰色面共享一条棱。他将一些立方体面对面粘在一起。下图展示了两个立方体粘合后，露出 3 个灰色面的情形。他至少需要粘合多少个小立方体，才能确保无论怎样旋转整个图形，都看不到任何灰色面？

正确答案：A · 分值：1

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2026 AMC8 #16 · Number Theory · ★★★
Consider all positive four-digit integers consisting of only even digits. What fraction of these integers are divisible by 4?
考虑所有由偶数数字组成的四位正整数。其中有多少比例的数能被 4 整除？

正确答案：D · 分值：1

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2026 AMC8 #17 · Counting, Probability & Statistics · ★★★
Four students are seated in a row. They chat with the people sitting next to them, then rearrange themselves so that they are no longer seated next to any of the same people. How many rearrangements are possible?
四名学生坐在一排。他们先和相邻的人聊天，然后重新排列座位，使得每个人都不再与之前相邻的人坐在一起。有多少种这样的重新排列方式？

正确答案：A · 分值：1

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2026 AMC8 #18 · Number Theory · ★★★
In how many ways can 60 be written as the sum of two or more consecutive odd positive integers that are arranged in increasing order?
有多少种方式可以将 60 表示为两个或更多个连续奇正整数（按递增顺序排列）的和？

正确答案：B · 分值：1

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2026 AMC8 #19 · Algebra · ★★★
Miguel is walking with his dog, Luna. When they reach the entrance to a park, Miguel throws a ball straight ahead and continues to walk at a steady pace. Luna sprints toward the ball, which stops by a tree. As soon as the dog reaches the ball, she brings it back to Miguel. Luna runs 5 times faster than Miguel walks. What fraction of the distance from the entrance to the tree will Miguel have walked when Luna returns the ball to him?
Miguel 带着他的狗 Luna 散步。当他们走到公园入口时，Miguel 向前扔出一个球并继续匀速行走。Luna 冲向球，球停在一棵树旁。Luna 一拿到球就立刻跑回 Miguel 身边。Luna 的奔跑速度是 Miguel 步行速度的 5 倍。当 Luna 把球送回给 Miguel 时，Miguel 已经走了从入口到树这段距离的几分之几？

正确答案：D · 分值：1

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2026 AMC8 #20 · Counting, Probability & Statistics · ★★★
The land of Catania uses gold coins and silver coins. Gold coins are 1 mm thick and silver coins are 3 mm thick. In how many ways can Taylor make a stack of coins that is 8 mm tall using any arrangement of gold and silver coins, assuming order matters?
Catania 国使用金币和银币。金币厚 1 毫米，银币厚 3 毫米。Taylor 想用任意数量和顺序的金币与银币堆叠出一个总高为 8 毫米的硬币堆（顺序不同视为不同方式）。共有多少种堆法？

正确答案：D · 分值：1

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2026 AMC8 #21 · Counting, Probability & Statistics · ★★★
Charlotte the spider is walking along a web shaped like a 5-pointed star, shown in the figure below. The web has 5 outer points and 5 inner points. Each time Charlotte reaches a point, she randomly chooses a neighboring point and moves to that point. Charlotte starts at one of the outer points and makes 3 moves (re-visiting points is allowed). What is the probability she is now at one of the outer points of the star?
Charlotte 是一只蜘蛛，她在一张形如五角星的网上爬行（如下图所示）。这张网有 5 个外顶点和 5 个内顶点。每次 Charlotte 到达一个顶点时，会随机选择一个相邻顶点并移动过去（允许重复访问）。她从一个外顶点出发，共移动 3 次。此时她位于外顶点的概率是多少？

正确答案：B · 分值：1

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2026 AMC8 #22 · Counting, Probability & Statistics · ★★★★★
The integers from 1 to 25 are arbitrarily separated into five groups of 5 numbers each. The median of each group is identified. Let M equal the median of the five medians. What is the least possible value of M?
将 1 到 25 的整数任意分成五组，每组 5 个数。找出每组的中位数，再求这五个中位数的中位数 M。M 的最小可能值是多少？

正确答案：A · 分值：1

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2026 AMC8 #23 · Geometry · ★★★★
Lakshmi has 5 round coins of diameter 4 centimeters. She arranges the coins in 2 rows on a table top, as shown below, and wraps an elastic band tightly around them. In centimeters, what will be the length of the band?
Lakshmi 有 5 枚直径为 4 厘米的圆形硬币。她将这些硬币按如下方式在桌面上排成两行，并用一根橡皮筋紧紧围住它们。橡皮筋的长度是多少厘米？

正确答案：C · 分值：1

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2026 AMC8 #24 · Number Theory · ★★★★
The notation n! (read "nn factorial") is defined as the product of the first nn positive integers. (For example, 3!=1⋅2⋅3=63! = 1 \cdot 2 \cdot 3 = 6.) Define the superfactorial of a positive number, denoted by n!n^!, to be the product of the first nn factorials. (For example, 3!=1!⋅2!⋅3!=123^! = 1! \cdot 2! \cdot 3! = 12.) How many factors of 7 appear in the prime factorization of 51!51^!, the superfactorial of 51?
记号 n!（读作"nn 阶乘"）定义为前 nn 个正整数的乘积（例如 3!=1⋅2⋅3=63! = 1 \cdot 2 \cdot 3 = 6）。定义超阶乘 n!n^! 为前 nn 个阶乘的乘积（例如 3!=1!⋅2!⋅3!=123^! = 1! \cdot 2! \cdot 3! = 12）。在 51!51^! 的质因数分解中，因子 7 出现了多少次？

正确答案：E · 分值：1

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2026 AMC8 #25 · Geometry · ★★★★
In an equiangular hexagon, all interior angles measure 120°. An example of such a hexagon with side lengths 2, 3, 1, 3, 2, and 2 is shown below, inscribed in equilateral triangle ABC. Consider all equiangular hexagons with positive integer side lengths that can be inscribed in △ABC, with all six vertices on the sides of the triangle. What is the total number of such hexagons? Hexagons that differ only by a rotation or a reflection are considered the same.
在一个等角六边形中，所有内角均为 120°。下图展示了一个边长依次为 2、3、1、3、2、2 的例子，它内接于一个等边三角形 ABC 中。考虑所有边长为正整数、且六个顶点都在 △ABC 三边上的等角六边形。若两个六边形仅通过旋转或反射重合，则视为相同。这样的六边形共有多少个？

正确答案：E · 分值：1

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2025 AMC8 #1 · Geometry · ★
The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire 4×44\times4 grid is covered by the star?
下图所示的八角星是一种流行的拼布图案。请问这个星形图案的面积占整个4×4网格的百分之多少？

正确答案：B · 分值：1

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2025 AMC8 #2 · Algebra · ★
The table below shows the ancient Egyptian hieroglyphs that were used to represent different numbers.
For example, the number 32 was represented by the hieroglyphs ∩∩∩∣∣\cap \cap \cap || . What number is represented by the following combination of hieroglyphs?
下表列出了古埃及象形文字中用来表示不同数字的符号。例如，数字32用（如图所示的象形文字）表示。请问以下这组象形文字表示的是哪个数字？

正确答案：B · 分值：1

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2025 AMC8 #3 · Algebra · ★
Buffalo Shuffle-o is a card game in which all the cards are distributed evenly among all players at the start of the game. When Annika and 3 of her friends play Buffalo Shuffle-o, each player is dealt 15 cards. Suppose 2 more friends join the next game. How many cards will be dealt to each player?
Buffalo Shuffle-o是一款卡牌游戏。游戏开始时，所有卡牌会平均分配给所有玩家。Annika和她的三位朋友一起玩Buffalo Shuffle-o时，每位玩家会得到15张卡牌。假设下一局又有2位朋友加入，请问每位玩家将会得到多少张卡牌？

正确答案：C · 分值：1

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2025 AMC8 #4 · Algebra · ★
Lucius is counting backward by 7 s. His first three numbers are 100 , 93 , and 86 . What is his 10 th number?
Lucius正在以7为间隔进行倒数。他倒数的前三个数是100、93和86。请问倒数的第10个数是多少？

正确答案：B · 分值：1

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2025 AMC8 #5 · Geometry · ★★
Betty drives a truck to deliver packages in a neighborhood whose street map is shown below. Betty starts at the factory (labled FF ) and drives to location AA , then BB , then CC , before returning to FF . What is the shortest distance, in blocks, she can drive to complete the route?
Betty驾驶卡车在一个社区送货，该社区的街道地图如下所示。Betty从工厂（标记为F）出发，依次到达A地、B地、C地，最后返回F地。请问她驾车走完这条路线的最短距离是多少？以街区为单位。

正确答案：C · 分值：1

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2025 AMC8 #6 · Number Theory · ★
Sekou writes the numbers 15, 16, 17, 18, 19. After he erases one of his numbers, the sum of the remaining four numbers is a multiple of 4. Which number did he erase?
Sekou写下数字15、16、17、18、19。他擦去其中一个数字后，剩下的四个数字之和是4的倍数。请问他擦去了哪个数字？

正确答案：C · 分值：1

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2025 AMC8 #7 · Counting, Probability & Statistics · ★★
On the most recent exam on Prof. Xochi's class,
5 students earned a score of at least 95% , 13 students earned a score of at least 90% , 27 students earned a score of at least 85% , 50 students earned a score of at least 80% ,
How many students earned a score of at least 80% and less than 90% ?
在Xochi教授班上最近的一次考试中，
5名学生的得分率至少达到了95%， 13名学生的得分率至少达到了90%， 27名学生的得分率至少达到了85%， 50名学生的得分率至少达到了80%。
请问有多少名学生的得分率至少达到了80%，但小于90%？

正确答案：D · 分值：1

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2025 AMC8 #8 · Geometry · ★★
Isaiah cuts open a cardboard cube along some of its edges to form the flat shape shown on the right, which has an area of 18 square centimeters. What is the volume of the cube in cubic centimeters?
Isaiah沿着一个硬纸板立方体的部分边缘将其剪开，形成右下图所示的平面图形，该图形的面积为18平方厘米。请问这个立方体的体积是多少立方厘米？

正确答案：A · 分值：1

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2025 AMC8 #9 · Counting, Probability & Statistics · ★★
Ningli looks at the 6 pairs of numbers directly across from each other on a clock. She takes the average of each pair of numbers. What is the average of the resulting 6 numbers?
Ningli观察时钟上6对正对着的数字，并计算每对数字的平均值。请问经过计算后得到的6个数的平均值是多少？

正确答案：B · 分值：1

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2025 AMC8 #10 · Geometry · ★★
In the figure below, ABCDABCD is a rectangle with sides of length AB = 5 inches and AD = 3 inches. Rectangle ABCDABCD is rotated 90∘90^\circ clockwise around the midpoint of side DCDC to give a second rectangle. What is the total area, in square inches, covered by the two overlapping rectangles?
如图所示，ABCD是一个长方形，其边长AB = 5英寸，AD = 3英寸。长方形ABCD绕DC边的中点顺时针旋转90°，得到第二个长方形。请问这两个重叠长方形覆盖的总面积是多少平方英寸？

正确答案：D · 分值：1

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2025 AMC8 #11 · Geometry · ★★★
AAtetromino\textit{tetromino} consists of four squares connected along their edges. There are five possible tetromino shapes, II , OO , LL , TT , and SS , shown below, which can be rotated or flipped over. Three tetrominoes are used to completely cover a 3×43\times4 rectangle. At least one of the tiles is an SS tile. What are the other two tiles?
一个四格拼板由四个正方形沿边相连组成。下图展示了五种可能的四格拼板形状：I、O、L、T和S，这些形状可以旋转或翻转。用三个四格拼板可以完全覆盖一个3×4的矩形，其中至少有一个是S形拼板。请问另外两个拼板的形状是什么？

正确答案：C · 分值：1

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2025 AMC8 #12 · Geometry · ★★★
The region shown below consists of 24 squares, each with side length 1 centimeter. What is the area, in square centimeters, of the largest circle that can fit inside the region, possibly touching the boundaries?
下图所示区域由24个边长为1厘米的正方形组成。请问该区域内正好能够容纳的最大圆的面积是多少平方厘米？（最大圆可能会接触到边界）

正确答案：C · 分值：1

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2025 AMC8 #13 · Number Theory · ★★★
Each of the even numbers 2,4,6,…,502, 4, 6, \ldots, 50 is divided by 7 . The remainders are recorded. Which histogram displays the number of times each remainder occurs?
将偶数2、4、6、……、50分别除以7，并记录下余数。请问下方哪个直方图显示了每个余数出现的次数？

正确答案：A · 分值：1

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2025 AMC8 #14 · Counting, Probability & Statistics · ★★★
A number NN is inserted into the list 2 , 6 , 7 , 7 , 28 . The mean is now twice as great as the median. What is NN ?
在一列数字2、6、7、7、28中插入一个数字N，使得这列数字的平均值是中位数的两倍。请问N是多少？

正确答案：E · 分值：1

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2025 AMC8 #15 · Counting, Probability & Statistics · ★★★
Kei draws a 6 -by- 6 grid. He colors 13 of the unit squares silver and the remaining squares gold. Kei then folds the grid in half vertically, forming pairs of overlapping unit squares. Let mm and MM equal the least and greatest possible number of gold-on-gold pairs, respectively. What is the value of m+M ?
Kei画了一个6×6的网格，并将其中13个单元格涂成银色，其余单元格涂成金色。然后，Kei将网格垂直对折，形成若干对重叠的单元格。设m和M分别为两个金色单元格重叠对数的最小和最大可能值。请问m + M的值是多少？

正确答案：C · 分值：1

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2025 AMC8 #16 · Counting, Probability & Statistics · ★★★
Five distinct integers from 1 to 10 are chosen, and five distinct integers from 11 to 20 are chosen. No two numbers differ by exactly 10 . What is the sum of the ten chosen numbers?
从1到10之间选择五个不同的整数，从11到20之间选择五个不同的整数。其中，没有两个数的差值恰好为10。请问选出的这十个数之和是多少？

正确答案：C · 分值：1

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2025 AMC8 #17 · Algebra · ★★★
In the land of Markovia, there are three cities: AA , BB , and CC . There are 100 people who live in AA , 120 who live in BB , and 160 who live in CC . Everyone works in one of the three cities, and a person may work in the same city where they live. In the figure below, an arrow pointing from one city to another is labeled with the fraction of people living in the first city who work in the second city. (For example, 14\displaystyle \frac{1}{4} of the people who live in AA work in BB .) How many people work in AA ?
马克维亚大陆有三座城市：A城、B城和C城。A城有100人居住，B城有120人居住，C城有160人居住。每个人都在A城、B城或C城中的一个城市工作，且有的人可能在自己居住的城市工作。下图中，从一座城市指向另一座城市的箭头上，标注了居住在第一座城市的人群中，在第二座城市工作的比例。（例如，居住在A城的人中，有1/4在B城工作。）请问有多少人在A城工作？

正确答案：D · 分值：1

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2025 AMC8 #18 · Geometry · ★★★
The circle shown below on the left has a radius of 1 unit. The region between the circle and the inscribed square is shaded. In the circle shown on the right, one quarter of the region between the circle and the inscribed square is shaded. The shaded regions in the two circles have the same area. What is the radius RR , in units, of the circle on the right?
左下图的圆的半径为1个单位，阴影部分为圆和其内接正方形之间的区域。在右下图的圆中，阴影部分为圆和其内接正方形之间区域的四分之一。两个圆中的阴影区域面积相同。请问右下图的圆的半径R是多少个单位？

正确答案：B · 分值：1

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2025 AMC8 #19 · Algebra · ★★★
Two towns, AA and BB , are connected by a straight road that is 15 miles long. Travelling from city AA to town BB , the speed limit changes every 5 miles: from 25 to 40 to 20 miles per hour (mph). Two cars, one at town AA and one at town BB , start moving toward each other at the same time. They drive at exactly the speed limit in each portion of the road. How far from town AA , in miles, will the two cars meet?
A镇和B镇之间由一条15英里长的笔直公路相连。从A镇行驶到B镇，限速每5英里变化一次：依次为25英里/小时、40英里/小时和20英里/小时。两辆汽车，一辆在A镇，另一辆在B镇，它们同时出发相向而行。两车在各路段上都严格按照限速行驶。请问两车将在距离A镇多少英里处相遇？

正确答案：D · 分值：1

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2025 AMC8 #20 · Algebra · ★★★
Sarika, Dev, and Rajiv are sharing a large block of cheese. They take turns cutting off half of what remains and eating it: first Sarika eats half of the cheese, then Dev eats half of the remaining half, then Rajiv eats half of what remains, then back to Sarika, and so on. They stop when the cheese is too small to see. About what fraction of the original block of cheese does Sarika eat in total?
Sarika、Dev和Rajiv正在分享一大块奶酪。他们轮流切下奶酪剩余部分的一半并吃掉：首先Sarika吃掉一半奶酪，接着Dev吃掉剩余部分的一半，随后Rajiv吃掉剩余部分的一半，然后又轮到Sarika，如此循环往复，直到奶酪小到看不见为止。请问Sarika一共大约吃掉了这块奶酪的几分之几？

正确答案：A · 分值：1

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2025 AMC8 #21 · Counting, Probability & Statistics · ★★★★
The Konigsberg School has assigned grades 1 through 7 to pods AA through GG , one grade per pod. Some of the pods are connected by walkways, as shown in the figure below. The school noticed that each pair of connected pods has been assigned grades differing by 1 or more grade levels. (For example, grades 1 and 2 will not be in pods directly connected by a walkway.) What is the sum of the grade levels assigned to pods C, E , and FF ?
哥尼斯堡学校将1至7年级的学生分配到A至G教学区，每个教学区分配一个年级。如下图所示，部分教学区通过走廊相连。学校注意到，每两个相连的教学区分配的年级数之差不低于2（例如，1年级和2年级的教学区不会直接通过走廊相连）。请问，分配到C、E和F教学区的年级数总和是多少？

正确答案：C · 分值：1

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2025 AMC8 #22 · Number Theory · ★★★★
A classroom has a row of 35 coat hooks. Paulina likes coats to be equally spaced, so that there is the same number of empty hooks before the first coat, after the last coat, and between every coat and the next one. Suppose there is at least 1 coat and at least 1 empty hook. How many different numbers of coats can satisfy Paulina's pattern?
教室里有一排35个衣钩。Paulina希望衣服之间的间隔相等，使得第一件衣服前、最后一件衣服后以及每两件衣服之间的空衣钩数量相同。假设至少有1件衣服且至少有1个空衣钩。请问有多少种不同的衣服数量可以满足Paulina的要求？

正确答案：D · 分值：1

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2025 AMC8 #23 · Number Theory · ★★★★
How many four-digit numbers have all three of the following properties?
(I) The tens and ones digit are both 9.
(II) The number is 1 less than a perfect square.
(III) The number is the product of exactly two prime numbers.
请问有多少个四位数同时满足以下三个条件？
（一）十位上的数字和个位上的数字都是9。
（二）该数比一个完全平方数小1。
（三）该数正好是两个质数的乘积。

正确答案：B · 分值：1

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2025 AMC8 #24 · Geometry · ★★★★
In trapezoid ABCDABCD , angles BB and CC measure 60∘60^\circ and AB = DC . The side lengths are all positive integers, and the perimeter of ABCDABCD is 30 units. How many non-congruent trapezoids satisfy all of these conditions?
在梯形ABCD中，∠B = ∠C = 60°，且AB = DC。该梯形的各边长均为正整数，其周长为30个单位。请问一共有多少个满足以上全部条件的非全等梯形？

正确答案：E · 分值：1

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2025 AMC8 #25 · Counting, Probability & Statistics · ★★★★★
Makayla finds all the possible ways to draw a path in a 5×55 \times 5 diamond-shaped grid. Each path starts at the bottom of the grid and ends at the top, always moving one unit northeast or northwest. She computes the area of the region between each path and the right side of the grid. Two examples are shown in the figures below. What is the sum of the areas determined by all possible paths?
Makayla在一个5×5的菱形网格中找到了所有可能的绘制路径的方式。每条路径从网格底部开始，到网格的顶部结束，总是朝东北或西北方向移动一个单位。她计算了每条路径与网格右侧边缘之间的区域面积。下图展示了两个示例。请问所有可能路径与网格右侧边缘之间的区域面积之和是多少？

正确答案：B · 分值：1

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2024 AMC8 #1 · Algebra · ★
What is the ones digit of
请问下方算式的个位数是几？
222,222−22,222−2,222−222−22−2?222,222 - 22,222 - 2,222 - 222 - 22 - 2?

正确答案：B · 分值：1

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2024 AMC8 #2 · Algebra · ★
What is the value of this expression in decimal form? 4411+11044+441100\displaystyle \frac{44}{11} + \frac{110}{44} + \frac{44}{1100}
请问下列表达式的值用小数可以表示为哪一项？

正确答案：C · 分值：1

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2024 AMC8 #3 · Geometry · ★★
Four squares of side length 4, 7, 9, and 10 units are arranged in increasing size order so that their left edges and bottom edges align. The squares alternate in color white-gray-white-gray, respectively, as shown in the figure. What is the area of the visible gray region in square units?
将四个边长分别为 4、7、9、10 个单位的正方形从小到大依次排列，使得它们的左侧边和底边分别对齐。四个正方形的颜色按照白色-灰色-白色-灰色的顺序交替出现，如图所示。请问灰色可见区域的面积为多少个平方单位？

正确答案：E · 分值：1

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2024 AMC8 #4 · Number Theory · ★
When Yunji added all the integers from 1 through 9, she mistakenly left out a number. Her incorrect sum turned out to be a square number. Which number did Yunji leave out?
Yunji 将 1到 9之间的所有整数相加时，漏加了一个数字，得到的错误结果是一个平方数。请问Yunji 漏加的是哪个数字？

正确答案：E · 分值：1

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2024 AMC8 #5 · Counting, Probability & Statistics · ★★
Aaliyah rolls two standard 6-sided dice. She notices that the product of the two numbers rolled is a multiple of 6. Which of the following integers cannot be the sum of the two numbers?
Aaliyah投掷两枚标准的六面殷子。她发现掷出的两个点数之积是6的倍数，请问下列哪个整数不可能是这两个点数之和？

正确答案：B · 分值：1

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2024 AMC8 #6 · Geometry · ★★
Sergei skated around an ice rink, gliding along different paths. The gray lines in the figures below show four of the paths labeled P, Q, R, and S. What is the sorted order of the four paths from shortest to longest?
Sergei在滑冰场沿着不同路径滑冰。下图中的灰色线条表示4条不同路径，分别标记为P、Q、R、S。请问这4条路径从短到长的正确排列顺序是什么？

正确答案：D · 分值：1

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2024 AMC8 #7 · Geometry · ★★
AA3×73 \times 7 rectangle is covered without overlap by 3 shapes of tiles: 2×22 \times 2, 1×41\times4, and 1×11\times1, shown below. What is the minimum possible number of 1×11\times1 tiles used?
一个3×7的矩形被下方3种规格分别为2×2、1×4和1×1的瓷砖所覆盖，且各瓷砖之间互不重叠。请问最少可能会用到多少个1×1的瓷砖？

正确答案：E · 分值：1

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2024 AMC8 #8 · Counting, Probability & Statistics · ★★
On Monday Taye has $2. Every day, he either gains $3 or doubles the amount of money he had on the previous day. How many different dollar amounts could Taye have on Thursday, 3 days later?
周一那天，Taye有2美元。每天，他要么获得3美元，要么拥有的金额变成前一天的两倍。请问三天后，也就是周四，Taye 拥有的金额可能有多少种不同的结果?

正确答案：D · 分值：1

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2024 AMC8 #9 · Algebra · ★★
All of the marbles in Maria's collection are red, green, or blue. Maria has half as many red marbles as green marbles and twice as many blue marbles as green marbles. Which of the following could be the total number of marbles in Maria's collection?
Maria收藏有红色、绿色、蓝色三种颜色的大理石，其中红色大理石的数量是绿色大理石数量的一半，蓝色大理石数量是绿色大理石数量的两倍。请问Maria收藏的大理石总数可能是多少？

正确答案：E · 分值：1

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2024 AMC8 #10 · Algebra · ★
In January 1980, the Mauna Loa Observatory recorded carbon dioxide (CO₂) levels of 338 ppm (parts per million).
Over the years, the average CO₂ reading has increased by about 1.515 ppm per year.
What is the expected CO₂ level in January 2030, in ppm? Round your answer to the nearest integer.
1980年1月，莫纳罗亚天文台记录的二氧化碳浓度为338ppm（百万分之一)。近年来，二氧化碳浓度平均每年增加约1.515ppm。请问2030年1月的二氧化碳浓度预计为多少ppm？将答案四舍五入到最接近的整数。

正确答案：B · 分值：1

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2024 AMC8 #11 · Geometry · ★★★
The coordinates of △ABC are A(5, 7), B(11, 7), and C(3, y), with y > 7.
The area of △ABC is 12.
What is the value of y?
△ABC 的顶点坐标分别为 A(5,7)、B(11,7)和 C(3,y)，其中 y>7。已知△ABC 的面积为12，请问y的值为多少？

正确答案：D · 分值：1

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2024 AMC8 #12 · Algebra · ★★★
Rohan keeps a total of 90 guppies in 4 fish tanks. • There is 1 more guppy in the 2nd tank than in the 1st tank. • There are 2 more guppies in the 3rd tank than in the 2nd tank. • There are 3 more guppies in the 4th tank than in the 3rd tank.
How many guppies are in the 4th tank?
Rohan 的 4 个鱼缸中一共有 90 条孔雀鱼。
• 第二个鱼缸比第一个鱼缸多 1 条孔雀鱼。 • 第三个鱼缸比第二个鱼缸多 2 条孔雀鱼。 • 第四个鱼缸比第三个鱼缸多 3 条孔雀鱼。
请问第四个鱼缸中有多少条孔雀鱼？

正确答案：E · 分值：1

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2024 AMC8 #13 · Counting, Probability & Statistics · ★★★
Buzz Bunny is hopping up and down a set of stairs, one step at a time.
In how many ways can Buzz Bunny start on the ground, make a sequence of 6 hops, and end up back on the ground?
(For example, one sequence of hops is up-up-down-down-up-down.)
小兔子Buzz在台阶上跳上跳下，每次跳一个台阶。Buzz从地面开始跳跃，连续跳跃6次。请问Buzz有几种方式，最后可以跳回地面？ （例如其中一种方式为上-上-下下-上-下。）

正确答案：B · 分值：1

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2024 AMC8 #14 · Counting, Probability & Statistics · ★★★
The one-way routes connecting towns A, M, C, X, Y, and Z are shown in the figure below (not drawn to scale).
The distances in kilometers along each route are marked.
Traveling along these routes, what is the shortest distance from A to Z in kilometers?
如图所示，A、M、C、X、Y、Z几座小镇之间通过单行道相连。图中标明了每条单行道的长度，单位为千米。请问沿单行道从A行驶到Z的最短距离为多少千米？（图形未按比例绘制）

正确答案：A · 分值：1

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2024 AMC8 #15 · Number Theory · ★★★
Let the letters F, L, Y, B, U, and G represent distinct digits.
Suppose F‾ L‾ Y‾ F‾ L‾ Y‾\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}}\,\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} is the greatest six-digit number that satisfies the following equation:
8⋅F‾ L‾ Y‾ F‾ L‾ Y‾=B‾ U‾ G‾ B‾ U‾ G‾8 \cdot \underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}}\,\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} = \underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}\,\underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}
What is the value of F‾ L‾ Y‾+B‾ U‾ G‾\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} + \underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}?
用 F、L、Y、B、U、G 表示不同数字。
若 F‾ L‾ Y‾ F‾ L‾ Y‾\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}}\,\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} 为满足下列等式的最大六位数：
8⋅F‾ L‾ Y‾ F‾ L‾ Y‾=B‾ U‾ G‾ B‾ U‾ G‾8 \cdot \underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}}\,\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} = \underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}\,\underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}}
求 F‾ L‾ Y‾+B‾ U‾ G‾\underline{\mathrm{F}}\,\underline{\mathrm{L}}\,\underline{\mathrm{Y}} + \underline{\mathrm{B}}\,\underline{\mathrm{U}}\,\underline{\mathrm{G}} 的值。

正确答案：C · 分值：1

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2024 AMC8 #16 · Counting, Probability & Statistics · ★★★
Minh enters the numbers 1 through 81 into the cells of a 9 × 9 grid in some order. She calculates the product of the numbers in each row and column. What is the least number of rows and columns that could have a product divisible by 3?
Minh按照某种顺序将数字1到81填入一个9×9的网格中，并计算出每行每列的数字之积。请问至少有多少行和列的乘积可以被3整除？

正确答案：D · 分值：1

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2024 AMC8 #17 · Counting, Probability & Statistics · ★★★
A chess king is said to attack all the squares one step away from it, horizontally, vertically, or diagonally. For instance, a king on the center square of a 3 × 3 grid attacks all 8 other squares, as shown below. Suppose a white king and a black king are placed on different squares of a 3 × 3 grid so that they do not attack each other. In how many ways can this be done?
在国际象棋中，"国王"可以进攻横向、纵向或对角线方向上所有距离一步的棋格。如下图所示，在一个3×3棋盘中，位于中心位置的"国王"可以进攻其他8个棋格。假设要在一个3×3棋盘的不同方格中放入一枚白色"国王"和一枚黑色"国王"，请问有多少种放置方式可以使得这两个"国王"不会互相进攻？

正确答案：E · 分值：1

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2024 AMC8 #18 · Geometry · ★★★
Three concentric circles centered at O have radii of 1, 2, and 3. Points B and C lie on the largest circle. The region between the two smaller circles is shaded, as is the portion of the region between the two larger circles bounded by central angle ∠BOC, as shown in the figure below. Suppose the shaded and unshaded regions are equal in area. What is the measure of ∠BOC in degrees?
以点 O 为圆心的三个同心圆的半径分别为 1、2、3。点 B 和点 C 位于最大圆上。两个较小圆之间的区域被涂上阴影，两个较大圆之间且位于圆心角 ∠BOC 内的区域也被涂上阴影，如图所示。若阴影区域与非阴影区域面积相等，请问 ∠BOC 的度数是多少？

正确答案：A · 分值：1

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2024 AMC8 #19 · Counting, Probability & Statistics · ★★★
Jordan owns 15 pairs of sneakers.
Three fifths of the pairs are red and the rest are white. Two thirds of the pairs are high-top and the rest are low-top.
The red high-top sneakers make up a fraction of the collection. What is the least possible value of this fraction?
Jordan 有 15 双运动鞋。其中 35\displaystyle \frac{3}{5} 的鞋是红色，其余为白色；其中 23\displaystyle \frac{2}{3} 的鞋是高帮，其余为低帮。红色高帮运动鞋的数量占全部鞋数的一个分数。这个分数的最小可能值是多少？

正确答案：C · 分值：1

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2024 AMC8 #20 · Geometry · ★★★
Any three vertices of the cube PQRSTUVW, shown in the figure below, can be connected to form a triangle.
For example, vertices P, Q, and R can be connected to form an isosceles △PQR.
How many of these triangles are equilateral and contain P as a vertex?
如图所示，立方体PQRSTUVW上任意三个顶点相连可以构成一个三角形（例如，顶点P,Q，R相连可以构成一个等腰三角形△PQR）。请问在上述三角形中， 有多少个是以P为一个顶点的等边三角形？

正确答案：D · 分值：1

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2024 AMC8 #21 · Algebra · ★★★
A group of frogs (called an army) is living in a tree. A frog turns green when in the shade and turns yellow when in the sun. Initially, the ratio of green to yellow frogs was 3:1. Then 3 green frogs moved to the sunny side and 5 yellow frogs moved to the shady side. Now the ratio is 4:1. What is the difference between the number of green frogs and the number of yellow frogs now?
一群青蛙（号称青蛙军团）生活在树上。它们在树荫中呈绿色，在阳光下又变成黄色。刚开始，绿色青蛙和黄色青蛙的数量之比是3：1。随后，3只绿色青蛙跳到阳光下，5只黄色青蛙跳到树荫下，此时数量之比变成4：1。请问现在绿色青蛙和黄色青蛙的数量相差多少？

正确答案：E · 分值：1

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2024 AMC8 #22 · Geometry · ★★★★
A roll of tape is 4 inches in diameter and is wrapped around a ring that is 2 inches in diameter. A cross section of the tape is shown in the figure below. The tape is 0.015 inches thick. If the tape is completely unrolled, approximately how long would it be? Round your answer to the nearest 100 inches.
下图为一卷胶带的横截面。胶带直径为4英寸，其中包裹着一个直径为2英寸的圆环。胶带厚度为0.015英寸。请问这卷胶带全部展开大约有多少英寸？请将答案四舍五入到最接近的百位数。

正确答案：B · 分值：1

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2024 AMC8 #23 · Geometry · ★★★★★
Rodrigo has a very large piece of graph paper. First he draws a line segment connecting point (0, 4) to point (2, 0) and colors the 4 cells whose interiors intersect the segment, as shown below. Next Rodrigo draws a line segment connecting point (2000, 3000) to point (5000, 8000). Again he colors the cells whose interiors intersect the segment. How many cells will he color this time?
Rodrigo有一张非常大的方格纸。他先画了一条线段连接点（O,4)和点（2,0），然后为内部与该线段相交的4个方格上色，如图所示。紧接着Rodrigo又画了一条线段连接点(2000,3000）和点（5000,8000)，并为内部与该线段相交的方格上色。 请问这次Rodrigo要给多少个方格上色？

正确答案：C · 分值：1

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2024 AMC8 #24 · Geometry · ★★★★
Jean made a piece of stained glass art in the shape of two mountains, as shown in the figure below.
One mountain peak is 8 feet high and the other peak is 12 feet high. Each peak forms a 90° angle, and the straight sides of the mountains form 45° angles with the ground.
The artwork has an area of 183 square feet. The sides of the mountains meet at an intersection point near the center of the artwork, h feet above the ground.
What is the value of h?
Jean制作了一件两座山形状的彩色玻璃艺术品，如下图所示。一座山峰高8英尺，另一座山峰高12英尺。每座山的顶部都形成一个90°的角，两座山的直边都与地面形成一个45°的夹角。这件艺术品的面积为183平方英尺。两座山的另一边在艺术品中心附近的位置相交，相交点距离地面h英尺。请问h的值是多少？

正确答案：B · 分值：1

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2024 AMC8 #25 · Counting, Probability & Statistics · ★★★★
A small airplane has 4 rows of seats with 3 seats in each row. Eight passengers have boarded the plane and are distributed randomly among the seats. A married couple is next to board. What is the probability there will be 2 adjacent seats in the same row for the couple?
一架小型飞机有4排座位，每排3个座位。目前已有8位乘客随机入座。接下来一对夫妻登机。这对夫妻能坐到同一排且相邻两个座位的概率是多少？

正确答案：C · 分值：1

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2023 AMC8 #2 · Geometry · ★★
A square piece of paper is folded twice into four equal quarters, as shown below, then cut along the dashed line. When unfolded, the paper will match which of the following figures?
如下图所示，将一张正方形纸对折两次，变成四等分，然后沿虚线裁剪。问这张纸展开后会是下面哪个图形？

正确答案：E · 分值：1

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2023 AMC8 #3 · Algebra · ★
Wind chill is a measure of how cold people feel when exposed to wind outside. A good estimate for wind chill can be found using this calculation:
(wind chill)=(air temperature)−0.7×(wind speed)(\text{wind chill}) = (\text{air temperature}) - 0.7 \times (\text{wind speed})
where temperature is measured in degrees Fahrenheit (∘F^{\circ}\mathrm{F}) and wind speed is measured in miles per hour (mph). Suppose the air temperature is 36∘F36^{\circ}\mathrm{F} and the wind speed is 18 mph. Which of the following is closest to the approximate wind chill?
风寒指数衡量人们在室外受风时感受到的寒冷程度。可用下面的关系式较好地估算风寒指数：
(风寒指数)=(气温)−0.7×(风速)\text{(风寒指数)} = \text{(气温)} - 0.7 \times \text{(风速)}
其中气温以华氏度（∘F^{\circ}\mathrm{F}）计量，风速以英里每小时（mph）计量。设气温为 36∘F36^{\circ}\mathrm{F}，风速为 18 mph。下列哪一项最接近此时的风寒指数？

正确答案：B · 分值：1

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2023 AMC8 #4 · Number Theory · ★★
The numbers from 1 to 49 are arranged in a spiral pattern on a square grid, beginning at the center. The first few numbers have been entered into the grid below. Consider the four numbers that will appear in the shaded squares, on the same diagonal as the number 7. How many of these four numbers are prime?
在正方形方格表上，数 1 到 49 从中心开始，按螺旋式方式排列。前面几个数已经填入到下面的方格表中。考虑与数 7 出现在同一个对角线上的阴影方格中的四个数。问这四个数中有几个质数？

正确答案：D · 分值：1

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2023 AMC8 #5 · Algebra · ★
A lake contains 250 trout, along with a variety of other fish. When a marine biologist catches and releases a sample of 180 fish from the lake, 30 are identified as trout. Assume that the ratio of trout to the total number of fish is the same in both the sample and the lake. How many fish are there in the lake?
湖里有 250 条鳟鱼，以及其他一些鱼类。当一位海洋生物学家从湖中捕获并释放 180 条鱼的样本时，他发现其中 30 条鱼是鳟鱼。假设在样本中鳟鱼所占的比例和湖里鳟鱼在全部鱼类中所占的比例相同。问湖里有多少条鱼？

正确答案：B · 分值：1

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2023 AMC8 #6 · Algebra · ★★
The digits 2, 0, 2, and 3 are placed in the expression below, one digit per box. What is the maximum possible value of the expression?
将数字2，0，2，3填入下面的表达式中，每个方框内填一个数字．问表达式的最大可能值是多少?

正确答案：C · 分值：1

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2023 AMC8 #7 · Geometry · ★★
A rectangle, with sides parallel to the x-axis and y-axis, has opposite vertices at (15, 3) and (16, 5). A line is drawn through A(0,0) and B(3,1). Another line is drawn through C(0,10) and D(2,9). How many points on the rectangle lie on at least one of the two lines?
有一个矩形，它的边平行于 x 轴和 y轴，两个相对的顶点分别是（15，3）与（16，5）。过点 A(0,0) 与 B(3,1) 作一条直线，再过点 C(0,10) 与 D(2,9) 作另一条直线。问矩形的边界上有多少个点落在两条直线中至少一条上？

正确答案：B · 分值：1

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2023 AMC8 #8 · Counting, Probability & Statistics · ★★
Lola, Lolo, Tiya, and Tiyo participated in a ping pong tournament. Each player competed against each of the other three players exactly twice. Shown below are the win-loss records for the players. The numbers 1 and 0 represent a win or loss, respectively. For example, Lola won five matches and lost the fourth match. What was Tiyo’s win-loss record?
Lola，Lolo，Tiya，Tiyo参加一场乒乓球锦标赛．每名选手与其他三名选手中的每个人比赛恰好两次. 下面显示的是选手的胜负记录. 数字1和0分别代表赢或输. 例如Lola一共赢了五场比赛，第四场比赛输了. 问Tiyo的胜负记录是怎样的?

正确答案：A · 分值：1

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2023 AMC8 #9 · Counting, Probability & Statistics · ★
Malaika is skiing on a mountain. The graph below shows her elevation, in meters, above the base of the mountain as she skis along a trail. In total, how many seconds does she spend at an elevation between 4 and 7 meters?
正在山上滑雪下图显示了她沿着小径滑雪时以山脚为基准的海拔高度 (单位为米)．问她在4米到7米之间的高度共停留了多少秒？

正确答案：B · 分值：1

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2023 AMC8 #10 · Algebra · ★★
Harold made a plum pie to take on a picnic. He was able to eat only 14\displaystyle \frac{1}{4} of the pie, and he left the rest for his friends. A moose came by and ate 13\displaystyle \frac{1}{3} of what Harold left behind. After that, a porcupine ate 13\displaystyle \frac{1}{3} of what the moose left behind. How much of the original pie still remained after the porcupine left?
Harold 做了一个李子派带去野餐。他只吃了这个派的 14\displaystyle \frac{1}{4}，剩下的留给他的朋友们。一只驼鹿经过，吃掉了 Harold 剩下的 13\displaystyle \frac{1}{3}。在那之后，一只豪猪吃掉了驼鹿剩下的派的 13\displaystyle \frac{1}{3}。问豪猪走后，原来的派还剩下多少？

正确答案：D · 分值：1

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2023 AMC8 #11 · Algebra · ★★★
NASA's Perseverance Rover was launched on July 30, 2020. After traveling 292,526,838292{,}526{,}838 miles, it landed on Mars in Jezero Crater about 6.5 months later. Which of the following is closest to the Rover's average interplanetary speed in miles per hour?
美国国家航空航天局（NASA）的「毅力号」火星车于 2020 年 7 月 30 日发射。它在飞行了 292,526,838 英里后，于大约 6.5 个月后着陆在火星的耶泽罗陨石坑。以下哪一个选项最接近毅力号在星际航行中的平均速度（英里每小时）？

正确答案：C · 分值：1

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2023 AMC8 #12 · Geometry · ★★★
The figure below shows a large white circle with a number of smaller white and shaded circles in its interior. What fraction of the interior of the large white circle is shaded?
如图所示，在一个大的白色圆圈内部有许多较小的白色和灰色圆圈．问灰色部分在大的白色圆圈内部所占的比例是多少？

正确答案：B · 分值：1

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2023 AMC8 #13 · Algebra · ★★★
Along the route of a bicycle race, 7 water stations are evenly spaced between the start and finish lines, as shown in the figure below. There are also 2 repair stations evenly spaced between the start and finish lines. The 3rd water station is located 2 miles after the 1st repair station. How long is the race in miles?
如下图所示，在自行车比赛路线的起点和终点之间均匀分布着7个饮用水补给站. 另外，在起点和终点之间还均匀分布着2个维修站.第三个饮用水补给站在第一个维修站后2英里处：问比赛的全程是多少英里？

正确答案：D · 分值：1

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2023 AMC8 #14 · Number Theory · ★★★
Nicolas is planning to send a package to his friend Anton, who is a stamp collector. To pay for the postage, Nicolas would like to cover the package with a large number of stamps. Suppose he has a collection of 5-cent, 10-cent, and 25-cent stamps, with exactly 20 of each type. What is the greatest number of stamps Nicolas can use to make exactly $7.10 in postage?
(Note: The amount $7.10 corresponds to 7 dollars and 10 cents. One dollar is worth 100 cents.)
Nicolas计划将一个包裹寄给爱好集邮的朋友Anton．为了支付邮资，Nicolas准备在包裹上贴大量的邮票．假设他有5美分，10美分，25美分的邮票，每种邮票恰好各有20张. Nicolas最多可以使用多少张邮票来恰好支付$7.10的邮资？ (注意：金额$7.10是指7美元10美分, 1美元是100美分.)

正确答案：E · 分值：1

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2023 AMC8 #15 · Algebra · ★★★
Viswam walks half a mile to get to school each day. His route consists of 10 city blocks of equal length and he takes 1 minute to walk each block. Today, after walking 5 blocks, Viswam discovers he has to make a detour, walking 3 blocks of equal length instead of 1 block to reach the next corner. From the time he starts his detour, at what speed, in mph, must he walk in order to get to school at his usual time?
Viswam 每天要步行半英里去上学，他上学的路线由 10 个等长的街区组成，每走 1 个街区需要一分钟。今天，在走了 5 个街区后，Viswam 发现他必须绕路：要走 3 个等长的街区而不是 1 个街区才能到达下一个交叉路口。从他绕行开始，Viswam 必须以每小时多少英里的速度步行，才能像平常一样准时到校？

正确答案：B · 分值：1

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2023 AMC8 #16 · Algebra · ★★★
The letters P\text{P}, Q\text{Q}, and R\text{R} are entered into a 20×2020\times 20 table according to the pattern shown below. How many P\text{P}'s, Q\text{Q}'s, and R\text{R}'s will appear in the completed table?
将字母 P\text{P}、Q\text{Q}、R\text{R} 按下图所示的规律填入 20×2020\times 20 的方格表中。问在完成的表中，各会出现多少个 P\text{P}、多少个Q\text{Q}、多少个R\text{R}？

正确答案：C · 分值：1

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2023 AMC8 #17 · Geometry · ★★★
A regular octahedron has eight equilateral triangle faces with four faces meeting at each vertex. Jun will make the regular octahedron shown on the right by folding the piece of paper shown on the left. Which numbered face will end up to the right of QQ?
正八面体有八个面，都是等边三角形，在每个顶点处有四个面相交。如图所示，Jun 把左边的纸片折成了右边的正八面体。问出现在 Q 的右边的那个面上的数是几？

正确答案：A · 分值：1

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2023 AMC8 #18 · Number Theory · ★★★
Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump 5 pads to the right or 3 pads to the left. What is the fewest number of jumps Greta must make to reach the lily pad located 2023 pads to the right of her starting position?
蚱锰Greta坐在池塘里一排长长的睡莲叶上：从任何睡莲叶出发，Greta都可以向右跳5个叶片或者向左跳3个叶片. 问Greta最少跳多少次才能到达位于她起始位置右侧的第2023片睡莲叶上？

正确答案：D · 分值：1

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2023 AMC8 #19 · Geometry · ★★★
An equilateral triangle is placed inside a larger equilateral triangle so that the region between them can be divided into three congruent trapezoids, as shown below. The side length of the inner triangle is 23\displaystyle \frac{2}{3} the side length of the larger triangle. What is the ratio of the area of one trapezoid to the area of the inner triangle?
如图所示，一个等边三角形在另一个更大的等边三角形内部，它们之间的区域可以分成三个全等的梯形．内部三角形的边长是大三角形边长的23\displaystyle \frac{2}{3}，问一个梯形的面积与内部三角形的面积之比是多少？

正确答案：C · 分值：1

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2023 AMC8 #20 · Counting, Probability & Statistics · ★★★
Two integers are inserted into the list 3, 3, 8, 11, 28 to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers?
将两个整数加入数据列表3，3，8，11，28使得它的极差加倍，而众数和中位数保持不变．问所添加的两个数之和的最大可能值是多少？

正确答案：D · 分值：1

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2023 AMC8 #21 · Counting, Probability & Statistics · ★★★★
Alina writes the numbers 1,2,…,91, 2, \dots, 9 on separate cards, one number per card. She wishes to divide the cards into 3 groups of 3 cards so that the sum of the numbers in each group will be the same. In how many ways can this be done?
Alina将数1,2,…,91, 2, \dots, 9写在不同的卡片上，每张卡片上有一个数.她希望将卡片分成3组，每组3张卡片，使得每组中的各数之和相同. 问有多少种这样的分组方法?

正确答案：C · 分值：1

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2023 AMC8 #22 · Number Theory · ★★★★
In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term is 4000. What is the first term?
在一个正整数数列中，第二项之后的每一项都是前面两项的乘积. 数列中的第六项是4000. 问第一项是多少?

正确答案：D · 分值：1

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2023 AMC8 #23 · Counting, Probability & Statistics · ★★★★
Each square in a 3×33\times 3 grid is randomly filled with one of the 4 gray and white tiles shown below on the right. What is the probability that the tiling will contain a large gray diamond in one of the smaller 2×22\times 2 grids? Below is an example of such a tiling.
将3×3方格表中的每个小方格随机的用如下图左侧所示的4个灰白双色方块之一嵌入，有一个大灰色菱形将出现在某个2×2子方格表中的概率是多少？一个这样的镶嵌方案的例子如下图右侧所示，

正确答案：C · 分值：1

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2023 AMC8 #24 · Geometry · ★★★★
Isosceles triangle ABCABC has equal side lengths ABAB and BCBC. In the figures below, segments are drawn parallel to AC‾\overline{AC} so that the shaded portions of △ABC\triangle ABC have the same area. The heights of the two unshaded portions are 11 and 5 units, respectively. What is the height hh of △ABC\triangle ABC?
在等腰三角形ABC中，边AB和BC的长度相等．在下图中，由平行于AC的线段形成的△ABC中的两个阴影部分具有相同的面积. 两个空白部分的高度分别为 11和5. 问△ABC的高h是多少?

正确答案：A · 分值：1

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2023 AMC8 #25 · Algebra · ★★★★
Fifteen integers a1,a2,…,a15a_1, a_2, \dots, a_{15} are arranged in order on a number line. The integers are equally spaced and have the property that
1≤a1≤10,13≤a2≤20,and241≤a15≤250.1 \le a_1 \le 10,\quad 13 \le a_2 \le 20,\quad \text{and}\quad 241 \le a_{15} \le 250.
What is the sum of the digits of a14a_{14}?
十五个整数 a1,a2,…,a15a_1,a_2,\dots,a_{15}依次排列在数轴上．这些整数呈等距排列，并且具有以下特性
1≤a1≤10,13≤a2≤20,241≤a15≤250.1 \le a_1 \le 10,\quad 13 \le a_2 \le 20,\quad 241 \le a_{15} \le 250.
问 a14a_{14} 的各位数字之和是多少？

正确答案：A · 分值：1

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2022 AMC8 #1 · Geometry · ★
The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches?
在由边长为 1 英寸的正方形组成的方格纸上，数学小组设计了一个类似乘法符号的标志，如下图所示。问该标志的面积是多少平方英寸？

正确答案：A · 分值：1

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2022 AMC8 #2 · Algebra · ★
Consider these two operations as shown below. What is the value of (5 ⧫ 3) ★ 6(5 \, \blacklozenge \, 3) \, \bigstar \, 6?
考虑下图所示的两种运算。那么 (5 ⧫ 3) ★ 6(5 \, \blacklozenge \, 3) \, \bigstar \, 6 的值是多少？

正确答案：D · 分值：1

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2022 AMC8 #3 · Number Theory · ★★
When three positive integers aa, bb, and cc are multiplied together, their product is $100$. Suppose a < b < c. In how many ways can the numbers be chosen?
当三个正整数a、b和c相乘时，它们的乘积是 100。假设a＜b＜c。问这些数共有多少种选择方法？

正确答案：E · 分值：1

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2022 AMC8 #4 · Geometry · ★★
The letter M in the figure below is first reflected over the line q and then reflected over the line p . What is the resulting image?
下图中的字母 M 首先沿着直线q反射，然后沿着直线p反射。问所得到的图像是怎样的？

正确答案：E · 分值：1

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2022 AMC8 #5 · Algebra · ★★
Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned 6 years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is 30 years. How many years older than Bella is Anna?
nna 和 Bella 正在一起庆祝她们的生日。五年前，当 Bella 到 6 岁的时候，她收到了一只新生的小猫作为生日礼物。今天，两个孩子与小猫的年龄之和是 30 岁。问 Anna 比 Bella 大多少岁？

正确答案：C · 分值：1

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2022 AMC8 #6 · Algebra · ★★
Three positive integers are equally spaced on a number line. The middle number is 15, and the largest number is 4 times the smallest number. What is the smallest of these three numbers?
三个正整数在数轴线上等距排列。中间的数是 15，最大的数是最小的数的 4 倍。问这三个数中最小的数是多少？

正确答案：C · 分值：1

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2022 AMC8 #7 · Algebra · ★
When the World Wide Web first became popular in the 1990 s, download speeds reached a maximum of about 56 kilobits per second. Approximately how many minutes would the download of a 4.2 -megabyte song have taken at that speed? (Note that there are 8000 kilobits in a megabyte.)
当全球互联网刚开始在 20 世纪 90 年代流行时，下载速度最高为每秒 56 千比特。以这样的速度下载一首 4.2 兆字节的歌曲大约需要多少分钟？（请注意，一兆字节相当于 8000 千比特）

正确答案：B · 分值：1

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2022 AMC8 #9 · Algebra · ★★
A cup of boiling water ( 212∘F212^{\circ}\text{F} ) is placed to cool in a room whose temperature remains constant at 68∘F68^{\circ}\text{F} . Suppose the difference between the water temperature and the room temperature is halved every 5 minutes. What is the water temperature, in degrees Fahrenheit, after 15 minutes?
一杯开水（212 华氏度）被放置在一个温度恒定为 68 华氏度的房间里进行冷却。假设水的温度和房间温度的差值每 5 分钟减半。问在 15 分钟后，水的温度是多少华氏度？

正确答案：B · 分值：1

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2022 AMC8 #10 · Algebra · ★★
One sunny day, Ling decided to take a hike in the mountains. She left her house at 8 AM , drove at a constant speed of 45 miles per hour, and arrived at the hiking trail at 10 AM . After hiking for 3 hours, Ling drove home at a constant speed of 60 miles per hour. Which of the following graphs best illustrates the distance between Ling's car and her house over the course of her trip?
在一个晴朗的日子，Ling 决定去山里远足。她早上 8 时离开家，以每小时 45 英里的恒定速度开车，在早上 10 时到达登山径。徒步运动 3 小时后，Ling 以每小时 60 英里的恒定速度开车回家。以下哪张图最好的表达了 Ling 的行程中她的汽车和她家之间的距离？

正确答案：E · 分值：1

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2022 AMC8 #11 · Algebra · ★★★
Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating 3 inches of pasta from the middle of one piece. In the end, he has $10$ pieces of pasta whose total length is 17 inches. How long, in inches, was the piece of pasta he started with?
驴 Henry 有一根很长的面条。他咬了几口面条，每次都是从一段面条的中间吃掉 3 英寸。最后，他还有 10 段面条，总长度为 17 英寸。问他开始吃的时候，那根面条的长度是多少英寸？

正确答案：D · 分值：1

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2022 AMC8 #12 · Counting, Probability & Statistics · ★★★
The arrows on the two spinners shown below are spun. Let the number N equal 10 times the number on Spinner A\text{A}, added to the number on Spinner B\text{B}. What is the probability that N is a perfect square number?
下图所示的两个转盘上的箭头可自由旋转。数 N 等于 10 乘以转盘 A 上箭头所指的数，再加上转盘 B 上箭头所指的数。问 N 是完全平方数的概率是多少？

正确答案：B · 分值：1

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2022 AMC8 #13 · Number Theory · ★★★
How many positive integers can fill the blank in the sentence below? “One positive integer is _____ more than twice another, and the sum of the two numbers is 28 .”
有多少个正整数可以填在下面句子的横线上？ “一个正整数是另一个的两倍加上，并且这两个数的和是 28”。

正确答案：D · 分值：1

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2022 AMC8 #14 · Counting, Probability & Statistics · ★★★
In how many ways can the letters in BEEKEEPER\textbf{BEEKEEPER} be rearranged so that two or more E\textbf{E} s do not appear together?
将 BEEKEEPER 中的字母重新排列，使得没有两个或更多的 E 连排在一起，共有多少种排列方式？

正确答案：D · 分值：1

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2022 AMC8 #15 · Counting, Probability & Statistics · ★★★
Laszlo went online to shop for black pepper and found thirty different black pepper options varying in weight and price, shown in the scatter plot below. In ounces, what is the weight of the pepper that offers the lowest price per ounce?
Laszlo 在网上选购黑胡椒，发现有三十种不同的黑胡椒，重量和价格不尽相同，如下面的散点图所示。问每盎司价格最低的那种胡椒的重量是多少盎司？

正确答案：C · 分值：1

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2022 AMC8 #16 · Algebra · ★★★
Four numbers are written in a row. The average of the first two is 21, the average of the middle two is 26, and the average of the last two is 30. What is the average of the first and last of the numbers?
四个数写在一行。前两个数的平均值是 21，中间两个数的平均值是 26，最后两个数的平均值是 30,。问第一个数和最后一个数的平均值是多少？

正确答案：B · 分值：1

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2022 AMC8 #17 · Number Theory · ★★★
If n is an even positive integer, the double factorial notation n!! represents the product of all the even integers from 2 to n . For example, 8!!=2⋅4⋅6⋅88!! = 2 \cdot 4 \cdot 6 \cdot 8 . What is the units digit of the following sum? 2!!+4!!+6!!+⋯+2018!!+2020!!+2022!!2!! + 4!! + 6!! + \cdots + 2018!! + 2020!! + 2022!!
如果 n 是一个正整数，那么双阶乘记号 n！！代表从 2 到 n 的所有偶整数的乘积。例如， 8!!=2·4·6·8。问下面和式的个位数字是几？ 2！！+4！！+6！！+ … +2018！！+2020！！+2022！！

正确答案：B · 分值：1

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2022 AMC8 #18 · Geometry · ★★★
The midpoints of the four sides of a rectangle are (-3,0), (2,0), (5,4), and (0,4). What is the area of the rectangle?
一个长方形的四条边的中点是(-3，0)，(2，0)，(5，4)和(0，4)。问这个长方形的面积是多少？

正确答案：C · 分值：1

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2022 AMC8 #19 · Counting, Probability & Statistics · ★★★
Mr. Ramos gave a test to his class of 20 students. The dot plot below shows the distribution of test scores. Later Mr. Ramos discovered that there was a scoring error on one of the questions. He regraded the tests, awarding some of the students 5 extra points, which increased the median test score to 85 . What is the minimum number of students who received extra points? (Note that the median test score equals the average of the 2 scores in the middle if the 20 test scores are arranged in increasing order.)
Ramos 先生给他班上的 20 名学生进行了一次测试。下面的点图显示了考试成绩的分布。后来， Ramos 先生发现有一道题的评分有误。他重新批改，给一些学生各加了 5 分，使得考试成绩的中位数增加到了 85。问最少有多少名学生获得了加分？（请注意，如果 20 个考试成绩按递增顺序排列，那么中位数等于中间 2 个考试成绩的平均值。）

正确答案：C · 分值：1

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2022 AMC8 #20 · Algebra · ★★★
The grid below is to be filled with integers in such a way that the sum of the numbers in each row and the sum of the numbers in each column are the same. Four numbers are missing. The number x in the lower left corner is larger than the other three missing numbers. What is the smallest possible value of x ?
在下面的方格表中要填入整数，使得每行的各数之和与每列的各数之和都相同。现在有四个数缺失。左下角的数 比其他三个缺失的数都大。问 的最小可能值是多少？

正确答案：D · 分值：1

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2022 AMC8 #21 · Algebra · ★★★★
Steph scored 15 baskets out of 20 attempts in the first half of a game, and 10 baskets out of 10 attempts in the second half. Candace took 12 attempts in the first half and 18 attempts in the second. In each half, Steph scored a higher percentage of baskets than Candace. Surprisingly they ended with the same overall percentage of baskets scored. How many more baskets did Candace score in the second half than in the first?
Steph 在一场比赛的上半场有 20 次上篮，其中 15 次得分；下半场有 10 次上篮，并且 10 次都得分。Candace 在上半场有 12 次上篮，在下半场有 18 次上篮。在每个半场，Steph 的上篮得分率都比 Candace 高。但令人惊讶的是，他们整场的上篮得分率是相同的。问 Candace 在下半场比上半场上多得分几次？

正确答案：C · 分值：1

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2022 AMC8 #22 · Algebra · ★★★★
A bus takes 2 minutes to drive from one stop to the next, and waits 1 minute at each stop to let passengers board. Zia takes 5 minutes to walk from one bus stop to the next. As Zia reaches a bus stop, if the bus is at the previous stop or has already left the previous stop, then she will wait for the bus. Otherwise she will start walking toward the next stop. Suppose the bus and Zia start at the same time toward the library, with the bus 3 stops behind. After how many minutes will Zia board the bus?
一辆公共汽车从一个站开到下一个站需要 2 分钟，在每个站乘客上下车需要等待 1 分钟。Zia 从一个公共汽车站走到下一个站需要 5 分钟。当 Zia 到达一个公共汽车站时，如果公共汽车是在上一站或已经离开上一站，那么她会等待公共汽车。否则，她将走向下一站。假设公共汽车和 Zia 同时出发前往图书馆，公共汽车落后 3 站。问多少分钟以后，Zia 将登上公共汽车？

正确答案：A · 分值：1

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2022 AMC8 #23 · Counting, Probability & Statistics · ★★★★
AA△\triangle or ◯\bigcirc is placed in each of the nine squares in a 3 -by- 3 grid. Shown below is a sample configuration with three △\triangles in a line. How many configurations will have three △\triangles in a line and three ◯\bigcircs in a line?
在 3×3 方格表的九个单元格的每个中放置△或○。下图是一种有三个△在一条线上的放置方法。问在有三个△在一条线上，并且有三个○在一条线上的放置方法有多少种？

正确答案：D · 分值：1

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2022 AMC8 #24 · Geometry · ★★★★
The figure below shows a polygon ABCDEFGH , consisting of rectangles and right triangles. When cut out and folded on the dotted lines, the polygon forms a triangular prism. Suppose that AH = EF = 8 and GH = 14 . What is the volume of the prism?
下图所示的多边形 ABCDEFGH 由长方形和直角三角形组成。当把它剪出并沿虚线折叠后，该多边形可以形成一个底面是三角形的棱柱。假设 AH=EF=8，GH=14。问该棱柱的体积是多少？

正确答案：C · 分值：1

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2022 AMC8 #25 · Counting, Probability & Statistics · ★★★★★
A cricket randomly hops between 4 leaves, on each turn hopping to one of the other 3 leaves with equal probability. After 4 hops what is the probability that the cricket has returned to the leaf where it started?
一只蟋蟀随机地在 4 片叶子之间跳来跳去，每次都以相同的概率跳到其它的 3 片叶子上。问经过 4 次跳跃，蟋蟀回到它开始的那片叶子的概率是多少？

正确答案：E · 分值：1

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2020 AMC8 #1 · Algebra · ★
Luka is making lemonade to sell at a school fundraiser. His recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. He uses 3 cups of lemon juice. How many cups of water does he need?
Luka 正在做柠檬水，准备在学校的募捐会上出售。他的配料表需要的水是糖的四倍，糖是柠檬汁的两倍。他用了 3 杯柠檬汁。他需要多少杯水？

正确答案：E · 分值：1

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2020 AMC8 #2 · Algebra · ★
Four friends do yardwork for their neighbors over the weekend, earning $15, $20, $25, and $40, respectively. They decide to split their earnings equally among themselves. In total, how much will the friend who earned $40 give to the others?
四个朋友在周末为他们的邻居打扫院子，收入分别为＄15，＄20，＄25 和＄40。他们决定平分收入。那么赚了 40 美元的那个朋友总共会给其他人多少钱？

正确答案：C · 分值：1

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2020 AMC8 #3 · Algebra · ★
Carrie has a rectangular garden that measures 6 feet by 8 feet. She plants the entire garden with strawberry plants. Carrie is able to plant 4 strawberry plants per square foot, and she harvests an average of 10 strawberries per plant. How many strawberries can she expect to harvest?
Carrie 有一个矩形的花园，尺寸是 6 英尺ｘ8 英尺。她在整个花园里都种植了草莓。Carrie 每平方英尺种植 4 棵草莓苗，并且每棵草莓苗上她可以收获 10 颗草莓。那么她可以期望总共收获多少颗草莓？

正确答案：D · 分值：1

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2020 AMC8 #4 · Algebra · ★★
Three hexagons of increasing size are shown below. Suppose the dot pattern continues so that each successive hexagon contains one more band of dots. How many dots are in the next hexagonal?
三个面积逐渐增大的六边形如下图所示。假设这种点阵模式以此规律继续，使得后一个六边形比前一个多一层点带。那么图中下一个六边形中有多少个点？

正确答案：B · 分值：1

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2020 AMC8 #5 · Algebra · ★
Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 5 cups. What percent of the total capacity of the pitcher did each cup receive?
一个水罐装了总容积四分之三的菠萝汁，把水罐里所有的菠萝汁平均倒到 5 个杯子里。那么每个杯子里菠萝汁的量占了水罐总容量的百分之几？

正确答案：C · 分值：1

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2020 AMC8 #6 · Counting, Probability & Statistics · ★★
Aaron, Darren, Karen, Maren, and Sharon rode on a small train that has five cars that seat one person each. Maren sat in the last car. Aaron sat directly behind Sharon. Darren sat in one of the cars in front of Aaron. At least one person sat between Karen and Darren. Who sat in the middle car?
Aaron，Darren，Karen，Maren 和 Sharon 乘坐一列小火车，火车有五节车厢，每节车厢可坐一人。Maren 坐在最后一节车厢里。Aaron 坐在 Sharon 的正后方。Darren 坐在 Aaron 前面的某节车厢里。至少有一个人坐在 Karen 和 Darren 之间。谁坐在中间的那节车厢里？

正确答案：A · 分值：1

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2020 AMC8 #7 · Counting, Probability & Statistics · ★★
How many integers between 2020 and 2400 have four distinct digits arranged in increasing order? (For example, 2347 is one integer.).
2020 和 2400 之间有多少个整数，满足四个位上的数字都不相同，且按照升序排列？（例如，2347 就是满足题意的一个数）

正确答案：C · 分值：1

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2020 AMC8 #8 · Algebra · ★★
Ricardo has $2020$ coins, some of which are pennies ( 1 -cent coins) and the rest of which are nickels ( 5 -cent coins). He has at least one penny and at least one nickel. What is the difference in cents between the greatest possible and least amounts of money that Ricardo can have?
Ricardo 有 2020 枚硬币，其中一些是便士（1 美分硬币），其余的是镍币（5 美分硬币）。他有至少一枚一分便士和一枚五分镍币。Ricardo 可能拥有的最大金额和可能拥有的最小金额相差多少美分？

正确答案：C · 分值：1

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2020 AMC8 #9 · Geometry · ★★
Akash's birthday cake is in the form of a 4×4×44 \times 4 \times 4 inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into 64 smaller cubes, each measuring 1×1×11 \times 1 \times 1 inch, as shown below. How many small pieces will have icing on exactly two sides?
Akash 的生日蛋糕是一个 4ｘ4ｘ4 的正方体（边长单位：英寸）。这个立方体的顶部和 4 个侧面都有冰覆盖，但底而没有。假设这个正方体被分成 64 个 1ｘ1ｘ1 英寸的小正方体，如下图所示。那么这些小正方体中有多少个恰好两面有冰？

正确答案：D · 分值：1

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2020 AMC8 #10 · Counting, Probability & Statistics · ★★
Zara has a collection of 4 marbles: an Aggie, a Bumblebee, a Steelie, and a Tiger. She wants to display them in a row on a shelf, but does not want to put the Steelie and the Tiger next to one another. In how many ways can she do this?
Zara 有 4 个玻璃球，分别叫 Aggie，Bumblebee，Steelie 和 Tiger。她想把它们在架子上排成一行，但不想让 Steelie 和 Tiger 相邻。那么她有多少种排列方法？

正确答案：C · 分值：1

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2020 AMC8 #11 · Algebra · ★★★
After school, Maya and Naomi headed to the beach, 6 miles away. Maya decided to bike while Naomi took a bus. The graph below shows their journeys, indicating the time and distance traveled. What was the difference, in miles per hour, between Naomi's and Maya's average speeds?
放学后，Maya 和 Naomi 出发去距学校 6 英里的沙滩。Maya 决定骑车去，而 Naomi 坐公交车去。下图展示了他们的行程，显示了时间和所走路程的关系。那么 Naomi 和 Maya 的平均速度之差是多少英里每小时？

正确答案：E · 分值：1

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2020 AMC8 #12 · Number Theory · ★★★
For a positive integer nn , the factorial notation n! represents the product of the integers from nn to 1 . What value of NN satisfies the following equation?
5!⋅9!=12⋅N!5!\cdot 9!=12\cdot N!
对一个正整数 n，符号 n！表示从 n 到 1 的所有整数的乘积。例如， 6！=6·5·4·3·2·3.2·1 则 N 为何值时，满足下面的方程？

正确答案：A · 分值：1

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2020 AMC8 #13 · Algebra · ★★★
Jamal has a drawer containing 6 green socks, 18 purple socks, and 12 orange socks. After adding more purple socks, Jamal noticed that there is now a 60% chance that a sock randomly selected from the drawer is purple. How many purple socks did Jamal add?
Jamal 有个抽屉，里面有 6 只绿色袜子，18 只紫色袜子，12 只橙色袜子。当加了更多紫色袜子后，Jamal 发现，从抽屉里随机抽取一只袜子，有 60％的概率是紫色的。那么 Jamal 加了多少只紫袜子？

正确答案：B · 分值：1

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2020 AMC8 #14 · Counting, Probability & Statistics · ★★★
There are 20 cities in the County of Newton. Their populations are shown in the bar chart below. The average population of all the cities is indicated by the horizontal dashed line. Which of the following is closest to the total population of all 20 cities?
牛顿县有 20 座城市。下面的条形图显示了各个城市的人口数。所有城市的平均人口数用一条水平虚线表示。以下哪一项最接近这 20 座城市的总人口？

正确答案：D · 分值：1

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2020 AMC8 #15 · Algebra · ★★★
Suppose 15% of xx equals 20% of $y.$ What percentage of xx is $y?$
假设 x 的 15％等于 y 的 20％．那么 x 的百分之几是 y?

正确答案：C · 分值：1

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2020 AMC8 #16 · Counting, Probability & Statistics · ★★★
Each of the points A,B,C,D,E, and F in the figure below represents a different digit from 1 to 6. Each of the five lines shown passes through some of these points. The digits along each line are added to produce five sums, one for each line. The total of the five sums is 47. What is the digit represented by B?
下图中 A，B，C，D，E，F 中的每个点代表 1 到 6 之间的一个不同的数字。图中所示的 5 条直线，每条都会通过其中几个点。每条直线上的几个数字相加得到 5 个和，每条直线一个和。把这 5 个和相加，结果为 47，那么 B 代表的数字是多少？

正确答案：E · 分值：1

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2020 AMC8 #17 · Number Theory · ★★★
How many positive integer factors of 2020 have more than 3 factors? (As an example, 12 has $6$ factors, namely 1,2,3,4,6, and 12. )
2020 有多少个正整数因子，它们各自的因子个数都大于 3?（例如，12 有 6 个因子， 即 1， 2，3，4，6，12.）

正确答案：B · 分值：1

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2020 AMC8 #18 · Geometry · ★★★
Rectangle ABCD is inscribed in a semicircle with diameter FE‾\overline{FE}, as shown in the figure. Let DA=16, and let FD=AE=9. What is the area of ABCD?
如图所示，矩形 ABCDABCD 内接于以 FE‾\overline{FE} 为直径的半圆中。已知 DA=16，FD=AE=9。那么 ABCDABCD 的面积是多少？

正确答案：A · 分值：1

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2020 AMC8 #19 · Number Theory · ★★★
A number is called flippy if its digits alternate between two distinct digits. For example, 2020 and 37373 are flippy, but 3883 and 123123 are not. How many five-digit flippy numbers are divisible by $15?$
若一个数的各个位上数字在 2 个不同的数字之间交替出现，那么这个数称为 flippy.例如， 2020 和 37373 都是 flippy 数，但是 3883 和 123123 不是。有多少个 5 位 flippy 数能被 15 整除？

正确答案：B · 分值：1

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2020 AMC8 #20 · Number Theory · ★★★
A scientist walking through a forest recorded as integers the heights of 5 trees standing in a row. She observed that each tree was either 2 times as tall or half as tall as the one to its right. Unfortunately some of her data was lost when rain fell on her notebook. Her notes are shown below, with blanks indicating the missing numbers. Based on her observations, the scientist was able to reconstruct the lost data. What was the average height of the trees, in meters?
一个穿过森林的科学家将一排 5 棵树的高度都记录了下来，这 5 棵树的高度均为整数。她观察到，每棵树的高度要么是右边树高的 2 倍，要么是它的一半。不幸的是，由于雨水落在她的笔记本上，导致部分数据丢失。她的笔记如下图所示，空白部分表示丢失的数据。根据她的观察，这个科学家最终能够重建丢失的数据。那么这 5 棵树的平均高度是多少米？

正确答案：B · 分值：1

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2020 AMC8 #21 · Counting, Probability & Statistics · ★★★
A game board consists of 64 squares that alternate in color between black and white. The figure below shows square P in the bottom row and square Q in the top row. A marker is placed at P. A step consists of moving the marker onto one of the adjoining white squares in the row above. How many 7 -step paths are there from P to Q? (The figure shows a sample path.)
一种游戏板由 64 个黑白相间的方块组成。下图显示了底行中的一个正方形 P 和顶行中的一个正方形 Q。在正方形 P 上放了一个标记，将标记移到上面一行中相邻的一个白色正方形上，这个操作称为一步。从 P 到 Q 有多少种 7 步路径？（图中显示了一种可能的示例路径）。

正确答案：A · 分值：1

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2020 AMC8 #22 · Number Theory · ★★★★
When a positive integer NN is fed into a machine, the output is a number calculated according to the rule shown below. For example, starting with an input of N = 7, the machine will output 3⋅7+1=223 \cdot 7 + 1 = 22. Then if the output is repeatedly inserted into the machine five more times, the final output is 26: 7→22→11→34→17→52→267 \to 22 \to 11 \to 34 \to 17 \to 52 \to 26. When the same 6-step process is applied to a different starting value of NN, the final output is $1$. What is the sum of all such integers NN?
当把一个正整数 N 输入一个机器，输出的是一个根据下面规则计算得到的数字：
例如，一开始输入的是 N=7，那么机器将输出接着如果把输出再输入机器这样继续重复 5 次，那么最后的输出将是 7→22→11→34→ 17 → 52 → 26。当把上述同样的 6 步过程再作用于另一个不同的初始值 N，最终的输出是 1，那么 N 的所有可能值之和是多少?

正确答案：E · 分值：1

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2020 AMC8 #23 · Counting, Probability & Statistics · ★★★★
Five different awards are to be given to three students. Each student will receive at least one award. In how many different ways can the awards be distributed?
把 5 个不同的奖章分配给 3 个学生，每个学生得到至少一个奖章。那么一共有多少种不同的分配方法？

正确答案：B · 分值：1

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2020 AMC8 #24 · Algebra · ★★★★
A large square region is paved with n^2 gray square tiles, each measuring s inches on a side. A border d inches wide surrounds each tile. The figure below shows the case for n=3 . When n=24 , the 576 gray tiles cover 64% of the area of the large square region. What is the ratio ds\displaystyle \frac{d}{s} for this larger value of n?
一个大正方形区域用 n2n^2 块灰色方形瓷砖铺成，每块边长为 ss 英寸。每块瓷砖四周都有宽 dd 英寸的边框。下图为 n=3 的情形。当 n=24 时，576 块灰色瓷砖覆盖了大正方形面积的 64％。那么对于这个较大的 nn 值，ds\displaystyle \frac{d}{s} 的比值是多少？

正确答案：A · 分值：1

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2020 AMC8 #25 · Geometry · ★★★★
Rectangles R_1 and R_2, and squares S_1, S_2,  and S_3, shown below, combine to form a rectangle that is 3322 units wide and 2020 units high. What is the side length of S_2 in units?
如图所示，矩形 R1R_1、R2R_2 和正方形 S1S_1、S2S_2、S3S_3 拼成了一个宽 3322、高 2020 的大矩形。求 S2S_2 的边长是多少？

正确答案：A · 分值：1

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2019 AMC8 #1 · Algebra · ★
Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy?
Ike 和 Mike 带着总共 30 美元去一家三明治商店，每块三明治价格 4.5 美元，每瓶软饮价格 1 美元。Ike 和 Mike 打算尽可能多的买三明治，然后用剩下的钱去买软饮料，那么三明治和软饮总个数加起来，他们将买多少件物品？

正确答案：D · 分值：1

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2019 AMC8 #2 · Geometry · ★★
Three identical rectangles are put together to form rectangle ABCD , as shown in the figure below. Given that the length of the shorter side of each of the rectangles is 5 feet, what is the area in square feet of rectangle ABCD ?
如图，把三个全等矩形拼在一起形成矩形 ABCD，已知每个小的矩形的短边为 5 英尺，求矩形 ABCD 的面积是多少平方英尺？

正确答案：E · 分值：1

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2019 AMC8 #3 · Algebra · ★★
Which of the following is the correct order of the fractions 1511,1915\displaystyle \frac{15}{11},\frac{19}{15}, and 1713\displaystyle \frac{17}{13}, from least to greatest?
下列哪个是把分数 1511\displaystyle \frac{15}{11}、1915\displaystyle \frac{19}{15}、1713\displaystyle \frac{17}{13} 从小到大排列的正确顺序？

正确答案：E · 分值：1

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2019 AMC8 #4 · Geometry · ★★
Quadrilateral ABCD is a rhombus with perimeter 52 meters. The length of diagonal AC‾\overline{AC} is 24 meters. What is the area in square meters of rhombus ABCD ?
四边形 ABCD 是个周长为 52 米的菱形。对角线是多少平方米？

正确答案：D · 分值：1

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2019 AMC8 #5 · Algebra · ★
A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance dd traveled by the two animals over time tt from start to finish?
乌龟向野兔发起挑战赛跑，野兔开心的同意了，然后迅速跑到了前面，把行动迟缓的乌龟甩在了后面，野兔很自信自己会赢，于是停下来打了个盹，同时，乌龟以缓慢但恒定的速度走完了全程。野兔醒了，当它跑到终点时，发现乌龟已经在那里了。下面哪张图和上述对比赛的描述相匹配，并正确的展示了这 2 只动物走过的距离 d 与从开始到结束这段时间 t 的关系？

正确答案：B · 分值：1

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2019 AMC8 #6 · Counting, Probability & Statistics · ★★
There are 81 grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point P is in the center of the square. Given that point Q is randomly chosen among the other 80 points, what is the probability that the line PQ is a line of symmetry for the square?
在下图所示的正方形中，一共有 81 个格点（均匀分布），包括边上的点。点 P 位于正方形的中心。已知点 Q 是从其他 80 个点中随机选择的一个点，问直线 PQ 是正方形的一条对称轴的概率是多少？

正确答案：C · 分值：1

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2019 AMC8 #7 · Counting, Probability & Statistics · ★★
Shauna takes five tests, each worth a maximum of 100 points. Her scores on the first three tests are 76 , 94 , and 87 . In order to average 81 for all five tests, what is the lowest score she could earn on one of the other two tests?
Shauna 一共考了 5 场考试，每场的满分都是 100 分。前三场考试的得分是 76，94 和 87，为了使得所有 5 场考试的平均分是 81 分，那么剩下 2 场考试中其中 1 场考试的最低得分可以是多少分？

正确答案：A · 分值：1

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2019 AMC8 #8 · Algebra · ★★
Gilda has a bag of marbles. She gives 20% of them to her friend Pedro. Then Gilda gives 10% of what is left to another friend, Ebony. Finally, Gilda gives 25% of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?
Gilda 有一包玻璃球，她把其中 20％给了她的朋友 Pedro，接着她把剩下的 10％给了另一个朋友 Ebony，最后 Gilda 把包里当前剩下的 25％给了她弟弟 Jimmy。问 Gilda 给她自己留了原来玻璃球总数的百分之多少？

正确答案：E · 分值：1

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2019 AMC8 #9 · Geometry · ★
Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are 6 cm in diameter and 12 cm high. Felicia buys cat food in cylindrical cans that are 12 cm in diameter and 6 cm high. What is the ratio of the volume of one of Alex's cans to the volume of one of Felicia's cans?
Alex 和 Felicia 他们都有宠物猫。Alex 买的宠物猫粮是装在底面直径为 6 厘米，高度 12 厘米的圆柱形罐子里的。Felicia 买的猫粮则装在底面直径是 12 厘米，高为 6 厘米的圆柱形罐子里。问 Alex 的罐子的体积和 Felicia 的罐子的体积之比是多少?

正确答案：B · 分值：1

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2019 AMC8 #10 · Counting, Probability & Statistics · ★★
The diagram shows the number of students at soccer practice each weekday during last week. After computing the mean and median values, Coach discovers that there were actually 21 participants on Wednesday. Which of the following statements describes the change in the mean and median after the correction is made?
下面这张图展示了上周的每个工作日某个足球训练场的学生数。在计算完平均值和中位数之后，教练发现周三实际有 21 个参加者。那么当纠正了这个错误后，下面对于平均数和中位数的改变的论断中，哪个是正确的？

正确答案：B · 分值：1

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2019 AMC8 #11 · Counting, Probability & Statistics · ★★★
The eighth grade class at Lincoln Middle School has $93$ students. Each student takes a math class or a foreign language class or both. There are 70 eighth graders taking a math class, and there are 54 eighth graders taking a foreign language class. How many eighth graders take only a math class and not a foreign language class?
林肯中学的八年级总共有 93 个学生。每个学生都会上一门数学课或者一门外语课或者两者都上。已知有 70 个八年级学生上一门数学课，54 个八年级学生上一门外语课。问有多少个八年级学生只上数学课而不上外语课？

正确答案：D · 分值：1

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2019 AMC8 #12 · Geometry · ★★★
The faces of a cube are painted in six different colors: red (R) , white (W) , green (G) , brown (B) , aqua (A) , and purple (P) . Three views of the cube are shown below. What is the color of the face opposite the aqua face?
用六种不同的颜色给一个正方体的六个面涂色：红色（R），白色（W），绿色（G），棕色（B），湖绿色（A）和紫色（P）。下图展示了这个正方体的 3 个不同视图。那么和湖绿色面相对的那个面的颜色是什么颜色？

正确答案：A · 分值：1

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2019 AMC8 #13 · Number Theory · ★★★
A palindrome is a number that has the same value when read from left to right or from right to left. (For example, 12321 is a palindrome.) Let NN be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of NN ?
回环数是指从左向右读和从右向左读，读数是一样的数（例如，12321 是个回环数）。N 是满足以下条件的最小三位整数：它不是个回环数，并且它是 3 个不同的两位回环数的和。问 N 的各个位上的数字之和是多少？

正确答案：A · 分值：1

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2019 AMC8 #14 · Number Theory · ★★★
Isabella has $6$ coupons that can be redeemed for free ice cream cones at Pete's Sweet Treats. In order to make the coupons last, she decides that she will redeem one every 10 days until she has used them all. She knows that Pete's is closed on Sundays, but as she circles the 6 dates on her calendar, she realizes that no circled date falls on a Sunday. On what day of the week does Isabella redeem her first coupon?
Isabella 有 6 张优惠券，可用于在 Pete 甜品店里免费兑换冰激凌。为了最后使用优惠券，她决定每 10 天兑换一次直到所有的优惠券都使用完毕。已知 Pete 甜品店周日是不营业的，当她在日历上圈出兑换冰激凌的这 6 天时，发现没有哪天是周日。问 Isabella 兑换她的第一个优惠券是在周几？

正确答案：C · 分值：1

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2019 AMC8 #15 · Counting, Probability & Statistics · ★★★
On a beach, 50 people are wearing sunglasses and 35 people are wearing caps. Some people are wearing both sunglasses and caps. If one of the people wearing a cap is selected at random, the probability that this person is also wearing sunglasses is 25\displaystyle \frac{2}{5} . If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?
在一个沙滩上，50 人戴着太阳镜，35 人戴着帽子，有些人同时戴着太阳镜和帽子。如果从戴着帽子的人当中随机选一人，那么这个人同时也戴着太阳镜的概率是 。相反，如果从戴着太阳镜的人当中随机选择一人，那么这个人同时也戴着帽子的概率是多少？

正确答案：B · 分值：1

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2019 AMC8 #16 · Algebra · ★★★
Qiang drives 15 miles at an average speed of 30 miles per hour. How many additional miles will he have to drive at 55 miles per hour to average 50 miles per hour for the entire trip?
Qiang 以 30 英里每小时的平均速度行驶了 15 英里。问他还需要以 55 英里每小时的速度行驶多少英里，这样可以使得全程的平均速度为 50 英里每小时？

正确答案：D · 分值：1

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2019 AMC8 #18 · Counting, Probability & Statistics · ★★★
The faces of each of two fair dice are numbered 1 , 2 , 3 , 5 , 7 , and 8 . When the two dice are tossed, what is the probability that their sum will be an even number?
两个标准骰子的 6 个面都标有数字 1，2，3，5，7，8.当掷了这两个骰子，问它们的数字和是个偶数的概率是多少？

正确答案：C · 分值：1

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2019 AMC8 #19 · Counting, Probability & Statistics · ★★★
In a tournament there are six teams that play each other twice. A team earns $3$ points for a win, 1 point for a draw, and 0 points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible number of total points for each of the top three teams?
在一场循环赛中，一共有 6 支队伍，每两支队伍之间都要比赛 2 次。某个队伍赢一次得 3 分，平局得 1 分，输了则得 0 分。当所有比赛都结束后，结果发现排名前三的队伍得分相同。问排名前三的队伍每支队最多可能得多少分？

正确答案：C · 分值：1

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2019 AMC8 #20 · Algebra · ★★★
How many different real numbers xx satisfy the equation
(x2−5)2=16?(x^{2}-5)^{2}=16?
有多少个不同的实数 x 满足方程

正确答案：D · 分值：1

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2019 AMC8 #21 · Geometry · ★★★
What is the area of the triangle formed by the lines y=5 , y=1+x , and y=1-x ?
由三条直线 y=5，y=1+x 和 y=1-x 所包围的三角形的面积是多少？

正确答案：E · 分值：1

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2019 AMC8 #22 · Algebra · ★★★★
A store increased the original price of a shirt by a certain percent and then lowered the new price by the same amount. Given that the resulting price was 84% of the original price, by what percent was the price increased and decreased?
一家商店把衬衫的原价提高了某个百分数，然后又把新价降低了同样的百分数。已知最终的价格是原价的 84％.问价格升高和降低了百分之多少?

正确答案：E · 分值：1

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2019 AMC8 #23 · Number Theory · ★★★★
After Euclid High School's last basketball game, it was determined that 14\displaystyle \frac{1}{4} of the team's points were scored by Alexa and 27\displaystyle \frac{2}{7} were scored by Brittany. Chelsea scored 15 points. None of the other 7 team members scored more than 2 points. What was the total number of points scored by the other 7 team members?
在 Euclid 高中最近的篮球赛后，发现队伍总分的 是 Alexa 获得的， 是 Brittany 获得的， Chelsea 得了 15 分。队伍中的其他 7 个队员没有一个得分超过 2 分。问其他 7 个队员获得的总分是多少分？

正确答案：B · 分值：1

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2019 AMC8 #24 · Geometry · ★★★★★
In triangle ABC , point D divides side AC‾\overline{AC} so that AD:DC=1:2 . Let E be the midpoint of BD‾\overline{BD} and let F be the point of intersection of line BC and line AE . Given that the area of △ABC\triangle ABC is 360 , what is the area of △EBF\triangle EBF?
在三角形 ABC 中，点 D 把边分成的两段满足 AD:DC＝1:2，点 E 是线段 BD 的中点，F 是直线 BC 和 AE 的交点。已知 ΔABC 的面积是 360，问 ΔEBF 的面积是多少？

正确答案：B · 分值：1

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2019 AMC8 #25 · Counting, Probability & Statistics · ★★★★
Alice has $24$ apples. In how many ways can she share them with Becky and Chris so that each of the three people has at least two apples?
Alice 有 24 个苹果。她有多少种和 Becky 与 Chris 分享苹果的方式，使得三人中的每个人都至少有 2 个苹果？

正确答案：C · 分值：1

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2018 AMC8 #1 · Algebra · ★
An amusement park has a collection of scale models, with a ratio of 1:201: 20 , of buildings and other sights from around the country. The height of the United States Capitol is 289 feet. What is the height in feet of its duplicate to the nearest whole number?
一个游乐公园有一系列美国国内建筑和其他景观的模型，与实际建筑的比例为 1：20．美国国会大厦的实际高为 289 英尺，那么它的模型复制品的高度是多少英尺？结果四舍五入到整数。

正确答案：A · 分值：1

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2018 AMC8 #3 · Counting, Probability & Statistics · ★★
Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a 7 as a digit (such as 47) or is a multiple of 7 that person leaves the circle and the counting continues. Who is the last one present in the circle?
Arn，Bob，Cyd，Dan，Eve 和 Fon 以这样的顺序围成一圈。他们开始数数：Arn 先开始，然后 Bob，以此类推。当数包含数字 7(例如 47)或者是 7 的倍数时，那个人就离开圆圈，数数继续进行。最后一个离开圆圈的是谁？

正确答案：D · 分值：1

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2018 AMC8 #4 · Geometry · ★★
The twelve-sided figure shown has been drawn on 1 cm×1 cm1\text{ cm}\times 1\text{ cm} graph paper. What is the area of the figure in cm2\text{cm}^2?
如下图所示的十二边形画在 1cmｘ1cm 的画纸上。那么这个十二边形的面积是多少平方厘米？

正确答案：C · 分值：1

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2018 AMC8 #6 · Algebra · ★★
On a trip to the beach, Anh traveled 50 miles on the highway and 10 miles on a coastal access road. He drove three times as fast on the highway as on the coastal road. If Anh spent 30 minutes driving on the coastal road, how many minutes did his entire trip take?
在去海滩的路上，Anh 先在高速上开了 50 英里，然后在沿海通道上开了 10 英里。他在高速上的开车速度是在沿海通道上的 3 倍。若 Anh 在沿海通道上开了 30 分钟，那么他全程开了多少分钟？

正确答案：C · 分值：1

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2018 AMC8 #7 · Number Theory · ★★
The 5-digit number 2‾  0‾  1‾  8‾  U‾\underline{2}\;\underline{0}\;\underline{1}\;\underline{8}\;\underline{U} is divisible by 9. What is the remainder when this number is divided by 8?
5 位数 2‾ 0‾ 1‾ 8‾ U‾\underline{2}\,\underline{0}\,\underline{1}\,\underline{8}\,\underline{U} 能被 9 整除。这个数除以 8 所得余数为多少？

正确答案：B · 分值：1

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2018 AMC8 #8 · Counting, Probability & Statistics · ★★
Mr. Garcia asked the members of his health class how many days last week they exercised for at least 30 minutes. The results are summarized in the following bar graph, where the heights of the bars represent the number of students. What was the mean number of days of exercise last week, rounded to the nearest hundredth, reported by the students in Mr. Garcia's class?
先生调查了他健康课的学生上周有多少天他们运动了至少 30 分钟，结果如下图柱状图所示，其中柱的高度表示学生数。那么 Garcia 先生班里的学生上周平均运动的天数是多少天？结果保留到百分位。

正确答案：C · 分值：1

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2018 AMC8 #9 · Geometry · ★★
Tyler is tiling the floor of his 12-foot by 16-foot living room. He plans to place one-foot by one-foot square tiles to form a border along the edges of the room and to fill in the rest of the floor with two-foot by two-foot square tiles. How many tiles will he use?
正在将他起居室 12 英尺ｘ16 英尺的地面用瓷砖贴起来。他打算用 1 英尺ｘ1 英尺的方形瓷砖沿着地板的边缘贴起来，地板的其他部分用 2 英尺ｘ2 英尺的方形瓷砖填满。问他最终总共使用了多少块瓷砖？

正确答案：B · 分值：1

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2018 AMC8 #10 · Algebra · ★
The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of 1, 2, and 4?
一组数的调和平均值定义为这组数各自的倒数的平均值的倒数。那么 1,2 和 4 的调和平均值是多少？

正确答案：C · 分值：1

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2018 AMC8 #11 · Counting, Probability & Statistics · ★★★
Abby, Bridget, and four of their classmates will be seated in two rows of three for a group picture, as shown. If the seating positions are assigned randomly, what is the probability that Abby and Bridget are adjacent to each other in the same row or the same column?
和其他四个同班同学坐在如下所示的两行三列的座位上准备拍集体照。 如果座位是随机分配的，那么 Abby 和 Bridget 坐在同一行或者同一列的相邻位置上的概率是多少？

正确答案：C · 分值：1

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2018 AMC8 #12 · Algebra · ★★★
The clock in Sri's car, which is not accurate, gains time at a constant rate. One day as he begins shopping, he notes that his car clock and his watch (which is accurate) both say 12:00 noon. When he is done shopping, his watch says 12:30 and his car clock says 12:35. Later that day, Sri loses his watch. He looks at his car clock and it says 7:00. What is the actual time?
的汽车上的钟表是不准确的，以一个恒定的速度增加时间。一天当他开始购物时，他发现他汽车上的钟表和他的手表(手表是准确的)的读数都是中午 12：00．当他结束购物后，他的手表读数是 12：30，而他的汽车钟表显示 12：35．那一天晚些时候，Sri 丢了手表，他看了看汽车钟表，读数为晚上 7：00，则实际时间是晚上几点？

正确答案：B · 分值：1

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2018 AMC8 #13 · Algebra · ★★★
Lalia took five math tests, each worth a maximum of 100 points. Laila's score on each test was an integer between 0 and 100, inclusive. Laila received the same score on the first four tests, and she received a higher score on the last test. Her average score on the five tests was 82. How many values are possible for Laila's score on the last test?
参加了 5 场数学考试，每场考试的满分都是 100 分。Laila 每场考试的得分都是 0 到 100 之间(包括 0 和 100)的整数。Laila 前四场考试得分相同，最后一场考试得分比前四场每场得分都高。已知五场考试的平均分是 82 分，那么最后一场考试的得分可能有多少个取值？

正确答案：A · 分值：1

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2018 AMC8 #14 · Number Theory · ★★★
Let NN be the greatest five-digit number whose digits have a product of 120 . What is the sum of the digits of NN ?
表示各个位上数字之积为 120 的最大的五位数。那么 N 的各个位上数字之和是多少？

正确答案：D · 分值：1

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2018 AMC8 #15 · Geometry · ★★★
In the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller circles have a combined area of 1 square unit, then what is the area of the shaded region, in square units?
如下图所示，2 个小圆各自的直径都是大圆的半径，如果这 2 个小圆的面积之和是 1 平方单位，那么图中阴影部分的面积是多少平方单位？

正确答案：D · 分值：1

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2018 AMC8 #16 · Counting, Probability & Statistics · ★★★
Professor Chang has nine different language books lined up on a bookshelf: two Arabic, three German, and four Spanish. How many ways are there to arrange the nine books on the shelf keeping the Arabic books together and keeping the Spanish books together?
教授有 9 本不同的书在书架上排成一排：2 本阿拉伯语书，3 本德语书和 4 本西班牙语书。有多少种把这些书排成一排的方式，要求阿拉伯语书在一起，并且西班牙语书也要在一起？

正确答案：C · 分值：1

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2018 AMC8 #17 · Algebra · ★★★
Bella begins to walk from her house toward her friend Ella's house. At the same time, Ella begins to ride her bicycle toward Bella's house. They each maintain a constant speed, and Ella rides 5 times as fast as Bella walks. The distance between their houses is 2 miles, which is 10,560 feet, and Bella covers 212\displaystyle 2\tfrac{1}{2} feet with each step. How many steps will Bella take by the time she meets Ella?
Bella 开始从她家步行去她朋友 Ella 的家。同时，Ella 骑着自行车开始向 Bella 的家出发。她们均保持各自恒定的速度，并且 Ella 骑车的速度是 Bella 行走速度的 5 倍。她们家相距 2 英里，即 10,560 英尺，已知 Bella 每步长为 212\displaystyle 2\tfrac{1}{2} 英尺，那么当 Bella 和 Ella 相遇时，Bella 走了多少步？

正确答案：A · 分值：1

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2018 AMC8 #19 · Counting, Probability & Statistics · ★★★
In a sign pyramid a cell gets a "+" if the two cells below it have the same sign, and it gets a "-" if the two cells below it have different signs. The diagram below illustrates a sign pyramid with four levels. How many possible ways are there to fill the four cells in the bottom row to produce a "+" at the top of the pyramid?
在一种符号金字塔中，如果下面 2 个方块的符号相同，那么这 2 个方块上面的方块就得到一个"＋"号；若下面 2 个方块的符号不同，那么这 2 个方块上面的方块就得到一个"-＂号。 下图展示了一个 4 层的符号金字塔。为了使得金字塔的最顶层是个＂＋＂，那么最底层的 4 个方块有多少种赋予符号的方法？

正确答案：C · 分值：1

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2018 AMC8 #20 · Geometry · ★★★
In △ABC\triangle ABC, a point EE is on AB‾\overline{AB} with AE=1 and EB=2. Point DD is on AC‾\overline{AC} so that DE‾∥BC‾\overline{DE} \parallel \overline{BC} and point FF is on BC‾\overline{BC} so that EF‾∥AC‾\overline{EF} \parallel \overline{AC}. What is the ratio of the area of CDEFCDEF to the area of △ABC\triangle ABC?
在 △ABC\triangle ABC 中，点 EE 在边 AB‾\overline{AB} 上，满足 AE=1，EB=2。点 DD 在边 AC‾\overline{AC} 上，满足 DE‾∥BC‾\overline{DE} \parallel \overline{BC}；点 FF 在边 BC‾\overline{BC} 上，满足 EF‾∥AC‾\overline{EF} \parallel \overline{AC}。则 CDEFCDEF 的面积与 △ABC\triangle ABC 的面积之比是多少？

正确答案：A · 分值：1

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2018 AMC8 #21 · Number Theory · ★★★★
How many positive three-digit integers have a remainder of 2 when divided by 6, a remainder of 5 when divided by 9, and a remainder of 7 when divided by 11?
有多少个 3 位正整数，满足：当除以 6 余数为 2，当除以 9 余数为 5，当除以 11 余数为 7？

正确答案：E · 分值：1

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2018 AMC8 #22 · Geometry · ★★★★
Point EE is the midpoint of side CD‾\overline{CD} in square ABCDABCD, and BE‾\overline{BE} meets diagonal AC‾\overline{AC} at FF. The area of quadrilateral AFEDAFED is 45. What is the area of ABCDABCD?
在正方形 ABCDABCD 中，EE 是边 CD‾\overline{CD} 的中点，BE‾\overline{BE} 和对角线 AC‾\overline{AC} 交于点 FF。四边形 AFEDAFED 的面积是 45，问 ABCDABCD 的面积是多少？

正确答案：B · 分值：1

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2018 AMC8 #23 · Counting, Probability & Statistics · ★★★★
From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the probability that at least one of the sides of the triangle is also a side of the octagon?
如下图所示的正八边形中，从 8 个顶点中任选 3 个并连接起来形成一个三角形。那么这个三角形至少有一条边也是八边形的一条边的概率是多少？

正确答案：D · 分值：1

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2018 AMC8 #24 · Geometry · ★★★★
In the cube ABCDEFGHABCDEFGH with opposite vertices CC and EE, JJ and II are the midpoints of edges FB‾\overline{FB} and HD‾\overline{HD}, respectively. Let RR be the ratio of the area of the cross-section EJCIEJCI to the area of one of the faces of the cube. What is R2R^2?
在正方体 ABCDEFGHABCDEFGH 中，顶点 CC 和 EE 相对，点 JJ 和点 II 分别是棱 FB‾\overline{FB} 和 HD‾\overline{HD} 的中点。RR 表示横截面 EJCIEJCI 的面积和正方体的一个面的面积之比，求 R2R^2。

正确答案：C · 分值：1

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2018 AMC8 #25 · Number Theory · ★★★★
How many perfect cubes lie between 28+12^8+1 and 218+12^{18}+1, inclusive?
在 28+12^8+1 和 218+12^{18}+1 之间（包括 28+12^8+1 和 218+12^{18}+1）的完全立方数有多少个？

正确答案：E · 分值：1

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2017 AMC8 #2 · Counting, Probability & Statistics · ★
Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received 36 votes, then how many votes were cast all together?
Alicia，Brenda 和 Colby 是最近的一次竞选学生主席的 3 个候选人。下面的饼图显示了这 3 人候选人的投票分布。若 Brenda 得到了 36 票，那么总共投了多少票？

正确答案：E · 分值：1

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2017 AMC8 #3 · Algebra · ★★
What is the value of the expression 1684\sqrt{16\sqrt{8\sqrt{4}}} ?
表达式

正确答案：C · 分值：1

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2017 AMC8 #4 · Algebra · ★
When 0.000315 is multiplied by 7,928,564 the product is closest to which of the following?
当 0.000315 乘以 7,928,564，乘积最接近下面哪个数？

正确答案：D · 分值：1

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2017 AMC8 #6 · Geometry · ★
If the degree measures of the angles of a triangle are in the ratio 3:3:4 , what is the degree measure of the largest angle of the triangle?
如果一个三角形的三个角度数之比为 3：3：4，那么这个三角形的最大的角是多少度？

正确答案：D · 分值：1

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2017 AMC8 #7 · Number Theory · ★★
Let ZZ be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of ZZ ?
Z 表示一个 6 位的正整数，例如 247247，从左往右前三位数字和后三位的数字一样。下面哪个数一定也是 Z 的一个因子？

正确答案：A · 分值：1

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2017 AMC8 #8 · Number Theory · ★★
Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true." (1) It is prime. (2) It is even. (3) It is divisible by 7. (4) One of its digits is 9. This information allows Malcolm to determine Isabella's house number. What is its units digit?
今天放学后 Malcolm 准备访问 Isabella，他知道 Isabella 住的街道号，但不知道门牌号。 Isabella 告诉他：“我的门牌号是个两位数，并且下面的 4 个关于我家门牌号的论断，恰好只有 3 个是对的。” （1）它是质数。 （2）它是偶数。 （3）它能被 7 整除。 （4）其中一个数字是 9。 这些信息可以让 Malcolm 确定 Isabella 的门牌号。那么门牌号的个位数字是多少？

正确答案：D · 分值：1

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2017 AMC8 #9 · Algebra · ★★
All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Marcy could have?
Marcy 的玻璃球只有蓝色，红色，绿色和黄色这 4 种颜色。她的玻璃缘的三分之一是蓝色，四分之一是红色，6 个玻璃球是绿色，那么黄色玻璃球的最小数目是多少个？

正确答案：D · 分值：1

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2017 AMC8 #10 · Counting, Probability & Statistics · ★★
A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?
一个盒子装了标有 1,2,3,4,5 的 5 张卡片。从中不放回的随机选择 3 张卡片，问 4 是选择的最大的数的概率是多少？

正确答案：C · 分值：1

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2017 AMC8 #11 · Algebra · ★★★
A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?
一个正方形的地板由一些全等的方形瓷砖覆盖。若两条对角线上的瓷砖总个数是 37，那么铺这个地板总共用了多少块瓷砖？

正确答案：C · 分值：1

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2017 AMC8 #12 · Number Theory · ★★★
The smallest positive integer greater than 1 that leaves a remainder of 1 when divided by 4, 5, and 6 lies between which of the following pairs of numbers?
大于 1 且除以 4,5 和 6 所得余数均为 1 的最小正整数在下面哪两个数之间？

正确答案：D · 分值：1

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2017 AMC8 #13 · Counting, Probability & Statistics · ★★★
Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost 2 games. Emma won 3 games and lost 3 games. If Kyler lost 3 games, how many games did he win?
Peter，Emma 和 Kyler 相互之间下棋。Peter 赢了 4 局，输了 2 局，Emma 赢了 3 局，输了 3 局，如果 Kyler 输了 3 局，那么他赢了几局？

正确答案：B · 分值：1

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2017 AMC8 #14 · Algebra · ★★★
Chloe and Zoe are both students in Ms. Demeanor's math class. Last night, they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only 80% of the problems she solved alone, but overall 88% of her answers were correct. Zoe had correct answers to 90% of the problems she solved alone. What was Zoe's overall percentage of correct answers?
Chloe 和 Zoe 都是 Demeanor 女士数学课上的学生。昨晚她俩各自解决了家庭作业上一半的题目，接着共同解决了剩下的一半。Chloe 自己单独解决的题目里，正确率是 80％，但算上共同完成的题目，总的来说，她的正确率是 88％．Zoe 自已单独解决的题目里，正确率是 90％，问总的来说，Zoe 的正确率是多少？

正确答案：C · 分值：1

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2017 AMC8 #15 · Counting, Probability & Statistics · ★★★
In the arrangement of letters and numerals below, by how many different paths can one spell AMC8? Beginning at the A in the middle, a path allows only moves from one letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture.
在下图所示的字母和数字的排布中，拼写出 AMC8 有多少种方法？要求从中间的 A 开始，移动的路径只允许从一个字母移到和这个字母相邻的字母（上，下，左，右，但不允许是对角线）。一种可能的路径标示在图中。

正确答案：D · 分值：1

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2017 AMC8 #16 · Geometry · ★★★
In the figure below, choose point D on BC‾\overline{BC} so that △ACD\triangle ACD and △ABD\triangle ABD have equal perimeters. What is the area of △ABD\triangle ABD?
如下图所示，在 BC‾\overline{BC} 上取点 DD，使得 △ACD\triangle ACD 和 △ABD\triangle ABD 的周长相等。那么 △ABD\triangle ABD 的面积是多少？

正确答案：D · 分值：1

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2017 AMC8 #17 · Algebra · ★★★
Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2 treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had $3$ gold coins left over. How many gold coins did I have?
我有一些金币和若干财宝箱。我尝试在每个财宝箱里放 9 枚金币，那么还剩 2 个财宝箱是空的。若我在每个财宝箱里放 6 枚金币，那么还剩 3 枚金币无处可放。问我有多少枚金币？

正确答案：C · 分值：1

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2017 AMC8 #18 · Geometry · ★★★
In the non-convex quadrilateral ABCD shown below, ∠BCD\angle BCD is a right angle, AB=12 , BC=4 , CD=3 , and AD=13 . What is the area of quadrilateral ABCD ?
在如下图所示的非凸四边形 ABCD 中， AD=13.那么四边形 ABCD 的面积是多少？

正确答案：B · 分值：1

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2017 AMC8 #19 · Number Theory · ★★★★★
For any positive integer MM , the notation M! denotes the product of the integers 1 through MM . What is the largest integer nn for which 5n5^n is a factor of the sum 98!+99!+100! ?
对于任何正整数 M 来说，符号 M！表示从 1 到 M 的所有整数的乘积。使得 ＋100！的一个因子的最大整数 n 是多少？
是 98！＋99！

正确答案：D · 分值：1

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2017 AMC8 #20 · Counting, Probability & Statistics · ★★★
An integer between 1000 and 9999, inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinct?
从 1000 到 9999 之间（包含 1000 和 9999）随机选择一个整数，问这个数是一个各个位上数字都不一样的奇数的概率是多少？

正确答案：B · 分值：1

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2017 AMC8 #21 · Algebra · ★★★★
Suppose a , b , and c are nonzero real numbers, and a+b+c=0 . What are the possible value(s) for a∣a∣+b∣b∣+c∣c∣+abc∣abc∣\displaystyle \frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}+\frac{abc}{|abc|} ?
设 aa、bb、cc 都是非零实数，且 a+b+c=0。那么 a∣a∣+b∣b∣+c∣c∣+abc∣abc∣\displaystyle \frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}+\frac{abc}{|abc|} 的可能取值有哪些？

正确答案：A · 分值：1

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2017 AMC8 #22 · Geometry · ★★★★
In the right triangle ABC , AC=12 , BC=5 , and angle C is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircle?
在直角三角形 ABC 中，AC=12，BC=5，且角 C 是个直角。一个半圆如下图所示内切于三角形中，那么这个半圆的半径是多少？

正确答案：D · 分值：1

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2017 AMC8 #23 · Number Theory · ★★★★
Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by 5 minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?
四天里的每一天，Linda 每天都旅行 1 小时，并且每天的旅行速度都满足这样的要求：保证旅行 1 英里所花的分钟数都是整数。第一天之后的每一天，她的速度不断降低，使得旅行 1 英里后一天所花的分钟数比前一天多 5 分钟。这 4 天的每一天，她所旅行的路程也都是个整数。那么这 4 天的总路程是多少英里？

正确答案：C · 分值：1

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2017 AMC8 #24 · Counting, Probability & Statistics · ★★★★
Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31, 2016. On how many days during the next year did she not receive a phone call from any of her grandchildren?
Sanders 女士有 3 个定期给她打电话的孙子．其中一个每三天通话一次，一个每四天通话一次，还有一个每五天通话一次。这 3 个孙子在 2016 年 12 月 31 号这天同时给她通了话。问下一年中有多少天她一个电话也没收到？

正确答案：D · 分值：1

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2017 AMC8 #25 · Geometry · ★★★★
In the figure shown, US‾\overline{US} and UT‾\overline{UT} are line segments each of length 2, and m∠TUS=60∘m\angle TUS = 60^\circ. Arcs TR⌢\overset{\frown}{TR} and SR⌢\overset{\frown}{SR} are each one-sixth of a circle with radius 2. What is the area of the region shown?
如下图所示，US‾\overline{US} 和 UT‾\overline{UT} 是两条长度都为 2 的线段，且 m∠TUS=60∘m\angle TUS = 60^\circ。弧 TR⌢\overset{\frown}{TR} 和 SR⌢\overset{\frown}{SR} 各是半径为 2 的圆的六分之一。那么图中所示区域的面积是多少？

正确答案：B · 分值：1

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2016 AMC8 #1 · Algebra · ★
The longest professional tennis match ever played lasted a total of 11 hours and 5 minutes. How many minutes was this?
时间最长的职业网球赛总共持续了 11 小时 5 分钟。问一共多少分钟？

正确答案：C · 分值：1

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2016 AMC8 #2 · Geometry · ★
In rectangle ABCD , AB=6 and AD=8 . Point M is the midpoint of AD‾\overline{AD}. What is the area of △AMC\triangle AMC?
在矩形 ABCD 中，AB=6，AD=8，点 M 是

正确答案：A · 分值：1

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2016 AMC8 #3 · Counting, Probability & Statistics · ★
Four students take an exam. Three of their scores are 70, 80, and 90 . If the average of their four scores is 70 , then what is the remaining score?
4 个学生参加一个考试。其中 3 个的分数是 70，80，90．若他们的平均分是 70 分，那么剩下那个学生的分数是多少分？

正确答案：A · 分值：1

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2016 AMC8 #4 · Algebra · ★★
When Cheenu was a boy, he could run 15 miles in 3 hours and 30 minutes. As an old man, he can now walk 10 miles in 4 hours. How many minutes longer does it take for him to walk a mile now compared to when he was a boy?
当 Cheenu 还是个孩子时，他 3 小时 30 分钟内可以跑 15 英里，现在他是个老人，4 小时内可以走 10 英里。现在的他和当他还是个孩子时比起来，行过 1 英里需要多花多少分钟？

正确答案：B · 分值：1

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2016 AMC8 #5 · Number Theory · ★★
The number N is a two-digit number. • When N is divided by 9, the remainder is 1. • When N is divided by 10, the remainder is 3. What is the remainder when N is divided by 11?
N 是个两位数。 ·当 N 除以 9，余数为 1． ·当 N 除以 10，余数为 3． 当 N 除以 11 时，余数是多少？

正确答案：E · 分值：1

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2016 AMC8 #6 · Counting, Probability & Statistics · ★★
The following bar graph represents the length (in letters) of the names of 19 people. What is the median length of these names?
下面的柱状图代表了 19 个人的名字的长度（字母个数）。那么这些名字长度的中位数是多少？
Frequency | 频率
Name length | 名字长度

正确答案：B · 分值：1

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2016 AMC8 #7 · Number Theory · ★★
Which of the following numbers is not a perfect square?
下面哪个数不是完全平方数？

正确答案：B · 分值：1

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2016 AMC8 #8 · Algebra · ★★
Find the value of the expression: 100−98+96−94+92−90+⋯+8−6+4−2100-98+96-94+92-90+\cdots+8-6+4-2.
计算下面表达式的值

正确答案：C · 分值：1

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2016 AMC8 #9 · Number Theory · ★★
What is the sum of the distinct prime integer divisors of 2016 ?
2016 的不同质因数之和是多少？

正确答案：B · 分值：1

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2016 AMC8 #10 · Algebra · ★★
Suppose that a * b means 3a-b. What is the value of xx if
2∗(5∗x)=12 * (5 * x)=1
假设 a * b 表示 3a-b。若 2 * (5 * x) = 1，那么 xx 的值是多少？

正确答案：D · 分值：1

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2016 AMC8 #11 · Algebra · ★★★
Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is 132.
有多少个两位数满足下面的性质：当把这个两位数的十位数字和个位数字调换位置所形成的新的数与原来的数相加，所得的和是 132．

正确答案：B · 分值：1

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2016 AMC8 #12 · Algebra · ★★★
Jefferson Middle School has the same number of boys and girls. 34\displaystyle \frac{3}{4} of the girls and 23\displaystyle \frac{2}{3} of the boys went on a field trip. What fraction of the students on the field trip were girls?
Jefferson 中学的男生和女生数目相同。 的女生和 的男生去郊游。那么这些去郊游的学生中，有多少比例是女生？

正确答案：B · 分值：1

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2016 AMC8 #13 · Counting, Probability & Statistics · ★★★
Two different numbers are randomly selected from the set {−2,−1,0,3,4,5}\{ - 2, -1, 0, 3, 4, 5\} and multiplied together. What is the probability that the product is 0 ?
从集合 {−2,−1,0,3,4,5}\{-2, -1, 0, 3, 4, 5\} 中随机选取两个不同的数相乘。那么乘积为 0 的概率是多少？

正确答案：D · 分值：1

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2016 AMC8 #14 · Algebra · ★★★
Karl's car uses a gallon of gas every 35 miles, and his gas tank holds 14 gallons when it is full. One day, Karl started with a full tank of gas, drove 350 miles, bought 8 gallons of gas, and continued driving to his destination. When he arrived, his gas tank was half full. How many miles did Karl drive that day?
Karl 的汽车每开 35 英里就需要 1 加仑汽油，且当他的油缸加满时，可以装 14 加仑的汽油。 一天，Karl 开始他的行程前，把油缸加满了汽油，接着开了 350 英里，之后买了 8 加仑汽油，然后继续开到目的地。当他到达目的地时，他的油缸只剩下一半汽油。问 Karl 那天总共开了多少英里？

正确答案：A · 分值：1

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2016 AMC8 #15 · Number Theory · ★★★
What is the largest power of 2 that is a divisor of 134−11413^4 - 11^4 ?
是

正确答案：C · 分值：1

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2016 AMC8 #16 · Algebra · ★★★
Annie and Bonnie are running laps around a 400 -meter oval track. They started together, but Annie has pulled ahead, because she runs 25% faster than Bonnie. How many laps will Annie have run when she first passes Bonnie?
Annie 和 Bonnie 绕着 400 米椭圆跑道跑步。他们同时起跑，但是因为 Annie 的速度比 Bonnie 快了 25％，所以她跑到了 Bonnie 的前面。当 Annie 第一次经过 Bonnie 时，Annie 已经跑了多少圈了？

正确答案：D · 分值：1

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2016 AMC8 #17 · Counting, Probability & Statistics · ★★★
An ATM password at Fred's Bank is composed of four digits from 0 to 9 , with repeated digits allowable. If no password may begin with the sequence 9,1,1, then how many passwords are possible?
Fred 银行的取款机密码由 0 到 9 中的 4 个数字组成，且允许重复，如果密码不允许以序列 9,1,1 开头，那么一共有多少种可能的密码？

正确答案：D · 分值：1

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2016 AMC8 #18 · Counting, Probability & Statistics · ★★★
In an All-Area track meet, 216 sprinters enter a 100- meter dash competition. The track has $6$ lanes, so only 6 sprinters can compete at a time. At the end of each race, the five non-winners are eliminated, and the winner will compete again in a later race. How many races are needed to determine the champion sprinter?
在一次全区田径比赛中，共有 216 个短跑运动员角逐 100 米冲刺赛。比赛一共有 6 个赛道，因此一次只允许 6 个短跑运动员同时比赛。每场比赛结束后，会淘汰掉其中 5 人，胜者将参与到下一次比赛中。问一共需要多少场比赛才能确定整个比赛最终的冠军？

正确答案：C · 分值：1

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2016 AMC8 #19 · Algebra · ★★★
The sum of 25 consecutive even integers is 10,000 . What is the largest of these 25 consecutive integers?
25 个连续的偶数之和是 10,000，问这 25 个连续的整数中，最大的数是多少？

正确答案：E · 分值：1

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2016 AMC8 #20 · Number Theory · ★★★
The least common multiple of aa and bb is 12 , and the least common multiple of bb and cc is 15 . What is the least possible value of the least common multiple of aa and cc ?
a 和 b 的最小公倍数是 12，b 和 c 的最小公倍数是 15，问 a 和 c 的最小公倍数的最小可能值是多少？

正确答案：A · 分值：1

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2016 AMC8 #21 · Counting, Probability & Statistics · ★★★★
A top hat contains 3 red chips and 2 green chips. Chips are drawn randomly, one at a time without replacement, until all 3 of the reds are drawn or until both green chips are drawn. What is the probability that the 3 reds are drawn?
一个罐子里装有 3 个红色筹码和 2 个绿色筹码。现在将筹码一个个随机抽出且不放回，直到 3 个红色筹码被全部取出或者 2 个绿色筹码被全部取出，这时取出动作立即停止，那么取出 3 个红色筹码的概率是多少？

正确答案：B · 分值：1

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2016 AMC8 #22 · Geometry · ★★★★
Rectangle DEFA below is a 3×43 \times 4 rectangle with DC=CB=BA=1 . What is the area of the "bat wings" (shaded region)?
wings" (shaded area) is？

正确答案：C · 分值：1

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2016 AMC8 #23 · Geometry · ★★★★
Two congruent circles centered at points AA and BB each pass through the other circle's center. The line containing both AA and BB is extended to intersect the circles at points CC and DD . The circles intersect at two points, one of which is EE . What is the degree measure of ∠CED\angle CED ?
两个圆心分别在点 A 和点 B 的全等圆各自通过对方的圆心。连接点 A 和点 B 的直线和这 2 个圆交于点 C 和点 D。这 2 个圆交于 2 个点，其中之一是点 E．那么的度数是多少？

正确答案：C · 分值：1

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2016 AMC8 #24 · Number Theory · ★★★★
The digits 1 , 2 , 3 , 4 , and 5 are each used once to write a five-digit number PQRSTPQRST . The three-digit number PQRPQR is divisible by 4 , the three-digit number QRSQRS is divisible by 5 , and the three-digit number RSTRST is divisible by 3 . What is PP ?
数字 1，2，3，4，5 各使用一次组成一个五位数 PQRST，其中三位数 PQR 能被 4 整除，三位数 QRS 能被 5 整除，三位数 RST 能被 3 整除。问 P 是多少？

正确答案：A · 分值：1

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2016 AMC8 #25 · Geometry · ★★★★
A semicircle is inscribed in an isosceles triangle with base 16 and height 15 so that the diameter of the semicircle is contained in the base of the triangle as shown. What is the radius of the semicircle?
如图所示，一个底边为 16，高为 15 的等腰三角形内有一个半圆与两条腰相切，并且半圆的直径与三角形的底边重合，问这个半圆的半径是多少？

正确答案：B · 分值：1

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2015 AMC8 #1 · Algebra · ★
Onkon wants to cover his room's floor with his favourite red carpet. How many square yards of red carpet are required to cover a rectangular floor that is 12 feet long and 9 feet wide? (There are 3 feet in a yard.)
要覆盖长 12 英尺，宽 9 英尺的长方形地板，需要多少平方码的地毯？（1 码等于 3 英尺）

正确答案：A · 分值：1

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2015 AMC8 #2 · Geometry · ★★
Point OO is the center of the regular octagon ABCDEFGHABCDEFGH, and XX is the midpoint of the side AB‾\overline{AB}. What fraction of the area of the octagon is shaded?
点 OO 是正八边形 ABCDEFGHABCDEFGH 的中心，XX 是边 AB‾\overline{AB} 的中点。问在整个八边形面积中，图中阴影部分面积所占的比例是多少？

正确答案：D · 分值：1

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2015 AMC8 #3 · Algebra · ★
Jack and Jill are going swimming at a pool that is one mile from their house. They leave home simultaneously. Jill rides her bicycle to the pool at a constant speed of 10 miles per hour. Jack walks to the pool at a constant speed of 4 miles per hour. How many minutes before Jack does Jill arrive?
Jack 和 Jill 要去距离他们家 1 英里的游泳池去游泳。他们同时从家出发。Jill 以 10 英里每小时的速度骑车去泳池，Jack 以 4 英里每小时的速度走过去。那么 Jill 比 Jack 早到多少分钟？

正确答案：D · 分值：1

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2015 AMC8 #4 · Counting, Probability & Statistics · ★
The Centerville Middle School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible?
Centerville 中学的国际象棋队由 2 个男生和 3 个女生组成。一家报社的摄影师想给他们拍张照片放到报纸上。她决定让他们坐成一排，需要 2 个男生坐两端，3 个女生坐中间。一共有多少种可能的安排方法？

正确答案：E · 分值：1

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2015 AMC8 #5 · Counting, Probability & Statistics · ★★
Billy's basketball team scored the following points over the course of the first 11 games of the season:
42,47,53,53,58,58,58,61,64,65,7342, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73
If his team scores 40 in the 12th12^{th} game, which of the following statistics will show an increase?
Billy 的篮球队在本季度前 11 场比赛中的得分分别是：42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73。若他的篮球队在第 12 场比赛中得到 40 分，那么下面哪个统计数据会升高？

正确答案：A · 分值：1

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2015 AMC8 #6 · Geometry · ★★
In △ABC\bigtriangleup ABC , AB=BC=29 , and AC=42 . What is the area of △ABC\bigtriangleup ABC ?
在 △ABC\triangle ABC 中，AB=BC=29，AC=42。那么 △ABC\triangle ABC 的面积是多少？

正确答案：B · 分值：1

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2015 AMC8 #7 · Counting, Probability & Statistics · ★★
Each of two boxes contains three chips numbered 1 , 2 , 3 . A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even?
有两个盒子，每个盒子内都有分别标有 1,2,3 的三个筹码。从每个盒子里都随机抽取一个筹码，并把上面标的数字相乘，那么乘积是偶数的概率是多少？

正确答案：E · 分值：1

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2015 AMC8 #8 · Geometry · ★★★
What is the smallest whole number larger than the perimeter of any triangle with a side of length 5 and a side of length 19 ?
一个三角形的其中两条边长度分别是 5 和 19，那么大于这个三角形周长的最小整数是多少？

正确答案：D · 分值：1

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2015 AMC8 #9 · Algebra · ★★
On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working 20 days?
Janabel 在她上班的第一天卖出了 1 个器具，第二天卖出了 3 个器具，第三天卖出了 5 个器具，且在往后的每一天，她都比前一天多卖出 2 个器具，那么当她工作了 20 天后，共卖出多少个器具？

正确答案：D · 分值：1

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2015 AMC8 #10 · Counting, Probability & Statistics · ★★
How many integers between 1000 and 9999 have four distinct digits?
1000 和 9999 之间有多少个四位数，满足这个数的四个位上数字都不相同？

正确答案：B · 分值：1

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2015 AMC8 #11 · Counting, Probability & Statistics · ★★★
In the small country of Mathland, all automobile license plates have four symbols. The first must be a vowel (A, E, I, O, or U), the second and third must be two different letters among the 21 non-vowels, and the fourth must be a digit (0 through 9). If the symbols are chosen at random subject to these conditions, what is the probability that the plate will read "AMC8"?
在 Mathland 这个小国家，所有汽车的牌照都有 4 个符号。第一个符号必须是个韵母（A,E,I,O 或 U），第二个和第三个符号必须是 21 个非韵母中不同的两个字母，第四个必须是一个数字 （0 到 9），如果符号都是按照这些规则随机选择的，那么牌照上显示的是“AMC8”概率是多少？

正确答案：B · 分值：1

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2015 AMC8 #12 · Geometry · ★★★
How many pairs of parallel edges, such as AB‾\overline{AB}, and GH‾\overline{GH}, or EH‾\overline{EH}, and FG‾\overline{FG}, does a cube have? Repeating parallel edges do not count toward the final answer.
在一个正方体中，有多少对平行的棱（例如 AB‾\overline{AB} 和 GH‾\overline{GH}，或者 EH‾\overline{EH} 和 FG‾\overline{FG}）？重复的平行棱不计入最终答案。

正确答案：C · 分值：1

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2015 AMC8 #13 · Counting, Probability & Statistics · ★★★
How many subsets of two elements can be removed from the set {1,2,3,4,5,6,7,8,9,10,11}\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\} so that the mean (average) of the remaining numbers is 6?
有多少个两元素的子集可以从集合｛1,2,3,4,5,6,7,8,9,10,11｝中移走，使得集合中剩下的元素的平均值是 6？

正确答案：D · 分值：1

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2015 AMC8 #14 · Number Theory · ★★★
Which of the following integers cannot be written as the sum of four consecutive odd integers?
下面哪个整数无法写成 4 个连续奇数之和？

正确答案：D · 分值：1

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2015 AMC8 #15 · Counting, Probability & Statistics · ★★★
At Euler Middle School, 198 students voted on two issues in a school referendum with the following results: 149 voted in favor of the first issue and 119 voted in favor of the second issue. If there were exactly 29 students who voted against both issues, how many students voted in favor of both issues?
在 Euler 中学，198 名学生参与了一次针对两项议题的全校投票，结果如下：149 名学生赞成第一项议题，119 名学生赞成第二项议题。如果恰好有 29 名学生对这两项议题都反对，那么有多少名学生对这两项议题都赞成？

正确答案：D · 分值：1

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2015 AMC8 #16 · Algebra · ★★★
In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If 13\displaystyle \frac{1}{3} of all the ninth graders are paired with 25\displaystyle \frac{2}{5} of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?
在一所中学的一项导师项目中，由六年级学生和九年级学生成对组队完成项目。每个九年级学生都不能和超过 1 个六年级学生组成队友。如果 的所有九年级学生和 的所有六年级成对，那么已经组成队友的学生占了六年级和九年级总人数的比例是多少？

正确答案：B · 分值：1

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2015 AMC8 #17 · Algebra · ★★★
Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far in miles is it to school?
Jeremy 的爸爸在交通高峰期把他送到学校需要 20 分钟。这一天路上车不多，因此他爸爸开车的速度提高了 18 英里每小时，把他送到学校花了 12 分钟，那么从他家到学校的距离有多少英里？

正确答案：D · 分值：1

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2015 AMC8 #18 · Algebra · ★★★
An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant to the previous term. For example, 2,5,8,11,14 is an arithmetic sequence with five terms, in which the first term is 2 and the constant added is 3 . Each row and each column in this 5×55\times5 array is an arithmetic sequence with five terms. The square in the center is labelled X as shown. What is the value of X ?
一个等差数列是这样一种数列：第一项后面的每一项，都可以通过把前面一项加上一个常数得到。例如，2,5,8,11,14 是个 5 项的等差数列，其中第 1 项是 2，所加的常数是 3．下图所示的 5ｘ5 的方阵中，每一行每一列都是 5 项的等差数列。正方形中心的数字标记为 X，问 X 的值是多少？

正确答案：B · 分值：1

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2015 AMC8 #19 · Geometry · ★★★
A triangle with vertices as A=(1,3) , B=(5,1) , and C=(4,4) is plotted on a 6×56\times5 grid. What fraction of the grid is covered by the triangle?
三个顶点为 A＝(1,3)，B＝(5,1)，C＝（4,4）的三角形画在一张 6ｘ5 的方格纸上，这张方格纸上被三角形覆盖的面积所占总面积的比例是多少？

正确答案：A · 分值：1

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2015 AMC8 #20 · Number Theory · ★★★
Ralph went to the store and bought 12 pairs of socks for a total of $24 . Some of the socks he bought cost $1 a pair, some of the socks he bought cost $3 a pair, and some of the socks he bought cost $4 a pair. If he bought at least one pair of each type, how many pairs of $1 socks did Ralph buy?
Ralph 去商店买了 12 双袜子，总共花了 24 美元。在她买的这些袜子中，有的是 1 美元一双，有的是 3 美元一双，还有的是 4 美元一双。如果她每种袜子都至少买了 1 双，那么 1 美元一双的袜子她买了多少双？

正确答案：D · 分值：1

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2015 AMC8 #21 · Geometry · ★★★★
In the given figure hexagon ABCDEF is equiangular, ABJI and FEHG are squares with areas 18 and 32 respectively, △JBK\triangle JBK is equilateral and FE=BC . What is the area of △KBC\triangle KBC?
如图所示，六边形 ABCDEF 是个等角六边形，ABJI 和 FEHG 是面积分别为 18 和 32 的正方形。 是等边三角形，且 FE=BC，则的面积是多少？

正确答案：C · 分值：1

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2015 AMC8 #22 · Number Theory · ★★★★
On June 1, a group of students is standing in rows, with 15 students in each row. On June 2, the same group is standing with all of the students in one long row. On June 3, the same group is standing with just one student in each row. On June 4, the same group is standing with 6 students in each row. This process continues through June 12 with a different number of students per row each day. However, on June 13, they cannot find a new way of organizing the students. What is the smallest possible number of students in the group?
7 月 1 号那天，一群学生站成几行，每行 15 个学生；7 月 2 号那天，这群学生站成一行；7 月 3 号那天，这群学生站成若干行，每行只有 1 个学生；7 月 4 号那天，这群学生站成若干行，每行 6 个学生。这个过程一直持续到 7 月 12 号，每天每行的人数都不一样。然而，到了 7 月 13 号这天，他们再也没有办法找到一种新的方式去安排这些学生，那么这群学生最少有多少人？

正确答案：C · 分值：1

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2015 AMC8 #23 · Counting, Probability & Statistics · ★★★★
Tom has twelve slips of paper which he wants to put into five cups labeled AA , BB , CC , DD , EE . He wants the sum of the numbers on the slips in each cup to be an integer. Furthermore, he wants the five integers to be consecutive and increasing from AA to EE . The numbers on the papers are 2, 2, 2, 2.5, 2.5, 3, 3, 3, 3, 3.5, 4, and 4.5 . If a slip with 2 goes into cup EE and a slip with 3 goes into cup BB , then the slip with 3.5 must go into what cup?
Tom 想把 12 张纸条放进 5 个标有 A，B，C，D，E 的杯子中。他希望每个杯子中的纸条上的数字之和均为整数。并且，他希望这 5 个整数是连续的整数，从 A 到 E 递增。这 12 张纸条上的数字分别是 2，2，2，2.5，2.5，3，3，3，3，3.5，4，4.5．如果写有 2 的那张纸条放进了杯子 E，写有 3 的那张纸条放进了杯子 B，那么写有 3.5 的那张纸一定放进了哪个杯子？

正确答案：D · 分值：1

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2015 AMC8 #24 · Number Theory · ★★★★
A baseball league consists of two four-team divisions. Each team plays every other team in its division NN games. Each team plays every team in the other division MM games with N>2M and M>4 . Each team plays a 76 game schedule. How many games does a team play within its own division?
一个棒球联盟有两组组成，每组 4 支队伍。每组里面的每支队伍和自己组内的其他每支队伍都打 N 场比赛。每支队伍和另一组的每支队伍都打 M 场比赛，且 N>2M，M>4，每支队伍共需要打 76 场比赛，那么每支队伍和自己组内的队伍共需要打多少场比赛？

正确答案：B · 分值：1

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2015 AMC8 #25 · Geometry · ★★★★
One-inch squares are cut from the corners of this 5 inch square. What is the area in square inches of the largest square that can fit into the remaining space?
从边长为 5 英寸的大正方形的四个角落裁去 4 个边长为 1 英寸的小正方形，则能够放入剩余图形中的最大正方形的面积是多少平方英寸？

正确答案：C · 分值：1

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2014 AMC8 #1 · Algebra · ★
Harry and Terry are each told to calculate 8-(2+5) . Harry gets the correct answer. Terry ignores the parentheses and calculates 8-2+5 . If Harry's answer is HH and Terry's answer is TT , what is H-T ?
Harry 和 Terry 都被要求计算 $8-(2+5)$。Harry 算对了，而 Terry 忽略了括号，计算的是 8-2+5。若 Harry 的答案是 HH，Terry 的答案是 TT，那么 H-T 是多少？

正确答案：A · 分值：1

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2014 AMC8 #2 · Algebra · ★
Paul owes Paula 35 cents and has a pocket full of 5-cent coins, 10-cent coins, and 25-cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her?
Paul 欠了 Paula 35 美分。Paula 目前口袋里有一堆 5 美分，10 美分和 25 美分的硬币可以用来还钱，他可用于还钱的最多硬币数目和最少硬币数目的差是多少？

正确答案：E · 分值：1

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2014 AMC8 #3 · Algebra · ★
Isabella had a week to read a book for a school assignment. She read an average of 36 pages per day for the first three days and an average of 44 pages per day for the next three days. She then finished the book by reading 10 pages on the last day. How many pages were in the book?
Isabella 的学校作业是花一周的时间读一本书。她前三天每天平均读 36 页，后三天平均每天读 44 页，之后在最后一天读了 10 页把整本书读完了。问这本书总共有多少页？

正确答案：B · 分值：1

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2014 AMC8 #4 · Number Theory · ★★
The sum of two prime numbers is 85 . What is the product of these two prime numbers?
两个质数之和为 85，问这两个质数的乘积是多少？

正确答案：E · 分值：1

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2014 AMC8 #5 · Algebra · ★
Margie's car can go 32 miles on a gallon of gas, and gas currently costs $4 per gallon. How many miles can Margie drive on $20 worth of gas?
Margie 的汽车 1 加仑的汽油可以开 32 英里，汽油的当前价格是每加仑 4 美元。那么 20 美元可以让 Margie 的汽车开多少英里？

正确答案：C · 分值：1

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2014 AMC8 #6 · Algebra · ★
Six rectangles each with a common base width of 2 have lengths of 1, 4, 9, 16, 25 , and 36 . What is the sum of the areas of the six rectangles?
6 个矩形共同的宽是 2，它们的长分别是 1,4,9,16,25 和 36．那么这 6 个矩形的面积之和是多少？

正确答案：D · 分值：1

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2014 AMC8 #7 · Algebra · ★★
There are four more girls than boys in Ms. Raub's class of 28 students. What is the ratio of number of girls to the number of boys in her class?
Raub 女士的课上总共有 28 个学生，而女生比男生多 4 个。那么她班上女生和男生的个数之比是多少？

正确答案：B · 分值：1

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2014 AMC8 #8 · Number Theory · ★★
Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. They paid their guest speaker $1‾A‾2‾\$\underline{1} \underline{A} \underline{2} . What is the missing digit AA of this 3 -digit number?
中学数学俱乐部的 11 个成员为了邀请一个客座演讲人在他们的数学俱乐部会议上讲授解题技巧，每个人都支付了同样的美元金额数且这个数是个整数。他们总共支付给客座演讲人，这个三位数中的 A 代表什么数字？

正确答案：D · 分值：1

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2014 AMC8 #9 · Geometry · ★★
In △ABC\bigtriangleup ABC, D is a point on side AC‾\overline{AC} such that BD=DC and ∠BCD\angle BCD measures 70∘70^\circ. What is the degree measure of ∠ADB\angle ADB?
在 △ABC\triangle ABC 中，DD 是边 AC‾\overline{AC} 上一点，使得 BD=DC，且 ∠BCD=70∘\angle BCD = 70^\circ。那么 ∠ADB\angle ADB 的度数是多少？

正确答案：D · 分值：1

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2014 AMC8 #10 · Algebra · ★★
The first AMC 8 was given in 1985 and it has been given annually since that time. Samantha turned 12 years old the year that she took the seventh AMC 8 . In what year was Samantha born?
第一次 AMC8 考试在 1985 年举行，那年之后的每一年都举办一次。Samantha 参加第 7 次 AMC8 考试的那一年，她 12 岁，那么 Samantha 是哪年出生的？

正确答案：A · 分值：1

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2014 AMC8 #11 · Counting, Probability & Statistics · ★★★
Jack wants to bike from his house to Jill's house, which is located three blocks east and two blocks north of Jack's house. After biking each block, Jack can continue either east or north, but he needs to avoid a dangerous intersection one block east and one block north of his house. In how many ways can he reach Jill's house by biking a total of five blocks?
Jack 想从他家骑车到 Jill 家去，Jill 家位于 Jack 家向东 3 个街区，向北 2 个街区的位置。当 Jack 骑车经过每个街区后，他可以选择继续向东或者向北，但他必须绕开离他家向东 1 个街区，向北 1 个街区的一个危险的十字路口。那么他经过 5 个街区骑车到 Jill 的家一共有多少种路线？

正确答案：A · 分值：1

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2014 AMC8 #12 · Counting, Probability & Statistics · ★★★
A magazine printed photos of three celebrities along with three photos of the celebrities as babies. The baby pictures did not identify the celebrities. Readers were asked to match each celebrity with the correct baby pictures. What is the probability that a reader guessing at random will match all three correctly?
一家杂志社打印了 3 位名人的照片，以及这 3 位名人婴儿时的照片。从婴儿照片上无法识别出对应的名人。杂志社要求读者把每位名人的照片和对应的婴儿照片正确匹配。某个读者随机匹配了这些照片，那么他把这 3 个名人都正确匹配的概率是多少？

正确答案：B · 分值：1

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2014 AMC8 #13 · Number Theory · ★★★
If nn and mm are integers and n2+m2n^2+m^2 is even, which of the following is impossible?
若 nn 和 mm 都是整数，且 n2+m2n^2+m^2 是偶数，那么下列哪种情况是不可能的？

正确答案：D · 分值：1

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2014 AMC8 #14 · Geometry · ★★★
Rectangle ABCD and right triangle DCE have the same area. They are joined to form a trapezoid, as shown. What is DE ?
矩形 ABCD 和直角三角形 DCE 的面积相同。他们拼起来形成了一个梯形，如下图所示。那么 DE 的长度是多少？

正确答案：B · 分值：1

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2014 AMC8 #15 · Geometry · ★★★
The circumference of the circle with center O is divided into 12 equal arcs, marked the letters A through L as seen below. What is the number of degrees in the sum of the angles x and y ?
如下图所示，圆心为 O 的圆被分成 12 个相等的圆弧，由字母 A 到 L 标识。那么角 x 和角 y 的度数之和是多少？

正确答案：C · 分值：1

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2014 AMC8 #16 · Counting, Probability & Statistics · ★★★
The "Middle School Eight" basketball conference has $8$ teams. Every season, each team plays every other conference team twice (home and away), and each team also plays 4 games against non-conference opponents. What is the total number of games in a season involving the "Middle School eight" teams?
“中学八队”篮球联盟共有 8 支球队。每一个赛季，篮球联盟内的每支球队都会与联盟内的其他球队进行两场比赛（主客场），联盟内的每支球队也会与非联盟对手进行 4 场比赛。“中学八队”球队在一个赛季中的比赛总数是多少？

正确答案：B · 分值：1

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2014 AMC8 #17 · Algebra · ★★★
George walks 1 mile to school. He leaves home at the same time each day, walks at a steady speed of 3 miles per hour, and arrives just as school begins. Today he was distracted by the pleasant weather and walked the first 12\displaystyle \frac{1}{2} mile at a speed of only 2 miles per hour. At how many miles per hour must George run the last 12\displaystyle \frac{1}{2} mile in order to arrive just as school begins today?
George 每天同一时间以恒定的 3 英里每小时的速度从家步行 1 英里去学校，且恰好准时到校。今天他被好天气吸引，因此前 英里路程的速度仅为 2 英里每小时。那么后面 英里的路程他应该以多少英里每小时的速度奔跑才能准时到校？

正确答案：B · 分值：1

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2014 AMC8 #18 · Counting, Probability & Statistics · ★★★
Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or a girl. Which of the following outcomes is most likely?
昨天城市医院出生了 4 个婴儿，假设每个婴儿是男孩还是女孩的概率是相等的。那么下面哪种结果是最有可能的？

正确答案：D · 分值：1

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2014 AMC8 #19 · Geometry · ★★★
A cube with 3-inch edges is to be constructed from 27 smaller cubes with 1-inch edges. Twenty-one of the cubes are colored red and 6 are colored white. If the 3-inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white?
一个边长为 3 英寸的大正方体是由 27 个边长为 1 英寸的小正方体组成的。其中 21 个小正方体是红色的，6 个是白色的。若要求大的正方体的表面积中白色部分越少越好，那么表面积的白色部分所占总表面积的比例是多少？

正确答案：A · 分值：1

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2014 AMC8 #20 · Geometry · ★★★
Rectangle ABCD has sides CD=3 and DA=5 . A circle with a radius of 1 is centered at A , a circle with a radius of 2 is centered at B , and a circle with a radius of 3 is centered at C . Which of the following is closest to the area of the region inside the rectangle but outside all three circles?
长方形 ABCD 的边长 CD＝3，DA＝5．圆 A 的半径为 1，圆 B 的半径为 2，圆 C 的半径为 3．那么在长方形内部但在三个圆外部的区域的面积最接近下面哪个数？

正确答案：B · 分值：1

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2014 AMC8 #21 · Number Theory · ★★★★
The 7 -digit numbers 7‾4‾A‾5‾2‾B‾1‾\underline{7} \underline{4} \underline{A} \underline{5} \underline{2} \underline{B} \underline{1} and 3‾2‾6‾A‾B‾4‾C‾\underline{3} \underline{2} \underline{6} \underline{A} \underline{B} \underline{4} \underline{C} are each multiples of 3 . Which of the following could be the value of CC ?
七位数 7‾ 4‾ A‾ 5‾ 2‾ B‾ 1‾\underline{7}\,\underline{4}\,\underline{A}\,\underline{5}\,\underline{2}\,\underline{B}\,\underline{1} 和 3‾ 2‾ 6‾ A‾ B‾ 4‾ C‾\underline{3}\,\underline{2}\,\underline{6}\,\underline{A}\,\underline{B}\,\underline{4}\,\underline{C} 都是 3 的倍数。那么 CC 可能是下列哪个值？

正确答案：A · 分值：1

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2014 AMC8 #22 · Number Theory · ★★★★
AA2 -digit number is such that the product of the digits plus the sum of the digits is equal to the number. What is the units digit of the number?
一个两位数满足：各个位上数字之积加上各个位上数字之和，所得结果等于原来的两位数。 那么原来两位数的个位数字是多少？

正确答案：E · 分值：1

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2014 AMC8 #23 · Number Theory · ★★★★
Three members of the Euclid Middle School girls' softball team had the following conversation. Ashley: I just realized that our uniform numbers are all 2 -digit primes. Bethany : And the sum of your two uniform numbers is the date of my birthday earlier this month. Caitlin: That's funny. The sum of your two uniform numbers is the date of my birthday later this month. Ashley: And the sum of your two uniform numbers is today's date. What number does Caitlin wear?
Euclid 中学女子垒球队的 3 名成员有如下对话： Ashley：我刚意识到原来我们的球衣编号都是 2 位质数。 Bethany：并且你们两个人的球衣编号之和是这个月的早些时候我生日的日期。 Caitlin：真有趣。你们俩的球衣编号之和是这个月晚些时候我生日的日期。 Ashley：并且你们俩的球衣编号之和就是今天的日期。 那么 Caitlin 的球衣编号是多少？

正确答案：A · 分值：1

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2014 AMC8 #24 · Counting, Probability & Statistics · ★★★★
One day the Beverage Barn sold 252 cans of soda to 100 customers, and every customer bought at least one can of soda. What is the maximum possible median number of cans of soda bought per customer on that day?
一天 Beverage Barn 向 100 个顾客卖出了 252 罐苏打水，且每个顾客买了至少一罐苏打水。 那么那天每个顾客所买苏打水的罐数的中位数最大可能是多少？

正确答案：C · 分值：1

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2014 AMC8 #25 · Geometry · ★★★★
A straight one-mile stretch of highway, 40 feet wide, is closed. Robert rides his bike on a path composed of semicircles as shown. If he rides at 5 miles per hour, how many hours will it take to cover the one-mile stretch? Note: 1 mile = 5280 feet
一段长为 1 英里，宽 40 英尺的高速公路被关闭了。Robert 沿着如下图中由一系列半圆组成的路径骑着自行车。若他骑车的速度是 5 英里每小时，那么走过这段 1 英里的高速公路需要多少小时？ 注意：1 英里＝5280 英尺

正确答案：B · 分值：1

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2013 AMC8 #1 · Number Theory · ★
Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way?
Danica 想把她的模型汽车排成每行 6 辆的若干行，她现在有 23 辆模型汽车，那么她还需要至少买多少辆模型汽车才能完成上述安排？

正确答案：A · 分值：1

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2013 AMC8 #2 · Algebra · ★
A sign at the fish market says, "50 % off, today only: half-pound packages for just $3 per package." What is the regular price for a full pound of fish, in dollars?
鱼市上的一则标语写着：“降价 50％，仅限今天：半磅重的一包鱼仅需 3 美元。”那么一磅重的鱼原价是多少美元？

正确答案：D · 分值：1

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2013 AMC8 #3 · Algebra · ★★
What is the value of 4⋅(−1+2−3+4−5+6−7+⋯+1000)4 \cdot (-1+2-3+4-5+6-7+\cdots+1000) ?
4⋅(−1+2−3+4−5+6−7+⋯+1000)4 \cdot (-1+2-3+4-5+6-7+\cdots+1000) 的值是多少？

正确答案：E · 分值：1

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2013 AMC8 #4 · Algebra · ★★
Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $2.50 to cover her portion of the total bill. What was the total bill?
8 个朋友在餐馆吃饭，并且商定均摊费用。因为 Judi 忘记带钱了，她的其他 7 个朋友帮她垫付了费用，因此 7 个人每人额外多付了 2.5 美元。那么餐费总共是多少美元？

正确答案：C · 分值：1

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2013 AMC8 #5 · Counting, Probability & Statistics · ★
Hammie is in 6th6^\text{th} grade and weighs 106 pounds. His quadruplet sisters are tiny babies and weigh 5, 5, 6, and 8 pounds. Which is greater, the average (mean) weight of these five children or the median weight, and by how many pounds?
Hammie 目前六年级，重 106 磅。她的四胞胎妹妹们现在还是婴儿，分别重 5，5，6，8 磅。 问这 5 个小孩的平均重量和重量的中位数，哪个大？大多少磅？

正确答案：E · 分值：1

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2013 AMC8 #6 · Algebra · ★★
The number in each box below is the product of the numbers in the two boxes that touch it in the row above. For example, 30=6×530 = 6\times5. What is the missing number in the top row?
下图中每个方格中的数字等于上一层和它相接触的两个方格内的数字之积。例如，30=6ｘ5. 那么在顶层的方格中，空白方格里的数字是多少？

正确答案：C · 分值：1

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2013 AMC8 #7 · Algebra · ★★
Trey and his mom stopped at a railroad crossing to let a train pass. As the train began to pass, Trey counted 6 cars in the first 10 seconds. It took the train 2 minutes and 45 seconds to clear the crossing at a constant speed. Which of the following was the most likely number of cars in the train?
Trey 和他妈妈为了让一辆火车通过，在铁路的交叉口停了下来。当火车开始通过时，在前 10 秒他们数到了 6 节车厢。火车以恒定的速度完全通过这个交叉口耗时 2 分钟 45 秒，那么这列火车最有可能有多少节车厢？

正确答案：C · 分值：1

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2013 AMC8 #8 · Counting, Probability & Statistics · ★★
A fair coin is tossed 3 times. What is the probability of at least two consecutive heads?
一枚标准的硬币被掷了 3 次，至少有 2 次连续正面朝上的概率是多少？

正确答案：C · 分值：1

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2013 AMC8 #9 · Algebra · ★★
The Incredible Hulk can double the distance he jumps with each succeeding jump. If his first jump is 1 meter, the second jump is 2 meters, the third jump is 4 meters, and so on, then on which jump will he first be able to jump more than 1 kilometer (1,000 meters)?
绿巨人浩克每次跳的长度都是前面一次的两倍。若它第一次跳了 1 米，第二次跳了 2 米，第三次跳了 4 米，以此类推，那么第几次跳的长度超过 1 公里？

正确答案：C · 分值：1

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2013 AMC8 #10 · Number Theory · ★★
What is the ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594?
180 和 594 的最小公倍数和最大公约数的比值是多少？

正确答案：C · 分值：1

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2013 AMC8 #11 · Algebra · ★★★
Ted's grandfather used his treadmill on 3 days this week. He went 2 miles each day. On Monday he jogged at a speed of 5 miles per hour. He walked at the rate of 3 miles per hour on Wednesday and at 4 miles per hour on Friday. If Grandfather had always walked at 4 miles per hour, he would have spent less time on the treadmill. How many minutes less?
Ted 的爷爷这周有 3 天使用跑步机跑步。他每天跑 2 英里。周一他跑步的速度是 5 英里每小时，周三是 3 英里每小时，周五是 4 英里每小时。若他爷爷这 3 天跑步的速度都保持在 4 英里每小时的话，他在跑步机上花费的时间会更少一些，那么少多少分钟？

正确答案：D · 分值：1

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2013 AMC8 #12 · Algebra · ★★★
At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $50, you get a second pair at a 40% discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage of the $150 regular price did he save?
在 2013 年温尼贝戈县博览会上，一位供应商提供了一款凉鞋的“展会特价”。如果以原价 50 元购买一双凉鞋，那么第二双价格降低 40％，第三双半价。Javier 利用“展会特价”买了三双凉鞋。那么对比原价 150 美元，他节省了百分之多少？

正确答案：B · 分值：1

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2013 AMC8 #13 · Number Theory · ★★★
When Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of one score. By which of the following might her incorrect sum have differed from the correct one?
当 Clara 把她的所有的考试分数相加时，她不小心把某个分数的十位数字和个位数字调换了。那么她不正确的总分和正确总分可能相差多少？

正确答案：A · 分值：1

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2013 AMC8 #14 · Counting, Probability & Statistics · ★★★
Abe holds 1 green and 1 red jelly bean in his hand. Bob holds 1 green, 1 yellow, and 2 red jelly beans in his hand. Each randomly picks a jelly bean to show the other. What is the probability that the colors match?
Abe 手里拿着一颗绿色的和一颗红色的果冻豆。Bob 手里拿着一颗绿色的、一颗黄色的和两颗红色的果冻豆。每个人随机挑选一个果冻豆给对方看。那么这两颗果冻豆颜色匹配的概率是多少？

正确答案：C · 分值：1

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2013 AMC8 #15 · Algebra · ★★★
If 3p+34=903^p + 3^4 = 90 , 2r+44=762^r + 44 = 76 , and 53+6s=14215^3 + 6^s = 1421 , what is the product of pp , rr , and ss ?
若 3p+34=903^p + 3^4 = 90，2r+44=762^r + 44 = 76，53+6s=14215^3 + 6^s = 1421，那么 pp、rr、ss 的乘积是多少？

正确答案：B · 分值：1

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2013 AMC8 #16 · Algebra · ★★★
A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of 8th8^\text{th} -graders to 6th6^\text{th} -graders is 5:35:3 , and the the ratio of 8th8^\text{th} -graders to 7th7^\text{th} -graders is 8:58:5 . What is the smallest number of students that could be participating in the project?
Fibonacci 中学的一些学生正在参加一项社区服务项目。其中，八年级和六年级学生的个数之比为 5：3，八年级学生和七年级学生的个数之比是 8：5．那么参加这个项目的学生数最少是多少个？

正确答案：E · 分值：1

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2013 AMC8 #17 · Algebra · ★★★
The sum of six consecutive positive integers is 2013. What is the largest of these six integers?
六个连续正整数之和是 2013，那么这六个整数中最大的整数是多少？

正确答案：B · 分值：1

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2013 AMC8 #18 · Geometry · ★★★
Isabella uses one-foot cubical blocks to build a rectangular fort that is 12 feet long, 10 feet wide, and 5 feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain?
Isabella 使用一些边长为 1 英尺的正方体砖块来建造一个长为 12 英尺，宽 10 英尺，高 5 英尺的堡垒。堡垒的地板和 4 堵墙的厚度都是 1 英尺。那么这个堡垒需要多少块砖块？

正确答案：B · 分值：1

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2013 AMC8 #19 · Counting, Probability & Statistics · ★★★
Bridget, Cassie, and Hannah are discussing the results of their last math test. Hannah shows Bridget and Cassie her test, but Bridget and Cassie don't show theirs to anyone. Cassie says, 'I didn't get the lowest score in our class,' and Bridget adds, 'I didn't get the highest score.' What is the ranking of the three girls from highest to lowest?
Bridget，Cassie 和 Hannah 正在讨论她们最近一次数学考试的成绩。Hannah 向 Bridget 和 Cassie 展示了她的分数，但是 Bridget 和 Cassie 没有把她们各自的分数告诉任何人。Cassie 说：“我的分数不是我们班最低的。”Bridget 补充道：“我没有得到最高的分数。”那么这 3 个女孩的分数从高到低排名是下面哪个？

正确答案：D · 分值：1

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2013 AMC8 #20 · Geometry · ★★★
AA1×21\times 2 rectangle is inscribed in a semicircle with longer side on the diameter. What is the area of the semicircle?
一个 1ｘ2 的矩形内接在一个半圆内，矩形的长边和圆的直径重合。那么这个半圆的面积是多少？

正确答案：C · 分值：1

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2013 AMC8 #21 · Counting, Probability & Statistics · ★★★
Samantha lives 2 blocks west and 1 block south of the southwest corner of City Park. Her school is 2 blocks east and 2 blocks north of the northeast corner of City Park. On school days she bikes on streets to the southwest corner of City Park, then takes a diagonal path through the park to the northeast corner, and then bikes on streets to school. If her route is as short as possible, how many different routes can she take?
Samantha 住在城市公园的西南角向西 2 个街区和向南 1 个街区的位置，而她的学校在城市公园的东北角向东两个街区和向北两个街区的位置。上学时，她首先沿着街道骑自行车到城市公园的西南角，然后沿着公园的一条对角线穿过公园到东北角，然后再沿着街道骑自行车到学校。如果她的路线尽可能短，她可以走多少条不同的路线？

正确答案：E · 分值：1

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2013 AMC8 #22 · Counting, Probability & Statistics · ★★★
Toothpicks are used to make a grid that is 60 toothpicks long and 32 toothpicks wide. How many toothpicks are used altogether?
下图所示的网格是用牙签做成的，网格长为 60 根牙签，宽为 32 根牙签。则总共用了多少根牙签？

正确答案：E · 分值：1

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2013 AMC8 #23 · Geometry · ★★★★
Angle ABC of △ABC\triangle ABC is a right angle. The sides of △ABC\triangle ABC are the diameters of semicircles as shown. The area of the semicircle on AB‾\overline{AB} equals 8π8\pi, and the arc of the semicircle on AC‾\overline{AC} has length 8.5π8.5\pi. What is the radius of the semicircle on BC‾\overline{BC}?
在内，∠ABC 是一个直角。 的三条边是如图所示的三个半圆的直径。 上的半圆面积是 8π，边上的半圆弧长为 8.5π．那么边上的半圆的半径是多少？
边

正确答案：B · 分值：1

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2013 AMC8 #24 · Geometry · ★★★★
Squares ABCD , EFGH , and GHIJ are equal in area. Points C and D are the midpoints of sides IH and HE , respectively. What is the ratio of the area of the shaded pentagon AJICB to the sum of the areas of the three squares?
正方形 ABCD，EFGH 和 GHIJ 的面积都相等。点 C 和点 D 分别是边 IH 和 HE 的中点。那么阴影部分五边形 AJICB 的面积和三个正方形面积总和的比值是多少？

正确答案：C · 分值：1

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2013 AMC8 #25 · Geometry · ★★★★
A ball with diameter 4 inches starts at point A to roll along the track shown. The track is comprised of 3 semicircular arcs whose radii are R_1 = 100 inches, R_2 = 60 inches, and R_3 = 80 inches, respectively. The ball always remains in contact with the track and does not slip. What is the distance the center of the ball travels over the course from A to B?
直径为 4 英寸的球从 A 开始沿着图示轨道滚动。轨道由 3 段半圆弧组成，半径分别为 R1=100 英寸，R2=60 英寸，R3=80 英寸。球全程都和轨道紧密接触，并且不会滑动。那么当球从 A 滚到 B，球心所经过的路程是多少英寸？

正确答案：A · 分值：1

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2012 AMC8 #1 · Algebra · ★
Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 hamburgers for a neighbourhood picnic?
Rachelle 用 3 磅肉为她的家人做了 8 个汉堡包。那么为邻里野餐做 24 个汉堡包需要多少磅肉？

正确答案：E · 分值：1

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2012 AMC8 #2 · Algebra · ★
In the country of East Westmore, statisticians estimate there is a baby born every 8 hours and a death every day. To the nearest hundred, how many people are added to the population of East Westmore each year?
在 East Westmore 这个国家，统计学家们估计，每 8 小时就会有 1 个婴儿出生，并且每天都会有一人去世。那么每年 East Westmore 国家的人口数会增加多少？结果精确到百位.

正确答案：B · 分值：1

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2012 AMC8 #3 · Algebra · ★
On February 13 The Oshkosh Northwester listed the length of daylight as 10 hours and 24 minutes, the sunrise was 6:57 AM , and the sunset as 8:15 PM . The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?
在 2 月 13 号这天，The Oshkosh Northwester 给出的白天时长是 10 小时 24 分钟，日出是早上 6：57，日落是晚上 8：15．白天时长和日出时间是对的，但日落时间不对。那么正确日落时间是多少？

正确答案：B · 分值：1

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2012 AMC8 #4 · Algebra · ★
Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat?
Peter 的家人晚餐订了一块 12 片的比萨。Peter 吃了一片，然后和他的弟弟 Paul 平分了另一片。那么 Peter 所吃的比萨饼占整块的比例是多少？

正确答案：C · 分值：1

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2012 AMC8 #5 · Geometry · ★★
In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note that the diagram is not drawn to scale. What is the length of X , in centimeters?
如下图所示，所有的角都是直角，并且边长都是以厘米为单位。注意图形没有按比例给出。 那么 X 代表的长度是多少厘米？

正确答案：E · 分值：1

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2012 AMC8 #6 · Geometry · ★
A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inches high and 10 inches wide. What is the area of the border, in square inches?
一张长方形的照片被放置在一个框架中，框架在照片的四周形成一个两英寸宽的边界。这张照片高 8 英寸，宽 10 英寸。边界的面积是多少平方英寸？

正确答案：E · 分值：1

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2012 AMC8 #7 · Algebra · ★★
Isabella must take four 100-point tests in her math class. Her goal is to achieve an average grade of 95 on the tests. Her first two test scores were 97 and 91. After seeing her score on the third test, she realized she can still reach her goal. What is the lowest possible score she could have made on the third test?
Isabella 必须参加 4 场满分都是 100 分的数学考试。她的目标是平均分达到 95 分。她的前 2 场考试的分数是 97 分和 91 分。当她看到第三场考试分数后，她意识到她还是可以达到她的目标的。那么第三场考试她可能考到的最低分数是多少？

正确答案：B · 分值：1

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2012 AMC8 #8 · Algebra · ★★
A shop advertises everything is "half price in today's sale." In addition, a coupon gives a 20% discount on sale prices. Using the coupon, the price today represents what percentage off the original price?
一家商店做了如下广告：“今天所有商品半价。”另外，还有可以使价格降低 20％的一张优惠券可以使用。若使用优惠券，那么今天的商品价格相当于原价降低了百分之多少？

正确答案：D · 分值：1

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2012 AMC8 #9 · Algebra · ★★
The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?
Fort Worth 动物园有一些两只腿的鸟，和一些 4 只腿的哺乳动物。一次 Margie 去动物园，数到了 200 个头，522 条腿。那么 Margie 数到的动物中，有多少是两只腿的鸟？

正确答案：C · 分值：1

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2012 AMC8 #10 · Counting, Probability & Statistics · ★★
How many 4-digit numbers greater than 1000 are there that use the four digits of 2012?
使用 2012 的四个数字，能组成多少个大于 1000 的四位数？

正确答案：D · 分值：1

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2012 AMC8 #11 · Counting, Probability & Statistics · ★★★
The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, and xx are all equal. What is the value of xx ?
正整数 3,4,5,6,6,7 和 x 组成的一组数，它们的平均数、中位数、唯一的众数都相等。那么 x 的值是多少？

正确答案：D · 分值：1

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2012 AMC8 #13 · Number Theory · ★★★
Jamar bought some pencils costing more than a penny each at the school bookstore and paid $1.43 . Sharona bought some of the same pencils and paid $1.87 . How many more pencils did Sharona buy than Jamar?
Jamar 在学校的书店买了一些铅笔，每支价格超过 1 美分，总共付了 1.43 美元。Sharona 也买了一些相同的铅笔，总共支付 1.87 美元。那么 Sharona 买的铅笔教比 Jamar 多多少支？

正确答案：C · 分值：1

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2012 AMC8 #14 · Counting, Probability & Statistics · ★★★
In the BIG N, a middle school football conference, each team plays every other team exactly once. If a total of 21 conference games were played during the 2012 season, how many teams were members of the BIG N conference?
在名为“BIG N”的中学足球联盟中，每个队需要与其他队比赛一次。如果 2012 赛季总共进行了 21 场比赛，那么这个足球联盟有多少支球队？

正确答案：B · 分值：1

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2012 AMC8 #15 · Number Theory · ★★★
The smallest number greater than 2 that leaves a remainder of 2 when divided by 3, 4, 5, or 6 lies between what numbers?
大于 2 且除以 3,4,5 或 6 所得余数均为 2 的最小整数在下面哪两个数之间？

正确答案：D · 分值：1

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2012 AMC8 #16 · Counting, Probability & Statistics · ★★★
Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?
用数字 0,1,2,3,4,5,6,7,8,9 组成两个 5 位数（每个数字只使用一次），使这两个五位数的和最大。下面哪个可能是这两个数之一？

正确答案：C · 分值：1

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2012 AMC8 #17 · Geometry · ★★★
A square with integer side length is cut into 10 squares, all of which have integer side length and at least 8 of which have area 1. What is the smallest possible value of the length of the side of the original square?
一个边长为整数的正方形被分割成 10 个小正方形，这些小正方形的边长也都是整数，并且至少有 8 个面积为 1．那么原来大正方形的边长的最小值是多少？

正确答案：B · 分值：1

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2012 AMC8 #18 · Number Theory · ★★★
What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?
有一个正整数，既不是质数，也不是完全平方数，且没有小于 50 的质因数。那么符合要求的最小正整数是多少？

正确答案：A · 分值：1

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2012 AMC8 #19 · Algebra · ★★★
In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and all but 4 are blue. How many marbles are in the jar?
一个罐子里装有红绿蓝三种颜色的玻璃球，除了 6 个之外的其他玻璃球都是红色的，除了 8 个之外的其他玻璃球都是绿色的，除了 4 个之外的其他玻璃球都是蓝色的。那么罐子里有多少个玻璃球？

正确答案：C · 分值：1

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2012 AMC8 #20 · Algebra · ★★★
What is the correct ordering of the three numbers 519,721\displaystyle \frac{5}{19} , \frac{7}{21}, and 923\displaystyle \frac{9}{23}, in increasing order?
把 519\displaystyle \frac{5}{19}、721\displaystyle \frac{7}{21}、923\displaystyle \frac{9}{23} 这三个数从小到大排列，正确的顺序是什么？

正确答案：B · 分值：1

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2012 AMC8 #21 · Geometry · ★★★
Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet?
Marla 有一个边长为 10 英尺的大的白色正方体。她同时还有能够粉刷 300 平方英尺的绿漆。 Marla 使用了全部的绿漆，将白色正方体涂成了这样的一个正方体：正方体的每个面的中央都有一个白色正方形，四周被绿边围绕。那么其中一个面上的白色正方形的面积是多少平方英尺？

正确答案：D · 分值：1

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2012 AMC8 #22 · Counting, Probability & Statistics · ★★★★
Let RR be a set of nine distinct integers. Six of the elements are 2 , 3 , 4 , 6 , 9 , and 14 . What is the number of possible values of the median of RR ?
R 是由 9 个不同的整数组成的集合。其中 6 个元素是 2,3,4,6,9 和 14．那么 R 的中位数有多少个可能的值？

正确答案：D · 分值：1

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2012 AMC8 #23 · Geometry · ★★★★
An equilateral triangle and a regular hexagon have equal perimeters. If the triangle's area is 4, what is the area of the hexagon?
一个等边三角形和一个正六边形的周长相等。若三角形的面积是 4，那么六边形的面积是多少？

正确答案：C · 分值：1

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2012 AMC8 #24 · Geometry · ★★★★
A circle of radius 2 is cut into four congruent arcs. The four arcs are joined to form the star figure shown. What is the ratio of the area of the star figure to the area of the original circle?
半径为 2 的圆被分割成 4 段相等的弧，这 4 段弧拼接成如图所示的星型。那么这个星型的面积和原来圆的面积的比值是多少？

正确答案：A · 分值：1

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2012 AMC8 #25 · Geometry · ★★★★
A square with area 4 is inscribed in a square with area 5, with one vertex of the smaller square on each side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length a , and the other of length b . What is the value of ab ?
一个面积为 4 的正方形内接在一个面积为 5 的正方形内，小正方形的每个顶点分别落在大正方形的每条边上。小正方形的某个顶点将大正方形的一条边分成了 2 条线段，长度分别是 a 和 b，那么 ab 的值是多少？

正确答案：C · 分值：1

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2011 AMC8 #1 · Algebra · ★
Margie bought 3 apples at a cost of 50 cents per apple. She paid with a 5-dollar bill. How much change did Margie receive?
Margie 买了 3 个苹果，每个 50 美分。她付了 5 美元，那么她应该找回多少零钱？

正确答案：E · 分值：1

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2011 AMC8 #2 · Geometry · ★
Karl's rectangular vegetable garden is 20 feet by 45 feet, and Makenna's is 25 feet by 40 feet. Whose garden is larger in area?
Karl 的长方形蔬菜园的尺寸是 20 英尺ｘ45 英尺，Makenna 的菜园是 25 英尺ｘ40 英尺。下面哪句话是对的？

正确答案：E · 分值：1

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2011 AMC8 #3 · Geometry · ★★
Extend the square pattern of 8 black and 17 white square tiles by attaching a border of black tiles around the square. What is the ratio of black tiles to white tiles in the extended pattern?
把下图所示的有 8 块黑色和 17 块白色方形瓷砖组成的正方形图案，通过围绕着这个大正方形的外周贴一圈黑色的瓷砖而进行拓展。那么拓展后的图形中，黑色瓷砖和白色瓷砖的个数的比值是多少？

正确答案：D · 分值：1

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2011 AMC8 #4 · Counting, Probability & Statistics · ★
Here is a list of the numbers of fish that Tyler caught in nine outings last summer:
2,0,1,3,0,3,3,1,2.2,0,1,3,0,3,3,1,2.
Which statement about the mean, median, and mode is true?
下面是 Tyler 去年夏天在 9 次出游中钓到的鱼的数量列表：2，0，1，3，0，3，3，1，2。关于平均值、中位数和众数的说法，下面哪个正确？ mean | 平均值
median | 中位数
mode | 众数

正确答案：C · 分值：1

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2011 AMC8 #5 · Algebra · ★★
What time was it 2011 minutes after midnight on January 1, 2011?
从 2011 年 1 月 1 日凌晨开始，经过 2011 分钟后是什么时间？ | 1 月 1 日下午 9:31 | 1 月 1 日下午 11:51 | 1 月 2 日上午 3:11 | 1 月 2 日上午 9:31 | 1 月 2 日下午 6:01

正确答案：D · 分值：1

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2011 AMC8 #6 · Counting, Probability & Statistics · ★★
In a town of 351 adults, every adult owns a car, motorcycle, or both. If 331 adults own cars and 45 adults own motorcycles, how many of the car owners do not own a motorcycle?
在一个有 351 个成年人的小镇，每个成年人都有汽车，摩托车或者两者兼具。若 331 人有汽车，45 人有摩托车，那么拥有汽车的人当中，有多少人没有摩托车？

正确答案：D · 分值：1

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2011 AMC8 #7 · Geometry · ★★
Each of the following four large congruent squares is subdivided into combinations of congruent triangles or rectangles and is partially bolded. What percent of the total area is partially bolded?
下面 4 个大的全等正方形，每个都被分成几个全等的三角形或者矩形，并且一部分用粗体表示。那么粗体部分的面积占了总面积的百分之多少？

正确答案：C · 分值：1

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2011 AMC8 #8 · Counting, Probability & Statistics · ★
Bag A has three chips labeled 1, 3, and 5. Bag B has three chips labeled 2, 4, and 6. If one chip is drawn from each bag, how many different values are possible for the sum of the two numbers on the chips?
口袋 A 中有标有 1，3，5 的三个筹码，口袋 B 中有标有 2，4，6 的三个筹码。若从每个口袋中随机抽出一个筹码，那么这 2 个筹码上的数字之和有多少种可能的不同值？

正确答案：B · 分值：1

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2011 AMC8 #9 · Algebra · ★★
Carmen takes a long bike ride on a hilly highway. The graph indicates the miles traveled during the time of her ride. What is Carmen's average speed for her entire ride in miles per hour?
卡门在一条丘陵公路上骑了很长时间的自行车。这张图表显示了她骑车时行驶的英里数。卡门整个旅程的平均速度是多少英里每小时？
Miles | 英里数
Hours | 小时数

正确答案：E · 分值：1

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2011 AMC8 #10 · Algebra · ★★
The taxi fare in Gotham City is $2.40 for the first 12\frac12 mile and additional mileage charged at the rate $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10 ?
高谭市的出租车前 英里收费 2.40 美元，后面每增加 0.1 英里收费 0.20 美元。你还打算给司机 2 美元小费，那么 10 美元你能坐多少英里？

正确答案：C · 分值：1

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2011 AMC8 #11 · Counting, Probability & Statistics · ★★★
The graph shows the number of minutes studied by both Asha (black bar) and Sasha (grey bar) in one week. On the average, how many more minutes per day did Sasha study than Asha?
下图显示了一周内 Asha（黑色长条）和 Sasha（灰色长条）的学习时间（分钟）。那么 Sasha 平均每天的学习时间比 Asha 多多少分钟？

正确答案：A · 分值：1

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2011 AMC8 #12 · Counting, Probability & Statistics · ★★★
Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?
Angie，Bridget，Carlos 和 Diego 随机围着一张方桌坐下，一人坐一边。那么 Angie 和 Carlos 面对面坐着的概率是多少？

正确答案：B · 分值：1

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2011 AMC8 #13 · Geometry · ★★★
Two congruent squares, ABCD and PQRS , have side length 15 . They overlap to form the 15 by 25 rectangle AQRD shown. What percent of the area of rectangle AQRD is shaded?
ABCD 和 PQRS 是两个全等的正方形，边长均为 15.它们重合形成一个 15ｘ25 的矩形 AQRD，如图所示。那么阴影部分占了矩形 AQRD 面积的百分之多少？

正确答案：C · 分值：1

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2011 AMC8 #14 · Algebra · ★★★
There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:45 : 4 . There are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4:54 : 5 . The two schools hold a dance and all students from both schools attend. What fraction of the students at the dance are girls?
Colfax 中学有 270 个学生，男生和女生的比例是 5:4。Winthrop 中学有 180 个学生，男生和女生的比例是 4:5。这两个学校举行了一次舞会，并且两个学校的学生都参加了这次舞会。 那么舞会上女生所占总学生数的比例是多少？

正确答案：C · 分值：1

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2011 AMC8 #15 · Number Theory · ★★★
How many digits are in the product 45⋅5104^5 \cdot 5^{10} ?
的乘积结果有多少位数字？

正确答案：D · 分值：1

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2011 AMC8 #16 · Geometry · ★★★
Let AA be the area of the triangle with sides of length 25, 25 , and 30 . Let BB be the area of the triangle with sides of length 25, 25, and 40 . What is the relationship between AA and BB ?
A 表示边长为 25，25，30 的三角形的面积，B 表示边长为 25，25，40 的三角形的面积，那么 A 和 B 的关系是什么？

正确答案：C · 分值：1

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2011 AMC8 #17 · Number Theory · ★★★
Let ww , xx , yy , and zz be whole numbers. If 2w⋅3x⋅5y⋅7z=5882^w \cdot 3^x \cdot 5^y \cdot 7^z = 588 , then what does 2w + 3x + 5y + 7z equal?
设 ww、xx、yy、zz 都是非负整数。若 2w⋅3x⋅5y⋅7z=5882^w \cdot 3^x \cdot 5^y \cdot 7^z = 588，那么 2w + 3x + 5y + 7z 等于多少？

正确答案：A · 分值：1

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2011 AMC8 #18 · Counting, Probability & Statistics · ★★★
A fair 6 sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number?
一个标准的 6 面骰子掷了两次，那么第一次正面朝上的数大于或等于第二次正面朝上的数的概率是多少？

正确答案：D · 分值：1

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2011 AMC8 #19 · Counting, Probability & Statistics · ★★★
How many rectangles are in this figure?
下图中有多少个长方形?

正确答案：D · 分值：1

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2011 AMC8 #20 · Geometry · ★★★
Quadrilateral ABCD is a trapezoid, AD = 15 , AB = 50 , BC = 20 , and the altitude is 12 . What is the area of the trapezoid?
四边形 ABCD 是个梯形，其中 AD＝15，AB＝50，BC＝20，且高为 12.那么这个梯形的面积是多少?

正确答案：D · 分值：1

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2011 AMC8 #21 · Number Theory · ★★★★
Students guess that Norb's age is 24, 28, 30, 32, 36, 38, 41, 44, 47 , and 49 . Norb says, "At least half of you guessed too low, two of you are off by one, and my age is a prime number." How old is Norb?
学生猜测 Norb 的年龄是 24，28，30，32，36，38，41，44，47 和 49 岁。Norb 说：“你们中至少有一半猜的太低，有 2 个同学猜的跟实际年龄相差 1 岁，并且我的年龄是个质数”。 那么 Norb 多大？

正确答案：C · 分值：1

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2011 AMC8 #23 · Counting, Probability & Statistics · ★★★★
How many 4-digit positive integers have four different digits, where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largest digit?
有多少个各个位上数字不同的 4 位数，满足以下条件：最高位不为 0，这个 4 位数是 5 的倍数，且 5 是最大的数字？

正确答案：D · 分值：1

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2011 AMC8 #24 · Number Theory · ★★★★
In how many ways can 10001 be written as the sum of two primes?
有多少种方法可以将 10001 写成两个质数之和?

正确答案：A · 分值：1

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2011 AMC8 #25 · Geometry · ★★★★
A circle with radius 1 is inscribed in a square and circumscribed about another square as shown. Which fraction is closest to the ratio of the circle's shaded area to the area between the two squares?
一个半径为 1 的圆内切于一个正方形中，并且外接于另一个正方形，如图所示。那么圆的阴影部分的面积和两个正方形之间的面积的比值最接近下面哪个分数？

正确答案：A · 分值：1

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2010 AMC8 #1 · Algebra · ★
At Euclid Middle School, the mathematics teachers are Miss Germain, Mr. Newton, and Mrs. Young. There are 11 students in Mrs. Germain's class, 8 students in Mr. Newton's class, and 9 students in Mrs. Young's class taking the AMC 8 this year. How many mathematics students at Euclid Middle School are taking the contest?
在欧几里得中学，数学老师是 Germain 小姐，Newton 先生和 Young 女士。Germain 小姐班上的 11 位学生，Newton 先生班上的 8 位学生和 Young 女士班上的 9 位学生今年参加 AMC8 竞赛。那么欧几里得中学今年有多少学数学的学生会参加这次竞赛？

正确答案：C · 分值：1

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2010 AMC8 #2 · Algebra · ★
If a @ b = a×ba+b\displaystyle \frac{a\times b}{a+b} for a,b positive integers, then what is 5 @ 10 ?
对于正整数 aa、bb，定义 a@b=a×ba+b\displaystyle a @ b = \frac{a\times b}{a+b}。那么 $5 @ 10$ 等于多少？

正确答案：D · 分值：1

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2010 AMC8 #3 · Algebra · ★★
The graph shows the price of five gallons of gasoline during the first ten months of the year. By what percent is the highest price more than the lowest price?
下图显示了前 10 个月 5 加仑汽油的价格。那么最高价比最低价多百分之几？

正确答案：C · 分值：1

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2010 AMC8 #4 · Counting, Probability & Statistics · ★
What is the sum of the mean, median, and mode of the numbers 2,3,0,3,1,4,0,3 ?
数字 2，3，0，3，1，4，0，3 的平均数，中位数，众数之和是多少？

正确答案：C · 分值：1

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2010 AMC8 #5 · Algebra · ★★
Alice needs to replace a light bulb located 10 centimeters below the ceiling in her kitchen. The ceiling is 2.4 meters above the floor. Alice is 1.5 meters tall and can reach 46 centimeters above the top of her head. Standing on a stool, she can just reach the light bulb. What is the height of the stool, in centimeters?
Alice 需要换掉厨房的一个灯泡，灯泡位于天花板下面 10 厘米，天花板离地面 2.4 米。 Alice 有 1.5 米高，并且可以碰到离她头顶 46 厘米高的地方。当她站在凳子上，她恰好可以碰到灯泡。那么凳子的高度是多少厘米？

正确答案：B · 分值：1

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2010 AMC8 #6 · Geometry · ★
Which of the following figures has the greatest number of lines of symmetry?
下面哪个图形对称轴的个数最多？

正确答案：E · 分值：1

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2010 AMC8 #7 · Counting, Probability & Statistics · ★★★
Using only pennies, nickels, dimes, and quarters, what is the smallest number of coins Freddie would need so he could pay any amount of money less than a dollar?
如果仅使用便士（1 分）、五分镍币、一角硬币（10 分）和 25 分硬币，Freddie 可以用于支付少于一美元的任何金额所需的硬币的最小数量是多少？

正确答案：B · 分值：1

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2010 AMC8 #8 · Algebra · ★★
As Emily is riding her bicycle on a long straight road, she spots Emerson skating in the same direction 1/2 mile in front of her. After she passes him, she can see him in her rear mirror until he is 1/2 mile behind her. Emily rides at a constant rate of 12 miles per hour, and Emerson skates at a constant rate of 8 miles per hour. For how many minutes can Emily see Emerson?
当 Emily 在一条长直公路上骑着她的自行车时，她发现前方 1/2 英里处 Emerson 正朝着同方向滑冰。当她经过他以后，她可以一直在后视镜里看到他，直到他在她后方 1/2 英里处。 Emily 骑车的速度是 12 英里每小时，而 Emerson 滑冰的速度是 8 英里每小时。那么 Emily 在多少分钟内可以一直看到 Emerson？

正确答案：D · 分值：1

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2010 AMC8 #9 · Algebra · ★★
Ryan got 80% of the problems correct on a 25 -problem test, 90% on a 40 -problem test, and 70% on a 10 -problem test. What percent of all the problems did Ryan answer correctly?
Ryan 在一次总共 25 题的考试里，做对 80％的题目，总共 40 题的考试里，做对 90％的题，在总共 10 题的考试里，做对 70％的题。那么总的来说，Ryan 所有的题的正确率是多少？

正确答案：D · 分值：1

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2010 AMC8 #10 · Geometry · ★★
Six pepperoni circles will exactly fit across the diameter of a 12 -inch pizza when placed. If a total of 24 circles of pepperoni are placed on this pizza without overlap, what fraction of the pizza is covered by pepperoni?
当把 6 个意大利香肠圈放在一个 12 英寸的比萨饼上时，正好可以穿过比萨饼的直径。若把 24 个意大利香肠圈没有重叠的放在这块比萨饼上，那么整块比萨饼被意大利香肠圈覆盖的比例是多少？

正确答案：B · 分值：1

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2010 AMC8 #11 · Algebra · ★★★
The top of one tree is 16 feet higher than the top of another tree. The heights of the two trees are in the ratio 3:43:4 . In feet, how tall is the taller tree?
一棵树的顶部比另一棵树的顶部高 16 英尺。这两棵树的高度之比是 3：4。那么较高的那棵树高多少英尺？

正确答案：B · 分值：1

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2010 AMC8 #12 · Algebra · ★★★
Of the 500 balls in a large bag, 80% are red and the rest are blue. How many of the red balls must be removed so that 75% of the remaining balls are red?
一个大包里的 500 个球中，有 80％是红球，其他是蓝球。需要从包中移走多少红球，使得包中剩下的球中，75％是红球？

正确答案：D · 分值：1

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2010 AMC8 #13 · Algebra · ★★★
The lengths of the sides of a triangle in inches are three consecutive integers. The length of the shortest side is 30% of the perimeter. What is the length of the longest side?
一个三角形的三条边长（单位：英寸）是 3 个连续的正整数。最短的边长是周长的 30％。那么最长的边长是多少？

正确答案：E · 分值：1

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2010 AMC8 #14 · Number Theory · ★★★
What is the sum of the prime factors of 2010 ?
2010 的质因子之和是多少？

正确答案：C · 分值：1

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2010 AMC8 #15 · Algebra · ★★★
A jar contains 5 different colors of gumdrops. 30% are blue, 20% are brown, 15% are red, 10% are yellow, and other 30 gumdrops are green. If half of the blue gumdrops are replaced with brown gumdrops, how many gumdrops will be brown?
一个罐子装有 5 种不同颜色的口香糖：30％是蓝色的，20％是棕色的，15％是红色的，10％ 是黄色的，且其他 30 个口香糖是绿色的。若蓝色口香糖的一半被棕色口香糖代替，那么有多少个口香糖将是棕色的？

正确答案：C · 分值：1

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2010 AMC8 #16 · Geometry · ★★★
A square and a circle have the same area. What is the ratio of the side length of the square to the radius of the circle?
一个正方形和一个圆有相同的面积。那么正方形的边长和圆的半径的比值是多少？

正确答案：B · 分值：1

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2010 AMC8 #17 · Geometry · ★★★
The diagram shows an octagon consisting of 10 unit squares. The portion below PQ‾\overline{PQ} is a unit square and a triangle with base 5 . If PQ‾\overline{PQ} bisects the area of the octagon, what is the ratio XQQY\displaystyle \frac{XQ}{QY}?
下图是一个由 10 个单位正方形组成的八边形。PQ‾\overline{PQ} 下方的部分是一个单位正方形和一个底边长为 5 的三角形。若 PQ‾\overline{PQ} 平分八边形的面积，那么 XQQY\displaystyle \frac{XQ}{QY} 的比值是多少？

正确答案：D · 分值：1

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2010 AMC8 #18 · Geometry · ★★★
A decorative window is made up of a rectangle with semicircles on either end. The ratio of AD to AB is 3:2 , and AB is 30 inches. What is the ratio of the area of the rectangle to the combined areas of the semicircles?
一种装饰性窗户是由一个矩形和位于两端的半圆组成。已知 AD：AB＝3：2，AB 长为 30 英寸，那么矩形的面积和两个半圆面积之和的比值是多少？

正确答案：C · 分值：1

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2010 AMC8 #19 · Geometry · ★★★
The two circles pictured have the same center C . Chord AD‾\overline{AD} is tangent to the inner circle at B , AC is 10 , and chord AD‾\overline{AD} has length 16 . What is the area between the two circles?
下图中的两个圆是同心圆，圆心都是 CC。弦 AD‾\overline{AD} 与内圆切于 BB，ACAC 长为 10，弦 AD‾\overline{AD} 长为 16。那么这两个圆之间区域的面积是多少？

正确答案：C · 分值：1

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2010 AMC8 #20 · Counting, Probability & Statistics · ★★★
In a room, 2/5 of the people are wearing gloves, and 3/4 of the people are wearing hats. What is the minimum number of people in the room wearing both a hat and gloves?
在一个房间里，2/5 的人戴着手套，3/4 的人戴着帽子。那么房间里同时戴着帽子和手套的人最少是多少个？

正确答案：A · 分值：1

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2010 AMC8 #21 · Algebra · ★★★★
Hui is an avid reader. She bought a copy of the best seller Math is Beautiful. On the first day, Hui read 1/5 of the pages plus 12 more, and on the second day she read 1/4 of the remaining pages plus 15 pages. On the third day she read 1/3 of the remaining pages plus 18 pages. She then realized that there were only 62 pages left to read, which she read the next day. How many pages are in this book?
Hui 很爱读她买的一本名叫《数学是美丽的》的畅销书，第一天，Hui 读了书的 1/5 再加 12 页，第二天，她读了剩下的 1/4 再加 15 页。第三天，她读了剩余页数的 1/3 再加 18 页。然后她发现还剩 62 页未读，隔天就把这剩下的 62 页读完了。问这本书总共多少页？

正确答案：C · 分值：1

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2010 AMC8 #22 · Number Theory · ★★★
The hundreds digit of a three-digit number is 2 more than the units digit. The digits of the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result?
一个三位数的百位比个位大 2。把这个三位数的各个位上数字颠倒，然后把原来的三位数减去这个数，所得最终结果的个位数字是多少？

正确答案：E · 分值：1

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2010 AMC8 #23 · Geometry · ★★★★
Semicircles POQ and ROS pass through the center of circle O . What is the ratio of the combined areas of the two semicircles to the area of circle O ?
半圆 POQ 和 ROS 通过圆 的圆心。则这两个半圆的面积总和与圆 的面积的比值是多少？

正确答案：B · 分值：1

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2010 AMC8 #24 · Number Theory · ★★★★
What is the correct ordering of the three numbers, 10^8, 5^12, and 2^24?
下面哪个是
,
和
,

正确答案：A · 分值：1

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2010 AMC8 #25 · Counting, Probability & Statistics · ★★★★
Everyday at school, Jo climbs a flight of 6 stairs. Jo can take the stairs 1 , 2 , or 3 at a time. For example, Jo could climb 3 , then 1 , then 2 . In how many ways can Jo climb the stairs?
Jo 每天在学校里都要爬 6 节楼梯。Jo 可以一次爬 1 节，2 节或者 3 节。例如，J0 可以先一次爬 3 节，然后 1 节，然后 2 节。则 Jo 爬楼梯一共有多少种可能的方法？

正确答案：E · 分值：1

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2009 AMC8 #1 · Algebra · ★★
Bridget bought a bag of apples at the grocery store. She gave half of the apples to Ann. Then she gave Cassie 3 apples, keeping 4 apples for herself. How many apples did Bridget buy?
Bridget 在水果店买了一包苹果。她把一半苹果给了 Ann，然后她把 3 个苹果了 Cassie，自己留了 4 个。那么 Bridget 总共买了多少个苹果？

正确答案：E · 分值：1

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2009 AMC8 #2 · Algebra · ★
On average, for every 4 sports cars sold at the local dealership, 7 sedans are sold. The dealership predicts that it will sell 28 sports cars next month. How many sedans does it expect to sell?
平均下来，当地经销商每售出 4 辆跑车，就售出 7 辆轿车。该经销商预计下个月将销售 28 辆跑车，那么预计销售多少辆轿车？

正确答案：D · 分值：1

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2009 AMC8 #3 · Algebra · ★
The graph shows the constant rate at which Suzanna rides her bike. If she rides a total of a half an hour at the same speed, how many miles would she have ridden?
下图显示了 Suzanna 以恒定的速度骑自行车。如果她以同样的速度骑了半个小时，她将骑多少英里？

正确答案：C · 分值：1

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2009 AMC8 #4 · Geometry · ★★
The five pieces shown below can be arranged to form four of the five figures shown in the choices. Which figure cannot be formed?
下面所示的 5 个图形可以重新组合成 5 个选项里其中 4 个图形。那么哪个选项里的图形无法形成？

正确答案：B · 分值：1

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2009 AMC8 #5 · Algebra · ★★
A sequence of numbers starts with 1 , 2 , and 3 . The fourth number of the sequence is the sum of the previous three numbers in the sequence: 1+2+3=6 . In the same way, every number after the fourth is the sum of the previous three numbers. What is the eighth number in the sequence?
一个数列以 1、2、3 开头。第四项是前三项之和：1+2+3=6。同样地，从第四项起每一项都是它前面三项之和。那么这个数列的第 8 项是多少？

正确答案：D · 分值：1

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2009 AMC8 #6 · Algebra · ★★
Steve's empty swimming pool will hold 24,000 gallons of water when full. It will be filled by 4 hoses, each of which supplies 2.5 gallons of water per minute. How many hours will it take to fill Steve's pool?
Steve 家的游泳池当装满水时，能装 24,000 加仑的水。现在将由 4 个水管同时灌水，每个水管每分钟灌水 2.5 加仑。那么将 Steve 家的泳池灌满水要多少小时？

正确答案：A · 分值：1

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2009 AMC8 #7 · Geometry · ★★
The triangular plot of ACD lies between Aspen Road, Brown Road and a railroad. Main Street runs east and west, and the railroad runs north and south. The numbers in the diagram indicate distances in miles. The width of the railroad track can be ignored. How many square miles are in the plot of land ACD?
三角形 ACD 区城处于 Aspen 公路，Brown 公路和一条铁路之间。Main 街道是东西向，铁路是南北向。图中的数字表示以英里为单位的距离。铁路轨道的宽度可以忽略。那么区域 ACD 的面积是多少平方英里？

正确答案：C · 分值：1

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2009 AMC8 #8 · Algebra · ★★
The length of a rectangle is increased by 10% percent and the width is decreased by 10% percent. What percent of the old area is the new area?
矩形的长增加了 10％，宽减小了 10％，那么新的矩形面积是原来的面积的百分之多少？

正确答案：B · 分值：1

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2009 AMC8 #9 · Geometry · ★★
Construct a square on one side of an equilateral triangle. On one non-adjacent side of the square, construct a regular pentagon, as shown. On a non-adjacent side of the pentagon, construct a hexagon. Continue to construct regular polygons in the same way, until you construct an octagon. How many sides does the resulting polygon have?
在一个等边三角形的一边上作一个正方形，然后在此正方形的另一条非相邻边上作一个正五边形，如下图所示。再在此五边形的一条非相邻边上作一个六边形。按照这种方法不断作出正多边形，直到作出一个八边形。那么最终形成的多边形有多少条边？

正确答案：B · 分值：1

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2009 AMC8 #10 · Counting, Probability & Statistics · ★★
On a checkerboard composed of 64 unit squares, what is the probability that a randomly chosen unit square does not touch the outer edge of the board?
在由 64 个单位正方形组成的棋盘上随机选择一个单位正方形，那么此单位正方形不接触棋盘外缘的概率是多少？

正确答案：D · 分值：1

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2009 AMC8 #11 · Number Theory · ★★★
The Amaco Middle School bookstore sells pencils costing a whole number of cents. Some seventh graders each bought a pencil, paying a total of $1.43. Some of the 30 sixth graders each bought a pencil, and they paid a total of $1.95. How many more sixth graders than seventh graders bought a pencil?
Amaco 中学的书店所卖的铅笔每根的价格是个整数（单位：美分）。一些七年级学生每个人买了一支铅笔，总共花了 1.43 美元。一些六年级学生（不超过 30 人）每人买了一支铅笔，总共花了 1.95 美元。买铅笔的人当中，六年级学生比七年级多多少人？

正确答案：D · 分值：1

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2009 AMC8 #12 · Counting, Probability & Statistics · ★★★
The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum of the numbers in the two sectors is prime?
如下所示的两个转盘各自转一次，每个转盘落在各自的某个扇形区域上。那么落在的这两个扇形区域的数字之和是个质数的概率是多少？

正确答案：D · 分值：1

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2009 AMC8 #13 · Counting, Probability & Statistics · ★★★
A three-digit integer contains one of each of the digits 1 , 3 , and 5 . What is the probability that the integer is divisible by 5 ?
一个三位整数包含了数字 1，3 和 5，且每个出现一次。那么这个整数能被 5 整除的概率是多少？

正确答案：B · 分值：1

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2009 AMC8 #14 · Algebra · ★★★
Austin and Temple are 50 miles apart along Interstate 35. Bonnie drove from Austin to her daughter's house in Temple, averaging 60 miles per hour. Leaving the car with her daughter, Bonnie rode a bus back to Austin along the same route and averaged 40 miles per hour on the return trip. What was the average speed for the round trip, in miles per hour?
奥斯汀和坦普尔沿 35 号州际公路相距 50 英里。Bonnic 从奥斯汀开车到她女儿位于坦普尔的家，平均时速为 60 英里。Bonnie 之后把车留给了女儿，接着沿着同一条路线乘公共汽车返回奥斯汀，回程平均速度为每小时 40 英里。那么她往返的平均速度是多少英里每小时？

正确答案：B · 分值：1

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2009 AMC8 #15 · Algebra · ★★★
A recipe that makes 5 servings of hot chocolate requires 2 squares of chocolate, 14\displaystyle \frac{1}{4} cup sugar, 1 cup water and 4 cups milk. Jordan has $5$ squares of chocolate, 2 cups of sugar, lots of water, and 7 cups of milk. If he maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate he can make?
一种制作 5 份热巧克力的配方需要 2 块巧克力、 杯糖、1 杯水和 4 杯牛奶。乔丹有 5 块巧克力，2 杯糖，大量的水和 7 杯牛奶。如果她保持相同的配料比例，那么她能做的热巧克力的最大份数是多少？

正确答案：D · 分值：1

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2009 AMC8 #16 · Counting, Probability & Statistics · ★★★
How many 3 -digit positive integers have digits whose product equals 24 ?
有多少个 3 位正整数，满足各个位上数字之积是 24？

正确答案：D · 分值：1

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2009 AMC8 #17 · Number Theory · ★★★
The positive integers xx and yy are the two smallest positive integers for which the product of 360 and xx is a square and the product of 360 and yy is a cube. What is the sum of xx and yy ?
x 和 y 是满足 360 和 x 之积为平方数，360 和 y 之积为立方数的最小正整数。那么 x 和 y 的和是多少？

正确答案：B · 分值：1

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2009 AMC8 #18 · Algebra · ★★★
The diagram represents a 7-foot-by-7-foot floor that is tiled with 1-square-foot black tiles and white tiles. Notice that the corners have white tiles. If a 15-foot-by-15-foot floor is to be tiled in the same manner, how many white tiles will be needed?
该图表示一块 7 英尺乘 7 英尺的地板，该地板由 1 平方英尺的黑色瓷砖和白色瓷砖铺成。请注意，四个角都是白色瓷砖。如果某个 15 英尺乘 15 英尺的地板要以同样的方式铺成，需要多少块白色瓷砖？

正确答案：C · 分值：1

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2009 AMC8 #19 · Geometry · ★★★
Two angles of an isosceles triangle measure 70∘70^\circ and x∘x^\circ . What is the sum of the three possible values of xx ?
一个等腰三角形其中两个角的度数是 70°和 x°。那么 的 3 个可能值之和是多少？

正确答案：D · 分值：1

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2009 AMC8 #20 · Geometry · ★★★
How many non-congruent triangles have vertices at three of the eight points in the array shown below?
以下图所示阵列 8 个，点中的 3 个为顶点，可以形成多少个不全等的三角形？

正确答案：D · 分值：1

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2009 AMC8 #21 · Algebra · ★★★★
Andy and Bethany have a rectangular array of numbers greater than 0 with 40 rows and 75 columns. Andy adds the numbers in each row. The average of his 40 sums is A . Bethany adds the numbers in each column. The average of her 75 sums is B . What is the value of AB\displaystyle \frac{A}{B} ?
Andy 和 Bethany 有一张 40 行 75 列的矩形正数阵列，Andy 把每行的数字都相加，得到的 40 个和的平均值是 A。Bethany 把每列的数字都相加，所得的 75 个和的平均值是 B。那么多少？

正确答案：D · 分值：1

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2009 AMC8 #22 · Counting, Probability & Statistics · ★★★★
How many whole numbers between 1 and 1000 do not contain the digit 1?
1 和 1000 之间有多少个整数不含有数字 1？
的值是

正确答案：D · 分值：1

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2009 AMC8 #23 · Number Theory · ★★★★
On the last day of school, Mrs. Wonderful gave jelly beans to her class. She gave each boy as many jelly beans as there were boys in the class. She gave each girl as many jelly beans as there were girls in the class. She brought 400 jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. How many students were in her class?
在学期的最后一天，苏威太太给全班同学送去了果冻豆。她给每个男孩的果冻豆数量和班上男孩的数量一样多，她给每个女孩的果冻豆数量和班上女孩的数量一样多。她一共带了 400 颗果冻豆，当她发完时，她还剩下 6 个果冻豆。她班上男生比女生多两个。她班上有多少学生？

正确答案：B · 分值：1

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2009 AMC8 #24 · Number Theory · ★★★★
The letters A , B , C and D represent digits. If the addition and subtraction shown below hold, what digit does D represent?
字母 AA、BB、CC、DD 代表数字。若下图所示的加法和减法都成立，那么 DD 代表哪个数字？

正确答案：E · 分值：1

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2009 AMC8 #25 · Geometry · ★★★★
A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cut is 1/2 foot from the top face. The second cut is 1/3 foot below the first cut, and the third cut is 1/17 foot below the second cut. From the top to the bottom the pieces are labeled A, B, C, and D. The pieces are then glued together end to end as shown in the second diagram. What is the total surface area of this solid in square feet?
一个 1 立方英尺的正方体被平行于立方体顶面的三个切口切成四块。第一个切口距离顶面 英尺。第二个切口比第一个切口低 英尺，第三个切口比第二个切口低 英尺。从上到下，切出的这 4 块立体图形被标记为 A、B、C 和 D。接着这 4 块立体图形被一个接一个地粘合在一起，如第二张图所示。那么新形成的立体图形的总表面积是多少平方英尺？

正确答案：E · 分值：1

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2008 AMC8 #1 · Algebra · ★
Susan had 50 dollars to spend at the carnival. She spent 12 dollars on food and twice as much on rides. How many dollars did she have left to spend?
苏珊在嘉年华会上有 50 美元可以消费。她在食物上花了 12 美元，在乘车上花了两倍的钱。 她还剩多少美元可以花？

正确答案：B · 分值：1

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2008 AMC8 #2 · Counting, Probability & Statistics · ★
The ten-letter code BEST OF LUCK\text{BEST OF LUCK} represents the ten digits 0-9 , in order. What 4-digit number is represented by the code word CLUE\text{CLUE} ?
十个字母的代码 BEST OF LUCK 按顺序依次表示 O—9 这十个数字。代码字 CLUE 代表的 4 位数是什么？

正确答案：A · 分值：1

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2008 AMC8 #3 · Number Theory · ★★
If February is a month that contains Friday the 13th13^{\text{th}} , what day of the week is February 1?
如果 2 月 13 号是周五，那么 2 月 1 号是周几？

正确答案：A · 分值：1

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2008 AMC8 #4 · Geometry · ★
In the figure, the outer equilateral triangle has area 16 , the inner equilateral triangle has area 1 , and the three trapezoids are congruent. What is the area of one of the trapezoids?
下图所示的四形中，外层等边三角形的面积为 16，内部边三角形的面积为 1，三个梯形都是全等的，那么其中一个梯形的面积是多少？

正确答案：C · 分值：1

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2008 AMC8 #5 · Algebra · ★★
Barney Schwinn notices that the odometer on his bicycle reads 1441 , a palindrome, because it reads the same forward and backward. After riding 4 more hours that day and 6 the next, he notices that the odometer shows another palindrome, 1661 . What was his average speed in miles per hour?
Barney Schwinn 注意到他自行车上的里程表读数为 1441，这是个回环数，因为它从前向后读和从后向前读读数都相同。那天又继续骑了 4 小时和第二天骑了 6 小时后，他注意到里程表显示了另一个回环数 1661。他的平均时速是多少英里每小时？

正确答案：E · 分值：1

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2008 AMC8 #6 · Geometry · ★★
In the figure, what is the ratio of the area of the gray squares to the area of the white squares?
如下图所示，灰色正方形的面积和白色正方形的面积的比值是多少？

正确答案：D · 分值：1

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2008 AMC8 #7 · Algebra · ★
If 35=M45=60N\displaystyle \frac{3}{5}=\frac{M}{45}=\frac{60}{N} , what is M+N ?
如果
,

正确答案：E · 分值：1

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2008 AMC8 #8 · Counting, Probability & Statistics · ★
Candy sales from the Boosters Club from January through April are shown. What were the average sales per month in dollars?
下图显示了 Boosters 俱乐部从 1 月到 4 月的糖果销售情况。每月的平均销售额是多少美元？

正确答案：D · 分值：1

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2008 AMC8 #9 · Algebra · ★★
In 2005 Tycoon Tammy invested 100 dollars for two years. During the first year her investment suffered a 15% loss, but during the second year the remaining investment showed a 20% gain. Over the two-year period, what was the change in Tammy's investment?
2005 年大亨塔米投资了 100 美元，投资时长为两年。在第一年，她的投资遭受了 15％的损失，但在第二年，剩余的投资获得了 20％的收益。则在这两年的时间里，塔米的投资发生了什么变化？

正确答案：D · 分值：1

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2008 AMC8 #10 · Counting, Probability & Statistics · ★★
The average age of the 6 people in Room A is 40 . The average age of the 4 people in Room B is 25 . If the two groups are combined, what is the average age of all the people?
A 房间里 6 个人的平均年龄是 40 岁。B 房间里 4 个人的平均年龄是 25 岁。如果把这两组人合起来，那么所有人的平均年龄是多少？

正确答案：D · 分值：1

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2008 AMC8 #11 · Counting, Probability & Statistics · ★★★
Each of the 39 students in the eighth grade at Lincoln Middle School has one dog or one cat or both a dog and a cat. Twenty students have a dog and 26 students have a cat. How many students have both a dog and a cat?
林肯中学八年级总共有 39 名学生，每名学生都有一条狗，或者一只猫，或者两者兼具。已知有 20 名学生有狗，有 26 名学生有猫。那么有多少名学生既有猫又有狗？

正确答案：A · 分值：1

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2008 AMC8 #12 · Algebra · ★★★
A ball is dropped from a height of 3 meters. On its first bounce it rises to a height of 2 meters. It keeps falling and bouncing to 23\displaystyle \frac{2}{3} of the height it reached in the previous bounce. On which bounce will it rise to a height less than 0.5 meters?
一个球从 3 米高处落下。它第一次弹起的高度是 2 米，之后不停地落下和弹起，弹起的高度都是前一次弹起高度的 。则第几次弹起的高度小于 0.5 米？

正确答案：C · 分值：1

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2008 AMC8 #13 · Algebra · ★★★
Mr. Harman needs to know the combined weight in pounds of three boxes he wants to mail. However, the only available scale is not accurate for weights less than 100 pounds or more than 150 pounds. So the boxes are weighed in pairs in every possible way. The results are 122 , 125 and 127 pounds. What is the combined weight in pounds of the three boxes?
哈曼太太需要知道他要邮寄的三个箱子的总重量是多少磅。然而，唯一可用的秤对于称量小于 100 磅或大于 150 磅的重物结果并不精确。因此，最后是以两两组合的方式同时称量 2 个箱子，结果是 122，125 和 127 磅。则这三个箱子的总重量是多少磅？

正确答案：C · 分值：1

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2008 AMC8 #14 · Counting, Probability & Statistics · ★★★
Three A’s\text{A's}, three B’s\text{B's}, and three C’s\text{C's} are placed in the nine spaces so that each row and column contain one of each letter. If A\text{A} is placed in the upper left corner, how many arrangements are possible?
把三个 A,三个 B 和三个 C 放置在九个空格中，使得每行和每列包含三个字母中的每一个字母。 如果 A 放置在左上角，那么一共有多少种安排方法？

正确答案：C · 分值：1

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2008 AMC8 #15 · Number Theory · ★★★
In Theresa's first 8 basketball games, she scored 7, 4, 3, 6, 8, 3, 1 and 5 points. In her ninth game, she scored fewer than 10 points and her points-per-game average for the nine games was an integer. Similarly in her tenth game, she scored fewer than 10 points and her points-per-game average for the 10 games was also an integer. What is the product of the number of points she scored in the ninth and tenth games?
在 Theresa 的前 8 场篮球比赛中，她的进球得分分别是 7，4，3，6，8，3，1 和 5 分。在她的第 9 场比赛中，她的得分少于 10 分，而她在这 9 场比赛中平均每场得分都是整数。同样，在她的第 10 场比赛中，她的得分少于 10 分，而她在这 10 场比赛中平均每场得分也都是整数。 那么她在第 9 场和第 10 场比赛中的得分的乘积是多少？

正确答案：B · 分值：1

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2008 AMC8 #16 · Geometry · ★★★
A shape is created by joining seven unit cubes, as shown. What is the ratio of the volume in cubic units to the surface area in square units?
如图所示，把 7 个单位正方体连接形成如下的立体图形。那么这个立体图形的体积和表面积的比值是多少？

正确答案：D · 分值：1

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2008 AMC8 #17 · Geometry · ★★★
Ms.Osborne asks each student in her class to draw a rectangle with integer side lengths and a perimeter of 50 units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles?
Osborne 女士要求班级里的每一个学生都画一个周长为 50，且每条边长度都是整数的矩形。每个学生都计算了自己所画矩形的面积。那么这些矩形中，最大可能的面积和最小可能的面积的差是多少？

正确答案：D · 分值：1

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2008 AMC8 #18 · Geometry · ★★★
Two circles that share the same center have radii 10 meters and 20 meters. An aardvark runs along the path shown, starting at A and ending at K . How many meters does the aardvark run?
两个同心圆的半径分别是 10 米和 20 米。一个土豚沿着图示路径运动，从 A 点开始到 K 点结束。则土豚总共运动了多少米？

正确答案：E · 分值：1

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2008 AMC8 #19 · Counting, Probability & Statistics · ★★★
Eight points are spaced around at intervals of one unit around a 2×22 \times 2 square, as shown. Two of the 8 points are chosen at random. What is the probability that the two points are one unit apart?
如图所示，八个点绕着一个 2×2 的正方形等间距分布，相邻点的距离均为 1 个单位。从这 8 个点中随机选择其中两个点，则这两点相距一个单位的概率是多少？

正确答案：B · 分值：1

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2008 AMC8 #20 · Algebra · ★★★
The students in Mr. Neatkin's class took a penmanship test. Two-thirds of the boys and 34\displaystyle \frac{3}{4} of the girls passed the test, and an equal number of boys and girls passed the test. What is the minimum possible number of students in the class?
Neatkin 先生班上的学生参加了某个笔试。三分之二的男孩和 的女孩通过了这个笔试，且通过这个笔试的男孩和女孩个数是一样的。则这个班最少可能是多少个学生？

正确答案：B · 分值：1

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2008 AMC8 #21 · Geometry · ★★★★
Jerry cuts a wedge from a 6 -cm cylinder of bologna as shown by the dashed curve. Which answer choice is closest to the volume of his wedge in cubic centimeters?
如图中虚线所示，Jery 从某个 6 厘米长的博洛尼亚圆柱上切下一个楔子。下面哪一个选项的答案最接近他的楔子的体积（单位：立方厘米）？

正确答案：C · 分值：1

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2008 AMC8 #22 · Number Theory · ★★★★
For how many positive integer values of n are both n3\displaystyle \frac{n}{3} and 3n three-digit whole numbers?
有多少个正整数 nn，使得 n3\displaystyle \frac{n}{3} 和 3n3n 都是三位整数？

正确答案：A · 分值：1

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2008 AMC8 #23 · Geometry · ★★★★
In square ABCE , AF=2FE and CD=2DE . What is the ratio of the area of △BFD\triangle BFD to the area of square ABCE ?
在正方形 ABCE 中，AF＝2FE，CD＝2DE，那么△BPD 的面积和正方形 ABCE 的面积的比值是多少？

正确答案：C · 分值：1

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2008 AMC8 #24 · Counting, Probability & Statistics · ★★★★
Ten tiles numbered 1 through 10 are turned face down. One tile is turned up at random, and a die is rolled. What is the probability that the product of the numbers on the tile and the die will be a square?
编号为 1 至 10 的十块瓷砖面朝下放置着。随机翻开其中一块瓷砖，然后再掷一枚般子。则瓷砖和骰子上的数的乘积为完全平方数的概率是多少？

正确答案：C · 分值：1

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2008 AMC8 #25 · Geometry · ★★★★
Margie's winning art design is shown. The smallest circle has radius 2 inches, with each successive circle's radius increasing by 2 inches. Which of the following is closest to the percent of the design that is black?
下图展示了 Margie 获奖的艺术设计作品。最小的圆的半径为 2 英寸，每个连续圆的半径增加 2 英寸。以下哪项最接近黑色图案占整个图案的百分比？

正确答案：A · 分值：1

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2007 AMC8 #1 · Counting, Probability & Statistics · ★
Theresa's parents have agreed to buy her tickets to see her favorite band if she spends an average of 10 hours per week helping around the house for 6 weeks. For the first 5 weeks she helps around the house for 8 , 11 , 7 , 12 and 10 hours. How many hours must she work for the final week to earn the tickets?
如果特蕾莎平均每周花 10 个小时在家里帮忙，一共帮忙 6 周，那么她的父母就同意给她买票去看她最喜欢的乐队。在最初的 5 周里，她在家里帮忙了 8，11，7，12 和 10 个小时。最后一周她必须工作多少小时才能挣到票？

正确答案：D · 分值：1

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2007 AMC8 #2 · Counting, Probability & Statistics · ★
650 students were surveyed about their pasta preferences. The choices were lasagna, manicotti, ravioli and spaghetti. The results of the survey are displayed in the bar graph. What is the ratio of the number of students who preferred spaghetti to the number of students who preferred manicotti?
调查了 650 个学生对意大利面的偏好。可供选择的食物有烤宽而条、意大利通心面、水饺和意大利细面条。调查结果显示在下面条形图中。喜欢意大利细面条的学生人数与喜欢意大利通心面的学生人数的比值是多少？

正确答案：E · 分值：1

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2007 AMC8 #3 · Number Theory · ★
What is the sum of the two smallest prime factors of 250 ?
250 的最小的两个质因子之和是多少？

正确答案：C · 分值：1

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2007 AMC8 #4 · Counting, Probability & Statistics · ★
A haunted house has six windows. In how many ways can Georgie the Ghost enter the house by one window and leave by a different window?
一间闹鬼的房子有 6 扇窗户。Georgie 这只鬼从其中一扇窗口进入房子，再从另一扇不同的窗户离开房子，一共有多少种方法？

正确答案：D · 分值：1

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2007 AMC8 #5 · Algebra · ★★
Chandler wants to buy a 500 dollar mountain bike. For his birthday, his grandparents send him 50 dollars, his aunt sends him 35 dollars and his cousin gives him 15 dollars. He earns $16$ dollars per week for his paper route. He will use all of his birthday money and all of the money he earns from his paper route. In how many weeks will he be able to buy the mountain bike?
Chandler 想买一辆 500 美元的山地车。在他生日的时候他爷爷奶奶给他 50 美元，阿姨给他 35 美元，表哥给他的 15 美元。另外，他送报每周能赚 16 美元。他将使用他生日收到的全部的钱和他送报赚来的钱来购买山地车，问几周后他能买到这辆山地车？

正确答案：B · 分值：1

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2007 AMC8 #6 · Algebra · ★★
The average cost of a long-distance call in the USA in 1985 was 41 cents per minute, and the average cost of a long-distance call in the USA in 2005 was 7 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call.
1985 年在美国打长途电话的平均费用是每分钟 41 美分，2005 年在美国打长途电话的平均费用是每分钟 7 美分。求长途电话每分钟费用减少的大致百分比。

正确答案：E · 分值：1

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2007 AMC8 #7 · Counting, Probability & Statistics · ★★
The average age of 5 people in a room is 30 years. An 18 -year-old person leaves the room. What is the average age of the four remaining people?
一个房间里 5 个人的平均年龄是 30 岁。一个 18 岁的人离开了这个房间。那么剩下的 4 人平均年龄是多少岁？

正确答案：D · 分值：1

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2007 AMC8 #8 · Geometry · ★★
In trapezoid ABCD , AD‾\overline{AD} is perpendicular to DC‾\overline{DC}, AD = AB = 3 , and DC = 6 . In addition, E is on DC‾\overline{DC}, and BE‾\overline{BE} is parallel to AD‾\overline{AD}. Find the area of △BEC\triangle BEC.
在梯形 ABCD 中，线段 AD 和线段 DC 垂直，AD＝AB＝3，DC＝6。另外，E 在线段 DC 上，BE 平行于 AD。求△BEC 的面积。

正确答案：B · 分值：1

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2007 AMC8 #9 · Counting, Probability & Statistics · ★★
To complete the grid below, each of the digits 1 through 4 must occur once in each row and once in each column. What number will occupy the lower right-hand square?
为完成下面的表格，要求数字 1 到 4 中的每个数字在表格的每一行和每一列都必须出现 1 次。 则表格的右下角方格里的数字是多少？

正确答案：B · 分值：1

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2007 AMC8 #10 · Number Theory · ★★
For any positive integer nn , define n\boxed{n} to be the sum of the positive factors of nn . For example, 6=1+2+3+6=12\boxed{6} = 1 + 2 + 3 + 6 = 12 . Find 11\boxed{\boxed{11}} .
对于任何正整数 n，定义
.
为 n 的正因子之和。例如，
。求
。

正确答案：D · 分值：1

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2007 AMC8 #11 · Counting, Probability & Statistics · ★★★
Tiles $I, II, III$ and IVIV are translated so one tile coincides with each of the rectangles A, B, C and DD . In the final arrangement, the two numbers on any side common to two adjacent tiles must be the same. Which of the tiles is translated to Rectangle CC ?
瓷砖 I，II，III 和 IV 被平移至与长方形 A，B，C，D 重合。排列完毕后，要求两块相邻的瓷砖的公共边上的数必须相等。那么哪块瓷砖平移到了长方形 C 上？

正确答案：D · 分值：1

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2007 AMC8 #12 · Geometry · ★★★
A unit hexagram is composed of a regular hexagon of side length 1 and its 6 equilateral triangular extensions, as shown in the diagram. What is the ratio of the area of the extensions to the area of the original hexagon?
一个单位六角星由一个边长为 1 的正六边形及其 6 个等边三角形形状的凸出部分组成，如图所示。则凸出部分的总面积与原来六边形的面积之比是多少？

正确答案：A · 分值：1

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2007 AMC8 #13 · Counting, Probability & Statistics · ★★★
Sets A and B, shown in the Venn diagram, have the same number of elements. Their union has 2007 elements and their intersection has 1001 elements. Find the number of elements in A.
如下图所示的文氏图中，集合 A 和集合 B 中的元素个数相等。它们的并集有 2007 个元素，且它们的交集有 1001 个元素。那么求集合 A 中的元素个数。

正确答案：C · 分值：1

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2007 AMC8 #14 · Geometry · ★★★
The base of isosceles △ABC\triangle ABC is 24 and its area is 60 . What is the length of one of the congruent sides?
等腰三角形△ABC 的底是 24，面积为 60。那么它的一条腰长是多少？

正确答案：C · 分值：1

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2007 AMC8 #15 · Algebra · ★★★
Let aa, bb and cc be numbers with 0 < a < b < c. Which of the following is impossible?
aa，bb，cc 是三个满足 0 < a < b < c 的实数。下面哪个选项不可能？

正确答案：A · 分值：1

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2007 AMC8 #16 · Algebra · ★★★
Amanda draws five circles with radii 1, 2, 3, 4 and 5. Then for each circle she plots the point (C,A), where C is its circumference and A is its area. Which of the following could be her graph?
Amanda 画了 5 个半径分别是 1，2，3，4 和 5 的圆。对于每个圆，她画了点（C，A），其中是这个园的周长，A 表示这个圆的面积。下面哪个可能是她画的图像？

正确答案：A · 分值：1

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2007 AMC8 #17 · Algebra · ★★★
A mixture of 30 liters of paint is 25% red tint, 30% yellow tint and 45% water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture?
一种 30 升的油漆混合物是由 25％的红色颜料，30％的黄色颜料和 45％的水组成。向原来混合物中再加入 5 升黄色颜料，那么新的混合物中黄色颜科所占的百分比是多少？

正确答案：C · 分值：1

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2007 AMC8 #18 · Number Theory · ★★★
The product of the two 99 -digit numbers 303,030,303,...,030,303 and 505,050,505,...,050,505 has thousands digit AA and units digit BB . What is the sum of AA and BB ?
两个 99 位数字 303,030,303,…,030,303 和 505,050,505,…,050,505 的乘积的千位数字为 A，个位数字是 B。那么 A 与 B 的和是多少？

正确答案：D · 分值：1

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2007 AMC8 #19 · Number Theory · ★★★
Pick two consecutive positive integers whose sum is less than 100 . Square both of those integers and then find the difference of the squares. Which of the following could be the difference?
选择两个连续的正整数，使得它们的和小于 100。将这两个整数平方后再相减，则下面哪个可能是所得到的差？

正确答案：C · 分值：1

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2007 AMC8 #20 · Algebra · ★★★
Before the district play, the Unicorns had won 45% of their basketball games. During district play, they won six more games and lost two, to finish the season having won half their games. How many games did the Unicorns play in all?
在地区赛之前，独角兽队已经赢得了他们所打过的篮球比赛的 45％。在地区赛期间，他们又赢了六场比赛，输了两场，最终整个赛季赢得了一半的比赛。则独角兽队总共打了多少场比赛？

正确答案：A · 分值：1

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2007 AMC8 #21 · Counting, Probability & Statistics · ★★★
Two cards are dealt from a deck of four red cards labeled AA , BB , CC , DD and four green cards labeled AA , BB , CC , DD . A winning pair is two of the same color or two of the same letter. What is the probability of drawing a winning pair?
从 4 张标有 A，B，C，D 的红牌和 4 张标有 A，B，C，D 的绿牌中选择 2 张牌。一对获胜的牌是指两张同色的牌或者两张字母一样的牌。那么抽到的 2 张牌是一对获胜的牌的概率是多少？

正确答案：D · 分值：1

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2007 AMC8 #22 · Geometry · ★★★★★
A lemming sits at a corner of a square with side length 10 meters. The lemming runs 6.2 meters along a diagonal toward the opposite corner. It stops, makes a 90∘90^{\circ} right turn and runs 2 more meters. A scientist measures the shortest distance between the lemming and each side of the square. What is the average of these four distances in meters?
一只旅鼠坐在一个边长为 10 米的正方形的某个角落里。旅鼠沿着对角线朝对面的角落跑了 6.2 米，然后停下来，右转 90 度，又继续跑了 2 米。一位科学家测量了旅鼠和正方形各边之间的最短距离。这四段距离的平均值是多少米？

正确答案：C · 分值：1

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2007 AMC8 #23 · Geometry · ★★★
What is the area of the shaded pinwheel shown in the 5×55 \times 5 grid?
下面 5×5 的网格中，阴影部分的面积是多少？

正确答案：B · 分值：1

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2007 AMC8 #24 · Counting, Probability & Statistics · ★★★★
A bag contains four pieces of paper, each labeled with one of the digits 1 , 2 , 3 or 4 , with no repeats. Three of these pieces are drawn, one at a time without replacement, to construct a three-digit number. What is the probability that the three-digit number is a multiple of 3 ?
一个包中有 4 张分别标有数字 1，2，3，4 的纸片，每个数字都不重复。从中不放回的选择 3 张纸片，构成一个三位数。则这个三位数是 3 的倍数的概率是多少？

正确答案：C · 分值：1

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2007 AMC8 #25 · Counting, Probability & Statistics · ★★★★
On the dart board shown in the figure, the outer circle has radius 6 and the inner circle has a radius of 3. Three radii divide each circle into three congruent regions, with point values shown. The probability that a dart will hit a given region is proportional to the area of the region. When two darts hit this board, the score is the sum of the point values in the regions. What is the probability that the score is odd?
在如下图所示的飞镖盘上，外圈的半径为 6，内圈的半径为 3。三个半径将每个圆分成三个全等区域，每个区域的分值如图所示。飞镖击中给定区域的概率与该区域的面积成正比。当两个飞镖击中此飞镖盘时，总分为所击中的各区域的分值之和。则总分为奇数的概率是多少？

正确答案：B · 分值：1

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2006 AMC8 #1 · Algebra · ★
Mindy made three purchases for $1.98 dollars, $5.04 dollars, and $9.89 dollars. What was her total, to the nearest dollar?
Mindy 买的三样东西价格分别为＄1.98，＄5.04 和＄9.89。那么她所需要支付的总价最接近多少美元？

正确答案：D · 分值：1

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2006 AMC8 #2 · Algebra · ★
On the AMC 8 contest Billy answers 13 questions correctly, answers 7 questions incorrectly and doesn't answer the last 5. What is his score?
在 AMC8 竞赛中，Billy 答对了 13 题，答错了 7 题，最后 5 题未作答，那么他的分数是多少？

正确答案：C · 分值：1

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2006 AMC8 #3 · Algebra · ★★
Elisa swims laps in the pool. When she first started, she completed 10 laps in 25 minutes. Now she can finish 12 laps in 24 minutes. By how many minutes has she improved her lap time?
Elisa 在游泳池里游了几圈。当她第一次开始时，她在 25 分钟内完成了 10 圈。现在她可以在 24 分钟内游完 12 圈。那么她游一圈所花的时间减少了多少分钟？

正确答案：A · 分值：1

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2006 AMC8 #4 · Geometry · ★★
Initially, a spinner points west. Chenille moves it clockwise 2142 \dfrac{1}{4} revolutions and then counterclockwise 3343 \dfrac{3}{4} revolutions. In what direction does the spinner point after the two moves?
最初，转盘的箭头指向西边。Chenille 将它顺时针旋转 2142\dfrac{1}{4} 圈，再逆时针旋转 3343\dfrac{3}{4} 圈。两次转动后，箭头指向哪个方向？

正确答案：B · 分值：1

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2006 AMC8 #5 · Geometry · ★★
Points A, B, C and D are midpoints of the sides of the larger square. If the larger square has area 60, what is the area of the smaller square?
点 A，B，C 和 D 是一个大正方形的各边的中点。若大正方形的面积为 60，那么小正方形的面积是多少？

正确答案：D · 分值：1

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2006 AMC8 #6 · Geometry · ★
The letter T is formed by placing two 2×42 \times 4 inch rectangles next to each other, as shown. What is the perimeter of the T, in inches?
将两个 2×4 英寸的矩形相邻放置，形成下图所示的 T 字形。那么这个 T 字形的周长是多少英寸？

正确答案：C · 分值：1

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2006 AMC8 #7 · Geometry · ★★
Circle X has a radius of π\pi. Circle Y has a circumference of 8π8 \pi. Circle Z has an area of 9π9 \pi. List the circles in order from smallest to largest radius.
圆 XX 的半径是 π\pi，圆 YY 的周长是 8π8\pi，圆 ZZ 的面积是 9π9\pi。将这三个圆按半径从小到大排序，正确的是？

正确答案：B · 分值：1

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2006 AMC8 #8 · Counting, Probability & Statistics · ★★
The table shows some of the results of a survey by radiostation KACL. What percentage of the males surveyed listen to the station?
下表列出了广播电台 KAMC 的一项调查所得到的某些结果。被调查的男性中，收听广播的男性占比是多少？

正确答案：E · 分值：1

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2006 AMC8 #10 · Algebra · ★★
Jorge's teacher asks him to plot all the ordered pairs (w, l) of positive integers for which w is the width and l is the length of a rectangle with area 12. What should his graph look like?
Jorget 的老师要求他画出所有的（w，l）正整数对，其中 w 和 l 分别是一个面积为 12 的矩形的宽和长。则他画的图应该是下面哪个？

正确答案：A · 分值：1

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2006 AMC8 #11 · Number Theory · ★★★
How many two-digit numbers have digits whose sum is a perfect square?
有多少个两位数，满足各个位上数字之和是个完全平方数？

正确答案：C · 分值：1

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2006 AMC8 #12 · Algebra · ★★★
Antonette gets 70 % on a 10-problem test, 80 % on a 20-problem test and 90 % on a 30-problem test. If the three tests are combined into one 60-problem test, which percent is closest to her overall score?
Antonette 在一场 10 道题的考试中得分为 70％，在一场 20 道题的考试中得分为 80％，在一场 30 道题的考试中得分为 90％.若这三场考试题合并成一场 60 道题的考试，那么下面哪个百分数最接近他的总分？

正确答案：D · 分值：1

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2006 AMC8 #13 · Algebra · ★★★
Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. She bikes at a uniform rate of 12 miles per hour. Brian leaves Marquette at 9:00 AM heading for Escanaba on his bike. He bikes at a uniform rate of 16 miles per hour. They both bike on the same 62-mile route between Escanaba and Marquette. At what time in the morning do they meet?
Cassie 早上 8：30 离开 Escanaba，骑自行车前往 Marquette.她以每小时 12 英里的均匀速度骑自行车。Brian 早上 9 点离开 Marquette，骑着自行车前往 Escanaba。他以每小时 16 英里的均匀速度骑自行车。他们俩骑自行车使用的都是在 Escanaba 和 Marquette 之间的同一条 62 英里长的路线。则他们早上什么时候相遇？

正确答案：D · 分值：1

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2006 AMC8 #14 · Algebra · ★★★
Problems 14, 15 and 16 involve Mrs. Reed's English assignment. A Novel Assignment The students in Mrs. Reed's English class are reading the same 760 -page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds. If Bob and Chandra both read the whole book, Bob will spend how many more seconds reading than Chandra?
Reed 老师英语课上的学生都在读同一本 760 页的小说。班上的三位朋友 Alice、Bob 和 Chandra 读书速度不同：Alice 每页用 20 秒，Bob 每页用 45 秒，Chandra 每页用 30 秒。如果 Bob 和 Chandra 都读完整本书，Bob 比 Chandra 多用多少秒？

正确答案：B · 分值：1

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2006 AMC8 #15 · Algebra · ★★★
Problems 14, 15 and 16 involve Mrs. Reed's English assignment. A Novel Assignment The students in Mrs. Reed's English class are reading the same 760-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds. Chandra and Bob, who each have a copy of the book, decide that they can save time by "team reading" the novel. In this scheme, Chandra will read from page 1 to a certain page and Bob will read from the next page through page 760, finishing the book. When they are through they will tell each other about the part they read. What is the last page that Chandra should read so that she and Bob spend the same amount of time reading the novel?
Chandra 和 Bob 各自都有这本书，他们决定通过”团队阅读”这本小说来节省时间。在这种方案下，Chandra 会从第一页读到某一页，Bob 会从下一页一直读到第 760 页，把书读完。当他们都完成各自的任务，他们会告诉对方自己所读的内容。那么为了使得 Chandra 和 Bob 阅读的时间相同，Chandra 所读的最后一页是第几页？

正确答案：C · 分值：1

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2006 AMC8 #16 · Algebra · ★★★
Problems 14, 15 and 16 involve Mrs. Reed's English assignment. A Novel Assignment The students in Mrs. Reed's English class are reading the same 760-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds. Before Chandra and Bob start reading, Alice says she would like to team read with them. If they divide the book into three sections so that each reads for the same length of time, how many seconds will each have to read?
在 Chandra 和 Bob 开始阅读前，Alice 说她想加入和他俩一起团队阅读。若他们把书分成 3 部分，使得每人阅读时间都相同，那么每人阅读时间是多少秒？

正确答案：E · 分值：1

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2006 AMC8 #17 · Counting, Probability & Statistics · ★★★
Jeff rotates spinners P , Q and R and adds the resulting numbers. What is the probability that his sum is an odd number?
Jeff 旋转转盘 P，Q 和 R，并把它们各自得到的数字相加。问所得到的和是个奇数的概率是多少？

正确答案：B · 分值：1

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2006 AMC8 #18 · Geometry · ★★★
A cube with 3-inch edges is made using 27 cubes with 1-inch edges. Nineteen of the smaller cubes are white and eight are black. If the eight black cubes are placed at the corners of the larger cube, what fraction of the surface area of the larger cube is white?
一个边长为 3 英寸的正方体是由 27 个边长为 1 英寸的正方体组成的。其中 19 个小正方体为白色，8 个是黑色。若这 8 个黑色正方体放在大的正方体的 8 个角落，那么大正方体的表面积中，白色部分的比例是多少？

正确答案：D · 分值：1

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2006 AMC8 #19 · Geometry · ★★★
Triangle ABC is an isosceles triangle with AB‾=BC‾\overline{AB}=\overline{BC}. Point D is the midpoint of both BC‾\overline{BC} and AE‾\overline{AE}, and CE‾\overline{CE} is 11 units long. Triangle ABD is congruent to triangle ECD . What is the length of BD‾\overline{BD}?
三角形 ABC 是个等腰三角形，。点 D 是线段的中点，同时也是线段的中点。 线段长度为 11 个单位。三角形 ABD 和三角形 ECD 全等的，则的长度是多少？

正确答案：D · 分值：1

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2006 AMC8 #20 · Counting, Probability & Statistics · ★★★
A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won 4 games, Ines won 3 games, Janet won 2 games, Kendra won 2 games and Lara won 2 games, how many games did Monica win?
某个单打比赛有六名选手。每个选手和其他每个选手都比赛一次，没有平局。如果 Helen 赢了 4 场比赛，Ines 赢了 3 场比赛，Janet 赢了 2 场比赛，Kendra 赢了 2 场比赛，Lara 赢了 2 场比赛，则 Monica（第六个选手）赢了多少场比赛？

正确答案：C · 分值：1

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2006 AMC8 #21 · Geometry · ★★★
An aquarium has a rectangular base that measures 100 cm by 40 cm and has a height of 50 cm. The aquarium is filled with water to a depth of 37 cm. A rock with volume 1000cm31000\text{cm}^3 is then placed in the aquarium and completely submerged. By how many centimeters does the water level rise?
一个鱼缸有一个尺寸为 100 厘米ｘ40 厘米的长方形底座，鱼缸高为 50 厘米。鱼缸里水深 37 厘米。将一块体积为 1000 立方厘米的石头放入鱼缸并完全浸没。问水位上升了多少厘米？

正确答案：A · 分值：1

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2006 AMC8 #22 · Algebra · ★★★★
Three different one-digit positive integers are placed in the bottom row of cells. Numbers in adjacent cells are added and the sum is placed in the cell above them. In the second row, continue the same process to obtain a number in the top cell. What is the difference between the largest and smallest numbers possible in the top cell?
将 3 个不同的 1 位正整数放入最底层的三个方格中。然后将相邻方格里的数字相加，得到的和放入位于这两个方格之上的方格内。对于第二层，重复同样的步骤得到顶层方格内的数字。则顶层方格内的数字的最大可能值和最小可能值的差是多少？

正确答案：D · 分值：1

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2006 AMC8 #23 · Number Theory · ★★★★
A box contains gold coins. If the coins are equally divided among six people, four coins are left over. If the coins are equally divided among five people, three coins are left over. If the box holds the smallest number of coins that meets these two conditions, how many coins are left when equally divided among seven people?
一个盒子内装有金币。若把这些金币均分给 6 个人，那么还剩 4 枚金币。若把这些金币均分给 5 个人，那么还剩 3 枚金币。若盒子里装有的金币个数是满足以上条件的最少的金币个数，那么当把这些金币均分给 7 个人，还剩多少枚金币？

正确答案：A · 分值：1

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2006 AMC8 #24 · Number Theory · ★★★★
In the multiplication problem below A , B , C , and D are different digits. What is A+B ?
在下面的乘法问题中，A，B，C，D 是不同的数字。那么 A＋B 是多少？

正确答案：A · 分值：1

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2006 AMC8 #25 · Number Theory · ★★★★
Barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. The sums of the two numbers on each of the three cards are equal. The three numbers on the hidden sides are prime numbers. What is the average of the hidden prime numbers?
Bary 在 3 张牌的两面各写了一个数，共写了 6 个不同的数字，然后把牌放在桌子上，如图所示。每张卡片上的两个数字之和都相等。没有翻开的三个面上的数字都是质数。则这 3 个没翻开的面上的质数的平均值是多少？

正确答案：B · 分值：1

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2005 AMC8 #1 · Algebra · ★
Connie multiplies a number by 2 and gets 60 as her answer. However, she should have divided the number by 2 to get the correct answer. What is the correct answer?
Connie 把一个数字乘以 2，得到答案为 60。然而，她本应该把数字除以 2 才能得到正确的答案。那么正确答案是什么？

正确答案：B · 分值：1

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2005 AMC8 #2 · Algebra · ★
Karl bought five folders from Pay-A-Lot at a cost of $2.50 each. Pay-A-Lot had a 20%-off sale the following day. How much could Karl have saved on the purchase by waiting a day?
Karl 从 Pay-A-Lot 买了五个文件夹，每个价格为 2.5 美元。Pay-A-Lot 第二天降价 20％。那么 Karl 如果等一天他本可以省下多少钱？

正确答案：C · 分值：1

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2005 AMC8 #3 · Geometry · ★★
What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal BD‾\overline{BD} of square ABCD ?
要使正方形 ABCDABCD 的一条对称轴落在对角线 BD‾\overline{BD} 上，至少需要把多少个小正方形涂成黑色？

正确答案：D · 分值：1

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2005 AMC8 #4 · Geometry · ★
A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.1 cm, 8.2 cm and 9.7 cm. What is the area of the square in square centimeters?
一个正方形和一个三角形的周长相等。三角形的三条边长分别是 6.1cm，8.2cm 和 9.7cm。那么正方形的面积是多少平方厘米？

正确答案：C · 分值：1

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2005 AMC8 #5 · Counting, Probability & Statistics · ★★
Soda is sold in packs of 6, 12 and 24 cans. What is the minimum number of packs needed to buy exactly 90 cans of soda?
苏打水以 6 罐、12 罐和 24 罐的包装出售。则购买 90 罐苏打水所需的最少包装数量是多少？

正确答案：B · 分值：1

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2005 AMC8 #6 · Algebra · ★★
Suppose dd is a digit. For how many values of dd is 2.00d5 > 2.005 ?
假设 dd 是一个数字。使 2.00d5 > 2.005 成立的 dd 有多少个？

正确答案：C · 分值：1

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2005 AMC8 #7 · Geometry · ★★
Bill walks 12\tfrac12 mile south, then 34\tfrac34 mile east, and finally 12\tfrac12 mile south. How many miles is he, in a direct line, from his starting point?
Bill 先向南行走 英里，然后向东行走 英里，最后向南行走 英里。那么他现在距离起点的直线距离是多少英里？

正确答案：B · 分值：1

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2005 AMC8 #8 · Number Theory · ★★
Suppose m and n are positive odd integers. Which of the following must also be an odd integer?
假设 m 和 n 都是正奇数，下面哪个一定也是奇数？

正确答案：E · 分值：1

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2005 AMC8 #9 · Geometry · ★★
In quadrilateral ABCD , sides AB‾\overline{AB} and BC‾\overline{BC} both have length 10, sides CD‾\overline{CD} and DA‾\overline{DA} both have length 17, and the measure of angle ADC is 60∘60^\circ. What is the length of diagonal AC‾\overline{AC}?
四边形 ABCDABCD 中，边 AB‾\overline{AB} 和 BC‾\overline{BC} 的长度都是 10，边 CD‾\overline{CD} 和 DA‾\overline{DA} 的长度都是 17，且 ∠ADC=60∘\angle ADC = 60^\circ。那么对角线 AC‾\overline{AC} 的长度是多少？

正确答案：D · 分值：1

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2005 AMC8 #10 · Algebra · ★★
Joe had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3 times as fast as he walked. Joe took 6 minutes to walk half way to school. How many minutes did it take Joe to get from home to school?
Joe 从家步行去学校，当他意识到自己已经迟到时，已经走了总路程的一半，他跑完了剩下的路程，跑步的速度是步行速度的 3 倍。已知 Joe 步行的一半路程耗时 6 分钟，那么他从家到学校总共花了多少分钟？

正确答案：D · 分值：1

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2005 AMC8 #11 · Algebra · ★★★
The sales tax rate in Rubenenkoville is 6%. During a sale at the Bergville Coat Closet, the price of a coat is discounted 20% from its $90.00 price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up $90.00 and adds 6% sales tax, then subtracts 20% from this total. Jill rings up $90.00, subtracts 20% of the price, then adds 6% of the discounted price for sales tax. What is Jack's total minus Jill's total?
Bergville 地区的销售税税率为 6％。在 Bergville 大衣柜的一次销售中，一件大衣的价格从原价 90 美元起打了 20％的折扣。Jack 和 Jill 两名职员独立计算账单。Jack 先将 90 美元加上 6％的销售税，然后从总额中减去 20％。Jill 先将 90.00 美元减去 20％，然后再在折扣价格的基础上加上 6％的销售税。则 Jack 所得到的价格减去 Jill 所得到的价格的结果是多少？

正确答案：C · 分值：1

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2005 AMC8 #12 · Algebra · ★★★
Big Al, the ape, ate 100 bananas from May 1 through May 5. Each day he ate six more bananas than on the previous day. How many bananas did Big Al eat on May 5?
从 5 月 1 日到 5 月 5 日，Big AL 这只大猩猩共吃了 100 根美味的黄香蕉。他每天比前一天多吃六根香蕉。那么它在 5 月 5 日这天吃了多少根美味的香蕉？

正确答案：D · 分值：1

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2005 AMC8 #13 · Geometry · ★★★
The area of polygon ABCDEF is 52 with AB=8 , BC=9 and FA=5 . What is DE+EF ?
多边形 ABCDEF 的面积是 52，其中 AB=8，BC=9，FA= 5。则 DE + EF 是多少？

正确答案：C · 分值：1

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2005 AMC8 #14 · Counting, Probability & Statistics · ★★★
The Little Twelve Basketball Conference has two divisions, with six teams in each division. Each team plays each of the other teams in its own division twice and every team in the other division once. How many conference games are scheduled?
小十二篮球联赛有两个赛区，每个赛区有六支球队。每支球队在各自的赛区内与其他球队比赛两次，且和另一个赛区内的每支球队比赛一次。则一共安排了多少场比赛？

正确答案：B · 分值：1

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2005 AMC8 #15 · Geometry · ★★★
How many different isosceles triangles have integer side lengths and perimeter 23?
有多少个不同的等腰三角形，满足各边长度均为整数，且周长为 23?

正确答案：C · 分值：1

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2005 AMC8 #16 · Counting, Probability & Statistics · ★★★
A five-legged Martian has a drawer full of socks, each of which is red, white or blue, and there are at least five socks of each color. The Martian pulls out one sock at a time without looking. How many socks must the Martian remove from the drawer to be certain there will be 5 socks of the same color?
一个五条腿的火星人有一个装满袜子的抽屉，每只袜子都是红色、白色或蓝色，每种颜色至少有五只袜子。火星人每次从抽屉只拿出一只袜子，且不看取出的是什么颜色。则火星人必须从抽屉里拿出多少只袜子才能确保会有 5 只相同颜色的袜子？

正确答案：D · 分值：1

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2005 AMC8 #17 · Algebra · ★★★
The results of a cross-country team's training run are graphed below. Which student has the greatest average speed?
越野队的训练结果如下图所示。则哪个学生的平均速度最高？
Distance | 距离
Time | 时间

正确答案：E · 分值：1

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2005 AMC8 #18 · Number Theory · ★★★
How many three-digit numbers are divisible by 13?
能被 13 整除的三位数有多少个?

正确答案：C · 分值：1

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2005 AMC8 #20 · Number Theory · ★★★
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
Alice 和 Bob 玩了一个游戏，游戏中有一个圆的周长被 12 个等距点分成 12 等份。这些点按顺时针方向从 1 到 12 编号。两个人都从第 12 个点开始。Alice 顺时针移动，而 Bob 逆时针移动。 在游戏的每个回合，Alice 顺时针移动 5 个点，Bob 逆时针移动 9 个点。当他们停在同一点上时，比赛结束。则到游戏结束一共需要经过多少个回合？

正确答案：A · 分值：1

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2005 AMC8 #21 · Counting, Probability & Statistics · ★★★
How many distinct triangles can be drawn using three of the dots below as vertices?
使用下图中其中 3 个点作为顶点，可以构成多少个不重叠的三角形？

正确答案：C · 分值：1

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2005 AMC8 #22 · Algebra · ★★★★
A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs 50% more than the small size and contains 20% less detergent than the large size. The large size contains twice as much detergent as the small size and costs 30% more than the medium size. Rank the three sizes from best to worst buy.
一家公司卖三种不同大小的盒子包装的洗涤剂：小盒子（S）、中盒子（M）和大盒子（L）。中号比小号贵 50％，且洗涤剂含量比大号少 20％．大号的洗涤剂含量是小号的两倍，价格比中号高 30％。请将这三种不同尺寸的洗涤剂按照性价比从高到低排列。

正确答案：E · 分值：1

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2005 AMC8 #23 · Geometry · ★★★★
Isosceles right triangle ABC encloses a semicircle of area 2π2\pi. The circle has its center O on hypotenuse AB‾\overline{AB} and is tangent to sides AC‾\overline{AC} and BC‾\overline{BC}. What is the area of triangle ABC ?
等腰直角三角形 ABCABC 内含一个面积为 2π2\pi 的半圆。该半圆圆心 OO 在斜边 AB‾\overline{AB} 上，且与边 AC‾\overline{AC} 和 BC‾\overline{BC} 相切。那么三角形 ABCABC 的面积是多少？

正确答案：B · 分值：1

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2005 AMC8 #24 · Counting, Probability & Statistics · ★★★★
A certain calculator has only two keys [+1] and [x2]. When you press one of the keys, the calculator automatically displays the result. For instance, if the calculator originally displayed "9" and you pressed [+1], it would display "10." If you then pressed [x2], it would display "20." Starting with the display "1," what is the fewest number of keystrokes you would need to reach "200"?
某个计算器只有两个键［＋1］和［x2］。按其中一个键时，计算器会自动显示计算结果，例如，如果计算器最初显示“9”，当你按下［＋1］，它将显示“10”。如果你接着再按下［x2］，它将显示“20”。从显示“1”开始，你最少需要按键多少次才能得到结果“200”？

正确答案：B · 分值：1

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2005 AMC8 #25 · Geometry · ★★★★
A square with side length 2.0 and a circle share the same center. The total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square. What is the radius of the circle?
一个边长为 2 的正方形和一个圆，两者中心重合。位于圆内且在正方形之外的区域的面积，等于位于圆外且在正方形之内的区域的面积。那么圆的半径是多少？

正确答案：A · 分值：1

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2004 AMC8 #1 · Algebra · ★
On a map, a 12 -centimeter length represents 72 kilometers. How many kilometers does a 17 -centimeter length represent?
在一张地图上，12 厘米长代表 72 公里。则 17 厘米长代表多少公里？

正确答案：B · 分值：1

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2004 AMC8 #2 · Counting, Probability & Statistics · ★★
How many different four-digit numbers can be formed by rearranging the four digits in 2004 ?
将 2004 的四个数字重新排列可以形成多少个不同的四位数?

正确答案：B · 分值：1

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2004 AMC8 #3 · Algebra · ★★
Twelve friends met for dinner at Oscar's Overstuffed Oyster House, and each ordered one meal. The portions were so large, there was enough food for 18 people. If they shared, how many meals should they have ordered to have just enough food for the 12 of them?
12 位朋友在奥斯卡的“牡蛎屋”共进晚餐，每人点了 1 份晚餐。食物份量很大，足够 18 人吃。如果他们一起分享晚餐，他们本应该只需点多少份就恰好够 12 人吃？

正确答案：A · 分值：1

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2004 AMC8 #4 · Counting, Probability & Statistics · ★
Ms. Hamilton’s eighth-grade class wants to participate in the annual three-person-team basketball tournament.
Lance, Sally, Joy, and Fred are chosen for the team. In how many ways can the three starters be chosen?
Hamilton 女士的八年级班级想参加一年一度的三人篮球团体赛。Lance，Sally，Joy 和 Fred 为待选队员。要从中选择三名作为先发球员，一共有多少种方法？

正确答案：B · 分值：1

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2004 AMC8 #5 · Counting, Probability & Statistics · ★★
Ms. Hamilton's eighth-grade class wants to participate in the annual three-person-team basketball tournament. The losing team of each game is eliminated from the tournament. If sixteen teams compete, how many games will be played to determine the winner?
Hamilton 女士八年级的班级想参加一年一度的三人篮球团体赛。每场比赛的败队被淘汰出局。如果有 16 支球队参加比赛，将进行多少场比赛来决定最终的冠军？

正确答案：D · 分值：1

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2004 AMC8 #6 · Algebra · ★★
After Sally takes 20 shots, she has made 55% of her shots. After she takes 5 more shots, she raises her percentage to 56% . How many of the last 5 shots did she make?
在 Sally 射击的 20 次中，有 55％的命中率。当她再多射击 5 次，则命中率提高到了 56％．那么最后射击的 5 次中，有几次命中？

正确答案：C · 分值：1

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2004 AMC8 #7 · Algebra · ★
An athlete's target heart rate, in beats per minute, is 80% of the theoretical maximum heart rate. The maximum heart rate is found by subtracting the athlete's age, in years, from 220 . To the nearest whole number, what is the target heart rate of an athlete who is 26 years old?
运动员的目标心率（以每分钟心跳数为单位）是理论最大心率的 80％．将 220 减去运动员的年龄（以年为单位），即可得到理论最大心率。则一名 26 岁的运动员的目标心率是多少（精确到整数）？

正确答案：B · 分值：1

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2004 AMC8 #8 · Counting, Probability & Statistics · ★★
Find the number of two-digit positive integers whose digits total 7 .
求各个位上数字之和为 7 的两位正整数的个数。

正确答案：B · 分值：1

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2004 AMC8 #9 · Counting, Probability & Statistics · ★★
The average of the five numbers in a list is 54 . The average of the first two numbers is 48 . What is the average of the last three numbers?
一列 5 个数的平均值为 54。已知前 2 个数的平均值为 48。则最后 3 个数的平均值是多少？

正确答案：D · 分值：1

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2004 AMC8 #10 · Algebra · ★★
Handy Aaron helped a neighbor 1141 \frac14 hours on Monday, 50 minutes on Tuesday, from 8:20 to 10:45 on Wednesday morning, and a half-hour on Friday. He is paid $3 per hour. How much did he earn for the week?
Handy Aaron 帮邻居干活：周一花了 114\displaystyle 1\frac{1}{4} 小时，周二花了 50 分钟，周三早上从 8:20 干到 10:45，周五花了半小时。已知他每小时工资是 3 美元，那么他这一周赚了多少钱？

正确答案：E · 分值：1

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2004 AMC8 #11 · Counting, Probability & Statistics · ★★★
The numbers -2, 4, 6, 9 and 12 are rearranged according to these rules:
1. The largest isn't first, but it is in one of the first three places. 2. The smallest isn't last, but it is in one of the last three places. 3. The median isn't first or last.
What is the average of the first and last numbers?
对－2，4，6，9 和 12 这些数按照如下规则重新排序： 最大的数不在第一个位置，但它位于前三个位置中的某个位置。 最小的数不在最后一个位置，但它位于后三个位置中的某个位置。 中位数不在第一个或者最后一个位置。 那么第一个数和最后一个数的平均值是多少？

正确答案：C · 分值：1

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2004 AMC8 #12 · Algebra · ★★★
Niki usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for 24 hours. If she is using it constantly, the battery will last for only 3 hours. Since the last recharge, her phone has been on 9 hours, and during that time she has used it for 60 minutes. If she doesn’t use it any more but leaves the phone on, how many more hours will the battery last?
Niki 的手机通常不关机。如果她的手机是开着的，但她实际上没有使用，那么电池将持续 24 小时。如果她一直使用手机，电池只能使用 3 个小时。自从最近一次充电以来，她的手机已经开机 9 小时，在这段时间里，她使用手机的时间是 60 分钟。如果她不再使用手机进行通话，而是让手机待机，那么电池还能用多少小时？

正确答案：B · 分值：1

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2004 AMC8 #13 · Counting, Probability & Statistics · ★★★
Amy, Bill and Celine are friends with different ages. Exactly one of the following statements is true.
I. Bill is the oldest. II. Amy is not the oldest. III. Celine is not the youngest.
Rank the friends from the oldest to youngest.
Amy，Bill 和 Celine 是不同年龄的朋友。下面的 3 个论断中，只有一个是正确的。 I.Bill 年龄最大 II.Amy 不是最大的. III.Celine 不是最小的. 请把这 3 个朋友按照年龄从大到小排列。

正确答案：E · 分值：1

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2004 AMC8 #14 · Geometry · ★★★
What is the area enclosed by the geoboard quadrilateral below?
由下图中几何板上的四边形包围的面积的是多少？

正确答案：C · 分值：1

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2004 AMC8 #15 · Geometry · ★★★
Thirteen black and six white hexagonal tiles were used to create the figure below. If a new figure is created by attaching a border of white tiles with the same size and shape as the others, what will be the difference between the total number of white tiles and the total number of black tiles in the new figure?
下图是由 13 块黑色瓷砖和 6 块白色瓷砖构成。若用同样大小和形状的若干块白色瓷砖在原来图形最外层再围成一圈，那么所形成的的新图形中，白色瓷砖的总个数和黑色瓷砖的总个数的差是多少？

正确答案：C · 分值：1

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2004 AMC8 #16 · Algebra · ★★★
Two 600 mL pitchers contain orange juice. One pitcher is 1/3 full and the other pitcher is 2/5 full. Water is added to fill each pitcher completely, then both pitchers are poured into one large container. What fraction of the mixture in the large container is orange juice?
两个容量为 600 mL 的罐子里装有橙汁。一个罐子装了 13\displaystyle \frac{1}{3}，另一个装了 25\displaystyle \frac{2}{5}。向每个罐子加水使其装满，然后把两个罐子的液体都倒入一个大容器中。那么大容器里的混合液中橙汁占的比例是多少？

正确答案：C · 分值：1

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2004 AMC8 #17 · Counting, Probability & Statistics · ★★★
Three friends have a total of 6 identical pencils, and each one has at least one pencil. In how many ways can this happen?
3 个朋友总共有 6 支一模一样的铅笔，并且每个人都有至少一支铅笔。那么一共有多少种可能的分配铅笔的方法？

正确答案：D · 分值：1

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2004 AMC8 #18 · Counting, Probability & Statistics · ★★★
Five friends compete in a dart-throwing contest. Each one has two darts to throw at the same circular target, and each individual's score is the sum of the scores in the target regions that are hit. The scores for the target regions are the whole numbers 1 through 10 . Each throw hits the target in a region with a different value. The scores are: Alice 16 points, Ben 4 points, Cindy 7 points, Dave 11 points, and Ellen 17 points. Who hits the region worth 6 points?
五个朋友参加掷镖比赛。每个人都有两个飞镖向同一个圆形目标投掷，每个人的得分是被他击中的目标区域分值的总和。各个目标区域的分值是 1 到 10 的整数。每次投掷都击中到不同分值的目标区域。他们的分数是：Alice 得 16 分、Ben 得 4 分、Cindy 得 7 分、Dave 得 11 分，Ellen 得 17 分。谁击中了分值为 6 分的目标区域？

正确答案：A · 分值：1

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2004 AMC8 #19 · Number Theory · ★★★
A whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5, and 6 . The smallest such number lies between which two numbers?
一个大于 2 的正整数分别除以 3，4，5 和 6，所得余数均为 2。那么这个正整数的最小可能值在哪两个数之间?

正确答案：B · 分值：1

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2004 AMC8 #20 · Algebra · ★★★
Two-thirds of the people in a room are seated in three-fourths of the chairs. The rest of the people are standing. If there are 6 empty chairs, how many people are in the room?
房间里的人坐在的椅子上。其余的人都站着。如果有 6 张空椅子，则房间里有多少人？

正确答案：D · 分值：1

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2004 AMC8 #21 · Counting, Probability & Statistics · ★★★
Spinners AA and BB are spun. On each spinner, the arrow is equally likely to land on each number. What is the probability that the product of the two spinners' numbers is even?
将转盘 A 和 B 各旋转一次。已知在每个转盘上，指针落在每个数字上的可能性都相同，那么这两个转盘上（指针所指的）数字之积为偶数的概率是多少？

正确答案：D · 分值：1

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2004 AMC8 #22 · Algebra · ★★★★
At a party there are only single women and married men with their wives. The probability that a randomly selected woman is single is 25\frac25 . What fraction of the people in the room are married men?
在某个聚会上，只有单身女性，以及已婚男性和他们的妻子。若随机选择一个女性，则她是单身的概率为 。那么这个房间的所有人中，已婚男性占了多少比例？

正确答案：B · 分值：1

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2004 AMC8 #23 · Algebra · ★★★
Tess runs counterclockwise around rectangular block JKLMJKLM . She lives at corner JJ . Which graph could represent her straight-line distance from home?
Tess 沿着长方形方块 JKLM 的边逆时针跑步。她住在角落 J，那么下面哪张图可以表示她距离家的直线距离？

正确答案：D · 分值：1

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2004 AMC8 #24 · Geometry · ★★★★
In the figure, ABCDABCD is a rectangle and EFGHEFGH is a parallelogram. Using the measurements given in the figure, what is the length dd of the segment that is perpendicular to HE‾\overline{HE} and FG‾\overline{FG} ?
如下图所示，ABCD 是个矩形，EFGH 是个平行四边形。使用图中所标线段的长度，则同时垂直于和的线段长度 d 是多少？

正确答案：C · 分值：1

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2004 AMC8 #25 · Geometry · ★★★★
Two 4×44 \times 4 squares intersect at right angles, bisecting their intersecting sides, as shown. The circle's diameter is the segment between the two points of intersection. What is the area of the shaded region created by removing the circle from the squares?
如图所示，两个 4ｘ4 正方形以直角相交，将其相交的边平分。圆的直径是两个交点之间的线段。从正方形中去除圆之后所得到的阴影部分的面积是多少？

正确答案：D · 分值：1

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2003 AMC8 #1 · Geometry · ★
Jamie counted the number of edges of a cube, Jimmy counted the numbers of corners, and Judy counted the number of faces. They then added the three numbers. What was the resulting sum?
Jamie 数了一个正方体的边数，Jimmy 数了它的顶点数，Judy 数了它的面数。然后他们把这三个数字相加。结果是多少？

正确答案：E · 分值：1

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2003 AMC8 #2 · Number Theory · ★
Which of the following numbers has the smallest prime factor?
下面哪个数有最小的质因子?

正确答案：C · 分值：1

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2003 AMC8 #3 · Algebra · ★
A burger at Ricky C's weighs 120 grams, of which 30 grams are filler. What percent of the burger is not filler?
Ricky C's 的汉堡重 120 克，其中 30 克是填料。汉堡的百分之多少不是填料？

正确答案：D · 分值：1

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2003 AMC8 #4 · Algebra · ★★
A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted 7 children and 19 wheels. How many tricycles were there?
一群骑自行车和三轮车的孩子经过 Billy Bob 的家。Billy Bob 数了数，一共数到了 7 个孩子和 19 个轮子，那么有多少辆三轮车？

正确答案：C · 分值：1

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2003 AMC8 #5 · Algebra · ★
If 20% of a number is 12 , what is 30% of the same number?
如果一个数的 20％是 12，那么这个数的 30％是多少？

正确答案：B · 分值：1

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2003 AMC8 #6 · Geometry · ★★
Given the areas of the three squares in the figure, what is the area of the interior triangle?
已知图中三个正方形的面积，求中间位置的三角形的面积是多少？

正确答案：B · 分值：1

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2003 AMC8 #7 · Algebra · ★★
Blake and Jenny each took four 100 -point tests. Blake averaged 78 on the four tests. Jenny scored 10 points higher than Blake on the first test, 10 points lower than him on the second test, and 20 points higher on both the third and fourth tests. What is the difference between Jenny's average and Blake's average on these four tests?
Blake 和 Jenny 每人参加了四次满分为 100 分的测验。Blake 在四次测试中平均得分为 78 分。 Jenny 在第一次测试中比 Blake 高 10 分，在第二次测试中比他低 10 分，在第三次和第四次测试中都比他高 20 分。那么 Jenny 和 Blake 在这四项测试中的平均分的差是多少？

正确答案：A · 分值：1

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2003 AMC8 #8 · Algebra · ★★
Problems 8, 9 and 10 use the data found in the accompanying paragraph and figures
Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
∘\circ Art's cookies are trapezoids.
∘\circ Roger's cookies are rectangles.
∘\circ Paul's cookies are parallelograms.
∘\circ Trisha's cookies are triangles.
Each friend uses the same amount of dough, and Art makes exactly 12 cookies. Who gets the fewest cookies from one batch of cookie dough?
每位朋友用的面团一样多，且 Art 恰好做了 12 块饼干。用一批面团，谁做出的饼干最少？

正确答案：A · 分值：1

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2003 AMC8 #9 · Algebra · ★★
Problems 8, 9 and 10 use the data found in the accompanying paragraph and figures
Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
∘\circ Art's cookies are trapezoids:
∘\circ Roger's cookies are rectangles:
∘\circ Paul's cookies are parallelograms:
∘\circ Trisha's cookies are triangles:
Each friend uses the same amount of dough, and Art makes exactly 12 cookies. Art's cookies sell for 60 cents each. To earn the same amount from a single batch, how much should one of Roger's cookies cost in cents?
每个朋友都用了等量的面团，Art 正好做了 12 块饼干。Art 的饼干每个卖 60 美分。为了从这批面团赚得同样的钱，那么 Roger 的饼干应该每个卖多少美分？

正确答案：C · 分值：1

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2003 AMC8 #10 · Algebra · ★★
Problems 8, 9 and 10 use the data found in the accompanying paragraph and figures
Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
∘\circ Art's cookies are trapezoids:
∘\circ Roger's cookies are rectangles:
∘\circ Paul's cookies are parallelograms:
∘\circ Trisha's cookies are triangles:
How many cookies will be in one batch of Trisha's cookies?
Trisha 能用这批面团做多少个饼干?

正确答案：E · 分值：1

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2003 AMC8 #11 · Algebra · ★★★
Business is a little slow at Lou's Fine Shoes, so Lou decides to have a sale. On Friday, Lou increases all of Thursday's prices by 10 percent. Over the weekend, Lou advertises the sale: "Ten percent off the listed price. Sale starts Monday." How much does a pair of shoes cost on Monday that cost 40 dollars on Thursday?
Lou 的精品鞋生意有点不景气，所以 Lou 决定降价促销。周五的时候，Lou 将周四的所有价格上调 10％。周末的时候，Lou 在广告中说： “降价百分之十。降价从周一开始。”一双周四时价格为 40 美元的鞋，在周一时价格是多少？

正确答案：B · 分值：1

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2003 AMC8 #12 · Counting, Probability & Statistics · ★★★
When a fair six-sided dice is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the faces that can be seen is divisible by 6 ?
当把一个标准的六面骰子掷到桌面上时，骰子底面数字无法看到。那么其他能看到的五个面上的数字之积能被 6 整除的概率是多少？

正确答案：E · 分值：1

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2003 AMC8 #13 · Geometry · ★★★
Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces
14 个白色正方体被放在一起形成右边的图形。图形的整个表面（包括底部）被涂成红色。接着将图形分割为各个正方体。有多少个正方体正好有四个红色的面？

正确答案：B · 分值：1

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2003 AMC8 #14 · Number Theory · ★★★
In this addition problem, each letter stands for a different digit:
TWO+TWOFOUR\begin{array}{r} TWO \\ +TWO \\ \hline FOUR \end{array}
If T = 7 and the letter OO represents an even number, what is the only possible value for WW?
在上面的加法竖式中，每个字母代表一个不同的数字。若 T = 7 且字母 OO 代表一个偶数，则 WW 的唯一可能值是多少？

正确答案：D · 分值：1

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2003 AMC8 #15 · Geometry · ★★★
A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?
一种图形是由若干个单位正方体组成。每个正方体都和其他正方体共用至少一个面。这个图形的正视图和侧视图如下图所示，则这个图形最少是由多少个正方体组成？
FRONT | 正面
SIDE | 侧面

正确答案：B · 分值：1

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2003 AMC8 #16 · Counting, Probability & Statistics · ★★★
Ali, Bonnie, Carlo, and Dianna are going to drive together to a nearby theme park. The car they are using has $4$ seats: 1 Driver seat, 1 front passenger seat, and 2 back passenger seats. Bonnie and Carlo are the only ones who know how to drive the car. How many possible seating arrangements are there?
Ali，Bonnic，Carlo 和 Dianna 将一起开车去附近的一个主题公园。他们使用的汽车有 4 个座椅：1 个驾驶员座椅、1 个前排乘客座椅和 2 个后排乘客座椅。车上只有 Bonnie 和 Carlo 会开车。则有多少种可能的安排座位的方法？

正确答案：D · 分值：1

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2003 AMC8 #17 · Counting, Probability & Statistics · ★★★
The six children listed in the table below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim's siblings?
下面列出的六名儿童来自两个家庭，每个家庭有三个兄弟姐妹。每个孩子都有蓝色或棕色的眼睛，和黑色或金色的头发。来自同一家庭的儿童至少有一个共同特征。哪两个孩子是 Jim 的兄弟姐妹？
Eye Color | 眼睛颜色
Hair Color | 头发颜色

正确答案：E · 分值：1

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2003 AMC8 #18 · Counting, Probability & Statistics · ★★★
Each of the twenty dots on the graph below represents one of Sarah's classmates. Classmates who are friends are connected with a line segment. For her birthday party, Sarah is inviting only the following: all of her friends and all of those classmates who are friends with at least one of her friends. How many classmates will not be invited to Sarah's party?
下图中的 20 个点中的每个点代表 Sarah 的一个同班同学。这些同班同学中，若某两人之间是朋友关系，则用线段将这两人相连。Sarah 只打算邀请符合下面条件的人参加她的生日聚会： 她的所有朋友，以及所有与她的至少一个朋友是朋友。有多少同学不会被邀请参加 Sarah 的聚会？

正确答案：D · 分值：1

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2003 AMC8 #19 · Number Theory · ★★★
How many integers between 1000 and 2000 have all three of the numbers 15, 20, and 25 as factors?
1000 和 2000 之间有多少个整数，满足 15，20 和 25 都是它的因子？

正确答案：C · 分值：1

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2003 AMC8 #20 · Geometry · ★★★
What is the measure of the acute angle formed by the hands of the clock at 4:20 PM?
下午 4:20 时，钟面上时针和分针所形成的的锐角是多少度？

正确答案：D · 分值：1

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2003 AMC8 #21 · Geometry · ★★★★
The area of trapezoid ABCDABCD is 164 cm2164\text{ cm}^2 . The altitude is 8 cm, ABAB is 10 cm, and CDCD is 17 cm. What is BCBC , in centimeters?
梯形 ABCD 的面积是 164 平方厘米，高为 8 厘米，AB 的长为 10 厘米，CD 的长为 17 厘米。则 BC 的长为多少厘米?

正确答案：B · 分值：1

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2003 AMC8 #22 · Geometry · ★★★
The following figures are composed of squares and circles. Which figure has a shaded region with largest area?
下图是由正方形和圆组成的图形。哪个图形的阴影部分的面积最大？

正确答案：C · 分值：1

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2003 AMC8 #23 · Number Theory · ★★★
In the pattern below, the cat moves clockwise through the four squares, and the mouse moves counterclockwise through the eight exterior segments of the four squares.
If the pattern is continued, where would the cat and mouse be after the 247th move?
在下面的图案里，猫顺时针在四个正方形里移动，老鼠逆时针沿着四个正方形外围的 8 根线段移动。如果照此规律继续移动，第 247 步后猫和老鼠分别在什么位置？

正确答案：A · 分值：1

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2003 AMC8 #24 · Algebra · ★★★
A ship travels from point AA to point BB along a semicircular path, centered at Island XX . Then it travels along a straight path from BB to CC . Which of these graphs best shows the ship's distance from Island XX as it moves along its course?
一艘船沿着以岛 X 为圆心的半圆形路径从点 A 航行到点 B。然后它沿着直线路径从 B 到 C。下面这些图表中哪一个最能显示当船沿航线行驶时，船与岛 X 的距离变化？

正确答案：B · 分值：1

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2003 AMC8 #25 · Geometry · ★★★★
In the figure, the area of square WXYZWXYZ is 25 cm225 \text{ cm}^2 . The four smaller squares have sides 1 cm long, either parallel to or coinciding with the sides of the large square. In △ABC\triangle ABC , AB = AC , and when △ABC\triangle ABC is folded over side BC‾\overline{BC} , point AA coincides with OO , the center of square WXYZWXYZ . What is the area of △ABC\triangle ABC , in square centimeters?
在下图中，正方形 WXYZ 的面积为 25 平方厘米。四个小正方形边长为 1 厘米，它们的各边与大正方形的边平行或重合。在中，，若将沿着边折叠，则点 A 和正方形的中心 重合。那么的面积是多少平方厘米？

正确答案：C · 分值：1

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2002 AMC8 #1 · Geometry · ★★
A circle and two distinct lines are drawn on a sheet of paper. What is the largest possible number of points of intersection of these figures?
在一张纸上画了一个圆和 2 条不同的直线，则这些图形的交点最多有多少个？

正确答案：D · 分值：1

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2002 AMC8 #2 · Number Theory · ★★
How many different combinations of $5 bills and $2 bills can be used to make a total of $17? Order does not matter in this problem.
有多少种方法可以将若干 5 元纸币和 2 元纸币组成总额为 17 元？这道题里不考虑顺序。

正确答案：A · 分值：1

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2002 AMC8 #3 · Algebra · ★
What is the smallest possible average of four distinct positive even integers?
4 个不同的正偶数的平均值最小可能是多少？

正确答案：C · 分值：1

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2002 AMC8 #4 · Number Theory · ★★
The year 2002 is a palindrome (a number that reads the same from left to right as it does from right to left). What is the product of the digits of the next year after 2002 that is a palindrome?
2002 年这个年份的数字是个回环数（是一个从左向右读和从右向左读一样的数）。那么 2002 年之后的下一个也是回环数的年份的各个位上数字之积是多少？

正确答案：B · 分值：1

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2002 AMC8 #5 · Number Theory · ★★
Carlos Montado was born on Saturday, November 9, 2002. On what day of the week will Carlos be 706 days old?
Carlos Montado 出生于 2002 年 11 月 9 日，这天周六。当 Carlos 年龄为 706 天时，这天是周几？

正确答案：C · 分值：1

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2002 AMC8 #6 · Algebra · ★★
A birdbath is designed to overflow so that it will be self-cleaning. Water flows in at the rate of 20 milliliters per minute and drains at the rate of 18 milliliters per minute. Which one of these graphs shows the volume of water in the birdbath during the filling time and continuing into the overflow time?
一种水盆设计为溢流式，以便能够自动清洗。水以每分钟 20 毫升的速度流入，以每分钟 18 毫升的速度排出。其中某一张图显示了从灌水开始，一直持续到不断溢出这段时间内，水盆中的水量。这张图是下面哪一个?

正确答案：A · 分值：1

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2002 AMC8 #7 · Counting, Probability & Statistics · ★
The students in Mrs. Sawyer's class were asked to do a taste test of five kinds of candy. Each student chose one kind of candy. A bar graph of their preferences is shown. What percent of her class chose candy E?
Sawyer 夫人班上的学生被要求对五种糖果进行口味测试。每个学生都选了一种糖果。下面的条形图显示了他们的个人喜好。她班有百分之几的学生选择了糖果 E?
Number of students | 学生数量
Kind of candy | 糖果种类

正确答案：E · 分值：1

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2002 AMC8 #8 · Counting, Probability & Statistics · ★★
Problems 8,9 and 10 use the data found in the accompanying paragraph and table:
Juan organizes the stamps in his collection by country and by the decade in which they were issued. The prices he paid for them at a stamp shop were: Brazil and France, 6 cents each, Peru 4 cents each, and Spain 5 cents each. (Brazil and Peru are South American countries and France and Spain are in Europe.)
How many of his European stamps were issued in the '80s?
他的欧洲邮票有多少张是在 80 年代发行的？

正确答案：D · 分值：1

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2002 AMC8 #9 · Counting, Probability & Statistics · ★★
Problems 8,9 and 10 use the data found in the accompanying paragraph and table:
Juan organizes the stamps in his collection by country and by the decade in which they were issued. The prices he paid for them at a stamp shop were: Brazil and France, 6 cents each, Peru 4 cents each, and Spain 5 cents each. (Brazil and Peru are South American countries and France and Spain are in Europe.)
In dollars and cents, how much did his South American stamps issued before the ’70s cost him?
他的 70 年代之前发行的南美邮票花了他多少钱?

正确答案：B · 分值：1

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2002 AMC8 #10 · Counting, Probability & Statistics · ★★
Problems 8,9 and 10 use the data found in the accompanying paragraph and table:
Juan organizes the stamps in his collection by country and by the decade in which they were issued. The prices he paid for them at a stamp shop were: Brazil and France, 6 cents each, Peru 4 cents each, and Spain 5 cents each. (Brazil and Peru are South American countries and France and Spain are in Europe.)
The average price of his '70s stamps is closest to
他的 70 年代的所有邮票的平均价格最接近多少？

正确答案：E · 分值：1

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2002 AMC8 #11 · Algebra · ★★★
A sequence of squares is made of identical square tiles. The edge of each square is one tile length longer than the edge of the previous square. The first three squares are shown. How many more tiles does the seventh square require than the sixth?
下面一系列正方形都是由若干相同的方形瓷砖组成的。每个正方形的边长比前一个正方形的边长多一个瓷砖长度。下图显示了前三个正方形。则第七个正方形比第六个正方形多需要多少块瓷砖？

正确答案：C · 分值：1

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2002 AMC8 #12 · Counting, Probability & Statistics · ★★
A board game spinner is divided into three regions labeled AA , BB and CC . The probability of the arrow stopping on region AA is 13\displaystyle \frac{1}{3} and on region BB is 12\displaystyle \frac{1}{2} . The probability of the arrow stopping on region CC is:
一种棋盘游戏的转盘分成 AA、BB、CC 三个区域。已知箭头停在区域 AA 的概率为 13\displaystyle \frac{1}{3}，停在区域 BB 的概率为 12\displaystyle \frac{1}{2}。那么箭头停在区域 CC 的概率是：

正确答案：B · 分值：1

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2002 AMC8 #13 · Geometry · ★★★
For his birthday, Bert gets a box that holds 125 jellybeans when filled to capacity. A few weeks later, Carrie gets a larger box full of jellybeans. Her box is twice as high, twice as wide and twice as long as Bert's. Approximately, how many jellybeans did Carrie get?
Bert 的生日礼物是一个装满 125 颗果冻豆的盒子。几周后，Carrie 得到了一个更大的装满果冻豆的盒子。她的箱子是 Bert 的两倍高、两倍宽、两倍长。那么 Carrie 大概得到了多少颗果冻豆？

正确答案：E · 分值：1

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2002 AMC8 #14 · Algebra · ★★★
A merchant offers a large group of items at 30% off. Later, the merchant takes 20% off these sale prices. The total discount is
一位商人以 30％的折扣提供大量商品。后来，商家又在此折扣价的基础上降低 20％，并声称这些商品的最终价格比原价低 50％。则商品的总折扣是

正确答案：B · 分值：1

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2002 AMC8 #15 · Geometry · ★★★
Which of the following polygons has the largest area?
下面哪个多边形的面积最大？

正确答案：E · 分值：1

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2002 AMC8 #16 · Geometry · ★★★
Right isosceles triangles are constructed on the sides of a right triangle, as shown. A capital letter represents the area of each triangle. Which one of the following is true?
如下图所示，在 3-4-5 直角三角形的三条边上作出三个等腰直角三角形。大写字母表示每个三角形的面积。下面哪个是正确的？
3−4−53-4-5

正确答案：E · 分值：1

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2002 AMC8 #17 · Algebra · ★★★
In a mathematics contest with ten problems, a student gains 5 points for a correct answer and loses 2 points for an incorrect answer. If Olivia answered every problem and her score was 29, how many correct answers did she have?
在一个有十道题的数学竞赛中，一个学生答对一题得 5 分，答错一题扣 2 分。如果 Olivia 回答了所有问题，她的分数是 29 分，那么她答对多少题？

正确答案：C · 分值：1

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2002 AMC8 #18 · Algebra · ★★★
Gage skated 1 hr 15 min each day for 5 days and 1 hr 30 min each day for 3 days. How long would he have to skate the ninth day in order to average 85 minutes of skating each day for the entire time?
Gage 连续 5 天每天滑冰 1 小时 15 分钟，连续 3 天每天滑冰 1 小时 30 分钟。那么第九天他需要滑多长时间才能使得在全部时间内每天平均滑 85 分钟？

正确答案：E · 分值：1

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2002 AMC8 #19 · Counting, Probability & Statistics · ★★★
How many whole numbers between 99 and 999 contain exactly one 0?
99 和 999 之间有多少整数恰好包含一个 0?

正确答案：D · 分值：1

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2002 AMC8 #20 · Geometry · ★★★
The area of triangle XYZXYZ is 8 square inches. Points AA and BB are midpoints of congruent segments XY‾\overline{XY} and XZ‾\overline{XZ} . Altitude XC‾\overline{XC} bisects YZ‾\overline{YZ} . The area (in square inches) of the shaded region is
三角形 XYZXYZ 的面积是 8 平方英寸。点 AA 和点 BB 分别是两条相等线段 XY‾\overline{XY} 和 XZ‾\overline{XZ} 的中点，高 XC‾\overline{XC} 平分 YZ‾\overline{YZ}。那么阴影部分的面积是多少平方英寸？

正确答案：D · 分值：1

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2002 AMC8 #21 · Counting, Probability & Statistics · ★★★★
Harold tosses a coin four times. The probability that he gets at least as many heads as tails is
Harold 掷一枚镍币掷了四次，那么他得到正面的次数至少和反面一样多的概率是多少？

正确答案：E · 分值：1

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2002 AMC8 #22 · Geometry · ★★★
Six cubes, each an inch on an edge, are fastened together, as shown. Find the total surface area in square inches. Include the top, bottom, and sides.
如下图所示，6 个边长为 1 的正方体被粘在一起。请求出这个立体的总表面积，包含顶面，底面和侧面（单位：平方英寸）。

正确答案：C · 分值：1

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2002 AMC8 #23 · Geometry · ★★★
A corner of a tiled floor is shown. If the entire floor is tiled in this way and each of the four corners looks like this one, then what fraction of the tiled floor is made of darker tiles?
图中显示了铺了瓷砖的地板的一个角。如果整个地板都是用这种方式铺成的，并且四个角中的每一个都和这个角一样，那么整个地板中有多少比例是用深色瓷砖铺成的？

正确答案：B · 分值：1

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2002 AMC8 #24 · Algebra · ★★★★
Miki has a dozen oranges of the same size and a dozen pears of the same size. Miki uses her juicer to extract 8 ounces of pear juice from 3 pears and 8 ounces of orange juice from 2 oranges. She makes a pear-orange juice blend from an equal number of pears and oranges. What percent of the blend is pear juice?
Miki 有一打同样大小的桔子和一打同样大小的梨。Miki 用榨汁机能从 3 个梨中榨取 8 盎司梨汁，并且从 2 个橙子中能榨取 8 盎司橙汁。她用同样数量的梨和橙子做成了梨橙混合汁。那么这个混合汁里有百分之多少是梨汁？

正确答案：B · 分值：1

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2002 AMC8 #25 · Algebra · ★★★★
Loki, Moe, Nick and Ott are good friends. Ott had no money, but the others did. Moe gave Ott one-fifth of his money, Loki gave Ott one-fourth of his money and Nick gave Ott one-third of his money. Each gave Ott the same amount of money. What fractional part of the group's money does Ott now have?
Loki，Moe，Nick 和 Ott 是好朋友。Ott 没有钱，但其他人有。Moe 给了 Ott 五分之一的钱， Loki 给了 Ott 四分之一的钱，Nick 给了 Ott 三分之一的钱。每个人都给了 Ott 同样的钱。那么现在 Ott 有的钱占了四个人全部的钱的几分之几？

正确答案：B · 分值：1

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2001 AMC8 #1 · Algebra · ★
Casey's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will he need to do his job?
Casey 的职业技能实践课是制作一个高尔夫奖杯。他必须在一个高尔夫球上画 300 个凹坑。如果他需要 2 秒钟才能画出一个凹坑，他需要多少分钟才能完成他的工作？

正确答案：D · 分值：1

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2001 AMC8 #2 · Algebra · ★
I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number?
我在想两个整数。他们的积是 24，和是 11。较大的那个数是多少？

正确答案：D · 分值：1

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2001 AMC8 #3 · Algebra · ★★
Granny Smith has $63. Elberta has $2 more than Anjou and Anjou has one-third as much as Granny Smith. How many dollars does Elberta have?
Smith 奶奶有 63 美元。Elberta 比 Anjou 多 2 美元，Anjou 的钱是 Smith 奶奶的三分之一。那么 Elberta 有多少美元？

正确答案：E · 分值：1

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2001 AMC8 #4 · Number Theory · ★★
The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible even five-digit number. The digit in the tens place is
数字 1，2，3，4 和 9 每个使用一次，形成最小的五位偶数。则这个数的十位数字是？

正确答案：E · 分值：1

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2001 AMC8 #5 · Algebra · ★★
On a dark and stormy night Snoopy suddenly saw a flash of lightning. Ten seconds later he heard the sound of thunder. The speed of sound is 1088 feet per second and one mile is 5280 feet. Estimate, to the nearest half-mile, how far Snoopy was from the flash of lightning.
在一个漆黑的暴风雨之夜，Snoopy 突然看到一道闪电。十秒钟后，他听到了雷声。音速是 1088 英尺每秒（一英里等于 5280 英尺）。请估算 Snoopy 离闪电有多少英里（结果精确到 0.5 英里）？

正确答案：C · 分值：1

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2001 AMC8 #6 · Algebra · ★★
Six trees are equally spaced along one side of a straight road. The distance from the first tree to the fourth is 60 feet. What is the distance in feet between the first and last trees?
六棵树在一条笔直公路的一侧等距分布。第一棵树和第四棵树相距 60 英尺。则第一棵树和最后一棵树之间的距离是多少英尺？

正确答案：B · 分值：1

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2001 AMC8 #7 · Geometry · ★★
To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display. The kites look like the one in the diagram. For her small kite Genevieve draws the kite on a one-inch grid. For the large kite she triples both the height and width of the entire grid.
What is the number of square inches in the area of the small kite?
小风筝的面积是多少平方英寸？

正确答案：A · 分值：1

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2001 AMC8 #8 · Geometry · ★★
To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display. The kites look like the one in the diagram. For her small kite Genevieve draws the kite on a one-inch grid. For the large kite she triples both the height and width of the entire grid.
Genevieve puts bracing on her large kite in the form of a cross connecting opposite corners of the kite. How many inches of bracing material does she need?
Genevieve 给大风筝制作了一个十字形的支架，支架即为风筝的两条对角线。她需要多少英寸的支架材料？

正确答案：E · 分值：1

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2001 AMC8 #9 · Geometry · ★★
To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display. The kites look like the one in the diagram. For her small kite Genevieve draws the kite on a one-inch grid. For the large kite she triples both the height and width of the entire grid.
The large kite is covered with gold foil. The foil is cut from a rectangular piece that just covers the entire grid. How many square inches of waste material are cut off from the four corners?
大风筝由一层金箔覆盖。箔材是从一张矩形金箔纸上切得，这张矩形金箔纸刚好能够覆盖整个网格。则从四个角上切下多少平方英寸的废料？

正确答案：D · 分值：1

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2001 AMC8 #10 · Algebra · ★★
A collector offers to buy state quarters for 2000% of their face value. At that rate how much will Bryden get for his four state quarters?
一位收藏家提出以面值的 2000％购买州政府发行的 25 美分硬币。按这个价格，Bryden 的 4 枚这样的 25 美分硬币能卖到多少钱？

正确答案：A · 分值：1

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2001 AMC8 #11 · Geometry · ★★★
Points AA, BB, CC and DD have these coordinates: A(3,2)A(3,2), B(3,−2)B(3,-2), C(−3,−2)C(-3,-2) and D(−3,0)D(-3, 0). The area of quadrilateral ABCDABCD is
点 AA，BB，CC 和 DD 有如下坐标：A(3,2)A(3,2)，B(3,−2)B(3,-2)，C(−3,−2)C(-3,-2)，D(−3,0)D(-3,0)，则四边形 ABCDABCD 的面积为

正确答案：C · 分值：1

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2001 AMC8 #12 · Algebra · ★★★
If a⊗b=a+ba−ba\otimes b = \dfrac{a + b}{a - b} , then (6⊗4)⊗3=(6\otimes 4)\otimes 3 =
若 a⊗b=a+ba−ba\otimes b = \dfrac{a + b}{a - b}，则 (6⊗4)⊗3=(6\otimes 4)\otimes 3 =

正确答案：A · 分值：1

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2001 AMC8 #13 · Counting, Probability & Statistics · ★★★
Of the 36 students in Richelle's class, 12 prefer chocolate pie, 8 prefer apple, and 6 prefer blueberry. Half of the remaining students prefer cherry pie and half prefer lemon. For Richelle's pie graph showing this data, how many degrees should she use for cherry pie?
在 Richelle 班的 36 名学生中，12 人喜欢巧克力派，8 人喜欢苹果，6 人喜欢蓝莓。剩下的学生中有一半喜欢樱桃派，另一半喜欢柠檬派。Richelle 的饼图显示了这些数据，她应该用多少角度表示樱桃派？

正确答案：D · 分值：1

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2001 AMC8 #14 · Counting, Probability & Statistics · ★★★
Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the order of food items is not important, how many different meals might he choose?
Meat: beef, chicken, pork Vegetables: baked beans, corn, potatoes, tomatoes Dessert: brownies, chocolate cake, chocolate pudding, ice cream
Tyler 进入了自助餐排队队列等待选餐，他可以选择一种肉，两种不同的蔬菜和一种甜点。如果食物的顺序不重要，这顿饭他能有多少种不同的组合？ ·肉：牛肉、鸡肉、猪肉 ·蔬菜：烤豆、玉米、土豆、西红柿 ·甜点：布朗尼，巧克力蛋糕，巧克力布丁，冰淇淋

正确答案：C · 分值：1

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2001 AMC8 #15 · Algebra · ★★★
Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute. Four minutes later Christen joined him and peeled at the rate of 5 potatoes per minute. When they finished, how many potatoes had Christen peeled?
Homer 开始以每分钟 3 个土豆的速度开始剥一堆土豆，这堆土豆总共有 44 个。四分钟后， Christen 加入他的行列，以每分钟 5 个土豆的速度剥皮。当他们完成时，Christen 剥了多少土豆？

正确答案：A · 分值：1

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2001 AMC8 #16 · Geometry · ★★★
A square piece of paper, 4 inches on a side, is folded in half vertically. Both layers are then cut in half parallel to the fold. Three new rectangles are formed, a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?
一张边长 4 英寸的正方形纸垂直对折。然后将这两层沿着平行于折痕的方向均切割成两半，形成了三个新矩形，1 个大矩形和 2 个小矩形。则其中一个小矩形的周长与大矩形的周长之比是多少？

正确答案：E · 分值：1

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2001 AMC8 #17 · Algebra · ★★★
For the game show Who Wants To Be A Millionaire?, the dollar values of each question are shown in the table below (where K = 1000). Between which two questions is the percent increase of the value the smallest?
对于游戏节目《谁想成为百万富翁？》，每个问题的价值（单位：美元）如下表所示（其中 K＝ 1000）。在哪两个问题之间，哪两个价值增加的百分比最小？

正确答案：B · 分值：1

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2001 AMC8 #18 · Counting, Probability & Statistics · ★★★
Two dice are thrown. What is the probability that the product of the two numbers is a multiple of 5?
掷两枚骰子，问得到的两个数之积为 5 的倍数的概率是多少？

正确答案：D · 分值：1

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2001 AMC8 #19 · Algebra · ★★★
Car M traveled at a constant speed for a given time. This is shown by the dashed line. Car N traveled at twice the speed for the same distance. If Car M and Car N's speed and time are shown as solid line, which graph illustrates this?
汽车 M 在给定的时间内以恒定的速度行驶，其速度和时间曲线用虚线所示。汽车 N 以两倍的速度行驶了相同的距离。如果 N 车的速度和时间曲线用实线表示，则下面哪张图表说明了这一点？

正确答案：D · 分值：1

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2001 AMC8 #20 · Counting, Probability & Statistics · ★★★
Kaleana shows her test score to Quay, Marty and Shana, but the others keep theirs hidden. Quay thinks, "At least two of us have the same score." Marty thinks, "I didn't get the lowest score." Shana thinks, "I didn't get the highest score." List the scores from lowest to highest for Marty (M), Quay (Q) and Shana (S).
Kaleana 向 Quay，Marty 和 Shana 展示了自己的考试成绩，但其他三人都隐藏了自己的成绩。 Quay 认为：“我们中至少有两个人有相同的分数。”Marty 认为：“我没有得到最低的分数。” Shana 认为： “我没有得到最高的分数。”请按从最低到最高的次序将 Marty（M）、Quay（Q）和 Shana（S）的分数列出来。

正确答案：A · 分值：1

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2001 AMC8 #21 · Counting, Probability & Statistics · ★★★★
The mean of a set of five different positive integers is 15. The median is 18. The maximum possible value of the largest of these five integers is
一组五个不同正整数的平均值是 15。中位数是 18。这五个整数中最大的那个数的最大可能值为

正确答案：D · 分值：1

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2001 AMC8 #22 · Number Theory · ★★★★
On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and each incorrect answer is worth 0 points. Which of the following scores is NOT possible?
在一项有 20 个问题的测试中，每个正确答案得 5 分，每个未回答的问题得 1 分，每个错误答案得 0 分。则以下哪个得分是不可能的？

正确答案：E · 分值：1

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2001 AMC8 #23 · Geometry · ★★★★
Points RR , SS and TT are vertices of an equilateral triangle, and points XX , YY and ZZ are midpoints of its sides. How many noncongruent triangles can be drawn using any three of these six points as vertices?
点 RR，SS 和 TT 是一个等边三角形的三个顶点，点 XX，YY 和 ZZ 分别是边的中点。使用这六个点中的任意三个作为顶点，可以画出多少个不全等的三角形？

正确答案：D · 分值：1

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2001 AMC8 #24 · Counting, Probability & Statistics · ★★★★
Each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. When the upper half is folded down over the centerline, 2 pairs of red triangles coincide, as do 3 pairs of blue triangles. There are 2 red-white pairs. How many white pairs coincide?
该图形的每一半由 3 个红色三角形、5 个蓝色三角形和 8 个白色三角形组成。当上半部分沿中心线向下折叠时，2 对红色三角形重合，3 对蓝色三角形重合。还有两对红－白对。那么有多少对白色三角形重合？

正确答案：B · 分值：1

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2001 AMC8 #25 · Number Theory · ★★★★
There are 24 four-digit whole numbers that use each of the four digits 2, 4, 5 and 7 exactly once. Only one of these four-digit numbers is a multiple of another one. Which of the following is it?
2、4、5 和 7 这四个数字每个恰好使用一次，一共可以组成 24 个四位整数。这 24 个四位整数中，只有一个是另一个的倍数。则这个数是下列哪一个？

正确答案：D · 分值：1

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2000 AMC8 #1 · Algebra · ★
Aunt Anna is 42 years old. Caitlin is 5 years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin?
Anna 阿姨现在 42 岁，Caitlin 比 Brianna 小 5 岁，Brianna 的年龄是 Anna 阿姨的一半。问 Caitlin 多大？

正确答案：B · 分值：1

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2000 AMC8 #2 · Algebra · ★★
Which of these numbers is less than its reciprocal?
下面哪个数比它的倒数小?

正确答案：A · 分值：1

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2000 AMC8 #3 · Algebra · ★
How many whole numbers lie in the interval between 53\displaystyle \frac{5}{3} and 2π2\pi?
在53\displaystyle \frac{5}{3}到2π2\pi之间有多少个整数？

正确答案：D · 分值：1

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2000 AMC8 #4 · Counting, Probability & Statistics · ★
In 1960 only 5% of the working adults in Carlin City worked at home. By 1970 the "at-home" work force had increased to 8%. In 1980 there were approximately 15% working at home, and in 1990 there were 30%. The graph that best illustrates this is:
在 1960 年，Carlin 城市只有 5％的劳动力在家办公，到 1970 年，在家办公的劳动力增加到了 8％，在 1980 年，大概有 15％的劳动力在家办公，在 1990 年，是 30％。下面的图像中，最能体现这一点的是

正确答案：E · 分值：1

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2000 AMC8 #5 · Counting, Probability & Statistics · ★★★
Each principal of Lincoln High School serves exactly one 3-year term. What is the maximum number of principals this school could have during an 8-year period?
林肯高中的每一任校长任期恰好都是3年，那么在某个8年期内，这所学校最多可能有多少任校长？

正确答案：C · 分值：1

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2000 AMC8 #6 · Geometry · ★★
Figure ABCDABCD is a square. Inside this square three smaller squares are drawn with the side lengths as labeled. The area of the shaded LL -shaped region is
ABCD 是个正方形。在这个正方形内画了 3 个小正方形，它们的边长如图所示。则 L 形状的阴影部分区域的面积是多少？

正确答案：A · 分值：1

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2000 AMC8 #7 · Algebra · ★★
What is the minimum possible product of three different numbers of the set {−8,−6,−4,0,3,5,7}\{-8,-6,-4,0,3,5,7\} ?
集合｛-8，-6，-4，0，3，5，7｝中的三个不同的元素的乘积的最小可能值是多少？

正确答案：B · 分值：1

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2000 AMC8 #8 · Counting, Probability & Statistics · ★★
Three dice with faces numbered 1 through 6 are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots NOT visible in this view is
3 个各个面上分别标有 1 到 6 的数字的骰子如图所示堆叠起来。18 个面只有 7 个面可见。其余 11 个面不可见（后面，底面以及两个骰子之间的面）。图示所示的角度所看不到的面上的点数总和是多少？

正确答案：D · 分值：1

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2000 AMC8 #9 · Number Theory · ★★
Three-digit powers of 2 and 5 are used in this "cross-number" puzzle. What is the only possible digit for the outlined square?
在这个交叉数字拼图中使用了 2 和 5 的幂，且都是三位数。则黑体所示的正方形内唯一可能的数字是多少？
ACROS|横着 DOWN|竖着

正确答案：D · 分值：1

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2000 AMC8 #10 · Algebra · ★★
Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grown half as many inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now?
Ara 和 Shea 以前身高一样。自那以后，Shea 身高增高了 20％，而 Ara 增长的高度是 Shea 增长高度的一半。Shea 现在身高 60 英寸，那么 Ara 现在身高是多少英寸？

正确答案：E · 分值：1

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2000 AMC8 #11 · Number Theory · ★★★
The number 64 has the property that it is divisible by its unit digit. How many whole numbers between 10 and 50 have this property?
64 这个数有这样的性质:它可以被它的个位所整除，那么 10 和 50 之间有多少个整数有这样的性质？

正确答案：C · 分值：1

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2000 AMC8 #12 · Counting, Probability & Statistics · ★★★
A block wall 100 feet long and 7 feet high will be constructed using blocks that are 1 foot high and either 2 feet long or 1 foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the ends. What is the smallest number of blocks needed to build this wall?
一堵墙 100 英尺长，7 英尺高，是由若干高度均为 1 英尺，长度为 2 英尺或者 1 英尺的砖块组成（不允许切割砖块）。砖块之间竖直的连接线必须如图所示交错开来，并且墙的两端要对齐。 则要建造这堵墙，需要的最少砖块数是多少？

正确答案：D · 分值：1

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2000 AMC8 #13 · Geometry · ★★★
In triangle CATCAT , we have ∠ACT=∠ATC\angle ACT =\angle ATC and ∠CAT=36∘\angle CAT = 36^\circ . If TR‾\overline{TR} bisects ∠ATC\angle ATC , then ∠CRT=\angle CRT =
在三角形 CATCAT 中，∠ACT=∠ATC\angle ACT = \angle ATC 且 ∠CAT=36∘\angle CAT = 36^\circ。若 TR‾\overline{TR} 平分 ∠ATC\angle ATC，则 ∠CRT=\angle CRT =

正确答案：C · 分值：1

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2000 AMC8 #14 · Number Theory · ★★★
What is the units digit of 1919+999919^{19} + 99^{99} ?
1919+999919^{19} + 99^{99} 的个位数字是多少？

正确答案：D · 分值：1

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2000 AMC8 #15 · Geometry · ★★★
Triangles ABCABC , ADEADE , and EFGEFG are all equilateral. Points DD and GG are midpoints of AC‾\overline{AC} and AE‾\overline{AE} , respectively. If AB = 4 , what is the perimeter of figure ABCDEFGABCDEFG ?
三角形 ABC，ADE 和 EFG 都是等边三角形。点 D 和 G 分别是形 ABCDEFG 的周长是多少？
和

正确答案：C · 分值：1

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2000 AMC8 #16 · Geometry · ★★★
In order for Mateen to walk a kilometer (1000m) in his rectangular backyard, he must walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen's backyard in square meters?
为了让 Mateen 在他的长方形后院里走 1 公里（1000 米），他必须沿着长方形的长走 25 次，或者沿着它的周长走 10 次．那么 Mateen 后院的面积是多少平方米?

正确答案：C · 分值：1

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2000 AMC8 #17 · Algebra · ★★★
The operation ⊗\otimes is defined for all nonzero numbers by a⊗b=a2b\displaystyle a\otimes b =\frac{a^{2}}{b} . Determine [(1⊗2)⊗3]−[1⊗(2⊗3)][(1\otimes 2)\otimes 3]-[1\otimes (2\otimes 3)] .
运算 ⊗\otimes 对所有非零数定义为 a⊗b=a2b\displaystyle a\otimes b = \frac{a^{2}}{b}。求 [(1⊗2)⊗3]−[1⊗(2⊗3)][(1\otimes 2)\otimes 3]-[1\otimes (2\otimes 3)] 的值。

正确答案：A · 分值：1

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2000 AMC8 #18 · Geometry · ★★★
Consider these two geoboard quadrilaterals. Which of the following statements is true?
考虑下面几何画板上的两个四边形。下面哪句话是对的？

正确答案：E · 分值：1

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2000 AMC8 #19 · Geometry · ★★★
Three circular arcs of radius 5 units bound the region shown. Arcs ABAB and ADAD are quarter-circles, and arc BCDBCD is a semicircle. What is the area, in square units, of the region?
三段半径为 5 个单位长的圆弧围成图示区域。弧 AB 和 AD 均为四分之一圆，弧 BCD 是个半圆。 那么这个区域的面积是多少平方单位？

正确答案：C · 分值：1

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2000 AMC8 #20 · Number Theory · ★★★
You have nine coins: a collection of pennies, nickels, dimes, and quarters having a total value of $1.02 , with at least one coin of each type. How many dimes must you have?
你有 9 枚硬币：若干便士，五分镍币，一角硬币和 25 分硬币，总价值是 1.02 美元，并且每种硬币都至少有一枚。那么你肯定有多少枚一角硬币？

正确答案：A · 分值：1

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2000 AMC8 #21 · Counting, Probability & Statistics · ★★★
Keiko tosses one penny and Ephraim tosses two pennies. The probability that Ephraim gets the same number of heads that Keiko gets is
Keiko 掷了一枚便士，Ephraim 掷了两枚便士。Ephraim 得到的正面的个数和 Keiko 得到的正面的个数一样多的概率是：

正确答案：B · 分值：1

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2000 AMC8 #22 · Geometry · ★★★
A cube has edge length 2 . Suppose that we glue a cube of edge length 1 on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. The percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid formed is closest to
一个正方体边长为 2。假设我们把一个边长为 1 的正方体粘贴到这个大的正方体的顶面，使得小正方体的一个面整个的放在大正方体的顶面上。则和原来大正方体的表面积（侧面，顶面，底面）相比较，所形成的新的立体图形的表面积增加的百分数最接近于百分之多少？

正确答案：C · 分值：1

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2000 AMC8 #23 · Algebra · ★★★★
There is a list of seven numbers. The average of the first four numbers is 5 , and the average of the last four numbers is 8 . If the average of all seven numbers is 647\displaystyle 6\frac{4}{7} , then the number common to both sets of four numbers is
有一组 7 个数。前 4 个数的平均值是 5，后 4 个数的平均值是 8。若这 7 个数的平均值是 647\displaystyle 6\frac{4}{7}，那么同时属于前 4 个数和后 4 个数的那个数是多少？

正确答案：B · 分值：1

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2000 AMC8 #24 · Geometry · ★★★★
If ∠A=20∘\angle A = 20^\circ and ∠AFG=∠AGF\angle AFG =\angle AGF , then ∠B+∠D=\angle B+\angle D =
若 ∠A=20∘\angle A = 20^\circ 且 ∠AFG=∠AGF\angle AFG = \angle AGF，则 ∠B+∠D=\angle B+\angle D =

正确答案：D · 分值：1

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2000 AMC8 #25 · Geometry · ★★★★
The area of rectangle ABCDABCD is 72 units squared. If point AA and the midpoints of BC‾\overline{BC} and CD‾\overline{CD} are joined to form a triangle, the area of that triangle is
矩形 ABCDABCD 的面积是 72 平方单位。若连接点 AA 与 BC‾\overline{BC}、CD‾\overline{CD} 的中点构成一个三角形，那么这个三角形的面积是多少？

正确答案：B · 分值：1

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1999 AMC8 #1 · Algebra · ★
(6?3) + 4 - (2 - 1) = 5. To make this statement true, the question mark between the 6 and the 3 should be replaced by
要使等式 (6?3) + 4 - (2 - 1) = 5 成立，6 和 3 之间的问号应替换为

正确答案：A · 分值：1

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1999 AMC8 #2 · Geometry · ★
What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock?
时钟在 10 点整时，时针和分针所形成较小角的度数是多少？

正确答案：C · 分值：1

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1999 AMC8 #3 · Algebra · ★
Which triplet of numbers has a sum NOT equal to 1?
下列哪组数字的和不等于 1？

正确答案：D · 分值：1

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1999 AMC8 #4 · Algebra · ★
The diagram shows the miles traveled by bikers Alberto and Bjorn. After four hours, about how many more miles has Alberto biked than Bjorn?
图中显示了骑行者 Alberto 和 Bjorn 行驶的英里数。四小时后，Alberto 比 Bjorn 大约多骑了多少英里？

正确答案：A · 分值：1

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1999 AMC8 #5 · Geometry · ★★
A rectangular garden 60 feet long and 20 feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden?
一个长 60 英尺、宽 20 英尺的矩形花园用围栏围起来。为了使花园更大，同时使用同样的围栏，将其形状改为正方形。这样花园面积扩大了多少平方英尺？

正确答案：D · 分值：1

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1999 AMC8 #6 · Counting, Probability & Statistics · ★★
Bo, Coe, Flo, Jo, and Moe have different amounts of money. Neither Jo nor Bo has as much money as Flo. Both Bo and Coe have more than Moe. Jo has more than Moe, but less than Bo. Who has the least amount of money?
Bo、Coe、Flo、Jo 和 Moe 各自拥有不同数量的钱。Jo 和 Bo 都没有 Flo 的钱多。Bo 和 Coe 都比 Moe 的钱多。Jo 比 Moe 的钱多，但比 Bo 的钱少。谁的钱最少？

正确答案：E · 分值：1

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1999 AMC8 #7 · Algebra · ★★
The third exit on a highway is located at milepost 40 and the tenth exit is at milepost 160. There is a service center on the highway located three-fourths of the way from the third exit to the tenth exit. At what milepost would you expect to find this service center?
某高速公路的第三个出口位于 40 英里处，第十个出口位于 160 英里处。该高速公路上有一个服务区，位于第三个出口到第十个出口之间四分之三的位置。该服务区大约在哪个英里标处？

正确答案：E · 分值：1

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1999 AMC8 #8 · Geometry · ★★
Six squares are colored, front and back, (R = red, B = blue, O = orange, Y = yellow, G = green, and W = white). They are hinged together as shown, then folded to form a cube. The face opposite the white face is
六个正方形，正面和背面分别涂有颜色（R = 红色，B = 蓝色，O = 橙色，Y = 黄色，G = 绿色，W = 白色）。它们如图所示铰接在一起，然后折叠形成一个正方体。白色面相对的面颜色是什么？

正确答案：A · 分值：1

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1999 AMC8 #9 · Counting, Probability & Statistics · ★★
Three flower beds overlap as shown. Bed A has 500 plants, bed B has 450 plants, and bed C has 350 plants. Beds A and B share 50 plants, while beds A and C share 100. The total number of plants is
三个花坛如图所示重叠。花坛 A 有 500 株植物，花坛 B 有 450 株，花坛 C 有 350 株。花坛 A 和 B 共享 50 株，花坛 A 和 C 共享 100 株。植物的总数是

正确答案：C · 分值：1

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1999 AMC8 #10 · Counting, Probability & Statistics · ★★
A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 seconds, yellow for 5 seconds, and red for 30 seconds. At a randomly chosen time, what is the probability that the light will NOT be green?
一个红绿灯的完整周期为 60 秒。每个周期中，绿灯亮 25 秒，黄灯亮 5 秒，红灯亮 30 秒。在随机一个时刻，灯不是绿色的概率是多少？

正确答案：E · 分值：1

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1999 AMC8 #11 · Counting, Probability & Statistics · ★★★
Each of the five numbers 1, 4, 7, 10, and 13 is placed in one of the five squares so that the sum of the three numbers in the horizontal row equals the sum of the three numbers in the vertical column. The largest possible value for the horizontal or vertical sum is
将五个数 1、4、7、10 和 13 分别放入五个方格中，使得横排三个数之和等于竖排三个数之和。水平或垂直和的最大可能值是

正确答案：D · 分值：1

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1999 AMC8 #12 · Algebra · ★★★
The ratio of the number of games won to the number of games lost (no ties) by the Middle School Middies is 11/4 . To the nearest whole percent, what percent of its games did the team lose?
中学 Middies 队赢的场数比输的场数（无平局）的比是 11/4。取最近的整数百分比，该队输掉的比赛占百分之多少？

正确答案：B · 分值：1

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1999 AMC8 #13 · Counting, Probability & Statistics · ★★★
The average age of the 40 members of a computer science camp is 17 years. There are 20 girls, 15 boys, and 5 adults. If the average age of the girls is 15 and the average age of the boys is 16, what is the average age of the adults?
一个计算机科学夏令营 40 名成员的平均年龄为 17 岁。其中有 20 名女生、15 名男生和 5 名成人。如果女生的平均年龄为 15 岁，男生的平均年龄为 16 岁，那么成人的平均年龄是多少？

正确答案：C · 分值：1

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1999 AMC8 #14 · Geometry · ★★★
In trapezoid ABCDABCD , the sides ABAB and CDCD are equal. The perimeter of ABCDABCD is
在梯形 ABCDABCD 中，边 ABAB 和 CDCD 相等。梯形 ABCDABCD 的周长是

正确答案：D · 分值：1

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1999 AMC8 #15 · Counting, Probability & Statistics · ★★★
Bicycle license plates in Flatville each contain three letters. The first is chosen from the set {C,H,L,P,R}, the second from {A,I,O}, and the third from {D,M,N,T}. When Flatville needed more license plates, they added two new letters. The new letters may both be added to one set or one letter may be added to one set and one to another set. What is the largest possible number of ADDITIONAL license plates that can be made by adding two letters?
Flatville 的自行车牌照各包含三个字母。第一个从 {C,H,L,P,R} 中选择，第二个从 {A,I,O} 中选择，第三个从 {D,M,N,T} 中选择。当 Flatville 需要更多牌照时，他们新增了两个新字母。这两个新字母可以都加入一个集合，或者一个字母加入一个集合、另一个加入另一个集合。通过添加两个字母，最多可以增加多少额外的牌照？

正确答案：D · 分值：1

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1999 AMC8 #16 · Algebra · ★★★
Tori's mathematics test had 75 problems: 10 arithmetic, 30 algebra, and 35 geometry problems. Although she answered 70% of the arithmetic, 40% of the algebra, and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% of the problems right. How many more problems would she have needed to answer correctly to earn a 60% passing grade?
Tori 的数学考试有 75 道题：10 道算术，30 道代数，35 道几何。虽然她做对了 70% 的算术题、40% 的代数题和 60% 的几何题，但她没有通过考试，因为她做对的题目不到 60%。她还需要多做对多少道题才能达到 60% 的及格成绩？

正确答案：B · 分值：1

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1999 AMC8 #17 · Algebra · ★★★
At Central Middle School the 108 students who take the AMC 8 meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, lists this items: 112\displaystyle 1\frac{1}{2} cups of flour, 2 eggs, 3 tablespoons butter, 34\displaystyle \frac{3}{4} cups sugar, and 1 package of chocolate drops. They will make only full recipes, not partial recipes. Walter can buy eggs by the half-dozen. How many half-dozens should he buy to make enough cookies? (Some eggs and some cookies may be left over.)
中央中学 108 名参加 AMC 8 的学生晚上聚会讨论题目，平均每人吃两块曲奇。Walter 和 Gretel 今年正在烤 Bonnie's Best Bar Cookies。他们的配方可以做一盘 15 块曲奇，配料表如下：112\displaystyle 1\frac{1}{2} 杯面粉、2 个鸡蛋、3 汤匙黄油、34\displaystyle \frac{3}{4} 杯糖、1 包巧克力豆。他们只做完整的配方，不做部分配方。
Walter 可以按半打买鸡蛋。他应该买多少个半打鸡蛋才能做足够的曲奇？（可能会剩下一些鸡蛋和一些曲奇。）

正确答案：C · 分值：1

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1999 AMC8 #18 · Algebra · ★★★
At Central Middle School the 108 students who take the AMC8 meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, lists this items: 112\displaystyle 1\frac{1}{2} cups flour, 2 eggs, 3 tablespoons butter, 34\displaystyle \frac{3}{4} cups sugar, and 1 package of chocolate drops. They will make only full recipes, not partial recipes. They learn that a big concert is scheduled for the same night and attendance will be down 25% . How many recipes of cookies should they make for their smaller party?
中央中学 108 名参加 AMC8 的学生晚上聚会讨论题目，平均每人吃两块曲奇。Walter 和 Gretel 今年正在烤 Bonnie's Best Bar Cookies。他们的配方可以做一盘 15 块曲奇，配料表如下：112\displaystyle 1\frac{1}{2} 杯面粉、2 个鸡蛋、3 汤匙黄油、34\displaystyle \frac{3}{4} 杯糖、1 包巧克力豆。他们只做完整的配方，不做部分配方。
他们得知当晚有一场大型音乐会，参加人数将减少 25%。他们应该为缩小后的聚会做多少份配方？

正确答案：E · 分值：1

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1999 AMC8 #19 · Algebra · ★★★
At Central Middle School, the 108 students who take the AMC 8 meet in the evening to talk about problems and eat an average of two cookies apiece. Hansel and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, lists these items: 112\displaystyle 1\frac{1}{2} cups flour, 2 eggs, 3 tablespoons butter, 34\displaystyle \frac{3}{4} cups sugar, and 1 package of chocolate drops. They will make full recipes, not partial recipes. Hansel and Gretel must make enough pans of cookies to supply 216 cookies. There are 8 tablespoons in a stick of butter. How many sticks of butter will be needed? (Some butter may be leftover, of course.)
中央中学 108 名参加 AMC 8 的学生晚上聚会讨论题目，平均每人吃两块曲奇。Hansel 和 Gretel 今年正在烤 Bonnie's Best Bar Cookies。他们的配方可以做一盘 15 块曲奇，配料表如下：112\displaystyle 1\frac{1}{2} 杯面粉、2 个鸡蛋、3 汤匙黄油、34\displaystyle \frac{3}{4} 杯糖、1 包巧克力豆。他们只做完整的配方，不做部分配方。
Hansel 和 Gretel 必须做足够的曲奇来供应 216 块。一条黄油有 8 汤匙。需要多少条黄油？（当然可能会剩下一些黄油。）

正确答案：B · 分值：1

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1999 AMC8 #20 · Geometry · ★★★
Figure 1 is called a "stack map." The numbers tell how many cubes are stacked in each position. Fig. 2 shows these cubes, and Fig. 3 shows the view of the stacked cubes as seen from the front.
Which of the following is the front view for the stack map in Fig. 4?
图 1 称为「堆叠图」。数字表示每个位置堆叠了多少个正方体。图 2 显示了这些正方体，图 3 显示了从前面看到的堆叠正方体的视图。
下列哪个是图 4 中堆叠图的前视图？

正确答案：B · 分值：1

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1999 AMC8 #22 · Algebra · ★★★
In a far-off land three fish can be traded for two loaves of bread and a loaf of bread can be traded for four bags of rice. How many bags of rice is one fish worth?
在某个遥远的地方，三条鱼可以换两条面包，一条面包可以换四袋米。一条鱼值多少袋米？

正确答案：D · 分值：1

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1999 AMC8 #23 · Geometry · ★★★★
Square ABCDABCD has sides of length 3. Segments CMCM and CNCN divide the square's area into three equal parts. How long is segment CMCM ?
正方形 ABCDABCD 的边长为 3。线段 CMCM 和 CNCN 将正方形的面积分成相等的三部分。线段 CMCM 的长度是多少？

正确答案：C · 分值：1

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1999 AMC8 #24 · Number Theory · ★★★★
When 199920001999^{2000} is divided by 5 , the remainder is
当 199920001999^{2000} 除以 5 时，余数是多少？

正确答案：B · 分值：1

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1999 AMC8 #25 · Geometry · ★★★★
Points BB , DD , and JJ are midpoints of the sides of right triangle ACGACG . Points KK , EE , II are midpoints of the sides of triangle JDGJDG , etc. If the dividing and shading process is done 100 times (the first three are shown) and AC=CG=6 , then the total area of the shaded triangles is nearest
点 BB、DD 和 JJ 是直角三角形 ACGACG 各边的中点。点 KK、EE、II 是三角形 JDGJDG 各边的中点，以此类推。如果分割和着色过程进行 100 次（前三次如图所示）且 AC=CG=6，则着色三角形的总面积最接近

正确答案：A · 分值：1

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1998 AMC8 #2 · Algebra · ★
If (abcd)=ad−bc\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc, then (2113)+(3214)=\begin{pmatrix} 2 & 1 \\ 1 & 3 \end{pmatrix} + \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} =
若 (abcd)=ad−bc\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc，则 (2113)+(3214)=\begin{pmatrix} 2 & 1 \\ 1 & 3 \end{pmatrix} + \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} =

正确答案：E · 分值：1

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1998 AMC8 #4 · Geometry · ★★
How many triangles are in this figure? (Some triangles may overlap other triangles.)
图中有多少个三角形？（有些三角形可能与其他三角形重叠。）

正确答案：E · 分值：1

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1998 AMC8 #6 · Geometry · ★★
Dots are spaced one unit apart, horizontally and vertically. The number of square units enclosed by the polygon is
点之间水平和垂直方向间距均为一个单位。该多边形围成的面积是多少平方单位？

正确答案：B · 分值：1

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1998 AMC8 #8 · Algebra · ★
A child's wading pool contains 200 gallons of water. If water evaporates at the rate of 0.5 gallons per day and no other water is added or removed, how many gallons of water will be in the pool after 30 days?
一个儿童戏水池装有 200 加仑水。如果水以每天 0.5 加仑的速度蒸发，且没有其他水的添加或移除，30 天后池中还有多少加仑水？

正确答案：C · 分值：1

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1998 AMC8 #9 · Algebra · ★★
For a sale, a store owner reduces the price of a $10 scarf by 20% . Later the price is lowered again, this time by one-half the reduced price. The price is now
为了促销，一家商店的老板将一条 $10 的围巾降价 20%。之后价格再次下调，这次是下调后价格的一半。现在的价格是

正确答案：C · 分值：1

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1998 AMC8 #10 · Number Theory · ★★
Each of the letters W\text{W} , X\text{X} , Y\text{Y} , and Z\text{Z} represents a different integer in the set {1,2,3,4}\{ 1,2,3,4\} , but not necessarily in that order. If WX−YZ=1\dfrac{\text{W}}{\text{X}} - \dfrac{\text{Y}}{\text{Z}}=1 , then the sum of W\text{W} and Y\text{Y} is
字母 W\text{W}、X\text{X}、Y\text{Y} 和 Z\text{Z} 各代表集合 {1,2,3,4}\{1,2,3,4\} 中不同的整数，但不一定按此顺序。若 WX−YZ=1\dfrac{\text{W}}{\text{X}} - \dfrac{\text{Y}}{\text{Z}}=1，则 W\text{W} 与 Y\text{Y} 之和为

正确答案：E · 分值：1

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1998 AMC8 #11 · Counting, Probability & Statistics · ★★★
Harry has 3 sisters and 5 brothers. His sister Harriet has S\text{S} sisters and B\text{B} brothers. What is the product of S\text{S} and B\text{B} ?
Harry 有 3 个姐妹和 5 个兄弟。他的姐妹 Harriet 有 S\text{S} 个姐妹和 B\text{B} 个兄弟。S\text{S} 和 B\text{B} 的乘积是多少？

正确答案：C · 分值：1

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1998 AMC8 #13 · Geometry · ★★★
What is the ratio of the area of the shaded square to the area of the large square? (The figure is drawn to scale)
着色正方形的面积与大正方形的面积之比是多少？（图形按比例绘制）

正确答案：C · 分值：1

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1998 AMC8 #14 · Algebra · ★★★
An Annville Junior High School, 30% of the students in the Math Club are in the Science Club, and 80% of the students in the Science Club are in the Math Club. There are 15 students in the Science Club. How many students are in the Math Club?
在 Annville 初中，数学俱乐部中 30% 的学生也在科学俱乐部，科学俱乐部中 80% 的学生也在数学俱乐部。科学俱乐部有 15 名学生。数学俱乐部有多少名学生？

正确答案：E · 分值：1

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1998 AMC8 #15 · Algebra · ★★★
Estimate the population of Nisos in the year 2050.
在 Irenic 海的中央坐落着美丽的 Nisos 群岛。1998 年这些岛屿上的人口仅为 200，但人口每 25 年翻三倍。Irene 女王已颁布法令，岛上每个人必须有至少 1.5 平方英里的空间。Nisos 群岛的总面积为 24,900 平方英里。
估计 2050 年 Nisos 的人口。

正确答案：D · 分值：1

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1998 AMC8 #16 · Algebra · ★★★
Estimate the year in which the population of Nisos will be approximately 6,000.
在 Irenic 海的中央坐落着美丽的 Nisos 群岛。1998 年这些岛屿上的人口仅为 200，但人口每 25 年翻三倍。Irene 女王已颁布法令，岛上每个人必须有至少 1.5 平方英里的空间。Nisos 群岛的总面积为 24,900 平方英里。
估计 Nisos 人口大约达到 6,000 的年份。

正确答案：B · 分值：1

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1998 AMC8 #17 · Algebra · ★★★
In how many years, approximately, from 1998 will the population of Nisos be as much as Queen Irene has proclaimed that the islands can support?
在 Irenic 海的中央坐落着美丽的 Nisos 群岛。1998 年这些岛屿上的人口仅为 200，但人口每 25 年翻三倍。Irene 女王已颁布法令，岛上每个人必须有至少 1.5 平方英里的空间。Nisos 群岛的总面积为 24,900 平方英里。
大约从 1998 年起多少年后，Nisos 的人口会达到 Irene 女王宣布的群岛可承载的数量？

正确答案：C · 分值：1

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1998 AMC8 #18 · Geometry · ★★★
As indicated by the diagram below, a rectangular piece of paper is folded bottom to top, then left to right, and finally, a hole is punched at X. What does the paper look like when unfolded?
如下图所示，将一张矩形纸从下往上折叠，再从左往右折叠，最后在 X 处打一个孔。展开后纸张是什么样子？

正确答案：B · 分值：1

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1998 AMC8 #19 · Counting, Probability & Statistics · ★★★
Tamika selects two different numbers at random from the set {8,9,10}\{ 8,9,10 \} and adds them. Carlos takes two different numbers at random from the set {3,5,6}\{3, 5, 6\} and multiplies them. What is the probability that Tamika's result is greater than Carlos' result?
Tamika 从集合 {8,9,10}\{8,9,10\} 中随机选两个不同的数并相加。Carlos 从集合 {3,5,6}\{3,5,6\} 中随机选两个不同的数并相乘。Tamika 的结果大于 Carlos 的结果的概率是多少？

正确答案：A · 分值：1

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1998 AMC8 #20 · Geometry · ★★★
Let PQRSPQRS be a square piece of paper. PP is folded onto RR and then QQ is folded onto SS . The area of the resulting figure is 9 square inches. Find the perimeter of square PQRSPQRS .
设 PQRSPQRS 为一张正方形纸。将 PP 折到 RR 上，再将 QQ 折到 SS 上。所得图形的面积为 9 平方英寸。求正方形 PQRSPQRS 的周长。

正确答案：D · 分值：1

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1998 AMC8 #21 · Geometry · ★★★
AA4×4×44\times 4\times 4 cubical box contains 64 identical small cubes that exactly fill the box. How many of these small cubes touch a side or the bottom of the box?
一个 4×4×44\times 4\times 4 的正方体盒子内装有 64 个完全相同的小正方体，恰好填满盒子。这些小正方体中有多少个接触盒子的侧面或底面？

正确答案：B · 分值：1

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1998 AMC8 #22 · Number Theory · ★★★★
Terri produces a sequence of positive integers by following three rules. She starts with a positive integer, then applies the appropriate rule to the result, and continues in this fashion. Rule 1: If the integer is less than 10, multiply it by 9. Rule 2: If the integer is even and greater than 9, divide it by 2. Rule 3: If the integer is odd and greater than 9, subtract 5 from it. A sample sequence: 23,18,9,81,76,….23, 18, 9, 81, 76, \ldots . Find the 98th98^\text{th} term of the sequence that begins 98,49,….98, 49, \ldots .
Terri 按照以下三条规则生成一个正整数序列。她从一个正整数开始，然后对结果应用适当的规则，并继续以此方式进行。
规则 1：如果整数小于 10，乘以 9。 规则 2：如果整数为偶数且大于 9，除以 2。 规则 3：如果整数为奇数且大于 9，减去 5。
示例序列：23,18,9,81,76,…23, 18, 9, 81, 76, \ldots。
求以 98,49,…98, 49, \ldots 开头的序列的第 98 项。

正确答案：D · 分值：1

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1998 AMC8 #23 · Algebra · ★★★★
If the pattern in the diagram continues, what fraction of eighth triangle would be shaded?
如果图中的图案继续下去，第八个三角形着色部分的比例是多少？

正确答案：C · 分值：1

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1998 AMC8 #24 · Number Theory · ★★★★
A rectangular board of 8 columns has squares numbered beginning in the upper left corner and moving left to right so row one is numbered 1 through 8, row two is 9 through 16, and so on. A student shades square 1, then skips one square and shades square 3, skips two squares and shades square 6, skips 3 squares and shades square 10, and continues in this way until there is at least one shaded square in each column. What is the number of the shaded square that first achieves this result?
一块有 8 列的矩形板，方格从左上角开始从左到右编号，第一行为 1 到 8，第二行为 9 到 16，以此类推。一个学生涂黑了方格 1，然后跳过一个方格涂黑方格 3，跳过两个方格涂黑方格 6，跳过 3 个方格涂黑方格 10，并继续按此方式操作，直到每一列至少有一个涂黑的方格。首次达到此结果时涂黑的方格编号是多少？

正确答案：E · 分值：1

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1998 AMC8 #25 · Algebra · ★★★★
Three generous friends, each with some money, redistribute the money as followed: Amy gives enough money to Jan and Toy to double each of their amounts. Jan then gives enough to Amy and Toy to double their amounts. Finally, Toy gives enough to Amy and Jan to double their amounts. If Toy had 36 dollars at the beginning and 36 dollars at the end, what is the total amount that all three friends have?
三位慷慨的朋友各自拥有一些钱，按如下方式重新分配：Amy 给 Jan 和 Toy 足够的钱，使他们各自的金额翻倍。然后 Jan 给 Amy 和 Toy 足够的钱，使他们的金额翻倍。最后，Toy 给 Amy 和 Jan 足够的钱，使他们的金额翻倍。如果 Toy 一开始有 36 美元，最后也有 36 美元，那么三位朋友共有多少钱？

正确答案：D · 分值：1

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1997 AMC8 #2 · Algebra · ★
Ahn chooses a two-digit integer, subtracts it from 200, and doubles the result. What is the largest number Ahn can get?
Ahn 选择一个两位整数，用 200 减去它，然后将结果加倍。Ahn 能得到的最大数是多少？

正确答案：D · 分值：1

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1997 AMC8 #4 · Algebra · ★
Julie is preparing a speech for her class. Her speech must last between one-half hour and three-quarters of an hour. The ideal rate of speech is 150 words per minute. If Julie speaks at the ideal rate, which of the following number of words would be an appropriate length for her speech?
Julie 正在为她的班级准备一篇演讲。她的演讲时长必须在半小时到三刻钟之间。理想的语速是每分钟 150 个单词。如果 Julie 以理想的语速讲话，以下哪个单词数对演讲来说是合适的长度？

正确答案：E · 分值：1

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1997 AMC8 #5 · Number Theory · ★★
There are many two-digit multiples of 7, but only two of the multiples have a digit sum of 10. The sum of these two multiples of 7 is
7 的两位数倍数有很多，但其中只有两个倍数的各位数字之和为 10。这两个 7 的倍数之和是

正确答案：A · 分值：1

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1997 AMC8 #6 · Algebra · ★★
In the number 74982.1035 the value of the place occupied by the digit 9 is how many times as great as the value of the place occupied by the digit 3?
在数 74982.1035 中，数字 9 所在数位的值是数字 3 所在数位的值的多少倍？

正确答案：C · 分值：1

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1997 AMC8 #7 · Geometry · ★
The area of the smallest square that will contain a circle of radius 4 is
能容纳一个半径为 4 的圆的最小正方形的面积是

正确答案：D · 分值：1

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1997 AMC8 #8 · Algebra · ★★
Walter gets up at 6:30 a.m., catches the school bus at 7:30 a.m., has 6 classes that last 50 minutes each, has 30 minutes for lunch, and has 2 hours additional time at school. He takes the bus home and arrives at 4:00 p.m. How many minutes has he spent on the bus?
Walter 早上 6:30 起床，7:30 赶校车，有 6 节课每节 50 分钟，有 30 分钟午饭时间，还有 2 小时额外在校时间。他乘校车回家，下午 4:00 到家。他在校车上花了多少分钟？

正确答案：B · 分值：1

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1997 AMC8 #9 · Counting, Probability & Statistics · ★★
Three students, with different names, line up single file. What is the probability that they are in alphabetical order from front-to-back?
三个名字各不相同的学生排成一列。他们从前到后按字母顺序排列的概率是多少？

正确答案：C · 分值：1

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1997 AMC8 #10 · Geometry · ★★
What fraction of this square region is shaded? Stripes are equal in width, and the figure is drawn to scale.
这个正方形区域中有多少比例被涂色？条纹宽度相等，图形按比例绘制。

正确答案：C · 分值：1

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1997 AMC8 #11 · Number Theory · ★★★
Let N\boxed{N} mean the number of whole number divisors of NN . For example, 3=2\boxed{3}=2 because 3 has two divisors, 1 and 3. Find the value of
11×20.\boxed{\boxed{11}\times\boxed{20}}.
令 N\boxed{N} 表示 NN 的正整数因数的个数。例如 3=2\boxed{3}=2，因为 3 有两个因数：1 和 3。求 11×20\boxed{\boxed{11}\times\boxed{20}} 的值。

正确答案：A · 分值：1

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1997 AMC8 #12 · Geometry · ★★★
∠1+∠2=180∘\angle 1 + \angle 2 = 180^\circ
∠3=∠4\angle 3 = \angle 4
Find ∠4.\angle 4.
求 ∠4\angle 4 的度数。

正确答案：D · 分值：1

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1997 AMC8 #13 · Algebra · ★★★
Three bags of jelly beans contain 26, 28, and 30 beans. The ratios of yellow beans to all beans in each of these bags are 50% , 25% , and 20% , respectively. All three bags of candy are dumped into one bowl. Which of the following is closest to the ratio of yellow jelly beans to all beans in the bowl?
三袋果冻豆分别装有 26、28 和 30 颗。这三袋中黄色豆与全部豆的比例分别是 50%、25% 和 20%。将三袋糖果全部倒入一个大碗中。黄色果冻豆与碗中全部果冻豆的比例最接近以下哪项？

正确答案：A · 分值：1

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1997 AMC8 #14 · Counting, Probability & Statistics · ★★★
There is a set of five positive integers whose average (mean) is 5, whose median is 5, and whose only mode is 8. What is the difference between the largest and smallest integers in the set?
有五个正整数组成的集合，其平均数为 5，中位数为 5，唯一的众数为 8。该集合中最大整数与最小整数之差是多少？

正确答案：D · 分值：1

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1997 AMC8 #15 · Geometry · ★★★
Each side of the large square in the figure is trisected (divided into three equal parts). The corners of an inscribed square are at these trisection points, as shown. The ratio of the area of the inscribed square to the area of the large square is
图中大正方形的每条边被三等分。在等分点处作内接正方形，如图所示。内接正方形的面积与大正方形的面积之比是

正确答案：B · 分值：1

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1997 AMC8 #16 · Algebra · ★★★
Penni Precisely buys $100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower. After one year, AA was up 20%, BB was down 25%, and CC was unchanged. For the second year, AA was down 20% from the previous year, BB was up 25% from the previous year, and CC was unchanged. If A, B, and C are the final values of the stock, then
Penni Precisely 购买三家公司各 $100 的股票：Alabama Almonds、Boston Beans 和 California Cauliflower。一年后，AA 上涨 20%，BB 下跌 25%，CC 不变。第二年，AA 在前一年的基础上下跌 20%，BB 在前一年的基础上上涨 25%，CC 不变。若 A、B、C 分别是这些股票的最终价值，则

正确答案：E · 分值：1

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1997 AMC8 #17 · Geometry · ★★★
A cube has eight vertices (corners) and twelve edges. A segment, such as xx , which joins two vertices not joined by an edge is called a diagonal. Segment yy is also a diagonal. How many diagonals does a cube have?
一个正方体有八个顶点和十二条棱。像 xx 这样连接两个不被棱相连的顶点的线段称为对角线。线段 yy 也是一条对角线。一个正方体有多少条对角线？

正确答案：E · 分值：1

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1997 AMC8 #18 · Algebra · ★★★
At the grocery store last week, small boxes of facial tissue were priced at 4 boxes for $5 . This week they are on sale at 5 boxes for $4 . The percent decrease in the price per box during the sale was closest to
上周在杂货店，小盒面巾纸的售价为 4 盒 $5。本周它们打折出售，5 盒 $4。打折期间每盒价格下降的百分比最接近

正确答案：B · 分值：1

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1997 AMC8 #19 · Algebra · ★★★
If the product 32⋅43⋅54⋅65⋅…⋅ab=9\dfrac{3}{2}\cdot \dfrac{4}{3}\cdot \dfrac{5}{4}\cdot \dfrac{6}{5}\cdot \ldots\cdot \dfrac{a}{b} = 9 , what is the sum of aa and bb ?
若乘积 32⋅43⋅54⋅65⋅…⋅ab=9\dfrac{3}{2}\cdot \dfrac{4}{3}\cdot \dfrac{5}{4}\cdot \dfrac{6}{5}\cdot \ldots\cdot \dfrac{a}{b} = 9，求 aa 与 bb 之和。

正确答案：D · 分值：1

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1997 AMC8 #20 · Counting, Probability & Statistics · ★★★
A pair of 8-sided dice have sides numbered 1 through 8. Each side has the same probability (chance) of landing face up. The probability that the product of the two numbers that land face-up exceeds 36 is
一对 8 面骰子，各面分别标有 1 到 8。每个面朝上的概率相同。两数乘积超过 36 的概率是

正确答案：A · 分值：1

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1997 AMC8 #21 · Geometry · ★★★★
Each corner cube is removed from this 3 cm×3 cm×3 cm3\text{ cm}\times 3\text{ cm}\times 3\text{ cm} cube. The surface area of the remaining figure is
从一个 3 cm×3 cm×3 cm3\text{ cm}\times 3\text{ cm}\times 3\text{ cm} 的正方体上移除每个角上的小正方体。剩余图形的表面积是

正确答案：D · 分值：1

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1997 AMC8 #22 · Algebra · ★★★
A two-inch cube (2×2×2)(2\times 2\times 2) of silver weighs 3 pounds and is worth 200 dollars. How much is a three-inch cube of silver worth?
一个 2 英寸的正方体 (2×2×2)(2\times 2\times 2) 银块重 3 磅，价值 200 美元。一个三英寸的正方体银块价值多少？

正确答案：E · 分值：1

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1997 AMC8 #23 · Number Theory · ★★★★
There are positive integers that have these properties: The sum of the squares of their digits is equal to 50 Each digit is larger than the one on it's left The product of the digits of the largest integer with both properties is
存在满足以下性质的正整数：各位数字的平方和等于 50，且每位数字都比它左边的数字大。同时满足这两个性质的最大整数，其各位数字之积是多少？

正确答案：C · 分值：1

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1997 AMC8 #24 · Geometry · ★★★★
Diameter ACEACE is divided at CC in the ratio 2:32:3 . The two semicircles, ABCABC and CDECDE , divide the circular region into an upper (shaded) region and a lower region. The ratio of the area of the upper region to that of the lower region is
直径 ACEACE 被点 CC 分成 2:32:3 的比例。两个半圆 ABCABC 和 CDECDE 将圆形区域分成上部（着色）区域和下部区域。上部区域与下部区域的面积之比是

正确答案：C · 分值：1

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1997 AMC8 #25 · Number Theory · ★★★★
All of the even numbers from 2 to 98 inclusive, excluding those ending in 0, are multiplied together. What is the rightmost digit (the units digit) of the product?
将 2 到 98（含）之间所有不以 0 结尾的偶数相乘。乘积的最右边数字（个位数字）是多少？

正确答案：D · 分值：1

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1996 AMC8 #1 · Number Theory · ★
How many positive factors of 36 are also multiples of 4?
36 的正因数中有多少个也是 4 的倍数？

正确答案：B · 分值：1

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1996 AMC8 #2 · Algebra · ★
Jose, Thuy, and Kareem each start with the number 10 . Jose subtracts 1 from the number 10 , doubles his answer, and then adds 2 . Thuy doubles the number 10 , subtracts 1 from her answer, and then adds 2 . Kareem subtracts 1 from the number 10 , adds 2 to his number, and then doubles the result. Who gets the largest final answer?
Jose、Thuy 和 Kareem 各从数字 10 开始。Jose 从 10 中减去 1，将结果加倍，然后加上 2。Thuy 将 10 加倍，从中减去 1，然后加上 2。Kareem 从 10 中减去 1，加上 2，然后将结果加倍。谁得到最大的最终答案？

正确答案：C · 分值：1

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1996 AMC8 #3 · Algebra · ★
The 64 whole numbers from 1 through 64 are written, one per square, on a checkerboard (an 8 by 8 array of 64 squares). The first 8 numbers are written in order across the first row, the next 8 across the second row, and so on. After all 64 numbers are written, the sum of the numbers in the four corners will be
1 到 64 的 64 个正整数被写在一个棋盘（8行8列共 64 格）上，每格一个数。前 8 个数按顺序写在第一行，接下来 8 个写在第二行，以此类推。所有 64 个数写完后，四个角落方格中的数之和是

正确答案：A · 分值：1

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1996 AMC8 #5 · Algebra · ★★
The letters PP , QQ , RR , SS , and TT represent numbers located on the number line as shown.
Which of the following expressions represents a negative number?
字母 PP、QQ、RR、SS 和 TT 表示数轴上的数，如图所示。
以下哪个表达式表示一个负数？

正确答案：A · 分值：1

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1996 AMC8 #6 · Algebra · ★★
What is the smallest result that can be obtained from the following process? Choose three different numbers from the set {3,5,7,11,13,17}\{3,5,7,11,13,17\} . Add two of these numbers. Multiply their sum by the third number.
以下过程可以得到的最小结果是多少？
从集合 {3,5,7,11,13,17}\{3,5,7,11,13,17\} 中选择三个不同的数。 将其中两个数相加。 将它们的和乘以第三个数。

正确答案：C · 分值：1

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1996 AMC8 #7 · Algebra · ★★
Brent has goldfish that quadruple (become four times as many) every month, and Gretel has goldfish that double every month. If Brent has 4 goldfish at the same time that Gretel has 128 goldfish, then in how many months from that time will they have the same number of goldfish?
Brent 的金鱼数量每个月翻四倍，Gretel 的金鱼数量每个月翻一倍。如果在 Brent 有 4 条金鱼的同时 Gretel 有 128 条金鱼，那么从那时起多少个月后他们的金鱼数量将相等？

正确答案：B · 分值：1

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1996 AMC8 #8 · Geometry · ★★
Points AA and BB are 10 units apart. Points BB and CC are 4 units apart. Points CC and DD are 3 units apart. If AA and DD are as close as possible, then the number of units between them is
点 AA 和 BB 相距 10 个单位。点 BB 和 CC 相距 4 个单位。点 CC 和 DD 相距 3 个单位。如果 AA 和 DD 尽可能接近，则它们之间的距离是多少个单位？

正确答案：B · 分值：1

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1996 AMC8 #9 · Algebra · ★★
If 5 times a number is 2, then 100 times the reciprocal of the number is
如果 5 乘某个数等于 2，则 100 乘该数的倒数等于

正确答案：D · 分值：1

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1996 AMC8 #10 · Algebra · ★★
When Walter drove up to the gasoline pump, he noticed that his gasoline tank was 1/8 full. He purchased 7.5 gallons of gasoline for 10 dollars. With this additional gasoline, his gasoline tank was then 5/8 full. The number of gallons of gasoline his tank holds when it is full is
当 Walter 开车到加油站时，他注意到他的油箱只有 1/8 满。他以 10 美元的价格买了 7.5 加仑汽油。加了这些额外的汽油后，他的油箱变为 5/8 满。油箱装满时的容量是多少加仑？

正确答案：D · 分值：1

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1996 AMC8 #11 · Algebra · ★★★
Let xx be the number
0.0000...0000⏟1996 zeros1,0.\underbrace{0000...0000}_{1996\text{ zeros}}1,
where there are 1996 zeros after the decimal point. Which of the following expressions represents the largest number?
设 xx 为上面所示的数（小数点后有 1996 个零）。以下哪个表达式表示最大的数？

正确答案：D · 分值：1

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1996 AMC8 #12 · Counting, Probability & Statistics · ★★★
What number should be removed from the list
1,2,3,4,5,6,7,8,9,10,111,2,3,4,5,6,7,8,9,10,11
so that the average of the remaining numbers is 6.1 ?
应该从列表 1,2,3,4,5,6,7,8,9,10,11 中移除哪个数，使剩余数的平均数为 6.1？

正确答案：B · 分值：1

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1996 AMC8 #13 · Algebra · ★★★
In the fall of 1996, a total of 800 students participated in an annual school clean-up day. The organizers of the event expect that in each of the years 1997, 1998, and 1999, participation will increase by 50% over the previous year. The number of participants the organizers will expect in the fall of 1999 is
1996 年秋季，共有 800 名学生参加了一年一度的学校清洁日。活动组织者预计在 1997、1998 和 1999 年每年，参与人数将在前一年的基础上增加 50%。组织者预计 1999 年秋季的参与人数是

正确答案：E · 分值：1

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1996 AMC8 #14 · Number Theory · ★★★
Six different digits from the set
{1,2,3,4,5,6,7,8,9}\{ 1,2,3,4,5,6,7,8,9\}
are placed in the squares in the figure shown so that the sum of the entries in the vertical column is 23 and the sum of the entries in the horizontal row is 12. The sum of the six digits used is
从集合 {1,2,3,4,5,6,7,8,9}\{1,2,3,4,5,6,7,8,9\} 中选取六个不同的数字填入图中所示的方格，使得竖列各项之和为 23，横行各项之和为 12。所用六个数字之和为

正确答案：B · 分值：1

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1996 AMC8 #15 · Number Theory · ★★★
The remainder when the product 1492⋅1776⋅1812⋅19961492\cdot 1776\cdot 1812\cdot 1996 is divided by 5 is
乘积 1492⋅1776⋅1812⋅19961492\cdot 1776\cdot 1812\cdot 1996 除以 5 的余数是

正确答案：E · 分值：1

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1996 AMC8 #16 · Algebra · ★★★
1−2−3+4+5−6−7+8+9−10−11+⋯+1992+1993−1994−1995+1996=1-2-3+4+5-6-7+8+9-10-11+\cdots + 1992+1993-1994-1995+1996=

正确答案：C · 分值：1

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1996 AMC8 #17 · Geometry · ★★★
Figure OPQROPQR is a square. Point OO is the origin, and point QQ has coordinates (2,2). What are the coordinates for TT so that the area of triangle PQTPQT equals the area of square OPQROPQR ?
NOT TO SCALE
图形 OPQROPQR 是一个正方形。点 OO 是原点，点 QQ 的坐标为 (2,2)。点 TT 的坐标应为何值，才能使三角形 PQTPQT 的面积等于正方形 OPQROPQR 的面积？
（图形未按比例绘制）

正确答案：C · 分值：1

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1996 AMC8 #18 · Algebra · ★★★
Ana's monthly salary was $2000 in May. In June she received a 20% raise. In July she received a 20% pay cut. After the two changes in June and July, Ana's monthly salary was
Ana 五月份的月薪是 $2000。六月份她获得了 20% 的加薪。七月份她的薪水被削减了 20%。经过六月和七月的两次变动后，Ana 的月薪是

正确答案：A · 分值：1

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1996 AMC8 #19 · Counting, Probability & Statistics · ★★★
The pie charts below indicate the percent of students who prefer golf, bowling, or tennis at East Junior High School and West Middle School. The total number of students at East is 2000 and at West, 2500. In the two schools combined, the percent of students who prefer tennis is
以下饼图显示了 East 初中和 West 中学喜欢高尔夫、保龄球或网球的学生百分比。East 共有 2000 名学生，West 共有 2500 名。两所学校合计，喜欢网球的学生的百分比是

正确答案：C · 分值：1

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1996 AMC8 #20 · Algebra · ★★★
Suppose there is a special key on a calculator that replaces the number xx currently displayed with the number given by the formula 1/(1-x) . For example, if the calculator is displaying 2 and the special key is pressed, then the calculator will display -1 since 1/(1-2)=-1 . Now suppose that the calculator is displaying 5. After the special key is pressed 100 times in a row, the calculator will display
假设计算器上有一个特殊键，将当前显示的数 xx 替换为公式 1/(1-x) 给出的数。例如，如果计算器显示 2 并按下特殊键，计算器将显示 -1，因为 1/(1-2)=-1。现在假设计算器显示 5。连续按下特殊键 100 次后，计算器将显示

正确答案：A · 分值：1

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1996 AMC8 #21 · Counting, Probability & Statistics · ★★★★
How many subsets containing three different numbers can be selected from the set {89,95,99,132,166,173}\{ 89,95,99,132,166,173 \} so that the sum of the three numbers is even?
从集合 {89,95,99,132,166,173}\{ 89,95,99,132,166,173 \} 中选取包含三个不同数的子集，使得三数之和为偶数，共有多少种选法？

正确答案：D · 分值：1

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1996 AMC8 #22 · Geometry · ★★★
The horizontal and vertical distances between adjacent points equal 1 unit. What is the area of triangle ABCABC ?
相邻点之间的水平和垂直距离均为 1 个单位。三角形 ABCABC 的面积是多少？

正确答案：B · 分值：1

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1996 AMC8 #23 · Algebra · ★★★★
The manager of a company planned to distribute a $50 bonus to each employee from the company fund, but the fund contained $5 less than what was needed. Instead the manager gave each employee a $45 bonus and kept the remaining $95 in the company fund. The amount of money in the company fund before any bonuses were paid was
某公司经理计划从公司基金中给每位员工发放 $50 的奖金，但基金比所需金额少 $5。于是经理改为给每位员工发放 $45 的奖金，并将剩余的 $95 保留在公司基金中。在发放任何奖金之前，公司基金中的金额是

正确答案：E · 分值：1

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1996 AMC8 #24 · Geometry · ★★★★
The measure of angle ABCABC is 50∘50^\circ , AD‾\overline{AD} bisects angle BACBAC , and DC‾\overline{DC} bisects angle BCABCA . The measure of angle ADCADC is
∠ABC\angle ABC 的度数为 50∘50^\circ，AD‾\overline{AD} 平分 ∠BAC\angle BAC，DC‾\overline{DC} 平分 ∠BCA\angle BCA。∠ADC\angle ADC 的度数是

正确答案：C · 分值：1

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1996 AMC8 #25 · Counting, Probability & Statistics · ★★★★
A point is chosen at random from within a circular region. What is the probability that the point is closer to the center of the region than it is to the boundary of the region?
在一个圆形区域内随机选取一个点。该点离圆心比离边界更近的概率是多少？

正确答案：A · 分值：1

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1995 AMC8 #1 · Algebra · ★
Walter has exactly one penny, one nickel, one dime and one quarter in his pocket. What percent of one dollar is in his pocket?
Walter 口袋里恰好有 1 枚 1 美分硬币、1 枚 5 美分硬币、1 枚 10 美分硬币和 1 枚 25 美分硬币。他口袋里的钱是 1 美元的百分之几？

正确答案：D · 分值：1

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1995 AMC8 #2 · Algebra · ★
Jose is 4 years younger than Zack. Zack is 3 years older than Inez. Inez is 15 years old. How old is Jose?
Jose 比 Zack 小 4 岁。Zack 比 Inez 大 3 岁。Inez 15 岁。Jose 多少岁？

正确答案：C · 分值：1

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1995 AMC8 #3 · Algebra · ★★
Which of the following operations has the same effect on a number as multiplying by 34\dfrac{3}{4} and then dividing by 35\dfrac{3}{5} ?
以下哪种运算对一个数的效果与先乘以 34\dfrac{3}{4} 再除以 35\dfrac{3}{5} 相同？

正确答案：E · 分值：1

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1995 AMC8 #4 · Algebra · ★
A teacher tells the class, "Think of a number, add 1 to it, and double the result. Give the answer to your partner. Partner, subtract 1 from the number you are given and double the result to get your answer." Ben thinks of 6 , and gives his answer to Sue. What should Sue's answer be?
老师对全班说：
"想一个数，加 1，然后将结果加倍。把答案告诉你的搭档。搭档，将你得到的数减 1，然后将结果加倍得出你的答案。"
Ben 想了 6，并将他的答案告诉了 Sue。Sue 的答案应是多少？

正确答案：C · 分值：1

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1995 AMC8 #5 · Algebra · ★
Find the smallest whole number that is larger than the sum
212+313+414+515.2\dfrac{1}{2}+3\dfrac{1}{3}+4\dfrac{1}{4}+5\dfrac{1}{5}.
求比上面各数之和大的最小整数。

正确答案：C · 分值：1

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1995 AMC8 #6 · Geometry · ★★
Figures II , IIII , and IIIIII are squares. The perimeter of II is 12 and the perimeter of IIII is 24 . The perimeter of IIIIII is
图形 II、IIII 和 IIIIII 是正方形。II 的周长是 12，IIII 的周长是 24。IIIIII 的周长是

正确答案：C · 分值：1

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1995 AMC8 #7 · Algebra · ★★
At Clover View Junior High, one half of the students go home on the school bus. One fourth go home by automobile. One tenth go home on their bicycles. The rest walk home. What fractional part of the students walk home?
在 Clover View 初中，二分之一的学生乘校车回家，四分之一乘汽车回家，十分之一骑自行车回家，其余步行回家。步行的学生占几分之几？

正确答案：B · 分值：1

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1995 AMC8 #8 · Algebra · ★★
An American traveling in Italy wishes to exchange American money (dollars) for Italian money (lire). If 3000 lire = 1.60, how much lire will the traveler receive in exchange for 1.00?
一位在意大利旅行的美国人想将美元兑换为意大利里拉。如果 3000 里拉 = 1.60 美元，旅行者用 1.00 美元能换多少里拉？

正确答案：D · 分值：1

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1995 AMC8 #9 · Geometry · ★★
Three congruent circles with centers PP , QQ , and RR are tangent to the sides of rectangle ABCDABCD as shown. The circle centered at QQ has diameter 4 and passes through points PP and RR . The area of the rectangle is
三个全等的圆，圆心分别为 PP、QQ 和 RR，如图所示与矩形 ABCDABCD 的边相切。以 QQ 为圆心的圆直径为 4 且经过点 PP 和 RR。矩形的面积是

正确答案：C · 分值：1

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1995 AMC8 #10 · Algebra · ★★
A jacket and a shirt originally sold for 80 dollars and 40 dollars, respectively. During a sale Chris bought the 80 dollar jacket at a 40% discount and the 40 dollar shirt at a 55% discount. The total amount saved was what percent of the total of the original prices?
一件夹克和一件衬衫原价分别为 80 美元和 40 美元。促销期间 Chris 以 40% 折扣买了 80 美元的夹克，以 55% 折扣买了 40 美元的衬衫。节省的总金额是原价总和的百分之多少？

正确答案：A · 分值：1

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1995 AMC8 #11 · Algebra · ★★★
Jane can walk any distance in half the time it takes Hector to walk the same distance. They set off in opposite directions around the outside of the 18-block area as shown. When they meet for the first time, they will be closest to
Jane 走任何距离所花的时间是 Hector 走同样距离所花时间的一半。他们从如图所示的 18 个街区区域的外围向相反方向出发。当他们第一次相遇时，他们最接近哪里？

正确答案：D · 分值：1

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1995 AMC8 #12 · Number Theory · ★★★
A lucky year is one in which at least one date, when written in the form month/day/year, has the following property: The product of the month times the day equals the last two digits of the year. For example, 1956 is a lucky year because it has the date and 7×8=567\times 8 = 56 . Which of the following is NOT a lucky year?
幸运年是指至少有一个日期，当写成月/日/年的格式时，满足：月份乘以日期等于年份的后两位数字。例如，1956 是一个幸运年，因为有日期 7/8/56 且 7×8=567\times 8 = 56。以下哪年不是幸运年？
7/8/567/8/56

正确答案：E · 分值：1

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1995 AMC8 #13 · Geometry · ★★★
In the figure, ∠A\angle A , ∠B\angle B , and ∠C\angle C are right angles. If ∠AEB=40∘\angle AEB = 40^\circ and ∠BED=∠BDE\angle BED = \angle BDE , then ∠CDE=\angle CDE =
在图中，∠A\angle A、∠B\angle B 和 ∠C\angle C 是直角。如果 ∠AEB=40∘\angle AEB = 40^\circ 且 ∠BED=∠BDE\angle BED = \angle BDE，则 ∠CDE=\angle CDE =

正确答案：E · 分值：1

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1995 AMC8 #14 · Algebra · ★★★
A team won 40 of its first 50 games. How many of the remaining 40 games must this team win so it will have won exactly 70 % of its games for the season?
一支队伍在前 50 场比赛中赢了 40 场。在剩下的 40 场比赛中他们必须赢多少场，才能使整个赛季的胜率恰好为 70%？

正确答案：B · 分值：1

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1995 AMC8 #15 · Number Theory · ★★★
What is the 100th100^\text{th} digit to the right of the decimal point in the decimal form of
4/37 的小数形式中，小数点右边第 100 位数字是多少？
4/37?4/37 ?

正确答案：B · 分值：1

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1995 AMC8 #16 · Algebra · ★★★
Students from three middle schools worked on a summer project. Seven students from Allen school worked for 3 days. Four students from Balboa school worked for 5 days. Five students from Carver school worked for 9 days. The total amount paid for the students' work was 774. Assuming each student received the same amount for a day's work, how much did the students from Balboa school earn altogether?
三所中学的学生参与了一个暑期项目。
Allen 学校的 7 名学生工作了 3 天。 Balboa 学校的 4 名学生工作了 5 天。 Carver 学校的 5 名学生工作了 9 天。
学生工作的总报酬为 774 美元。假设每个学生每天的工作报酬相同，Balboa 学校的学生总共挣了多少钱？

正确答案：C · 分值：1

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1995 AMC8 #17 · Counting, Probability & Statistics · ★★★
The table below gives the percent of students in each grade at Annville and Cleona elementary schools. Annville has 100 students and Cleona has 200 students. In the third grade, the number of students in Annville is what percent of the number of students in Cleona?
下表给出了 Annville 和 Cleona 两所小学各年级学生的百分比。Annville 有 100 名学生，Cleona 有 200 名学生。在三年级，Annville 的学生数是 Cleona 学生数的百分之几？

正确答案：D · 分值：1

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1995 AMC8 #18 · Geometry · ★★★
The area of each of the four congruent L-shaped regions of this 100-inch by 100-inch square is 3/16 of the total area. How many inches long is the side of the center square?
在这个 100 英寸 × 100 英寸的正方形中，四个全等 L 形区域各占总面积的 3/16。中心正方形的边长是多少英寸？

正确答案：C · 分值：1

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1995 AMC8 #19 · Counting, Probability & Statistics · ★★★
The graph shows the distribution of the number of children in the families of the students in Ms. Jordan's English class. The median number of children in the family for this distribution is
图表显示了 Ms. Jordan 英语班学生家庭中子女数量的分布。该分布中家庭子女数量的中位数是

正确答案：D · 分值：1

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1995 AMC8 #20 · Counting, Probability & Statistics · ★★★
Diana and Apollo each roll a standard die obtaining a number at random from 1 to 6 . What is the probability that Diana's number is larger than Apollo's number?
Diana 和 Apollo 各自掷一个标准骰子，随机得到 1 到 6 中的一个数。Diana 的数大于 Apollo 的数的概率是多少？

正确答案：B · 分值：1

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1995 AMC8 #21 · Geometry · ★★★★
A plastic snap-together cube has a protruding snap on one side and receptacle holes on the other five sides as shown. What is the smallest number of these cubes that can be snapped together so that only receptacle holes are showing?
一种塑料拼插正方体，一面有凸出的插头，其余五面有凹孔，如图所示。要使拼插后只露出凹孔，最少需要多少个这样的正方体？

正确答案：B · 分值：1

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1995 AMC8 #22 · Number Theory · ★★★★
The number 6545 can be written as a product of a pair of positive two-digit numbers. What is the sum of this pair of numbers?
6545 可以写成一对正两位数的乘积。这对数之和是多少？

正确答案：A · 分值：1

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1995 AMC8 #23 · Counting, Probability & Statistics · ★★★★
How many four-digit whole numbers are there such that the leftmost digit is odd, the second digit is even, and all four digits are different?
有多少个四位数满足：最左边一位是奇数，第二位是偶数，且四位数字各不相同？

正确答案：B · 分值：1

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1995 AMC8 #24 · Geometry · ★★★★
In parallelogram ABCDABCD , DE‾\overline{DE} is the altitude to the base AB‾\overline{AB} and DF‾\overline{DF} is the altitude to the base BC‾\overline{BC} . [Note: Both pictures represent the same parallelogram.] If DC=12 , EB=4 , and DE=6 , then DF=
在平行四边形 ABCDABCD 中，DE‾\overline{DE} 是底边 AB‾\overline{AB} 上的高，DF‾\overline{DF} 是底边 BC‾\overline{BC} 上的高。[注：两幅图表示同一平行四边形。] 若 DC=12，EB=4，DE=6，则 DF=

正确答案：C · 分值：1

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1995 AMC8 #25 · Algebra · ★★★★
Buses from Dallas to Houston leave every hour on the hour. Buses from Houston to Dallas leave every hour on the half hour. The trip from one city to the other takes 5 hours. Assuming the buses travel on the same highway, how many Dallas-bound buses does a Houston-bound bus pass in the highway (not in the station)?
从 Dallas 到 Houston 的巴士每小时正点发车。从 Houston 到 Dallas 的巴士每小时半点发车。从一城到另一城的行程需 5 小时。假设巴士在同一条高速公路上行驶，一辆从 Houston 出发的巴士在途中（不在车站）会与多少辆 Dallas 方向的巴士相遇？

正确答案：D · 分值：1

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1994 AMC8 #3 · Algebra · ★★
Each day Maria must work 8 hours. This does not include the 45 minutes she takes for lunch. If she begins working at 7:25 A.M.\text{7:25 A.M.} and takes her lunch break at noon, then her working day will end at
Maria 每天需要工作 8 小时，不包括 45 分钟的午休时间。如果她于上午 7:25\text{7:25} 开始工作，并在中午开始午休，那么她的工作日将结束于

正确答案：C · 分值：1

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1994 AMC8 #4 · Geometry · ★★
Which of the following represents the result when the figure shown below is rotated clockwise 120∘120^\circ about its center?
以下哪个表示将下图绕其中心顺时针旋转 120∘120^\circ 后的结果？

正确答案：B · 分值：1

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1994 AMC8 #5 · Algebra · ★
Given that 1 mile=8 furlongs\text{1 mile} = \text{8 furlongs} and 1 furlong=40 rods\text{1 furlong} = \text{40 rods}, the number of rods in one mile is
已知 \text{1 英里} = \text{8 弗隆}，\text{1 弗隆} = \text{40 杆}，则 1 英里等于多少杆？

正确答案：B · 分值：1

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1994 AMC8 #6 · Number Theory · ★★
The unit's digit (one's digit) of the product of any six consecutive positive whole numbers is
任意六个连续正整数的乘积的个位数字是

正确答案：A · 分值：1

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1994 AMC8 #7 · Geometry · ★★
If ∠A=60∘\angle A = 60^\circ , ∠E=40∘\angle E = 40^\circ and ∠C=30∘\angle C = 30^\circ , then ∠BDC=\angle BDC =
如果 ∠A=60∘\angle A = 60^\circ，∠E=40∘\angle E = 40^\circ，∠C=30∘\angle C = 30^\circ，则 ∠BDC=\angle BDC =

正确答案：B · 分值：1

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1994 AMC8 #8 · Number Theory · ★★
For how many three-digit whole numbers does the sum of the digits equal 25 ?
有多少个三位正整数，其各位数字之和等于 25？

正确答案：C · 分值：1

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1994 AMC8 #9 · Algebra · ★★
A shopper buys a 100 dollar coat on sale for 20% off. An additional 5 dollars are taken off the sale price by using a discount coupon. A sales tax of 8% is paid on the final selling price. The total amount the shopper pays for the coat is
一位顾客以 20% 折扣买了一件 100 美元的外套。使用折扣券再减 5 美元。最终售价需缴纳 8% 的销售税。顾客买这件外套总共支付多少钱？

正确答案：A · 分值：1

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1994 AMC8 #10 · Number Theory · ★★
For how many positive integer values of NN is the expression 36/N+2 an integer?
有多少个正整数值的 NN 能使表达式 36N+2\dfrac{36}{N+2} 为整数？

正确答案：A · 分值：1

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1994 AMC8 #11 · Counting, Probability & Statistics · ★★★
Last summer 100 students attended basketball camp. Of those attending, 52 were boys and 48 were girls. Also, 40 students were from Jonas Middle School and 60 were from Clay Middle School. Twenty of the girls were from Jonas Middle School. How many of the boys were from Clay Middle School?
去年夏天 100 名学生参加了篮球夏令营。参加者中 52 名男生，48 名女生。另有 40 名来自 Jonas 中学，60 名来自 Clay 中学。女生中有 20 名来自 Jonas 中学。男生中有多少名来自 Clay 中学？

正确答案：B · 分值：1

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1994 AMC8 #12 · Geometry · ★★★
Each of the three large squares shown below is the same size. Segments that intersect the sides of the squares intersect at the midpoints of the sides. How do the shaded areas of these squares compare?
下面所示的三个大正方形大小相同。与正方形边相交的线段在边的中点处相交。这些正方形的着色面积相比如何？

正确答案：A · 分值：1

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1994 AMC8 #13 · Algebra · ★★★
The number halfway between 16\dfrac{1}{6} and 14\dfrac{1}{4} is
16\dfrac{1}{6} 和 14\dfrac{1}{4} 正中间的数是多少？

正确答案：C · 分值：1

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1994 AMC8 #14 · Algebra · ★★★
Two children at a time can play pairball. For 90 minutes, with only two children playing at time, five children take turns so that each one plays the same amount of time. The number of minutes each child plays is
双人壁球每次只能两名儿童同时玩。在 90 分钟内，只有两名儿童同时在玩，五名儿童轮流上场，使得每人玩的时间相同。每名儿童玩多少分钟？

正确答案：E · 分值：1

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1994 AMC8 #15 · Number Theory · ★★★
If this path is to continue in the same pattern:
then which sequence of arrows goes from point 425 to point 427 ?
如果该路径按同样的模式继续：
那么从点 425 到点 427 应该是哪个箭头序列？

正确答案：A · 分值：1

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1994 AMC8 #16 · Geometry · ★★★
The perimeter of one square is 3 times the perimeter of another square. The area of the larger square is how many times the area of the smaller square?
一个正方形的周长是另一个正方形周长的 3 倍。大正方形的面积是小正方形面积的多少倍？

正确答案：E · 分值：1

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1994 AMC8 #17 · Algebra · ★★★
Pauline Bunyan can shovel snow at the rate of 20 cubic yards for the first hour, 19 cubic yards for the second, 18 for the third, etc., always shoveling one cubic yard less per hour than the previous hour. If her driveway is 4 yards wide, 10 yards long, and covered with snow 3 yards deep, then the number of hours it will take her to shovel it clean is closest to
Pauline Bunyan 第一小时可以铲 20 立方码的雪，第二小时 19 立方码，第三小时 18 立方码，以此类推，每小时比前一小时少铲一立方码。如果她的车道宽 4 码、长 10 码，覆盖着 3 码深的雪，那么她铲完雪所需的小时数最接近

正确答案：D · 分值：1

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1994 AMC8 #18 · Algebra · ★★★
Mike leaves home and drives slowly east through city traffic. When he reaches the highway he drives east more rapidly until he reaches the shopping mall where he stops. He shops at the mall for an hour. Mike returns home by the same route as he came, driving west rapidly along the highway and then slowly through city traffic. Each graph shows the distance from home on the vertical axis versus the time elapsed since leaving home on the horizontal axis. Which graph is the best representation of Mike's trip?
Mike 离开家，在城市交通中向东缓慢行驶。当他到达高速公路上时，他更快速地向东行驶，直到到达购物中心并停下来。他在购物中心购物一小时。Mike 按原路返回，沿高速公路快速向西行驶，然后缓慢通过城市交通到达家。每个图表的纵轴表示离家距离，横轴表示离家后经过的时间。哪张图能最好地表示 Mike 的行程？

正确答案：B · 分值：1

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1994 AMC8 #19 · Geometry · ★★★
Around the outside of a 4 by 4 square, construct four semicircles (as shown in the figure) with the four sides of the square as their diameters. Another square, ABCDABCD , has its sides parallel to the corresponding sides of the original square, and each side of ABCDABCD is tangent to one of the semicircles. The area of the square ABCDABCD is
在一个 4 × 4 正方形的四边外侧，以正方形的四条边为直径作四个半圆（如图所示）。另一个正方形 ABCDABCD 的各边与原正方形的对应边平行，且 ABCDABCD 的每条边都与一个半圆相切。正方形 ABCDABCD 的面积是

正确答案：E · 分值：1

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1994 AMC8 #20 · Algebra · ★★★
Let W,X,Y and ZZ be four different digits selected from the set {1,2,3,4,5,6,7,8,9}.\{ 1,2,3,4,5,6,7,8,9\}. If the sum WX+YZ\dfrac{W}{X} + \dfrac{Y}{Z} is to be as small as possible, then WX+YZ\dfrac{W}{X} + \dfrac{Y}{Z} must equal
设 W,X,Y 和 ZZ 是从集合 {1,2,3,4,5,6,7,8,9}\{1,2,3,4,5,6,7,8,9\} 中选出的四个不同数字。
若要和 WX+YZ\dfrac{W}{X} + \dfrac{Y}{Z} 尽可能小，则 WX+YZ\dfrac{W}{X} + \dfrac{Y}{Z} 必须等于

正确答案：D · 分值：1

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1994 AMC8 #21 · Counting, Probability & Statistics · ★★★
A gumball machine contains 9 red, 7 white, and 8 blue gumballs. The least number of gumballs a person must buy to be sure of getting four gumballs of the same color is
一台口香糖机装有 9 颗红色、7 颗白色和 8 颗蓝色口香糖。要确保得到四颗同色的口香糖，最少需要买多少颗？

正确答案：C · 分值：1

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1994 AMC8 #22 · Counting, Probability & Statistics · ★★★
The two wheels shown below are spun and the two resulting numbers are added. The probability that the sum is even is
如图所示，两个转盘各自旋转一次，将所得两数相加。和为偶数的概率是

正确答案：D · 分值：1

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1994 AMC8 #23 · Number Theory · ★★★★
If XX, YY and ZZ are different digits, then the largest possible 3-digit sum for the addition problem shown below has the form
若 XX、YY 和 ZZ 是不同的数字，则如下所示加法算式的最大可能三位数和的形式为

正确答案：D · 分值：1

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1994 AMC8 #24 · Counting, Probability & Statistics · ★★★★
A 2 by 2 square is divided into four 1 by 1 squares. Each of the small squares is to be painted either green or red. In how many different ways can the painting be accomplished so that no green square shares its top or right side with any red square? There may be as few as zero or as many as four small green squares.
一个 2 × 2 的正方形被分成四个 1 × 1 的小正方形。每个小正方形要被涂成绿色或红色。共有多少种不同的涂色方式，使得没有绿色正方形与任何红色正方形共享其顶边或右边？小绿色正方形的数量可以从零到四个不等。

正确答案：B · 分值：1

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1994 AMC8 #25 · Number Theory · ★★★★
Find the sum of the digits in the answer to 9999⋯99⏟94 nines×4444⋯44⏟94 fours\underbrace{9999\cdots 99}_{94\text{ nines}} \times \underbrace{4444\cdots 44}_{94\text{ fours}} where a string of 94 nines is multiplied by a string of 94 fours.
求以下乘积的各位数字之和：
\underbrace{9999\cdots 99}_{94\text{ 个 9}} \times \underbrace{4444\cdots 44}_{94\text{ 个 4}}
即 94 个 9 组成的数乘以 94 个 4 组成的数。

正确答案：A · 分值：1

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1993 AMC8 #1 · Algebra · ★
Which pair of numbers does NOT have a product equal to 36 ?
哪对数的乘积不等于 36？

正确答案：C · 分值：1

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1993 AMC8 #2 · Number Theory · ★
When the fraction 4984\dfrac{49}{84} is expressed in simplest form, then the sum of the numerator and the denominator will be
当分数 4984\dfrac{49}{84} 化为最简形式时，分子与分母之和是

正确答案：C · 分值：1

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1993 AMC8 #3 · Number Theory · ★★
Which of the following numbers has the largest prime factor?
以下哪个数有最大的质因数？

正确答案：B · 分值：1

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1993 AMC8 #5 · Counting, Probability & Statistics · ★
Which one of the following bar graphs could represent the data from the circle graph?
以下哪张柱状图可以表示圆形图中的数据？

正确答案：C · 分值：1

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1993 AMC8 #6 · Algebra · ★★
A can of soup can feed 3 adults or 5 children. If there are 5 cans of soup and 15 children are fed, then how many adults would the remaining soup feed?
一罐汤可以喂饱 3 个成人或 5 个儿童。如果有 5 罐汤且已喂饱了 15 个儿童，那么剩下的汤可以喂饱多少个成人？

正确答案：B · 分值：1

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1993 AMC8 #8 · Algebra · ★★
To control her blood pressure, Jill's grandmother takes one half of a pill every other day. If one supply of medicine contains 60 pills, then the supply of medicine would last approximately
为了控制血压，Jill 的祖母每隔一天服用半片药。如果一份药包含 60 片，那么这份药大约能持续多久？

正确答案：D · 分值：1

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1993 AMC8 #9 · Algebra · ★★
Consider the operation ∗\ast defined by the table below. What is (2∗4)∗1(2\ast 4)\ast 1?
考虑由下表定义的运算 ∗\ast。(2∗4)∗1(2\ast 4)\ast 1 等于多少？

正确答案：D · 分值：1

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1993 AMC8 #10 · Counting, Probability & Statistics · ★
This line graph represents the price of a trading card during the first 6 months of 1993 .
The greatest monthly drop in price occurred during
此折线图表示了 1993 年前 6 个月一张交易卡的价格。
价格月跌幅最大的是在

正确答案：B · 分值：1

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1993 AMC8 #11 · Counting, Probability & Statistics · ★★★
Consider this histogram of the scores for 81 students taking a test:
The median is in the interval labeled
考虑 81 名学生考试成绩的直方图：
中位数位于哪个标记的区间内？

正确答案：C · 分值：1

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1993 AMC8 #12 · Algebra · ★★★
If each of the three operation signs, +{+} , –\text{--} , ×\times , is used exactly ONCE in one of the blanks in the expression
5‾4‾6‾35\hspace{1 mm}\underline{\hspace{4 mm}}\hspace{1 mm}4\hspace{1 mm}\underline{\hspace{4 mm}}\hspace{1 mm}6\hspace{1 mm}\underline{\hspace{4 mm}}\hspace{1 mm}3
then the value of the result could equal
如果三个运算符号 +{+}、–\text{--}、×\times 各恰好使用一次，填入表达式
5‾4‾6‾35\hspace{1 mm}\underline{\hspace{4 mm}}\hspace{1 mm}4\hspace{1 mm}\underline{\hspace{4 mm}}\hspace{1 mm}6\hspace{1 mm}\underline{\hspace{4 mm}}\hspace{1 mm}3
的空白中，则结果的值可能等于

正确答案：E · 分值：1

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1993 AMC8 #13 · Counting, Probability & Statistics · ★★★
The word "HELP" in block letters is painted in black with strokes 1 unit wide on a 5 by 15 rectangular white sign with dimensions as shown. The area of the white portion of the sign, in square units, is
在一块 5×155 \times 15 的白色矩形标牌上，用宽度为 1 单位的笔划将单词「HELP」以块状字母涂成黑色，尺寸如图所示。标牌白色部分的面积（以平方单位计）是

正确答案：D · 分值：1

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1993 AMC8 #14 · Counting, Probability & Statistics · ★★★
The 3 by 3 grid below is to be filled so that every row and every column contains each of the numbers 1, 2, 3. Then A+B=
下面的 3 × 3 方格表需要填入数字，使得每行每列都包含 1、2、3 各一次。则 A+B=

正确答案：C · 分值：1

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1993 AMC8 #15 · Counting, Probability & Statistics · ★★★
The arithmetic mean (average) of four numbers is 85. If the largest of these numbers is 97, then the mean of the remaining three numbers is
四个数的算术平均数为 85。如果其中最大的数是 97，那么其余三个数的平均数是

正确答案：A · 分值：1

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1993 AMC8 #17 · Geometry · ★★★
Square corners, 5 units on a side, are removed from a 20 unit by 30 unit rectangular sheet of cardboard. The sides are then folded to form an open box. The surface area, in square units, of the interior of the box is
从一个 20 × 30 单位的矩形纸板上切掉四个边长为 5 单位的正方形角。然后将四边折叠形成一个开口的盒子。盒子内部的表面积是多少平方单位？

正确答案：B · 分值：1

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1993 AMC8 #18 · Geometry · ★★★
The rectangle shown has length AC=32 , width AE=20 , and BB and FF are midpoints of AC‾\overline{AC} and AE‾\overline{AE} , respectively. The area of quadrilateral ABDFABDF is
如图所示，矩形 AC=32，宽 AE=20，点 BB 和 FF 分别是 AC‾\overline{AC} 和 AE‾\overline{AE} 的中点。四边形 ABDFABDF 的面积是

正确答案：A · 分值：1

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1993 AMC8 #20 · Number Theory · ★★★
When 1093−9310^{93}-93 is expressed as a single whole number, the sum of the digits is
当 1093−9310^{93}-93 表示为一个整数时，其各位数字之和是

正确答案：D · 分值：1

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1993 AMC8 #21 · Algebra · ★★★
If the length of a rectangle is increased by 20% and its width is increased by 50% , then the area is increased by
如果矩形的长增加 20%，宽增加 50%，则面积增加了

正确答案：D · 分值：1

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1993 AMC8 #22 · Counting, Probability & Statistics · ★★★★
Pat Peano has a collection of numbers to label the pages of his scrapbook. He has an infinite number of 0's, 1's, 3's, 4's, 5's, 6's, 7's, 8's and 9's, but only twenty-two 2's. How far can he number the pages of his scrapbook with these digits?
Pat Peano 有一批数字用于给他的剪贴簿页码编号。他有无限多个 0、1、3、4、5、6、7、8 和 9，但只有二十二个 2。用这些数字他最多能将剪贴簿页码编到多少？

正确答案：D · 分值：1

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1993 AMC8 #23 · Counting, Probability & Statistics · ★★★★
Five runners, PP , QQ , RR , SS , TT , have a race, and PP beats QQ , PP beats RR , QQ beats SS , and TT finishes after PP and before QQ . Who could NOT have finished third in the race?
五名跑步者 PP、QQ、RR、SS、TT 参加比赛。PP 击败 QQ，PP 击败 RR，QQ 击败 SS，TT 在 PP 之后、QQ 之前完赛。谁不可能获得第三名？

正确答案：C · 分值：1

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1993 AMC8 #24 · Algebra · ★★★★
What number is directly above 142 in this array of numbers?
在此数字阵列中，142 正上方的数是多少？

正确答案：C · 分值：1

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1993 AMC8 #25 · Geometry · ★★★★
A checkerboard consists of one-inch squares. A square card, 1.5 inches on a side, is placed on the board so that it covers part or all of the area of each of nn squares. The maximum possible value of nn is
棋盘由边长为 1 英寸的方格组成。一张边长为 1.5 英寸的正方形卡片放在棋盘上，使其覆盖 nn 个方格的部分或全部面积。nn 的最大可能值是

正确答案：E · 分值：1

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1992 AMC8 #2 · Algebra · ★
Which of the following is not equal to 54\dfrac{5}{4} ?
以下哪个不等于 54\dfrac{5}{4}？

正确答案：D · 分值：1

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1992 AMC8 #3 · Algebra · ★
What is the largest difference that can be formed by subtracting two numbers chosen from the set {−16,−4,0,2,4,12}\{ -16,-4,0,2,4,12 \} ?
从集合 {−16,−4,0,2,4,12}\{-16,-4,0,2,4,12\} 中选两个数相减，能形成的最大差是多少？

正确答案：D · 分值：1

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1992 AMC8 #4 · Algebra · ★★
During the softball season, Judy had 35 hits. Among her hits were 1 home run, 1 triple and 5 doubles. The rest of her hits were single. What percent of her hits were single?
垒球赛季中，Judy 共有 35 次安打。其中包括 1 次本垒打、1 次三垒打和 5 次二垒打，其余均为一垒打。她的安打中有百分之几是一垒打？

正确答案：E · 分值：1

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1992 AMC8 #5 · Geometry · ★★
A circle of diameter 1 is removed from a 2×32\times 3 rectangle, as shown. Which whole number is closest to the area of the shaded region?
如图所示，从一个 2×32\times 3 的矩形中移除一个直径为 1 的圆。以下哪个整数最接近着色区域的面积？

正确答案：E · 分值：1

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1992 AMC8 #6 · Algebra · ★★
Suppose that means a+b-c . For example, is 5+4-6 = 3 . Then the sum is
设 a△b△ca\triangle b\triangle c 表示 a+b-c。例如 5△4△65\triangle 4\triangle 6 是 5+4-6 = 3。则 8△5△68\triangle 5\triangle 6 与 2△7△32\triangle 7\triangle 3 的和是

正确答案：D · 分值：1

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1992 AMC8 #7 · Number Theory · ★★
The digit-sum of 998 is 9+9+8=26 . How many 3-digit whole numbers, whose digit-sum is 26 , are even?
998 的各位数字之和是 9+9+8=26。有多少个三位正整数，其各位数字之和为 26，且为偶数？

正确答案：A · 分值：1

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1992 AMC8 #8 · Algebra · ★★
A store owner bought 1500 pencils at $ 0.10 each. If he sells them for $ 0.25 each, how many of them must he sell to make a profit of exactly $ 100.00 ?
一位店主以每支 $0.10 的价格购入 1500 支铅笔。如果他以每支 $0.25 的价格出售，他必须卖出多少支才能恰好获得 $100.00 的利润？

正确答案：C · 分值：1

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1992 AMC8 #9 · Counting, Probability & Statistics · ★★
The population of a small town is 480 . The graph indicates the number of females and males in the town, but the vertical scale-values are omitted. How many males live in the town?
一个小镇的人口是 480。图表显示了镇中女性和男性的数量，但纵轴刻度值被省略了。镇上有多少男性？

正确答案：B · 分值：1

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1992 AMC8 #10 · Geometry · ★★
An isosceles right triangle with legs of length 8 is partitioned into 16 congruent triangles as shown. The shaded area is
一个直角边长为 8 的等腰直角三角形被分成 16 个全等三角形，如图所示。着色面积是

正确答案：B · 分值：1

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1992 AMC8 #11 · Counting, Probability & Statistics · ★★★
The bar graph shows the results of a survey on color preferences. What percent preferred blue?
柱状图显示了一项颜色偏好调查的结果。偏好蓝色的百分比是多少？

正确答案：B · 分值：1

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1992 AMC8 #12 · Algebra · ★★★
The five tires of a car (four road tires and a full-sized spare) were rotated so that each tire was used the same number of miles during the first 30,000 miles the car traveled. For how many miles was each tire used?
一辆汽车的五只轮胎（四只行驶轮胎和一只全尺寸备胎）被轮换使用，使得在汽车行驶的前 30,000 英里中每只轮胎使用相同的里程。每只轮胎被使用了多少英里？

正确答案：C · 分值：1

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1992 AMC8 #13 · Counting, Probability & Statistics · ★★★
Five test scores have a mean (average score) of 90 , a median (middle score) of 91 and a mode (most frequent score) of 94 . The sum of the two lowest test scores is
五次考试成绩的平均数为 90，中位数为 91，众数为 94。两个最低成绩之和是

正确答案：B · 分值：1

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1992 AMC8 #14 · Algebra · ★★★
When four gallons are added to a tank that is one-third full, the tank is then one-half full. The capacity of the tank in gallons is
向一个三分之一满的油箱加入四加仑油后，油箱变为半满。油箱的容量是多少加仑？

正确答案：D · 分值：1

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1992 AMC8 #15 · Number Theory · ★★★
What is the 1992nd1992^\text{nd} letter in this sequence?
ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC⋯\text{ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC}\cdots
此序列中的第 1992 个字母是什么？

正确答案：C · 分值：1

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1992 AMC8 #16 · Geometry · ★★★
Which cylinder has twice the volume of the cylinder shown above?
哪个圆柱的体积是上图所示圆柱体积的两倍？

正确答案：B · 分值：1

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1992 AMC8 #17 · Geometry · ★★★
The sides of a triangle have lengths 6.5 , 10 , and ss , where ss is a whole number. What is the smallest possible value of ss ?
一个三角形的边长分别为 6.5、10 和 ss，其中 ss 是一个整数。ss 的最小可能值是多少？

正确答案：B · 分值：1

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1992 AMC8 #18 · Algebra · ★★★
On a trip, a car traveled 80 miles in an hour and a half, then was stopped in traffic for 30 minutes, then traveled 100 miles during the next 2 hours. What was the car's average speed in miles per hour for the 4 -hour trip?
在一次旅行中，一辆汽车用了一个半小时行驶 80 英里，然后在交通中停了 30 分钟，然后在接下来的 2 小时内行驶了 100 英里。这 4 小时行程中汽车的平均速度是多少英里/小时？

正确答案：A · 分值：1

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1992 AMC8 #19 · Counting, Probability & Statistics · ★★★
The distance between the 5th5^\text{th} and 26th26^\text{th} exits on an interstate highway is 118 miles. If any two consecutive exits are at least 5 miles apart, then what is the largest number of miles there can be between two consecutive exits that are between the 5th5^\text{th} and 26th26^\text{th} exits?
一条州际公路上第 5 个出口与第 26 个出口之间的距离是 118 英里。如果任意两个连续的出口至少相距 5 英里，那么位于第 5 个和第 26 个出口之间的两个连续出口之间，最大可能有多少英里？

正确答案：C · 分值：1

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1992 AMC8 #20 · Geometry · ★★★
Which pattern of identical squares could NOT be folded along the lines shown to form a cube?
以下哪种全等正方形的排列不能沿所示线条折叠成一个正方体？

正确答案：D · 分值：1

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1992 AMC8 #21 · Counting, Probability & Statistics · ★★★
Northside's Drum and Bugle Corps raised money for a trip. The drummers and bugle players kept separate sales records. According to the double bar graph, in what month did one group's sales exceed the other's by the greatest percent?
Northside 鼓号队为一次旅行筹款。鼓手和号手分别保留了销售记录。根据双柱状图，在哪个月其中一组的销售额超过另一组，且超出的百分比最大？

正确答案：B · 分值：1

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1992 AMC8 #22 · Geometry · ★★★★
Eight 1×11\times 1 square tiles are arranged as shown so their outside edges form a polygon with a perimeter of 14 units. Two additional tiles of the same size are added to the figure so that at least one side of each tile is shared with a side of one of the squares in the original figure. Which of the following could be the perimeter of the new figure?
八块 1×11\times 1 的方形瓷砖如图所示排列，其外缘形成一个周长为 14 个单位的多边形。在原图形上添加两块同样大小的瓷砖，使得每块新瓷砖至少有一条边与原图形中某块正方形的边共边。新图形的周长可能是以下哪个？

正确答案：C · 分值：1

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1992 AMC8 #23 · Counting, Probability & Statistics · ★★★
If two dice are tossed, the probability that the product of the numbers showing on the tops of the dice is greater than 10 is
掷两个骰子，朝上面的数字之积大于 10 的概率是

正确答案：B · 分值：1

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1992 AMC8 #24 · Geometry · ★★★★
Four circles of radius 3 are arranged as shown. Their centers are the vertices of a square. The area of the shaded region is closest to
四个半径为 3 的圆如图所示排列。它们的圆心是一个正方形的顶点。着色区域的面积最接近

正确答案：A · 分值：1

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1992 AMC8 #25 · Algebra · ★★★★
One half of the water is poured out of a full container. Then one third of the remainder is poured out. Continue the process: one fourth of the remainder for the third pouring, one fifth of the remainder for the fourth pouring, etc. After how many pourings does exactly one tenth of the original water remain?
从一个装满水的容器中倒出一半的水。然后倒出剩余水的三分之一。继续这个过程：第三次倒出剩余的四分之一，第四次倒出剩余的五分之一，依此类推。经过多少次倾倒后，恰好剩下原来水量的十分之一？

正确答案：D · 分值：1

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1991 AMC8 #5 · Geometry · ★★
A "domino" is made up of two small squares: Which of the "checkerboards" illustrated below CANNOT be covered exactly and completely by a whole number of non-overlapping dominoes?
一块"多米诺"骨牌由两个小正方形组成： 下面哪块"棋盘"不能被整数块不重叠的多米诺骨牌完全精确地覆盖？

正确答案：B · 分值：1

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1991 AMC8 #6 · Counting, Probability & Statistics · ★★
In the table shown, which number is the largest in its column and the smallest in its row?
在所示的表格中，哪个数在其所在列最大而在其所在行最小？

正确答案：C · 分值：1

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1991 AMC8 #7 · Algebra · ★★
The value of (487,000)(12,027,300)+(9,621,001)(487,000)(19,367)(0.05)\displaystyle \frac{(487,000)(12,027,300)+(9,621,001)(487,000)}{(19,367)(0.05)} is closest to
(487,000)(12,027,300)+(9,621,001)(487,000)(19,367)(0.05)\displaystyle \frac{(487,000)(12,027,300)+(9,621,001)(487,000)}{(19,367)(0.05)} 的值最接近

正确答案：D · 分值：1

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1991 AMC8 #8 · Algebra · ★★
What is the largest quotient that can be formed using two numbers chosen from the set {−24,−3,−2,1,2,8}\{ -24, -3, -2, 1, 2, 8 \} ?
从集合 {−24,−3,−2,1,2,8}\{-24, -3, -2, 1, 2, 8\} 中选两个数，能形成的最大商是多少？

正确答案：D · 分值：1

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1991 AMC8 #9 · Counting, Probability & Statistics · ★★
How many whole numbers from 1 through 46 are divisible by either 3 or 5 or both?
从 1 到 46 的正整数中，有多少个能被 3 或 5 或两者同时整除？

正确答案：B · 分值：1

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1991 AMC8 #10 · Geometry · ★★
The area in square units of the region enclosed by parallelogram ABCDABCD is
平行四边形 ABCDABCD 所围成区域的面积是多少平方单位？

正确答案：B · 分值：1

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1991 AMC8 #11 · Counting, Probability & Statistics · ★★★
There are several sets of three different numbers whose sum is 15 which can be chosen from {1,2,3,4,5,6,7,8,9}\{ 1,2,3,4,5,6,7,8,9 \} . How many of these sets contain a 5 ?
从 {1,2,3,4,5,6,7,8,9}\{1,2,3,4,5,6,7,8,9\} 中可以选出几组三个不同数的集合，其和为 15？这些集合中有多少个包含 5？

正确答案：B · 分值：1

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1991 AMC8 #12 · Algebra · ★★★
If 2+3+43=1990+1991+1992N\displaystyle \frac{2+3+4}{3}=\frac{1990+1991+1992}{N} , then N=
若 2+3+43=1990+1991+1992N\displaystyle \frac{2+3+4}{3}=\frac{1990+1991+1992}{N}，则 N=

正确答案：D · 分值：1

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1991 AMC8 #13 · Number Theory · ★★★
How many zeros are at the end of the product
25×25×25×25×25×25×25×8×8×8?25\times 25\times 25\times 25\times 25\times 25\times 25\times 8\times 8\times 8?
乘积
25×25×25×25×25×25×25×8×8×825\times 25\times 25\times 25\times 25\times 25\times 25\times 8\times 8\times 8
末尾有多少个零？

正确答案：C · 分值：1

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1991 AMC8 #14 · Counting, Probability & Statistics · ★★★
Several students are competing in a series of three races. A student earns 5 points for winning a race, 3 points for finishing second and 1 point for finishing third. There are no ties. What is the smallest number of points that a student must earn in the three races to be guaranteed of earning more points than any other student?
几名学生在三场系列赛中竞争。赢一场得 5 分，第二名得 3 分，第三名得 1 分。没有平局。一个学生在三场比赛中至少需要获得多少分，才能保证总分超过其他任何学生？

正确答案：D · 分值：1

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1991 AMC8 #15 · Geometry · ★★★
All six sides of a rectangular solid were rectangles. A one-foot cube was cut out of the rectangular solid as shown. The total number of square feet in the surface of the new solid is how many more or less than that of the original solid?
一个长方体的六个面都是矩形。如图所示，从该长方体中切掉一个一英尺的正方体。新立体表面的总平方英尺数比原立体多还是少多少？

正确答案：C · 分值：1

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1991 AMC8 #16 · Geometry · ★★★
The 16 squares on a piece of paper are numbered as shown in the diagram. While lying on a table, the paper is folded in half four times in the following sequence:
(1) fold the top half over the bottom half
(2) fold the bottom half over the top half
(3) fold the right half over the left half
(4) fold the left half over the right half.
Which numbered square is on top after step 4 ?
一张纸上的 16 个方格如图所示编号。纸张平放在桌上，按以下顺序对折四次：
(1) 将上半部分向下对折
(2) 将下半部分向上对折
(3) 将右半部分向左对折
(4) 将左半部分向右对折。
第 4 步之后，哪个编号的方格在最上面？

正确答案：B · 分值：1

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1991 AMC8 #17 · Counting, Probability & Statistics · ★★★
An auditorium with 20 rows of seats has 10 seats in the first row. Each successive row has one more seat than the previous row. If students taking an exam are permitted to sit in any row, but not next to another student in that row, then the maximum number of students that can be seated for an exam is
一个有 20 排座位的礼堂，第一排有 10 个座位。每一排比前一排多一个座位。如果参加考试的学生可以坐在任意一排，但不能与该排其他学生相邻，那么能安排考试的最大学生数是多少？

正确答案：C · 分值：1

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1991 AMC8 #18 · Counting, Probability & Statistics · ★★★
The vertical axis indicates the number of employees, but the scale was accidentally omitted from this graph. What percent of the employees at the Gauss company have worked there for 5 years or more?
纵轴表示员工数量，但此图意外遗漏了刻度。Gauss 公司员工中工作 5 年或以上的占百分之多少？

正确答案：C · 分值：1

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1991 AMC8 #19 · Counting, Probability & Statistics · ★★★
The average (arithmetic mean) of 10 different positive whole numbers is 10 . The largest possible value of any of these numbers is
10 个不同的正整数平均数为 10。这些数中最大可能值是多少？

正确答案：C · 分值：1

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1991 AMC8 #20 · Number Theory · ★★★
In the addition problem, each digit has been replaced by a letter. If different letters represent different digits then what is the value of CC ?
在下面的加法算式中，每个数字被替换为一个字母。如果不同的字母代表不同的数字，则 CC 的值是多少？

正确答案：A · 分值：1

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1991 AMC8 #21 · Algebra · ★★★
For every 3∘3^\circ rise in temperature, the volume of a certain gas expands by 4 cubic centimeters. If the volume of the gas is 24 cubic centimeters when the temperature is 32∘32^\circ , what was the volume of the gas in cubic centimeters when the temperature was 20∘20^\circ ?
温度每升高 3∘3^\circ，某气体的体积膨胀 4 立方厘米。如果温度为 32∘32^\circ 时气体体积为 24 立方厘米，则温度为 20∘20^\circ 时气体体积是多少立方厘米？

正确答案：A · 分值：1

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1991 AMC8 #22 · Counting, Probability & Statistics · ★★★
Each spinner is divided into 3 equal parts. The results obtained from spinning the two spinners are multiplied. What is the probability that this product is an even number?
每个转盘被分成 3 等份。两个转盘所得结果相乘。乘积为偶数的概率是多少？

正确答案：D · 分值：1

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1991 AMC8 #23 · Counting, Probability & Statistics · ★★★★
The Pythagoras High School band has 100 female and 80 male members. The Pythagoras High School orchestra has 80 female and 100 male members. There are 60 females who are members in both band and orchestra. Altogether, there are 230 students who are in either band or orchestra or both. The number of males in the band who are NOT in the orchestra is
Pythagoras 高中乐队有 100 名女生和 80 名男生。Pythagoras 高中管弦乐团有 80 名女生和 100 名男生。有 60 名女生同时参加乐队和管弦乐团。共有 230 名学生参加乐队或管弦乐团或两者都参加。乐队中不在管弦乐团的男生人数是

正确答案：A · 分值：1

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1991 AMC8 #24 · Geometry · ★★★★
A cube of edge 3 cm is cut into NN smaller cubes, not all the same size. If the edge of each of the smaller cubes is a whole number of centimeters, then N=
一个棱长为 3 cm 的正方体被切成 NN 个小正方体，不全部大小相同。如果每个小正方体的棱长都是整数厘米，则 N=

正确答案：E · 分值：1

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1991 AMC8 #25 · Algebra · ★★★★
An equilateral triangle is originally painted black. Each time the triangle is changed, the middle fourth of each black triangle turns white. After five changes, what fractional part of the original area of the black triangle remains black?
一个等边三角形最初被涂成黑色。每变换一次，每个黑色三角形中间的四分之一变成白色。经过五次变换后，原等边三角形的面积还剩几分之几是黑色的？

正确答案：C · 分值：1

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1990 AMC8 #1 · Counting, Probability & Statistics · ★★
What is the smallest sum of two 3 -digit numbers that can be obtained by placing each of the six digits 4,5,6,7,8,9 in one of the six boxes in this addition problem?
将六个数字 4,5,6,7,8,9 放入此加法算式的六个方框中各一次，能得到的两个三位数之和最小是多少？

正确答案：C · 分值：1

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1990 AMC8 #2 · Algebra · ★
Which digit of 0.12345 , when changed to 9 , gives the largest number?
将 0.12345 中的哪一位数字改为 9 能得到最大的数？

正确答案：A · 分值：1

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1990 AMC8 #4 · Number Theory · ★★
Which of the following could not be the unit's digit [one's digit] of the square of a whole number?
以下哪个数不可能是某个整数的平方的个位数字？

正确答案：E · 分值：1

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1990 AMC8 #5 · Algebra · ★
Which of the following is closest to the product (0.48017)(0.48017)(0.48017) ?
以下哪个最接近乘积 (0.48017)(0.48017)(0.48017)？

正确答案：B · 分值：1

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1990 AMC8 #7 · Algebra · ★★
When three different numbers from the set {−3,−2,−1,4,5}\{ -3, -2, -1, 4, 5 \} are multiplied, the largest possible product is
从集合 {−3,−2,−1,4,5}\{-3, -2, -1, 4, 5\} 中取三个不同的数相乘，最大可能的乘积是

正确答案：C · 分值：1

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1990 AMC8 #8 · Algebra · ★★
A dress originally priced at $80 was put on sale for 25% off. If 10% tax was added to the sale price, then the total selling price of the dress was
一件原价 $80 的连衣裙以 25% 折扣出售。如果打折价格再加 10% 税，则连衣裙的总售价是

正确答案：D · 分值：1

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1990 AMC8 #9 · Counting, Probability & Statistics · ★★
The grading scale shown is used at Jones Junior High. The fifteen scores in Mr. Freeman's class were: 89, 72, 54, 97, 77, 92, 85, 74, 75, 63, 84, 65, 76, 64, 67. In Mr. Freeman's class, what percent of the students received a grade of CC?
Jones 初中使用的评分标准如图所示。Mr. Freeman 班上的十五个成绩为：89, 72, 54, 97, 77, 92, 85, 74, 75, 63, 84, 65, 76, 64, 67。Mr. Freeman 班上获得 CC 成绩的学生占百分之多少？

正确答案：D · 分值：1

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1990 AMC8 #10 · Algebra · ★★
On this monthly calendar, the date behind one of the letters is added to the date behind C. If this sum equals the sum of the dates behind A and B, then the letter is
在这张月历上，其中一个字母背后的日期与 C 背后的日期相加。如果这个和等于 A 和 B 背后日期之和，则该字母是

正确答案：A · 分值：1

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1990 AMC8 #11 · Number Theory · ★★★
The numbers on the faces of this cube are consecutive whole numbers. The sum of the two numbers on each of the three pairs of opposite faces are equal. The sum of the six numbers on this cube is
此正方体面上的数字是连续的正整数。三组相对面上每组的两个数字之和相等。正方体上六个数字之和为

正确答案：E · 分值：1

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1990 AMC8 #12 · Counting, Probability & Statistics · ★★★
There are twenty-four 4-digit numbers that use each of the four digits 2, 4, 5, and 7 exactly once. Listed in numerical order from smallest to largest, the number in the 17th17\text{th} position in the list is
用数字 2、4、5、7 各用一次组成的四位数共有二十四个。按从小到大的顺序排列，第 17 个数是

正确答案：B · 分值：1

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1990 AMC8 #13 · Algebra · ★★★
One proposal for new postage rates for a letter was 30¢ for the first ounce and 22¢ for each additional ounce (or fraction of an ounce). The postage for a letter weighing 4.5 ounces was
一项新的信件邮资方案为：首盎司 30 美分，之后每盎司（或部分盎司）22 美分。一封重 4.5 盎司的信件邮资为

正确答案：C · 分值：1

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1990 AMC8 #14 · Counting, Probability & Statistics · ★★★
A bag contains only blue balls and green balls. There are 6 blue balls. If the probability of drawing a blue ball at random from this bag is 14\displaystyle \frac{1}{4} , then the number of green balls in the bag is
一个袋子里只有蓝球和绿球。有 6 个蓝球。如果从袋中随机抽到蓝球的概率是 14\displaystyle \frac{1}{4}，则袋中绿球的数量是

正确答案：B · 分值：1

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1990 AMC8 #15 · Geometry · ★★★
The area of this figure is 100 cm2100\text{ cm}^2 . Its perimeter is [figure consists of four identical squares]
此图形的面积为 100 cm2100\text{ cm}^2。其周长是
[图形由四个相同的正方形组成]

正确答案：E · 分值：1

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1990 AMC8 #17 · Geometry · ★★★
A straight concrete sidewalk is to be 3 feet wide, 60 feet long, and 3 inches thick. How many cubic yards of concrete must a contractor order for the sidewalk if concrete must be ordered in a whole number of cubic yards?
一条直的混凝土人行道宽 3 英尺、长 60 英尺、厚 3 英寸。如果混凝土必须按整立方码订购，承包商需要为这条人行道订购多少立方码混凝土？

正确答案：A · 分值：1

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1990 AMC8 #18 · Geometry · ★★★
Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have?
一个长方体每个角都被切掉了。显示了八个切口中的两个。新图形有多少条棱？

正确答案：C · 分值：1

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1990 AMC8 #19 · Counting, Probability & Statistics · ★★★
There are 120 seats in a row. What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone?
一排有 120 个座位。最少需要坐满多少个座位，才能使下一个入座的人必须挨着某人坐？

正确答案：B · 分值：1

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1990 AMC8 #20 · Counting, Probability & Statistics · ★★★
The annual incomes of 1,000 families range from $8200 to $98,000 . In error, the largest income was entered on the computer as $980,000 . The difference between the mean of the incorrect data and the mean of the actual data is
1,000 个家庭的年收入范围为 $8200 到 $98,000。错误地将最大收入输入为 $980,000。错误数据的平均数与实际数据的平均数之差为

正确答案：A · 分值：1

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1990 AMC8 #21 · Algebra · ★★★★
A list of 8 numbers is formed by beginning with two given numbers. Each new number in the list is the product of the two previous numbers. Find the first number if the last three are shown:
?‾, ‾, ‾, ‾, ‾,16‾,64‾,1024‾\text{\underline{\hspace{3 mm}?\hspace{3 mm}}\hspace{1 mm},\hspace{1 mm} \underline{\hspace{7 mm}}\hspace{1 mm},\hspace{1 mm} \underline{\hspace{7 mm}}\hspace{1 mm},\hspace{1 mm} \underline{\hspace{7 mm}}\hspace{1 mm},\hspace{1 mm} \underline{\hspace{7 mm}}\hspace{1 mm},\hspace{1 mm}\underline{\hspace{2 mm}16\hspace{2 mm}}\hspace{1 mm},\hspace{1 mm}\underline{\hspace{2 mm}64\hspace{2 mm}}\hspace{1 mm},\hspace{1 mm}\underline{\hspace{1 mm}1024\hspace{1 mm}}}
一个包含 8 个数的列表由两个给定的数开始形成。列表中每个新数都是前两个数的乘积。已知最后三个数如图所示，求第一个数。

正确答案：B · 分值：1

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1990 AMC8 #22 · Number Theory · ★★★★
Several students are seated at a large circular table. They pass around a bag containing 100 pieces of candy. Each person receives the bag, takes one piece of candy and then passes the bag to the next person. If Chris takes the first and last piece of candy, then the number of students at the table could be
几名学生围坐在一张大圆桌旁。他们传一袋装有 100 颗糖果的袋子。每人接过袋子，取一颗糖果，然后将袋子传给下一个人。如果 Chris 拿走第一颗也是最后一颗糖果，则桌旁的学生人数可能是

正确答案：B · 分值：1

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1990 AMC8 #23 · Algebra · ★★★
The graph relates the distance traveled [in miles] to the time elapsed [in hours] on a trip taken by an experimental airplane. During which hour was the average speed of this airplane the largest?
该图显示了一架实验飞机在一次飞行中已行驶距离[英里]与已用时间[小时]的关系。在哪一个小时中该飞机的平均速度最大？

正确答案：B · 分值：1

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1990 AMC8 #24 · Algebra · ★★★★
Three Δ\Delta 's and a ♢\diamondsuit will balance nine ∙\bullet 's. One Δ\Delta will balance a ♢\diamondsuit and a ∙\bullet .
How many ∙\bullet 's will balance the two ♢\diamondsuit 's in this balance?
三个 Δ\Delta 和一个 ♢\diamondsuit 能平衡九个 ∙\bullet。一个 Δ\Delta 能平衡一个 ♢\diamondsuit 和一个 ∙\bullet。
此天平中，多少个 ∙\bullet 能平衡两个 ♢\diamondsuit？

正确答案：C · 分值：1

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1990 AMC8 #25 · Counting, Probability & Statistics · ★★★★
How many different patterns can be made by shading exactly two of the nine squares? Patterns that can be matched by flips and/or turns are not considered different. For example, the patterns shown below are not considered different.
通过恰好给九个正方形中的两个着色，可以形成多少种不同的图案？通过翻转和/或旋转能重合的图案不算不同。例如，下面显示的图案不算不同。

正确答案：C · 分值：1

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1989 AMC8 #4 · Algebra · ★
Estimate to determine which of the following numbers is closest to 4010.205\displaystyle \frac{401}{0.205} .
估算 4010.205\displaystyle \frac{401}{0.205} 最接近以下哪个数。

正确答案：E · 分值：1

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1989 AMC8 #6 · Algebra · ★★
If the markings on the number line are equally spaced, what is the number yy ?
如果数轴上的标记是等间距的，数 yy 是多少？

正确答案：C · 分值：1

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1989 AMC8 #7 · Algebra · ★★
If the value of 20 quarters and 10 dimes equals the value of 10 quarters and nn dimes, then n=
如果 20 个 25 分硬币和 10 个 10 分硬币的总价值等于 10 个 25 分硬币和 nn 个 10 分硬币的总价值，则 n=

正确答案：D · 分值：1

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1989 AMC8 #9 · Algebra · ★★
There are 2 boys for every 3 girls in Ms. Johnson's math class. If there are 30 students in her class, what percent of them are boys?
Ms. Johnson 的数学班上每 2 个男生对应 3 个女生。如果她班上有 30 名学生，男生占百分之多少？

正确答案：C · 分值：1

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1989 AMC8 #10 · Geometry · ★★
What is the number of degrees in the smaller angle between the hour hand and the minute hand on a clock that reads seven o'clock?
时钟显示七点整时，时针和分针之间较小角的度数是多少？

正确答案：D · 分值：1

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1989 AMC8 #11 · Geometry · ★★★
Which of the five "T-like shapes" would be symmetric to the one shown with respect to the dashed line?
五个"T 形图形"中，哪个与所示图形关于虚线对称？

正确答案：B · 分值：1

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1989 AMC8 #14 · Counting, Probability & Statistics · ★★★
If a single digit is placed in each of the boxes of this subtraction problem, what is the smallest difference that is possible?
如果在每个方框中各放一个一位数字，这个减法算式的最小可能差是多少？

正确答案：C · 分值：1

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1989 AMC8 #15 · Geometry · ★★★
The area of the shaded region BEDCBEDC in parallelogram ABCDABCD is
平行四边形 ABCDABCD 中阴影区域 BEDCBEDC 的面积是

正确答案：D · 分值：1

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1989 AMC8 #16 · Number Theory · ★★★
In how many ways can 47 be written as the sum of two primes?
有多少种方式可以将 47 写成两个质数之和？

正确答案：A · 分值：1

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1989 AMC8 #17 · Algebra · ★★★
The number NN is between 9 and 17 . The average of 6 , 10 , and NN could be
数 NN 在 9 到 17 之间。6、10 和 NN 的平均数可能是

正确答案：B · 分值：1

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1989 AMC8 #18 · Algebra · ★★★
Many calculators have a reciprocal key 1x\displaystyle \boxed{\frac{1}{x}} that replaces the current number displayed with its reciprocal. For example, if the display is 00004\boxed{00004} and the 1x\displaystyle \boxed{\frac{1}{x}} key is depressed, then the display becomes 000.25\boxed{000.25} . If 00032\boxed{00032} is currently displayed, what is the fewest number of times you must depress the 1x\displaystyle \boxed{\frac{1}{x}} key so the display again reads 00032\boxed{00032} ?
许多计算器有一个倒数键 1x\displaystyle \boxed{\frac{1}{x}}，将当前显示的数替换为其倒数。例如，如果显示为 00004\boxed{00004} 并按下 1x\displaystyle \boxed{\frac{1}{x}} 键，则显示变为 000.25\boxed{000.25}。如果当前显示 00032\boxed{00032}，最少需要按多少次 1x\displaystyle \boxed{\frac{1}{x}} 键才能使显示再次变为 00032\boxed{00032}？

正确答案：B · 分值：1

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1989 AMC8 #19 · Counting, Probability & Statistics · ★★★
The graph below shows the total accumulated dollars (in millions) spent by the Surf City government during 1988 . For example, about 0.5 million had been spent by the beginning of February and approximately 2 million by the end of April. Approximately how many millions of dollars were spent during the summer months of June, July, and August?
下图显示了 1988 年 Surf City 政府累计支出总额（百万美元）。例如，到二月初已支出约 0.5 百万美元，到四月底约 2 百万美元。六月、七月和八月的夏季大约支出了多少百万美元？

正确答案：B · 分值：1

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1989 AMC8 #20 · Geometry · ★★★
The figure may be folded along the lines shown to form a number cube. Three number faces come together at each corner of the cube. What is the largest sum of three numbers whose faces come together at a corner?
此图可以沿所示线条折叠形成一个数字正方体。正方体的每个角上有三个数字面汇聚在一起。汇聚于一个角的三个数字之和最大是多少？

正确答案：D · 分值：1

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1989 AMC8 #21 · Algebra · ★★★
Jack had a bag of 128 apples. He sold 25% of them to Jill. Next he sold 25% of those remaining to June. Of those apples still in his bag, he gave the shiniest one to his teacher. How many apples did Jack have then?
Jack 有一袋 128 个苹果。他将其中的 25% 卖给了 Jill。接着他将剩下苹果中的 25% 卖给了 June。然后从袋中剩下的苹果中，他把最亮的那一个送给了老师。那时 Jack 还有多少个苹果？

正确答案：D · 分值：1

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1989 AMC8 #22 · Number Theory · ★★★★
The digits 1, 9, 8, 9 are "cycled" separately as shown and put together in a numbered list. What is the 7th7\text{th} number in the list?
数字 1、9、8、9 分别如图所示"循环"排列，并合在一起形成一个编号列表。列表中的第 7 个数是什么？

正确答案：C · 分值：1

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1989 AMC8 #23 · Geometry · ★★★
An artist has 14 cubes, each with an edge of 1 meter. She stands them on the ground to form a sculpture as shown. She then paints the exposed surface of the sculpture. How many square meters does she paint?
一位艺术家有 14 个棱长为 1 米的正方体。她将它们立在地上形成如图所示的雕塑。然后她对雕塑的暴露表面进行涂漆。她涂了多少平方米？

正确答案：C · 分值：1

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1989 AMC8 #24 · Geometry · ★★★★
Suppose a square piece of paper is folded in half vertically. The folded paper is then cut in half along the dashed line. Three rectangles are formed-a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?
假设一张正方形纸被垂直对折。折叠后的纸再沿虚线切成两半。形成三个矩形——一个大矩形和两个小矩形。一个小矩形的周长与大矩形的周长之比是多少？

正确答案：E · 分值：1

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1989 AMC8 #25 · Counting, Probability & Statistics · ★★★★
Every time these two wheels are spun, two numbers are selected by the pointers. What is the probability that the sum of the two selected numbers is even?
每次转动这两个转盘时，指针各选中一个数字。两个选中数字之和为偶数的概率是多少？

正确答案：C · 分值：1

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1988 AMC8 #1 · Algebra · ★
The diagram shows part of a scale of a measuring device. The arrow indicates an approximate reading of
图中显示了一个测量设备刻度的一部分。箭头所指的近似读数是

正确答案：D · 分值：1

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1988 AMC8 #2 · Algebra · ★
The product 8×0.25×2×0.125=8\times 0.25\times 2\times 0.125 =
乘积 8×0.25×2×0.125=8\times 0.25\times 2\times 0.125 =

正确答案：C · 分值：1

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1988 AMC8 #4 · Counting, Probability & Statistics · ★★
The figure consists of alternating light and dark squares. The number of dark squares exceeds the number of light squares by
该图形由深浅交替的正方形组成。深色正方形的数量比浅色正方形多

正确答案：B · 分值：1

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1988 AMC8 #5 · Geometry · ★
Problem If ∠CBD\angle CBD is a right angle, then this protractor indicates that the measure of ∠ABC\angle ABC is approximately
如果 ∠CBD\angle CBD 是直角，则该量角器显示 ∠ABC\angle ABC 的近似度数是

正确答案：C · 分值：1

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1988 AMC8 #7 · Algebra · ★
2.46×8.163×(5.17+4.829)2.46\times 8.163\times (5.17+4.829) is closest to
2.46×8.163×(5.17+4.829)2.46\times 8.163\times (5.17+4.829) 最接近

正确答案：B · 分值：1

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1988 AMC8 #8 · Algebra · ★★
Betty used a calculator to find the product 0.075×2.560.075 \times 2.56 . She forgot to enter the decimal points. The calculator showed 19200 . If Betty had entered the decimal points correctly, the answer would have been
Betty 用计算器求乘积 0.075×2.560.075 \times 2.56。她忘记输入小数点。计算器显示 19200。如果 Betty 正确输入了小数点，答案应该是

正确答案：B · 分值：1

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1988 AMC8 #9 · Geometry · ★★
An isosceles triangle is a triangle with two sides of equal length. How many of the five triangles on the square grid below are isosceles?
等腰三角形是有两条边长度相等的三角形。下面方格网格上的五个三角形中有多少个是等腰三角形？

正确答案：D · 分值：1

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1988 AMC8 #10 · Number Theory · ★★
Chris' birthday is on a Thursday this year. What day of the week will it be 60 days after her birthday?
今年 Chris 的生日在周四。她生日后的第 60 天是周几？

正确答案：A · 分值：1

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1988 AMC8 #12 · Algebra · ★★★
Suppose the estimated 20 billion dollar cost to send a person to the planet Mars is shared equally by the 250 million people in the U.S. Then each person's share is
假设送一个人去火星的估计成本为 200 亿美元，由美国 2.5 亿人平均分担。则每人应承担

正确答案：C · 分值：1

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1988 AMC8 #13 · Geometry · ★★★
If rose bushes are spaced about 1 foot apart, approximately how many bushes are needed to surround a circular patio whose radius is 12 feet?
如果玫瑰花丛间距约 1 英尺，环绕一个半径为 12 英尺的圆形露台大约需要多少花丛？

正确答案：D · 分值：1

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1988 AMC8 #14 · Number Theory · ★★★
♢\diamondsuit and Δ\Delta are whole numbers and ♢×Δ=36\diamondsuit \times \Delta =36 . The largest possible value of ♢+Δ\diamondsuit + \Delta is
♢\diamondsuit 和 Δ\Delta 是正整数，且 ♢×Δ=36\diamondsuit \times \Delta =36。♢+Δ\diamondsuit + \Delta 的最大可能值是

正确答案：E · 分值：1

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1988 AMC8 #15 · Algebra · ★★★
The reciprocal of (12+13)\displaystyle \left( \frac{1}{2}+\frac{1}{3}\right) is
(12+13)\displaystyle \left( \frac{1}{2}+\frac{1}{3}\right) 的倒数是

正确答案：C · 分值：1

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1988 AMC8 #16 · Counting, Probability & Statistics · ★★★
Placing no more than one X\text{X} in each small square, what is the greatest number of X\text{X} 's that can be put on the grid shown without getting three X\text{X} 's in a row vertically, horizontally, or diagonally?
每个小方格最多放一个 X\text{X}，在所示网格上最多能放多少个 X\text{X}，使得任意垂直、水平或对角线方向不会出现连续的三个 X\text{X}？

正确答案：E · 分值：1

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1988 AMC8 #17 · Geometry · ★★★
The shaded region formed by the two intersecting perpendicular rectangles, in square units, is
两个垂直相交矩形形成的着色区域面积是多少平方单位？

正确答案：B · 分值：1

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1988 AMC8 #18 · Counting, Probability & Statistics · ★★★
The average weight of 6 boys is 150 pounds and the average weight of 4 girls is 120 pounds. The average weight of the 10 children is
6 个男孩的平均体重是 150 磅，4 个女孩的平均体重是 120 磅。这 10 个孩子的平均体重是

正确答案：C · 分值：1

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1988 AMC8 #19 · Algebra · ★★★
What is the 100th100\text{th} number in the arithmetic sequence: 1,5,9,13,17,21,25,... ?
等差数列 1,5,9,13,17,21,25,... 中的第 100 个数是多少？

正确答案：A · 分值：1

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1988 AMC8 #20 · Algebra · ★★★
Problem The glass gauge on a cylindrical coffee maker shows that there are 45 cups left when the coffee maker is 36% full. How many cups of coffee does it hold when it is full?
一个圆柱形咖啡壶的玻璃刻度显示，当咖啡壶 36% 满时还剩下 45 杯。咖啡壶满的时候能装多少杯咖啡？

正确答案：C · 分值：1

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1988 AMC8 #21 · Counting, Probability & Statistics · ★★★★
A fifth number, nn , is added to the set {3,6,9,10}\{ 3,6,9,10 \} to make the mean of the set of five numbers equal to its median. The number of possible values of nn is
将第五个数 nn 加入集合 {3,6,9,10}\{3,6,9,10\} 中，使得这五个数的平均数等于其中位数。nn 的可能值有多少个？

正确答案：C · 分值：1

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1988 AMC8 #22 · Algebra · ★★★
Tom's Hat Shoppe increased all original prices by 25% . Now the shoppe is having a sale where all prices are 20% off these increased prices. Which statement best describes the sale price of an item?
Tom's Hat Shoppe 将所有原价提高 25%。现在该店正在进行促销，所有价格在提高后的基础上打 20% 折扣。以下哪句话最能描述商品的促销价格？

正确答案：E · 分值：1

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1988 AMC8 #23 · Algebra · ★★★
Maria buys computer disks at a price of 4 for $5 and sells them at a price of 3 for $5 . How many computer disks must she sell in order to make a profit of $100 ?
Maria 以 $5 买 4 张的价格购入计算机磁盘，以 $5 卖 3 张的价格出售。为获得 $100 利润，她必须卖出多少张磁盘？

正确答案：D · 分值：1

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1988 AMC8 #24 · Geometry · ★★★★
The square in the first diagram "rolls" clockwise around the fixed regular hexagon until it reaches the bottom. In which position will the solid triangle be in diagram 4 ?
第一个图中的正方形围绕固定的正六边形顺时针"滚动"，直到到达底部。图 4 中实心三角形将位于哪个位置？

正确答案：A · 分值：1

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1988 AMC8 #25 · Counting, Probability & Statistics · ★★★★
A palindrome is a whole number that reads the same forwards and backwards. If one neglects the colon, certain times displayed on a digital watch are palindromes. Three examples are: 1:011{:}01, 4:444{:}44, and 12:2112{:}21. How many times during a 12-hour period will be palindromes?
回文数是指正读和倒读都相同的整数。如果忽略冒号，数字手表上显示的某些时间是回文数。三个例子是：1:011{:}01、4:444{:}44 和 12:2112{:}21。在 12 小时内，共有多少个时间是回文数？

正确答案：A · 分值：1

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1987 AMC8 #4 · Algebra · ★★
Martians measure angles in clerts. There are 500 clerts in a full circle. How many clerts are there in a right angle?
火星人以 clert 为单位度量角度。一整个圆周有 500 clert。一个直角有多少 clert？

正确答案：C · 分值：1

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1987 AMC8 #6 · Algebra · ★★
The smallest product one could obtain by multiplying two numbers in the set {−7,−5,−1,1,3}\{ -7,-5,-1,1,3 \} is
将集合 {−7,−5,−1,1,3}\{-7,-5,-1,1,3\} 中的两个数相乘，能得到的最小乘积是

正确答案：B · 分值：1

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1987 AMC8 #7 · Geometry · ★★
The large cube shown is made up of 27 identical sized smaller cubes. For each face of the large cube, the opposite face is shaded the same way. The total number of smaller cubes that must have at least one face shaded is
所示大正方体由 27 个相同大小的小正方体组成。大正方体的每个面，其相对面的着色方式相同。至少有一个面被着色的小正方体总数是

正确答案：C · 分值：1

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1987 AMC8 #8 · Algebra · ★★
If the letters are replaced by digits so that the given addition problem is correct, then the number of digits (not necessarily different) in the sum of the three whole numbers is
若字母被数字替换使得给定的加法算式正确，则三个整数的和的位数（数字不必不同）为

正确答案：B · 分值：1

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1987 AMC8 #9 · Number Theory · ★★
When finding the sum 12+13+14+15+16+17\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7} , the least common denominator used is
求 12+13+14+15+16+17\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7} 的和时，使用的最小公分母是

正确答案：C · 分值：1

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1987 AMC8 #11 · Algebra · ★★★
The sum 217+312+5119\displaystyle 2\frac17+3\frac12+5\frac{1}{19} is between
和 217+312+5119\displaystyle 2\frac17+3\frac12+5\frac{1}{19} 在以下哪两个数之间？

正确答案：B · 分值：1

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1987 AMC8 #12 · Geometry · ★★★
What fraction of the large 12 by 18 rectangular region is shaded?
着色部分占 12 × 18 大矩形区域的几分之几？

正确答案：C · 分值：1

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1987 AMC8 #13 · Algebra · ★★★
Which of the following fractions has the largest value?
以下哪个分数值最大？

正确答案：E · 分值：1

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1987 AMC8 #14 · Algebra · ★★★
A computer can do 10,000 additions per second. How many additions can it do in one hour?
一台计算机每秒可以做 10,000 次加法。它在一小时内能做多少次加法？

正确答案：B · 分值：1

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1987 AMC8 #15 · Algebra · ★★★
The sale ad read: "Buy three tires at the regular price and get the fourth tire for $3. " Sam paid $240 for a set of four tires at the sale. What was the regular price of one tire?
促销广告写道："以原价购买三个轮胎，第四个轮胎仅需 $3。" Sam 在促销中以 $240 买了一套四个轮胎。一个轮胎的原价是多少？

正确答案：D · 分值：1

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1987 AMC8 #16 · Algebra · ★★★
Joyce made 12 of her first 30 shots in the first three games of this basketball season, so her seasonal shooting average was 40% . In her next game, she took 10 shots and raised her seasonal shooting average to 50% . How many of these 10 shots did she make?
Joyce 在本篮球赛季的前三场比赛中前 30 次出手命中 12 次，因此她的赛季命中率为 40%。在下一场比赛中，她出手 10 次并将赛季命中率提高到 50%。这 10 次出手她命中了多少次？

正确答案：E · 分值：1

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1987 AMC8 #17 · Counting, Probability & Statistics · ★★★
Abby, Bret, Carl, and Dana are seated in a row of four seats numbered #1 to #4 . Joe looks at them and says: \hspace{2em} "Bret is next to Carl." \hspace{2em} "Abby is between Bret and Carl." However each one of Joe's statements is false. Bret is actually sitting in seat #3 . Who is sitting in seat #2 ?
Abby、Bret、Carl 和 Dana 坐在编号为 #1 到 #4 的四个座位上。Joe 看着他们说：
\hspace{2em} "Bret 挨着 Carl。"
\hspace{2em} "Abby 在 Bret 和 Carl 之间。"
然而 Joe 的每句话都是假的。实际上 Bret 坐在 #3 号座位。谁坐在 #2 号座位？

正确答案：D · 分值：1

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1987 AMC8 #18 · Algebra · ★★★
Half the people in a room left. One third of those remaining started to dance. There were then 12 people who were not dancing. The original number of people in the room was
房间中一半的人离开了。剩下的人中有三分之一开始跳舞。此时有 12 人没有跳舞。房间里原来的人数是

正确答案：C · 分值：1

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1987 AMC8 #19 · Algebra · ★★★
A calculator has a squaring key x2\boxed{x^2} which replaces the current number displayed with its square. For example, if the display is          3\boxed{\ \ \ \ \ \ \ \ \ 3} and the x2\boxed{x^2} key is depressed, then the display becomes          9\boxed{\ \ \ \ \ \ \ \ \ 9} . If the display reads          2\boxed{\ \ \ \ \ \ \ \ \ 2} , how many times must you depress the x2\boxed{x^2} key to produce a displayed number greater than 500 ?
一个计算器有一个平方键 x2\boxed{x^2}，将当前显示的数替换为其平方。例如，如果显示为 3\boxed{3} 并按下 x2\boxed{x^2} 键，则显示变为 9\boxed{9}。如果显示 2\boxed{2}，需要按多少次 x2\boxed{x^2} 键才能产生一个大于 500 的显示数？

正确答案：A · 分值：1

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1987 AMC8 #20 · Number Theory · ★★★
"If a whole number nn is not prime, then the whole number n-2 is not prime." A value of nn which shows this statement to be false is
"如果一个正整数 nn 不是质数，则正整数 n-2 也不是质数。" 以下哪个 nn 的值能证明该陈述为假？

正确答案：A · 分值：1

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1987 AMC8 #21 · Algebra · ★★★
Suppose n∗n^{*} means 1n\displaystyle \frac{1}{n} , the reciprocal of nn . For example, 5∗=15\displaystyle 5^{*}=\frac{1}{5} . How many of the following statements are true? \hspace{2em} i) 3∗+6∗=9∗3^*+6^*=9^* \hspace{2em} ii) 6∗−4∗=2∗6^*-4^*=2^* \hspace{2em} iii) 2∗⋅6∗=12∗2^*\cdot 6^*=12^* \hspace{2em} iv) 10∗÷2∗=5∗10^*\div 2^* =5^*
设 n∗n^{*} 表示 1n\displaystyle \frac{1}{n}，即 nn 的倒数。例如 5∗=15\displaystyle 5^{*}=\frac{1}{5}。以下陈述中有多少条为真？
\hspace{2em} i) 3∗+6∗=9∗3^*+6^*=9^*
\hspace{2em} ii) 6∗−4∗=2∗6^*-4^*=2^*
\hspace{2em} iii) 2∗⋅6∗=12∗2^*\cdot 6^*=12^*
\hspace{2em} iv) 10∗÷2∗=5∗10^*\div 2^* =5^*

正确答案：C · 分值：1

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1987 AMC8 #22 · Geometry · ★★★★
ABCDABCD is a rectangle, DD is the center of the circle, and BB is on the circle. If AD=4 and CD=3 , then the area of the shaded region is between
ABCDABCD 是一个矩形，DD 是圆的圆心，BB 在圆上。如果 AD=4 且 CD=3，则着色区域的面积在以下哪两个数之间？

正确答案：D · 分值：1

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1987 AMC8 #23 · Counting, Probability & Statistics · ★★★
The table below gives the 1980 U.S. population for each of the four geographic regions and for each of two ethnic groups. To the nearest percent, what percent of the U.S. Black population lived in the South?
下表给出了 1980 年美国四个地理区域和两个族裔的人口。取整到最近的百分比，美国黑人人口中有百分之多少居住在南方？

正确答案：D · 分值：1

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1987 AMC8 #24 · Number Theory · ★★★★
A multiple choice examination consists of 20 questions. The scoring is +5 for each correct answer, -2 for each incorrect answer, and 0 for each unanswered question. John's score on the examination is 48 . What is the maximum number of questions he could have answered correctly?
一项选择题考试包含 20 道题。评分规则为：每答对一题 +5 分，每答错一题 -2 分，未答题 0 分。John 的考试分数为 48。他最多可能答对了多少道题？

正确答案：D · 分值：1

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1987 AMC8 #25 · Counting, Probability & Statistics · ★★★★
Ten balls numbered 1 to 10 are in a jar. Jack reaches into the jar and randomly removes one of the balls. Then Jill reaches into the jar and randomly removes a different ball. The probability that the sum of the two numbers on the balls removed is even is
一个罐子中有编号 1 到 10 的十个球。Jack 从罐中随机取出一个球。然后 Jill 从罐中随机取一个不同的球。取出的两个球上的数字之和为偶数的概率是

正确答案：A · 分值：1

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1986 AMC8 #1 · Algebra · ★
In July 1861, 366 inches of rain fell in Cherrapunji, India. What was the average rainfall in inches per hour during that month?
1861 年 7 月，印度 Cherrapunji 的降雨量为 366 英寸。该月平均每小时降雨量是多少英寸？

正确答案：A · 分值：1

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1986 AMC8 #2 · Algebra · ★
Which of the following numbers has the largest reciprocal?
以下哪个数的倒数最大？

正确答案：A · 分值：1

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1986 AMC8 #3 · Algebra · ★
The smallest sum one could get by adding three different numbers from the set {7,25,−1,12,−3}\{ 7,25,-1,12,-3 \} is
从集合 {7,25,−1,12,−3}\{7,25,-1,12,-3\} 中选三个不同的数相加，能得到的最小和是

正确答案：C · 分值：1

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1986 AMC8 #5 · Algebra · ★★
A contest began at noon one day and ended 1000 minutes later. At what time did the contest end?
某竞赛于一天中午开始，1000 分钟后结束。竞赛在什么时间结束？

正确答案：D · 分值：1

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1986 AMC8 #7 · Number Theory · ★★
How many whole numbers are between 8\sqrt8 and 80\sqrt80?
8\sqrt{8} 和 80\sqrt{80} 之间有多少个整数？

正确答案：B · 分值：1

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1986 AMC8 #9 · Counting, Probability & Statistics · ★★
Using only the paths and the directions shown, how many different routes are there from M\text{M} to N\text{N} ?
只使用所示路径和方向，从 M\text{M} 到 N\text{N} 有多少条不同路线？

正确答案：E · 分值：1

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1986 AMC8 #10 · Algebra · ★★
A picture 3 feet across is hung in the center of a wall that is 19 feet wide. How many feet from the end of the wall is the nearest edge of the picture?
一幅 3 英尺宽的画挂在宽 19 英尺的墙中央。画最近的边缘距离墙的末端有多少英尺？

正确答案：B · 分值：1

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1986 AMC8 #11 · Algebra · ★★★
If A∗B\text{A}*\text{B} means A+B2\displaystyle \frac{\text{A}+\text{B}}{2} , then ()*8 is
若 A∗B\text{A}*\text{B} 表示 A+B2\displaystyle \frac{\text{A}+\text{B}}{2}，则 (3*5)*8 等于
3∗53*5

正确答案：A · 分值：1

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1986 AMC8 #12 · Counting, Probability & Statistics · ★★★
Problem The table below displays the grade distribution of the 30 students in a mathematics class on the last two tests. For example, exactly one student received a 'D' on Test 1 and a 'C' on Test 2 (see circled entry). What percent of the students received the same grade on both tests?
下表显示了一个数学班 30 名学生最近两次考试的成绩分布。例如，恰好有一名学生考试一得了 'D'，考试二得了 'C'（见圈出的条目）。两次考试得分相同的学生占百分之多少？

正确答案：D · 分值：1

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1986 AMC8 #14 · Algebra · ★★★
If 200≤a≤400200\leq a \leq 400 and 600≤b≤1200600\leq b\leq 1200 , then the largest value of the quotient ba\displaystyle \frac{b}{a} is
若 200≤a≤400200\leq a \leq 400 且 600≤b≤1200600\leq b\leq 1200，则商 ba\displaystyle \frac{b}{a} 的最大值是

正确答案：C · 分值：1

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1986 AMC8 #15 · Algebra · ★★★
Sale prices at the Ajax Outlet Store are 50% below original prices. On Saturdays an additional discount of 20% off the sale price is given. What is the Saturday price of a coat whose original price is \textdollar180\textdollar 180?
Ajax 折扣店的促销价格为原价减 50%。周六在促销价的基础上再打 20% 的折扣。一件原价为 $180 的外套周六价格是多少？

正确答案：B · 分值：1

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1986 AMC8 #16 · Counting, Probability & Statistics · ★★★
A bar graph shows the number of hamburgers sold by a fast food chain each season. However, the bar indicating the number sold during the winter is covered by a smudge. If exactly 25% of the chain's hamburgers are sold in the fall, how many million hamburgers are sold in the winter?
一张柱状图显示了一家快餐连锁店每个季节的汉堡销量。但是，显示冬季销量的柱条被污渍遮盖了。如果该连锁店恰好 25% 的汉堡在秋季销售，冬季销售了多少百万个汉堡？

正确答案：A · 分值：1

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1986 AMC8 #17 · Number Theory · ★★★
Let oo be an odd whole number and let nn be any whole number. Which of the following statements about the whole number (o2+no)(o^2+no) is always true?
设 oo 为一个奇整数，nn 为任意整数。关于整数 (o2+no)(o^2+no)，以下哪条陈述一定成立？

正确答案：E · 分值：1

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1986 AMC8 #18 · Counting, Probability & Statistics · ★★★
A rectangular grazing area is to be fenced off on three sides using part of a 100 meter rock wall as the fourth side. Fence posts are to be placed every 12 meters along the fence including the two posts where the fence meets the rock wall. What is the fewest number of posts required to fence an area 36 m by 60 m?
一块矩形放牧区需用围墙三面围起，以一段 100 米的石墙作为第四边。围墙柱每隔 12 米竖一根，包括围墙与石墙相接处的两根柱子。围起 36 m × 60 m 的区域最少需要多少根柱子？

正确答案：B · 分值：1

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1986 AMC8 #19 · Algebra · ★★★
At the beginning of a trip, the mileage odometer read 56,200 miles. The driver filled the gas tank with 6 gallons of gasoline. During the trip, the driver filled his tank again with 12 gallons of gasoline when the odometer read 56,560 . At the end of the trip, the driver filled his tank again with 20 gallons of gasoline. The odometer read 57,060 . To the nearest tenth, what was the car's average miles-per-gallon for the entire trip?
旅行开始时，里程表读数为 56,200 英里。驾驶员给油箱加了 6 加仑汽油。旅行中，当里程表读数为 56,560 时，驾驶员又加了 12 加仑汽油。旅行结束时，驾驶员再次加满 20 加仑汽油。里程表读数为 57,060。精确到十分位，汽车整个旅行的平均每加仑英里数是多少？

正确答案：D · 分值：1

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1986 AMC8 #20 · Algebra · ★★★
The value of the expression (304)5(29.7)(399)4\displaystyle \frac{(304)^5}{(29.7)(399)^4} is closest to
表达式 (304)5(29.7)(399)4\displaystyle \frac{(304)^5}{(29.7)(399)^4} 的值最接近

正确答案：D · 分值：1

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1986 AMC8 #21 · Geometry · ★★★★
Suppose one of the eight lettered identical squares is included with the four squares in the T-shaped figure outlined. How many of the resulting figures can be folded into a topless cubical box?
假设八个标有字母的全等正方形之一与 T 形外框中的四个正方形合并。所得图形中有多少个可以折叠成一个无盖的正方体盒子？

正确答案：E · 分值：1

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1986 AMC8 #22 · Counting, Probability & Statistics · ★★★★
Alan, Beth, Carlos, and Diana were discussing their possible grades in mathematics class this grading period. Alan said, "If I get an A, then Beth will get an A." Beth said, "If I get an A, then Carlos will get an A." Carlos said, "If I get an A, then Diana will get an A." All of these statements were true, but only two of the students received an A. Which two received A's?
Alan、Beth、Carlos 和 Diana 正在讨论本评分周期他们可能的数学成绩。Alan 说："如果我得了 A，那么 Beth 会得 A。" Beth 说："如果我得了 A，那么 Carlos 会得 A。" Carlos 说："如果我得了 A，那么 Diana 会得 A。" 所有这些陈述都是真的，但只有两名学生得了 A。哪两人得了 A？

正确答案：C · 分值：1

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1986 AMC8 #23 · Geometry · ★★★★
The large circle has diameter AC\text{AC} . The two small circles have their centers on AC\text{AC} and just touch at O\text{O} , the center of the large circle. If each small circle has radius 1 , what is the value of the ratio of the area of the shaded region to the area of one of the small circles?
大圆的直径为 AC\text{AC}。两个小圆的圆心在 AC\text{AC} 上，且恰好在 O\text{O} 点（大圆的圆心）相切。如果每个小圆的半径为 1，着色区域与一个小圆的面积之比是多少？

正确答案：B · 分值：1

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1986 AMC8 #24 · Counting, Probability & Statistics · ★★★★
The 600 students at King Middle School are divided into three groups of equal size for lunch. Each group has lunch at a different time. A computer randomly assigns each student to one of three lunch groups. The probability that three friends, Al, Bob, and Carol, will be assigned to the same lunch group is approximately
King 中学的 600 名学生被平均分成三组用午餐。每组在不同的时间用餐。一台计算机随机将每名学生分配到三个午餐组之一。三个朋友 Al、Bob 和 Carol 被分到同一午餐组的概率大约是

正确答案：B · 分值：1

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1986 AMC8 #25 · Algebra · ★★★★
Which of the following sets of whole numbers has the largest average?
下列哪一组整数的平均数最大？

正确答案：D · 分值：1

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1985 AMC8 #4 · Geometry · ★★
The area of polygon ABCDEFABCDEF , in square units, is
多边形 ABCDEFABCDEF 的面积是多少平方单位？

正确答案：C · 分值：1

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1985 AMC8 #5 · Counting, Probability & Statistics · ★
The bar graph shows the grades in a mathematics class for the last grading period. If A, B, C, and D are satisfactory grades, what fraction of the grades shown in the graph are satisfactory?
柱状图显示了一个数学班上个评分周期的成绩。如果 A、B、C 和 D 是及格成绩，图表中显示的及格成绩占几分之几？

正确答案：C · 分值：1

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1985 AMC8 #6 · Algebra · ★★
A ream of paper containing 500 sheets is 5 cm thick. Approximately how many sheets of this type of paper would there be in a stack 7.5 cm high?
一令纸含有 500 张，厚度为 5 厘米。同类型的纸叠成 7.5 厘米高的一摞，大约有多少张？

正确答案：D · 分值：1

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1985 AMC8 #7 · Algebra · ★★
A "stair-step" figure is made of alternating black and white squares in each row. Rows 1 through 4 are shown. All rows begin and end with a white square. The number of black squares in the 37th37\text{th} row is
一个"阶梯"图形由每行交替的黑白正方形组成。图中显示了第 1 行到第 4 行。每行都以一个白色正方形开始和结束。第 37 行中黑色正方形的数量是

正确答案：C · 分值：1

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1985 AMC8 #8 · Algebra · ★★
If a = - 2 , the largest number in the set {−3a,4a,24a,a2,1}\displaystyle \{ - 3a, 4a, \frac {24}{a}, a^2, 1\} is
若 a = -2，集合 {−3a,4a,24a,a2,1}\displaystyle \{-3a, 4a, \frac{24}{a}, a^2, 1\} 中最大的数是

正确答案：A · 分值：1

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1985 AMC8 #10 · Algebra · ★★
The fraction halfway between 15\displaystyle \frac{1}{5} and 13\displaystyle \frac{1}{3} (on the number line) is
数轴上 15\displaystyle \frac{1}{5} 和 13\displaystyle \frac{1}{3} 正中间的分数是

正确答案：C · 分值：1

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1985 AMC8 #11 · Geometry · ★★★
A piece of paper containing six joined squares labeled as shown in the diagram is folded along the edges of the squares to form a cube. The label of the face opposite the face labeled X\text{X} is
一张纸上有六个相连的正方形，标记如图所示。将纸沿正方形的边折叠形成一个正方体。与面 X\text{X} 相对的面上的标记是

正确答案：E · 分值：1

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1985 AMC8 #12 · Geometry · ★★★
A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.2cm6.2 \text cm, 8.3cm8.3 \text cm and 9.5cm9.5 \text cm. The area of the square is
一个正方形和一个三角形周长相等。三角形三边长分别为 6.2 cm6.2 \text{ cm}、8.3 cm8.3 \text{ cm} 和 9.5 cm9.5 \text{ cm}。正方形的面积是

正确答案：B · 分值：1

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1985 AMC8 #13 · Algebra · ★★★
If you walk for 45 minutes at a rate of 4 mph4 \text{ mph} and then run for 30 minutes at a rate of 10 mph10\text{ mph} , how many miles will you have gone at the end of one hour and 15 minutes?
如果你以 4 mph4 \text{ mph} 的速度步行 45 分钟，然后以 10 mph10\text{ mph} 的速度跑步 30 分钟，那么在一小时 15 分钟结束时你走了多少英里？

正确答案：B · 分值：1

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1985 AMC8 #14 · Algebra · ★★★
The difference between a 6.5% sales tax and a 6% sales tax on an item priced at $20 before tax is
一件标价 $20 的商品，6.5% 销售税和 6% 销售税的差额是

正确答案：B · 分值：1

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1985 AMC8 #15 · Counting, Probability & Statistics · ★★★
How many whole numbers between 100 and 400 contain the digit 2 ?
100 到 400 之间有多少个整数包含数字 2？

正确答案：C · 分值：1

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1985 AMC8 #16 · Algebra · ★★★
The ratio of boys to girls in Mr. Brown's math class is 2:3. If there are 30 students in the class, how many more girls than boys are in the class?
Mr. Brown 的数学班上男生与女生的比例是 2:3。如果班上有 30 名学生，女生比男生多多少人？

正确答案：D · 分值：1

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1985 AMC8 #17 · Algebra · ★★★
If your average score on your first six mathematics tests was 84 and your average score on your first seven mathematics tests was 85, then your score on the seventh test was
如果你前六次数学考试的平均分是 84，前七次数学考试的平均分是 85，那么你第七次考试的分数是

正确答案：D · 分值：1

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1985 AMC8 #18 · Number Theory · ★★★
Nine copies of a certain pamphlet cost less than $10.00 while ten copies of the same pamphlet (at the same price) cost more than $11.00. How much does one copy of this pamphlet cost?
某种小册子九份的价钱低于 $10.00，而同一小册子十份的价钱（相同单价）高于 $11.00。该小册子一份多少钱？

正确答案：E · 分值：1

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1985 AMC8 #19 · Geometry · ★★★
If the length and width of a rectangle are each increased by 10%, then the perimeter of the rectangle is increased by
如果矩形的长和宽各增加 10%，则矩形的周长增加了

正确答案：B · 分值：1

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1985 AMC8 #20 · Number Theory · ★★★
In a certain year, January had exactly four Tuesdays and four Saturdays. On what day did January 1 fall that year?
某年一月份恰好有四个星期二和四个星期六。那年的一月一日是星期几？

正确答案：C · 分值：1

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1985 AMC8 #21 · Algebra · ★★★★
Mr. Green receives a 10% raise every year. His salary after four such raises has gone up by what percent?
Mr. Green 每年获得 10% 的加薪。经过四次这样的加薪后，他的工资上涨了百分之多少？

正确答案：E · 分值：1

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1985 AMC8 #22 · Counting, Probability & Statistics · ★★★★
Assume every 7-digit whole number is a possible telephone number except those that begin with 0 or 1 . What fraction of telephone numbers begin with 9 and end with 0 ?
假设除了以 0 或 1 开头的号码外，所有七位正整数都是可能的电话号码。以 9 开头且以 0 结尾的电话号码占几分之几？

正确答案：B · 分值：1

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1985 AMC8 #23 · Algebra · ★★★★
King Middle School has 1200 students. Each student takes 5 classes a day. Each teacher teaches 4 classes. Each class has 30 students and 1 teacher. How many teachers are there at King Middle School?
King 中学有 1200 名学生。每名学生每天上 5 节课。每位教师每天教 4 节课。每节课有 30 名学生和 1 名教师。King 中学有多少名教师？

正确答案：E · 分值：1

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1985 AMC8 #24 · Counting, Probability & Statistics · ★★★★
In a magic triangle, each of the six whole numbers 10-15 is placed in one of the circles so that the sum, SS , of the three numbers on each side of the triangle is the same. The largest possible value for SS is
在一个魔力三角形中，六个整数 10-15 各放入一个圆圈，使得三角形每条边上的三个数之和 SS 相同。SS 的最大可能值是

正确答案：D · 分值：1

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1985 AMC8 #25 · Counting, Probability & Statistics · ★★★★
Five cards are lying on a table as shown. Each card has a letter on one side and a whole number on the other side. Jane said, "If a vowel is on one side of any card, then an even number is on the other side." Mary showed Jane was wrong by turning over one card. Which card did Mary turn over?
如图所示，桌上放着五张卡片。每张卡片一面是字母、另一面是整数。Jane 说：「如果任何一张卡片的一面是元音字母，那么它的另一面就是偶数。」Mary 只翻开一张卡片就证明了 Jane 是错的。Mary 翻开的是哪张卡片？

正确答案：A · 分值：1

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