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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2025 AMC8 #14 · Counting, Probability & Statistics · ★★★
A number N is inserted into the list 2 , 6 , 7 , 7 , 28 . The mean is now twice as great as the median. What is N ? 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
用同分类同星级进入练习 →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 m and M 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2025 AMC8 #21 · Counting, Probability & Statistics · ★★★★
The Konigsberg School has assigned grades 1 through 7 to pods A through G , 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 F ? 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
用同分类同星级进入练习 →2025 AMC8 #25 · Counting, Probability & Statistics · ★★★★★
Makayla finds all the possible ways to draw a path in a 5×5 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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 53 的鞋是红色，其余为白色；其中 32 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2023 AMC8 #21 · Counting, Probability & Statistics · ★★★★
Alina writes the numbers 1,2,…,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,…,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
用同分类同星级进入练习 →2023 AMC8 #23 · Counting, Probability & Statistics · ★★★★
Each square in a 3×3 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 2×2 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
用同分类同星级进入练习 →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, added to the number on Spinner 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
用同分类同星级进入练习 →2022 AMC8 #14 · Counting, Probability & Statistics · ★★★
In how many ways can the letters in BEEKEEPER be rearranged so that two or more 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2022 AMC8 #23 · Counting, Probability & Statistics · ★★★★
A△ or ◯ is placed in each of the nine squares in a 3 -by- 3 grid. Shown below is a sample configuration with three △s in a line. How many configurations will have three △s in a line and three ◯s 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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 52 . 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2016 AMC8 #13 · Counting, Probability & Statistics · ★★★
Two different numbers are randomly selected from the set {−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} 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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: 42,47,53,53,58,58,58,61,64,65,73 If his team scores 40 in the 12th 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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} 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2015 AMC8 #23 · Counting, Probability & Statistics · ★★★★
Tom has twelve slips of paper which he wants to put into five cups labeled A , B , C , D , E . 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 A to E . 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 E and a slip with 3 goes into cup B , 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2013 AMC8 #5 · Counting, Probability & Statistics · ★
Hammie is in 6th 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2012 AMC8 #11 · Counting, Probability & Statistics · ★★★
The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, and x are all equal. What is the value of x ? 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2012 AMC8 #22 · Counting, Probability & Statistics · ★★★★
Let R 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 R ? 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
用同分类同星级进入练习 →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. 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2011 AMC8 #19 · Counting, Probability & Statistics · ★★★
How many rectangles are in this figure?
正确答案：D · 分值：1
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2008 AMC8 #2 · Counting, Probability & Statistics · ★
The ten-letter code BEST OF LUCK represents the ten digits 0-9 , in order. What 4-digit number is represented by the code word 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2008 AMC8 #14 · Counting, Probability & Statistics · ★★★
Three A’s, three B’s, and three C’s are placed in the nine spaces so that each row and column contain one of each letter. If 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
用同分类同星级进入练习 →2008 AMC8 #19 · Counting, Probability & Statistics · ★★★
Eight points are spaced around at intervals of one unit around a 2×2 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2007 AMC8 #11 · Counting, Probability & Statistics · ★★★
Tiles $I, II, III$ and IV are translated so one tile coincides with each of the rectangles A, B, C and D . 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 C ? 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2007 AMC8 #21 · Counting, Probability & Statistics · ★★★
Two cards are dealt from a deck of four red cards labeled A , B , C , D and four green cards labeled A , B , C , D . 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2004 AMC8 #8 · Counting, Probability & Statistics · ★★
Find the number of two-digit positive integers whose digits total 7 .
正确答案：B · 分值：1
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →2004 AMC8 #21 · Counting, Probability & Statistics · ★★★
Spinners A and B 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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?
正确答案：D · 分值：1
用同分类同星级进入练习 →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?
正确答案：B · 分值：1
用同分类同星级进入练习 →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
正确答案：E · 分值：1
用同分类同星级进入练习 →2002 AMC8 #12 · Counting, Probability & Statistics · ★★
A board game spinner is divided into three regions labeled A , B and C . The probability of the arrow stopping on region A is 31 and on region B is 21 . The probability of the arrow stopping on region C is: 一种棋盘游戏的转盘分成 A、B、C 三个区域。已知箭头停在区域 A 的概率为 31，停在区域 B 的概率为 21。那么箭头停在区域 C 的概率是： 正确答案：B · 分值：1
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →1998 AMC8 #11 · Counting, Probability & Statistics · ★★★
Harry has 3 sisters and 5 brothers. His sister Harriet has S sisters and B brothers. What is the product of S and B ? Harry 有 3 个姐妹和 5 个兄弟。他的姐妹 Harriet 有 S 个姐妹和 B 个兄弟。S 和 B 的乘积是多少？ 正确答案：C · 分值：1
用同分类同星级进入练习 →1998 AMC8 #19 · Counting, Probability & Statistics · ★★★
Tamika selects two different numbers at random from the set {8,9,10} and adds them. Carlos takes two different numbers at random from the set {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} 中随机选两个不同的数并相加。Carlos 从集合 {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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →1996 AMC8 #12 · Counting, Probability & Statistics · ★★★
What number should be removed from the list 1,2,3,4,5,6,7,8,9,10,11 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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} so that the sum of the three numbers is even? 从集合 {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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →1993 AMC8 #5 · Counting, Probability & Statistics · ★
Which one of the following bar graphs could represent the data from the circle graph?
正确答案：C · 分值：1
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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 5×15 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →1993 AMC8 #23 · Counting, Probability & Statistics · ★★★★
Five runners, P , Q , R , S , T , have a race, and P beats Q , P beats R , Q beats S , and T finishes after P and before Q . Who could NOT have finished third in the race? 五名跑步者 P、Q、R、S、T 参加比赛。P 击败 Q，P 击败 R，Q 击败 S，T 在 P 之后、Q 之前完赛。谁不可能获得第三名？ 正确答案：C · 分值：1
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →1992 AMC8 #19 · Counting, Probability & Statistics · ★★★
The distance between the 5th and 26th 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 5th and 26th 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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
正确答案：B · 分值：1
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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} . How many of these sets contain a 5 ? 从 {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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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 C? 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 C 成绩的学生占百分之多少？ 正确答案：D · 分值：1
用同分类同星级进入练习 →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 17th 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
用同分类同星级进入练习 →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 41 , 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 41，则袋中绿球的数量是 正确答案：B · 分值：1
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →1988 AMC8 #16 · Counting, Probability & Statistics · ★★★
Placing no more than one X in each small square, what is the greatest number of X 's that can be put on the grid shown without getting three X 's in a row vertically, horizontally, or diagonally? 每个小方格最多放一个 X，在所示网格上最多能放多少个 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？ 正确答案：E · 分值：1
用同分类同星级进入练习 →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
用同分类同星级进入练习 →1988 AMC8 #21 · Counting, Probability & Statistics · ★★★★
A fifth number, n , is added to the set {3,6,9,10} to make the mean of the set of five numbers equal to its median. The number of possible values of n is 将第五个数 n 加入集合 {3,6,9,10} 中，使得这五个数的平均数等于其中位数。n 的可能值有多少个？ 正确答案：C · 分值：1
用同分类同星级进入练习 →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: 1:01, 4:44, and 12:21. 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：1:01、4:44 和 12:21。在 12 小时内，共有多少个时间是回文数？ 正确答案：A · 分值：1
用同分类同星级进入练习 →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: "Bret is next to Carl." "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：
"Bret 挨着 Carl。" "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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →1986 AMC8 #9 · Counting, Probability & Statistics · ★★
Using only the paths and the directions shown, how many different routes are there from M to N ? 只使用所示路径和方向，从 M 到 N 有多少条不同路线？ 正确答案：E · 分值：1
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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
用同分类同星级进入练习 →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, S , of the three numbers on each side of the triangle is the same. The largest possible value for S 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 S 相同。S 的最大可能值是 正确答案：D · 分值：1
用同分类同星级进入练习 →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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