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
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？
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？
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?
Betty drives a truck to deliver packages in a neighborhood whose street map is shown below. Betty starts at the factory (labled F ) and drives to location A , then B , then C , before returning to F . What is the shortest distance, in blocks, she can drive to complete the route?
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% ?
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?
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?
In the figure below, ABCD is a rectangle with sides of length AB = 5 inches and AD = 3 inches. Rectangle ABCD is rotated 90∘ clockwise around the midpoint of side DC to give a second rectangle. What is the total area, in square inches, covered by the two overlapping rectangles?
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?
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?
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?
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?
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?
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?
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?
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?
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?
Harold made a plum pie to take on a picnic. He was able to eat only 41 of the pie, and he left the rest for his friends. A moose came by and ate 31 of what Harold left behind. After that, a porcupine ate 31 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 41，剩下的留给他的朋友们。一只驼鹿经过，吃掉了 Harold 剩下的 31。在那之后，一只豪猪吃掉了驼鹿剩下的派的 31。问豪猪走后，原来的派还剩下多少？
When three positive integers a, b, and c are multiplied together, their product is $100$. Suppose a < b < c. In how many ways can the numbers be chosen?
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？
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?
A cup of boiling water ( 212∘F ) is placed to cool in a room whose temperature remains constant at 68∘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?
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?
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?
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?
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?
Akash's birthday cake is in the form of a 4×4×4 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 1×1×1 inch, as shown below. How many small pieces will have icing on exactly two sides?
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?
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 ?
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?
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?
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?
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?
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？
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?
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?
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?
Let Z 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 Z ?
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？
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?
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?
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?
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?
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？
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?
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?
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 $1A2 . What is the missing digit A 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？
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?
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?
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=6×5. What is the missing number in the top row?
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?
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)?
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？
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?
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?
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?
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?
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?
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?
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?
The taxi fare in Gotham City is $2.40 for the first 21 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 ?
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?
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？
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?
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?
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?
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?
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?
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？
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?
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?
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?
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?
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?
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?
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.
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?
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?
Initially, a spinner points west. Chenille moves it clockwise 241 revolutions and then counterclockwise 343 revolutions. In what direction does the spinner point after the two moves?
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？
In quadrilateral ABCD , sides AB and BC both have length 10, sides CD and DA both have length 17, and the measure of angle ADC is 60∘. What is the length of diagonal AC?
四边形 ABCD 中，边 AB 和 BC 的长度都是 10，边 CD 和 DA 的长度都是 17，且 ∠ADC=60∘。那么对角线 AC 的长度是多少？
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？
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?
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？
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?
Handy Aaron helped a neighbor 141 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?
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？
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?
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.
∘ Art's cookies are trapezoids:
∘ Roger's cookies are rectangles:
∘ Paul's cookies are parallelograms:
∘ 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？
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?
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?
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?
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?
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
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：
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.
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?
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?
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?
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?
Figure ABCD is a square. Inside this square three smaller squares are drawn with the side lengths as labeled. The area of the shaded L -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？
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
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？
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?
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？
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?
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
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
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?
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
Each of the letters W , X , Y , and Z represents a different integer in the set {1,2,3,4} , but not necessarily in that order. If XW−ZY=1 , then the sum of W and Y is
字母 W、X、Y 和 Z 各代表集合 {1,2,3,4} 中不同的整数，但不一定按此顺序。若 XW−ZY=1，则 W 与 Y 之和为
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?
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} . Add two of these numbers. Multiply their sum by the third number.
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?
Points A and B are 10 units apart. Points B and C are 4 units apart. Points C and D are 3 units apart. If A and D are as close as possible, then the number of units between them is
点 A 和 B 相距 10 个单位。点 B 和 C 相距 4 个单位。点 C 和 D 相距 3 个单位。如果 A 和 D 尽可能接近，则它们之间的距离是多少个单位？
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
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?
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?
Three congruent circles with centers P , Q , and R are tangent to the sides of rectangle ABCD as shown. The circle centered at Q has diameter 4 and passes through points P and R . The area of the rectangle is
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?
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. 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 开始工作，并在中午开始午休，那么她的工作日将结束于
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
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?
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
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?
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 ?
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?
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?
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?
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?
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
Betty used a calculator to find the product 0.075×2.56 . She forgot to enter the decimal points. The calculator showed 19200 . If Betty had entered the decimal points correctly, the answer would have been
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
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
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?
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 37th row is