ΒΆ 2008 AMC8 Problems and Solutions
Problem Set Workbook
Access the downloadable workbook for 2008 AMC8 problems here.
Discussion Forum
Engage in discussion about the 2008 AMC8 math contest by visiting Random Math 2008 AMC8 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2008 AMC8 problems, please refer below:
Problem 1: Susan had to spend at the carnival. She spent on food and twice as much on rides. How many dollars did she have left to spend?
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Problem 2: The ten-letter code represents the ten digits , in order. What -digit number is represented by the code word
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Problem 3: If February is a month that contains Friday the , what day of the week is February
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A. Sunday
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E. Saturday
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Problem 4: In the figure, the outer equilateral triangle has area , the inner equilateral triangle has area , and the three trapezoids are congruent. What is the area of one of the trapezoids?
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Problem 5: Barney Schwinn notices that the odometer on his bicycle reads , a palindrome, because it reads the same forward and backward. After riding more hours that day and the next, he notices that the odometer shows another palindrome, . What was his average speed in miles per hour?
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Problem 6: In the figure, what is the ratio of the area of the gray squares to the area of the white squares?
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Problem 7: If , what is
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Problem 8: Candy sales of the Boosters Club for January through April are shown. What were the average sales per month in dollars?
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Problem 9: In Tycoon Tammy invested for two years. During the first year her investment suffered a loss, but during the second year the remaining investment showed a gain. Over the two-year period, what was the change in Tammy's investment?
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A. loss
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Problem 10: The average age of the people in Room is . The average age of the people in Room is . If the two groups are combined, what is the average age of all the people?
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Problem 11: Each of the 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 students have a cat. How many students have both a dog and a cat?
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Problem 12: A ball is dropped from a height of meters. On its first bounce it rises to a height of meters. It keeps falling and bouncing to of the height it reached in the previous bounce. On which bounce will it not rise to a height of meters?
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Problem 13: Mr. Harman needs to know the combined weight in pounds of three boxes he wants to mail. However, the only available scale is not accurate for weights less than pounds or more than pounds. So the boxes are weighed in pairs in every possible way. The results are and pounds. What is the combined weight in pounds of the three boxes?
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Problem 14: Three As, three Bs and three Cs 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?
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Problem 15: In Theresa's first basketball games, she scored , and points. In her ninth game, she scored fewer than points and her points-per-game average for the nine games was an integer. Similarly in her tenth game, she scored fewer than points and her points-per-game average for the games was also an integer. What is the product of the number of points she scored in the ninth and tenth games?
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Problem 16: A shape is created by joining seven unit cubes, as shown. What is the ratio of the volume in cubic units to the surface area in square units?
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Problem 17: Ms. Osborne asks each student in her class to draw a rectangle with integer side lengths and a perimeter of units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles?
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Problem 18: Two circles that share the same center have radii meters and meters. An aardvark runs along the path shown, starting at and ending at . How many meters does the aardvark run?
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Problem 19: Eight points are spaced at intervals of one unit around a square, as shown. Two of the points are chosen at random. What is the probability that the points are one unit apart?
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Problem 20: The students in Mr. Neatkin's class took a penmanship test. Two-thirds of the boys and of the girls passed the test, and an equal number of boys and girls passed the test. What is the minimum possible number of students in the class?
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Problem 21: Jerry cuts a wedge from a -cm cylinder of bologna as shown by the dashed curve. Which answer choice is closest to the volume of his wedge in cubic centimeters?
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Problem 22: For how many positive integer values of are both and three-digit whole numbers?
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Problem 23: In square and . What is the ratio of the area of to the area of square
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Problem 24: Ten tiles numbered through 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?
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Problem 25: Margie's winning art design is shown. The smallest circle has radius inches, with each successive circle's radius increasing by inches. Approximately what percent of the design is black?
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The problems on this page are the property of the MAA's American Mathematics Competitions