2002 AMC 8 Problems

Problem 1

A circle and two distinct lines are drawn on a sheet of paper. What is the largest possible number of points of intersection of these figures?

Solution

Problem 2

How many different combinations of <dollar/>5 bills and <dollar/>2 bills can be used to make a total of <dollar/>17? Order does not matter in this problem.

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Problem 3

What is the smallest possible average of four distinct positive even integers?

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Problem 4

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?

Solution

Problem 5

Carlos Montado was born on Saturday, November 9, 2002. On what day of the week will Carlos be 706 days old?

Solution

Problem 6

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. One of these graphs shows the volume of water in the birdbath during the filling time and continuing into the overflow time. Which one is it?

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Solution

Problem 7

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?

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Solution

Juan's Old Stamping Grounds

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.)

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Problem 8

How many of his European stamps were issued in the '80s?

Solution

Problem 9

His South American stamps issued before the '70s cost him

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Problem 10

The average price of his '70s stamps is closest to

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Problem 11

A sequence of squares is made of identical square tiles. The edge of each square is one tile length longer than the edge of the previous square. The first three squares are shown. How many more tiles does the seventh square require than the sixth?

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Solution

Problem 12

A board game spinner is divided into three regions labeled , and . The probability of the arrow stopping on region is and on region is . The probability of the arrow stopping on region is

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Solution

Problem 13

For his birthday, Bert gets a box that holds 125 jellybeans when filled to capacity. A few weeks later, Carrie gets a larger box full of jellybeans. Her box is twice as high, twice as wide and twice as long as Bert's. Approximately, how many jellybeans did Carrie get?

Solution

Problem 14

A merchant offers a large group of items at 30% off. Later, the merchant takes 20% off these sale prices and claims that the final price of these items is 50% off the original price. The total discount is

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Problem 15

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Problem 16

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Problem 17

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Problem 18

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Problem 19

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Problem 20

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Problem 21

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Problem 22

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Problem 23

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Problem 24

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Problem 25

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See Also

• AMC 8
• AMC 8 Problems and Solutions
• Mathematics competition resources