¶ 1987 AMC8 Problems and Solutions
Problem Set Workbook
Access the downloadable workbook for 1987 AMC8 problems here.
Discussion Forum
Engage in discussion about the 1987 AMC8 math contest by visiting Random Math 1987 AMC8 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 1987 AMC8 problems, please refer below:
Problem 1:
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Problem 2:
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Problem 4: Martians measure angles in clerts. There are clerts in a a full circle. How many clerts are there in a right angle?
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Problem 5: The area of the rectangular region is
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Problem 6: The smallest product one could obtain by multiplying two numbers in the set is
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Problem 7: The large cube shown is made up of 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
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Problem 8: If and are nonzero digits, then the number of three whole numbers is
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Problem 9: Wen finding the sum , the least common denominator used is
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Problem 11: The sum is between
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Problem 12: What fraction of the large by rectangular region is shaded?
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Problem 13: Which of the following fractions has the largest value?
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Problem 14: A computex can do additions per second. How many additions can it do in one hour?
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Problem 15: The sale ad read: "Buy three tires ar the regular price and get the fourth tire for Sam paid for a set of four tires at the sale. What was the regular price of one tire?
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Problem 16: Joyce made of her first shots in the first three games of this basketball season, so her seasonal shooting average was .
In her next game, she took shots and raised her seasonal shooting average to . How many of these shots did she make?
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Problem 17: Abby, Bret, Carl, and Dana are seated in a row on four seats numbered to . 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 . Who is sitting in seat
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Problem 18: Half the people in a room left. One third of those remaining started to dance. There were then people who were not dancing. The original number of people in the room was
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Problem 19: A calculator has a squaring key which replaces the current number displayed with its square. For example, if the display is and the key is depressed, then the display becomes . If the display reads , how many times must you depress the key to produce a displayed number greater than
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Problem 20: If a whole number is not prime, then the whole number is not prime." A value of which shows this statement to be false is
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Problem 21: Suppose means , the reciprocal of . For example, . How many of the following statements are true?
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Problem 22: is a rectangle, is the center of the circle, and is on the circle. If and , then the area of the shaded region is between
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Problem 23: Assume the adjoining chart shows the U.S. population, in millions, for each region by ethnic group. To the nearest
percent, what percent of the U.S. Black population lived in the South?
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Problem 24: A multiple choice examination consists of questions. The scoring is for each correct answer, for each incorrect answer, and for each unanswered question. John's score on the examination is . What is the maximum number of questions he could have answered correctly?
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Problem 25: Ten balls numbered to 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
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The problems on this page are the property of the MAA's American Mathematics Competitions