ΒΆ 1986 AMC8 Problems and Solutions
Problem Set Workbook
Access the downloadable workbook for 1986 AMC8 problems here.
Discussion Forum
Engage in discussion about the 1986 AMC8 math contest by visiting Random Math 1986 AMC8 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 1986 AMC8 problems, please refer below:
Problem 1: In July inches of rain fell in Cherrapunji, India. What was the average rainfall in inches per hour during that month?
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Problem 2: Which of the following numbers has the largest reciprocal?
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Problem 3: The smallest sum one could get by adding three different numbers from the set is
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Problem 4: The product is closest to
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Problem 5: A contest began at noon one day and ended minutes later. At what time did the contest end?
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A. p.m.
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E. a.m.
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Problem 6:
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Problem 7: How many whole numbers are between and
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Problem 8: In the product shown, is a digit. The value of is
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Problem 9: Using only the paths and the directions shown, how many different routes are there from to
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Problem 10: A picture feet across is hung in the center of a wall that is feet wide. How many feet from the end of the wall is the nearest edge of the picture?
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Problem 11: If means , then is
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Problem 12: The table to the right displays the grade distribution of the students in a mathematics class on the last two tests. For example, exactly one student received a '' on Test and a '' on Test (see circled entry). What percent of the students received
the same grade on both tests?
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Problem 13: The perimeter of the polygon shown is
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Problem 14: If and , then the largest value of the quotient is
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Problem 15: Sale prices at the Ajax Outlet Store are below original prices. On Saturdays an additional discount of off the sale price is given. What is the Saturday price of a coat whose original price is
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Problem 16: 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 of the chain's hamburgers are sold in the fall, how many million hamburgers are sold in the winter?
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Problem 17: Let be an odd whole number and let be any whole number. Which of the following statements about the whole number Is always true?
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A. it is always odd
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C. it is even onIy if is even
D. it is odd only if is odd
E. it is odd only if is even
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Problem 18: A rectangular grazing area is to be fenced off on three sides using part of a meter rock wall as the fourth side. Fence posts are to be placed every 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 by
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Problem 19: At the beginning of a trip, the mileage odometer read miles. The driver filled the gas tank wtth gallons of gasoline. During the trip, the driver filled his tank again with gallons of gasoline when the odometer read . At the end of the trip, the driver filled the tank agaln with gallons of gasoline. The odometer read . To the nearest tenth, what was the car's average miles-per-gallon for the entire trip?
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Problem 20: The value of the expression is closest to
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Problem 21: Suppose one of the eight lettered identical squares is included with the four squares in the T-shaped figure outlined. How many of the resulting figures can be folded into a topless cubical box?
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Problem 22: Alan, Beth, Carlos, and Diana were discussIng their possible grades in mathematics class this grading period. Alan said, "If I get an , then Beth will get an ." Beth said, "If I get an , then Carlos will get an ." Carlos said, "If I get an , then Diana will get an ." All of these statements were true, but only two of the students received an . Which two receΔ±ved 's?
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A. Alan, Beth
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Problem 23: The large circle has diameter . The two small circles have their centers on and just touch at , the center of the large circle. If each small circle has radius , what is the value of the ratio of the area of the shaded region to the area of one of the small circles?
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A. between and
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Problem 24: The 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 the three lunch groups. The probability that three friends, Al, Bob, and Carol, will be assigned to the same lunch group is approximately
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Problem 25: Which of the following sets of whole numbers has the largest average?
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A. multiples of between and
B. multiples of between and
C. multiples of between and
D. multiples of between and
E. multiples of between and
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The problems on this page are the property of the MAA's American Mathematics Competitions