¶ 1985 AMC8 Problems and Solutions
Problem Set Workbook
Access the downloadable workbook for 1985 AMC8 problems here.
Discussion Forum
Engage in discussion about the 1985 AMC8 math contest by visiting Random Math 1985 AMC8 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 1985 AMC8 problems, please refer below:
Problem 1:
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Problem 4: The area of polygon , In square units, is
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Problem 5: The bar graph shows the grades in a mathematics class for the last grading period. If A, B, C and D are satisfactory grades, what fraction of the grades shown in the graph are satisfactory?
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Problem 6: A ream of paper containing sheets is thick. Approximately how many sheets of this type of paper would there be in a stack
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Problem 7: A "stair-step" figure s made up of alternating black and white squares in each row. Rows through are shown. All rows begin and end with a white square. The number of black squares in the th row is
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Problem 8: If , the largest number in the set is
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Problem 9: The product of the factors
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Problem 10: The fraction halfway between and (on the number line) is
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Problem 11: A plece of paper containing six joined squares labeled as shown in the diagram is folded along the edges of the squares to form a cube. The label of the face opposite the face labeled is
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Problem 12: A square and a triangle have equal perimeters. The lengths of the three sides of the trlangle are and . The area of the square is
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Problem 13: If you walk for minutes at a rate of and then run for minutes at a rate of, , how many miles have you gone at the end of one hour and minutes?
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Problem 14: The difference between a sales tax and a sales tax on an item priced at before tax is
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Problem 15: How many whole numbers between and contain the digit
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Problem 16: The ratio of boys to girls in Mr. Brown's math class is . If there are students in the class, how many more girls than boys are in the class?
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Problem 17: If your average score on your first six mathematics tests was and your average score on your first seven mathematics tests was , then your score on the seventh test was
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Problem 18: Nine copies of a certain pamphlet cost less than while ten coples of the same pamphlet (at the same price) cost more than . How much does one copy of this pamphlet cost?
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Problem 19: If the length and width of a rectangle are each increased by , then the perimeter of the rectangle is increased by
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Problem 20: In a certain year, January had exactly four Tuesdays and four Saturdays. On what day did January fall that year?
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Problem 21: Mr. Green recelves a raise every year. His salary after four such raises has gone up by: what percent?
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Problem 22: Assume every -digit whole number is a possible telephone number except those which begin with or . What fraction of telephone numbers begin with and end with
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Problem 23: King Middle School has students. Each student takes classes a day. Each teacher teaches classes. Each class has students and teacher. How many teachers are there at King Middle School?
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Problem 24: In a magic trlangle, each of the six whole numbers is placed in one of the circles so that the sum, , of the three numbers on each side of the triangle is the same. The largest possible value for is
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Problem 25: Five cards are lying on a table as shown. Each card has a letter on one side and a whole number on the other side. Jane said, "If a vowel is on one side of any card, then an even number is on the other side." Mary showed Jane was wrong by turning over one card. Which card did Mary turn over?
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The problems on this page are the property of the MAA's American Mathematics Competitions