¶ 1992 AMC8 Problems and Solutions
Problem Set Workbook
Access the downloadable workbook for 1992 AMC8 problems here.
Discussion Forum
Engage in discussion about the 1992 AMC8 math contest by visiting Random Math 1992 AMC8 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 1992 AMC8 problems, please refer below:
Problem 1:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 2: Which of the following is not equal to
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 3:
What is the largest difference that can be formed by subtracting two numbers chosen from the set
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 4: During the softball season, Judy had hits. Among her hits were home run, triple and doubles. The rest of her hits were singles. What percent of her hits were singles?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 5: A circle of diameter is removed from a rectangle, as shown. Which whole number is closest to the area of the shaded region?
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 6: Suppose that
means . For example,
is . Then the sum
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 7: The digit-sum of is . How many -digit whole numbers, whose digit-sum is , are even?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 8: A store owner bought pencils at each. If he sells them for each, how many of them must he sell to make a profit of exactly
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 9: The population of a small town is . The graph indicates the number of females and males in the town, but the vertical scale-values are omitted. How many males live in the town?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 10: An isosceles right triangle with legs of length is partitioned into congruent triangles as shown. The shaded area is
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 11: The bar graph shows the results of a survey on color preferences. What percent preferred blue?
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 12: The five tires of a car (four road tires and a full-sized spare) were rotated so that each tire was used the same number of miles during the first miles the car traveled. For how many miles was each tire used?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 13: Five test scores have a mean (average score) of , a median (middle score) of and a mode (most frequent score) of . The sum of the two lowest test scores is
Answer Choices:
A.
B.
C.
D.
E. not determined by the information given
Solution:
Problem 14: When four gallons are added to a tank that is one-third full, the tank is then one-half full. The capacity of the tank in gallons is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 15: What is the letter in this sequence?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 16: Which cylinder has twice the volume of the cylinder shown below?
Answer Choices:
A. 
B. 
C. 
D. 
E. None of the above
Solution:
Problem 17: The sides of a triangle have lengths , and , where is a whole number. What is the smallest possible value of
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 18: On a trip, a car traveled miles in an hour and a half, then was stopped in traffic for minutes, then traveled miles during the next hours. What was the car's average speed in miles per hour for the -hour trip?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 19: The distance between the and exits on an interstate highway is miles. If any two exits are at least miles apart, then what is the largest number of miles there can be between two consecutive exits that are between the and exits?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 20: Which pattern of identical squares could NOT be folded along the lines shown to form a cube?
Answer Choices:
A.
.jpg)
.jpg)
.jpg)
.jpg)
Solution:
Problem 21: Northside's Drum and Bugle Corps raised money for a trip. The drummers and bugle players kept separate sales records. According to the double bar graph, in what month did one group's sales exceed the other's by the greatest percent?
.jpg)
Answer Choices:
A. Jan
B. Feb
C. Mar
D. Apr
E. May
Solution:
Problem 22: Eight square tiles are arranged as shown so their outside edges form a polygon with a perimeter of units. Two additional tiles of the same size are added to the figure so that at least one side of each tile is shared with a side of one of the squares in the original figure. Which of the following could be the perimeter of the new figure?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 23: If two dice are tossed, the probability that the product of the numbers showing on the tops of the dice is greater than is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 24: Four circles of radius are arranged as shown. Their centers are the vertices of a square. The area of the shaded region is closest to
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Problem 25: One half of the water is poured out of a full container. Then one third of the remainder is poured out. Continue the process: one fourth of the remainder for the third pouring, one fifth of the remainder for the fourth pouring, etc. After how many pourings does exactly one tenth of the original water remain?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions