1992 AJHSME Problems
1992 AJHSME (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
Problem 2
Which of the following is not equal to ?
Problem 3
What is the largest difference that can be formed by subtracting two numbers chosen from the set ?
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?
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?
Problem 6
Suppose that means . For example, is . Then the sum is
Problem 7
The digit-sum of is . How many 3-digit whole numbers, whose digit-sum is , are even?
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 ?
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?
Problem 10
An isosceles right triangle with legs of length is partitioned into congruent triangles as shown. The shaded area is
Problem 11
The bar graph shows the results of a survey on color preferences. What percent preferred blue?
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?
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
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
Problem 15
What is the letter in this sequence?
Problem 16
Which cylinder has twice the volume of the cylinder shown above?
Problem 17
The sides of a triangle have lengths , , and , where is a whole number. What is the smallest possible value of ?
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?
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?
Problem 20
Which pattern of identical squares could NOT be folded along the lines shown to form a cube?
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?
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?
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
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
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?
See also
1992 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by 1991 AJHSME |
Followed by 1993 AJHSME | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.