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1992 AMC 8

Question 1

What is the value of the following expression?

$$
\scriptsize \dfrac{10 - 9 + 8 - 7 + 6 - 5 + 4 - 3 + 2 - 1}{1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9}
$$
  1. $-1$
  2. $1$
  3. $5$
  4. $9$
  5. $10$

Question 2

Which of the following is **not** equal to $\dfrac54?$
  1. $\dfrac{10}{8}$
  2. $1\dfrac14$
  3. $1\dfrac{3}{12}$
  4. $1\dfrac15$
  5. $1\dfrac{10}{40}$

Question 3

What is the largest difference that can be formed by subtracting two numbers chosen from the set $\{-16, -4, 0, 2, 4, 12\}?$
  1. $10$
  2. $12$
  3. $16$
  4. $28$
  5. $48$

Question 4

During the softball season, Judy had $35$ hits. Among her hits were $1$ home run, $1$ triple, and $5$ doubles. The rest of her hits were singles. What percent of her hits were singles?
  1. $28\%$
  2. $35\%$
  3. $70\%$
  4. $75\%$
  5. $80\%$

Question 5

A circle of diameter $1$ is removed from a $2 \times 3$ rectangle, as shown. Which whole number is closest to the area of the shaded region?

Question illustration
  1. $1$
  2. $2$
  3. $3$
  4. $4$
  5. $5$

Question 6

A triangular expression with top entry $a$, lower-left entry $b$, and lower-right entry $c$ means $a+b-c$, as shown below. What is the indicated sum?

Question illustration
  1. $-2$
  2. $-1$
  3. $0$
  4. $1$
  5. $2$

Question 7

The digit-sum of $998$ is $9 + 9 + 8 = 26.$ How many $3$-digit whole numbers, whose digit-sum is $26$, are even?
  1. $1$
  2. $2$
  3. $3$
  4. $4$
  5. $5$

Question 8

A store owner bought $1500$ pencils at $\$0.10$ each. If he sells them for $\$0.25$ each, how many of them must he sell to make a profit of exactly $\$100.00?$
  1. $400$
  2. $667$
  3. $1000$
  4. $1500$
  5. $1900$

Question 9

The population of a small town is $480.$ The graph indicates the numbers of females and males in the town, but the vertical scale values are omitted. The bars labeled $F$ and $M$ represent females and males, respectively. How many males live in the town?

Question illustration
  1. $120$
  2. $160$
  3. $200$
  4. $240$
  5. $360$

Question 10

An isosceles right triangle with legs of length $8$ is partitioned into $16$ congruent triangles as shown. The shaded area is

Question illustration
  1. $10$
  2. $20$
  3. $32$
  4. $40$
  5. $64$

Question 11

The bar graph shows the results of a survey on color preferences. From left to right, the bars represent red, blue, brown, pink, and green. What percent preferred blue?

Question illustration
  1. $20\%$
  2. $24\%$
  3. $30\%$
  4. $36\%$
  5. $42\%$

Question 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 $30{,}000$ miles the car traveled. For how many miles was each tire used?
  1. $6000$
  2. $7500$
  3. $24{,}000$
  4. $30{,}000$
  5. $37{,}500$

Question 13

Five test scores have a mean (average score) of $90,$ a median (middle score) of $91,$ and a mode (most frequent score) of $94.$ The sum of the two lowest test scores is
  1. $170$
  2. $171$
  3. $176$
  4. $177$
  5. not determined by the information given

Question 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
  1. $8$
  2. $12$
  3. $20$
  4. $24$
  5. $48$

Question 15

What is the $1992$nd letter in this sequence?

ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC$\cdots$
  1. $A$
  2. $B$
  3. $C$
  4. $D$
  5. $E$

Question 16

Which cylinder has twice the volume of the cylinder shown at right?

Question illustration

**(A)** Question illustration

**(B)** Question illustration

**(C)** Question illustration

**(D)** Question illustration
  1. Choice A shown above
  2. Choice B shown above
  3. Choice C shown above
  4. Choice D shown above
  5. None of the above

Question 17

The sides of a triangle have lengths $6.5,$ $10,$ and $s,$ where $s$ is a whole number. What is the smallest possible value of $s?$
  1. $3$
  2. $4$
  3. $5$
  4. $6$
  5. $7$

Question 18

On a trip, a car traveled $80$ miles in an hour and a half, then was stopped in traffic for $30$ minutes, then traveled $100$ miles during the next $2$ hours. What was the car’s average speed in miles per hour for the $4$-hour trip?
  1. $45$
  2. $50$
  3. $60$
  4. $75$
  5. $90$

Question 19

The distance between the $5$th and $26$th exits on an interstate highway is $118$ miles. If any two exits are at least $5$ miles apart, then what is the largest number of miles there can be between two consecutive exits that are between the $5$th and $26$th exits?
  1. $8$
  2. $13$
  3. $18$
  4. $47$
  5. $98$

Question 20

Which pattern of identical squares could **not** be folded along the lines shown to form a cube?

**(A)** Question illustration

**(B)** Question illustration

**(C)** Question illustration

**(D)** Question illustration

**(E)** Question illustration
  1. Choice A shown above
  2. Choice B shown above
  3. Choice C shown above
  4. Choice D shown above
  5. Choice E shown above