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Difference between revisions of "1992 AJHSME Problems"
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== Problem 19 ==
 
== Problem 19 ==
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The distance between the <math>5^\text{th}</math> and <math>26^\text{th}</math> exits on an interstate highway is <math>118</math> miles.  If any two exits are at least <math>5</math> miles apart, then what is the largest number of miles there can be between two consecutive exits that are between the <math>5^\text{th}</math> and <math>26^\text{th}</math> exits?
 +
 +
<math>\text{(A)}\ 8 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 18 \qquad \text{(D)}\ 47 \qquad \text{(E)}\ 98</math>
  
 
[[1992 AJHSME Problems/Problem 19|Solution]]
 
[[1992 AJHSME Problems/Problem 19|Solution]]
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== Problem 23 ==
 
== Problem 23 ==
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 +
If two dice are tossed, the probability that the product of the numbers showing on the tops of the dice is greater than <math>10</math> is
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 +
<math>\text{(A)}\ \dfrac{3}{7} \qquad \text{(B)}\ \dfrac{17}{36} \qquad \text{(C)}\ \dfrac{1}{2} \qquad \text{(D)}\ \dfrac{5}{8} \qquad \text{(E)}\ \dfrac{11}{12}</math>
  
 
[[1992 AJHSME Problems/Problem 23|Solution]]
 
[[1992 AJHSME Problems/Problem 23|Solution]]
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== Problem 25 ==
 
== Problem 25 ==
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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?
 +
 +
<math>\text{(A)}\ 6 \qquad \text{(B)}\ 7 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 10</math>
  
 
[[1992 AJHSME Problems/Problem 25|Solution]]
 
[[1992 AJHSME Problems/Problem 25|Solution]]

Revision as of 21:48, 19 August 2009

Problem 1

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

$\text{(A)}\ -1 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 10$

Solution

Problem 2

Which of the following is not equal to $\dfrac{5}{4}$?

$\text{(A)}\ \dfrac{10}{8} \qquad \text{(B)}\ 1\dfrac{1}{4} \qquad \text{(C)}\ 1\dfrac{3}{12} \qquad \text{(D)}\ 1\dfrac{1}{5} \qquad \text{(E)}\ 1\dfrac{10}{40}$

Solution

Problem 3

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

$\text{(A)}\ 10 \qquad \text{(B)}\ 12 \qquad \text{(C)}\ 16 \qquad \text{(D)}\ 28 \qquad \text{(E)}\ 48$

Solution

Problem 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 single. What percent of her hits were single?

$\text{(A)}\ 28\% \qquad \text{(B)}\ 35\% \qquad \text{(C)}\ 70\% \qquad \text{(D)}\ 75\% \qquad \text{(E)}\ 80\%$

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

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

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 5$

Solution

Problem 8

A store owner bought $1500$ pencils at <dollar/>0.10 each. If he sells them for <dollar/>0.25 each, how many of them must he sell to make a profit of exactly <dollar/>100.00?

$\text{(A)}\ 400 \qquad \text{(B)}\ 667 \qquad \text{(C)}\ 1000 \qquad \text{(D)}\ 1500 \qquad \text{(E)}\ 1900$

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

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 $30,000$ miles the car traveled. For how many miles was each tire used?

$\text{(A)}\ 6000 \qquad \text{(B)}\ 7500 \qquad \text{(C)}\ 24,000 \qquad \text{(D)}\ 30,000 \qquad \text{(E)}\ 37,500$

Solution

Problem 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

$\text{(A)}\ 170 \qquad \text{(B)}\ 171 \qquad \text{(C)}\ 176 \qquad \text{(D)}\ 177 \qquad \text{(E)}\ \text{not determined by the information given}$

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

$\text{(A)}\ 8 \qquad \text{(B)}\ 12 \qquad \text{(C)}\ 20 \qquad \text{(D)}\ 24 \qquad \text{(E)}\ 48$

Solution

Problem 15

What is the $1992^\text{nd}$ letter in this sequence?

\[\text{ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC}\cdots\]

$\text{(A)}\ \text{A} \qquad \text{(B)}\ \text{B} \qquad \text{(C)}\ \text{C} \qquad \text{(D)}\ \text{D} \qquad \text{(E)}\ \text{E}$

Solution

Problem 16

Solution

Problem 17

Solution

Problem 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?

$\text{(A)}\ 45 \qquad \text{(B)}\ 50 \qquad \text{(C)}\ 60 \qquad \text{(D)}\ 75 \qquad \text{(E)}\ 90$

Solution

Problem 19

The distance between the $5^\text{th}$ and $26^\text{th}$ 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 $5^\text{th}$ and $26^\text{th}$ exits?

$\text{(A)}\ 8 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 18 \qquad \text{(D)}\ 47 \qquad \text{(E)}\ 98$

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

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 $10$ is

$\text{(A)}\ \dfrac{3}{7} \qquad \text{(B)}\ \dfrac{17}{36} \qquad \text{(C)}\ \dfrac{1}{2} \qquad \text{(D)}\ \dfrac{5}{8} \qquad \text{(E)}\ \dfrac{11}{12}$

Solution

Problem 24

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?

$\text{(A)}\ 6 \qquad \text{(B)}\ 7 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 10$

Solution

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
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