# Difference between revisions of "1987 AJHSME Problems"

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== Problem 14 == | == Problem 14 == | ||

+ | |||

+ | A computer can do <math>10,000</math> additions per second. How many additions can it do in one hour? | ||

+ | |||

+ | <math>\text{(A)}\ 6\text{ million} \qquad \text{(B)}\ 36\text{ million} \qquad \text{(C)}\ 60\text{ million} \qquad \text{(D)}\ 216\text{ million} \qquad \text{(E)}\ 360\text{ million}</math> | ||

[[1987 AJHSME Problems/Problem 14|Solution]] | [[1987 AJHSME Problems/Problem 14|Solution]] | ||

== Problem 15 == | == Problem 15 == | ||

+ | |||

+ | The sale ad read: "Buy three tires at the regular price and get the fourth tire for <dollar/>3." Sam paid <dollar/>240 for a set of four tires at the sale. What was the regular price of one tire? | ||

+ | |||

+ | <math>\text{(A)}\ 59.25\text{ dollars} \qquad \text{(B)}\ 60\text{ dollars} \qquad \text{(C)}\ 70\text{ dollars} \qquad \text{(D)}\ 79\text{ dollars} \qquad \text{(E)}\ 80\text{ dollars}</math> | ||

[[1987 AJHSME Problems/Problem 15|Solution]] | [[1987 AJHSME Problems/Problem 15|Solution]] | ||

== Problem 16 == | == Problem 16 == | ||

+ | |||

+ | Joyce made <math>12</math> of her first <math>30</math> shots in the first three games of this basketball game, so her seasonal shooting average was <math>40\% </math>. In her next game, she took <math>10</math> shots and raised her seasonal shooting average to <math>50\% </math>. How many of these <math>10</math> shots did she make? | ||

+ | |||

+ | <math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math> | ||

[[1987 AJHSME Problems/Problem 16|Solution]] | [[1987 AJHSME Problems/Problem 16|Solution]] | ||

== Problem 17 == | == Problem 17 == | ||

+ | |||

+ | Abby, Bret, Carl, and Dana are seated in a row of four seats numbered #1 to #4. Joe looks at them and says: | ||

+ | |||

+ | "Bret is next to Carl." | ||

+ | "Abby is between Bret and Carl." | ||

+ | |||

+ | However each one of Joe's statements is false. Bret is actually sitting in seat #3. Who is sitting in seat #2? | ||

+ | |||

+ | <math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math> | ||

[[1987 AJHSME Problems/Problem 17|Solution]] | [[1987 AJHSME Problems/Problem 17|Solution]] | ||

== Problem 18 == | == Problem 18 == | ||

+ | |||

+ | Half the people in a room left. One third of those remaining started to dance. There were then <math>12</math> people who were not dancing. The original number of people in the room was | ||

+ | |||

+ | <math>\text{(A)}\ 24 \qquad \text{(B)}\ 30 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 42 \qquad \text{(E)}\ 72</math> | ||

[[1987 AJHSME Problems/Problem 18|Solution]] | [[1987 AJHSME Problems/Problem 18|Solution]] | ||

== Problem 19 == | == Problem 19 == | ||

+ | |||

+ | A calculator has a squaring key <math>\boxed{x^2}</math> which replaces the current number displayed with its square. For example, if the display is <math>\boxed{000003}</math> and the <math>\boxed{x^2}</math> key is depressed, then the display becomes <math>\boxed{000009}</math>. If the display reads <math>\boxed{000002}</math>, how many times must you depress the <math>\boxed{x^2}</math> key to produce a displayed number greater than <math>500</math>? | ||

+ | |||

+ | <math>\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 250</math> | ||

[[1987 AJHSME Problems/Problem 19|Solution]] | [[1987 AJHSME Problems/Problem 19|Solution]] |

## Revision as of 21:34, 28 February 2009

## 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

## Problem 3

## Problem 4

Martians measure angles in clerts. There are clerts in a full circle. How many clerts are there in a right angle?

## Problem 5

The area of the rectangular region is

## Problem 6

The smallest product one could obtain by multiplying two numbers in the set is

## Problem 7

## Problem 8

## Problem 9

When finding the sum , the least common denominator used is

## Problem 10

## Problem 11

The sum is between

## Problem 12

What fraction of the large by rectangular region is shaded?

## Problem 13

Which of the following fractions has the largest value?

## Problem 14

A computer can do additions per second. How many additions can it do in one hour?

## Problem 15

The sale ad read: "Buy three tires at the regular price and get the fourth tire for <dollar/>3." Sam paid <dollar/>240 for a set of four tires at the sale. What was the regular price of one tire?

## Problem 16

Joyce made of her first shots in the first three games of this basketball game, so her seasonal shooting average was . In her next game, she took shots and raised her seasonal shooting average to . How many of these shots did she make?

## Problem 17

Abby, Bret, Carl, and Dana are seated in a row of four seats numbered #1 to #4. Joe looks at them and says:

"Bret is next to Carl." "Abby is between Bret and Carl."

However each one of Joe's statements is false. Bret is actually sitting in seat #3. Who is sitting in seat #2?

## Problem 18

Half the people in a room left. One third of those remaining started to dance. There were then people who were not dancing. The original number of people in the room was

## Problem 19

A calculator has a squaring key which replaces the current number displayed with its square. For example, if the display is and the key is depressed, then the display becomes . If the display reads , how many times must you depress the key to produce a displayed number greater than ?