# Difference between revisions of "1987 AJHSME Problems"

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== Problem 8 == | == Problem 8 == | ||

+ | |||

+ | If <math>\text{A}</math> and <math>\text{B}</math> are nonzero digits, then the number of digits (not necessarily different) in the sum of the three whole numbers is | ||

+ | |||

+ | <cmath>\begin{tabular}[t]{cccc} | ||

+ | 9 & 8 & 7 & 6 \\ | ||

+ | & A & 3 & 2 \\ | ||

+ | & & B & 1 \\ \hline | ||

+ | \end{tabular}</cmath> | ||

+ | |||

+ | |||

+ | <math>\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ \text{depends on the values of A and B}</math> | ||

[[1987 AJHSME Problems/Problem 8|Solution]] | [[1987 AJHSME Problems/Problem 8|Solution]] |

## Revision as of 20:43, 5 March 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

If and are nonzero digits, then the number of digits (not necessarily different) in the sum of the three whole numbers is

## 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 ?

## Problem 20

"If a whole number is not prime, then the whole number is not prime." A value of which shows this statement to be false is

## Problem 21

Suppose means , the reciprocal of . For example, . How many of the following statements are true?

i) ii) iii) iv)

## Problem 22

is a rectangle, is the center of the circle, and is on the circle. If and , then the area of the shaded region is between

## Problem 23

Assume the adjoining chart shows the U.S. population, in millions, for each region by ethnic group. To the nearest percent, what percent of the U.S. Black population lived in the South?

## Problem 24

A multiple choice examination consists of questions. The scoring is for each correct answer, for each incorrect answer, and for each unanswered question. John's score on the examination is . What is the maximum number of questions he could have answered correctly?

## Problem 25

Ten balls numbered to are in a jar. Jack reaches into the jar and randomly removes one of the balls. Then Jill reaches into the jar and randomly removes a different ball. The probability that the sum of the two numbers on the balls removed is even is