MathDB

1

1987 AJHSME Problem 25

1

to

10

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

\text{(A)}\ \frac{4}{9} \qquad \text{(B)}\ \frac{9}{19} \qquad \text{(C)}\ \frac{1}{2} \qquad \text{(D)}\ \frac{10}{19} \qquad \text{(E)}\ \frac{5}{9}

24

1

1987 AJHSME Problem 24

A multiple choice examination consists of

20

questions. The scoring is

+5

for each correct answer,

-2

for each incorrect answer, and

0

for each unanswered question. John's score on the examination is

48

. What is the maximum number of questions he could have answered correctly?

\text{(A)}\ 9 \qquad \text{(B)}\ 10 \qquad \text{(C)}\ 11 \qquad \text{(D)}\ 12 \qquad \text{(E)}\ 16

23

1

1987 AJHSME Problem 23

Assume the adjoining chart shows the

1980

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?
\begin{tabular}[t]{c|cccc} & NE & MW & South & West \\ \hline White & 42 & 52 & 57 & 35 \\ Black & 5 & 5 & 15 & 2 \\ Asian & 1 & 1 & 1 & 3 \\ Other & 1 & 1 & 2 & 4 \end{tabular}

\text{(A)}\ 20\% \qquad \text{(B)}\ 25\% \qquad \text{(C)}\ 40\% \qquad \text{(D)}\ 56\% \qquad \text{(E)}\ 80\%

22

1

1987 AJHSME Problem 22

\text{ABCD}

is a rectangle,

\text{D}

is the center of the circle, and

\text{B}

is on the circle. If

\text{AD}=4

and

\text{CD}=3

, then the area of the shaded region is between
[asy] pair A,B,C,D; A=(0,4); B=(3,4); C=(3,0); D=origin; draw(circle(D,5)); fill((0,5)..(1.5,4.7697)..B--A--cycle,black); fill(B..(4,3)..(5,0)--C--cycle,black); draw((0,5)--D--(5,0)); label("A",A,NW); label("B",B,NE); label("C",C,S); label("D",D,SW); [/asy]

\text{(A)}\ 4\text{ and }5 \qquad \text{(B)}\ 5\text{ and }6 \qquad \text{(C)}\ 6\text{ and }7 \qquad \text{(D)}\ 7\text{ and }8 \qquad \text{(E)}\ 8\text{ and }9

21

1

1987 AJHSME Problem 21

Suppose

n^{*}

means

\frac{1}{n}

, the reciprocal of

n

. For example,

5^{*}=\frac{1}{5}

. How many of the following statements are true?
i)

3^*+6^*=9^*

ii)

6^*-4^*=2^*

iii)

2^*\cdot 6^*=12^*

iv)

10^*\div 2^* =5^*

\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 4

20

1

1987 AJHSME Problem 20

"If a whole number

n

is not prime, then the whole number

n-2

is not prime." A value of

n

which shows this statement to be false is

\text{(A)}\ 9 \qquad \text{(B)}\ 12 \qquad \text{(C)}\ 13 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 23

19

1

1987 AJHSME Problem 19

A calculator has a squaring key

\boxed{x^2}

which replaces the current number displayed with its square. For example, if the display is

\boxed{000003}

and the

\boxed{x^2}

key is depressed, then the display becomes

\boxed{000009}

. If the display reads

\boxed{000002}

, how many times must you depress the

\boxed{x^2}

key to produce a displayed number greater than

500

?

\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 250

18

1

1987 AJHSME Problem 18

Half the people in a room left. One third of those remaining started to dance. There were then

12

people who were not dancing. The original number of people in the room was

\text{(A)}\ 24 \qquad \text{(B)}\ 30 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 42 \qquad \text{(E)}\ 72

17

1

1987 AJHSME 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?

\text{(A)}\ \text{Abby} \qquad \text{(B)}\ \text{Bret} \qquad \text{(C)}\ \text{Carl} \qquad \text{(D)}\ \text{Dana} \qquad \text{(E)}\ \text{There is not enough information to be sure.}

16

1

1987 AJHSME Problem 16

Joyce made

12

of her first

30

shots in the first three games of this basketball game, so her seasonal shooting average was

40\%

. In her next game, she took

10

shots and raised her seasonal shooting average to

50\%

. How many of these

10

shots did she make?

\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8

15

1

1987 AJHSME Problem 15

The sale ad read: "Buy three tires at the regular price and get the fourth tire for

\$3

." Sam paid

\$240

for a set of four tires at the sale. What was the regular price of one tire?

\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}

14

1

1987 AJHSME Problem 14

A computer can do

10,000

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

\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}

13

1

1987 AJHSME Problem 13

Which of the following fractions has the largest value?

\text{(A)}\ \frac{3}{7} \qquad \text{(B)}\ \frac{4}{9} \qquad \text{(C)}\ \frac{17}{35} \qquad \text{(D)}\ \frac{100}{201} \qquad \text{(E)}\ \frac{151}{301}

12

1

1987 AJHSME Problem 12

What fraction of the large

12

by

18

rectangular region is shaded?
[asy] draw((0,0)--(18,0)--(18,12)--(0,12)--cycle); draw((0,6)--(18,6)); for(int a=6; a<12; ++a) { draw((1.5a,0)--(1.5a,6)); } fill((15,0)--(18,0)--(18,6)--(15,6)--cycle,black); label("0",(0,0),W); label("9",(9,0),S); label("18",(18,0),S); label("6",(0,6),W); label("12",(0,12),W); [/asy]

\text{(A)}\ \frac{1}{108} \qquad \text{(B)}\ \frac{1}{18} \qquad \text{(C)}\ \frac{1}{12} \qquad \text{(D)}\ \frac29 \qquad \text{(E)}\ \frac13

11

1

1987 AJHSME Problem 11

The sum

2\frac17+3\frac12+5\frac{1}{19}

is between

\text{(A)}\ 10\text{ and }10\frac12 \qquad \text{(B)}\ 10\frac12 \text{ and } 11 \qquad \text{(C)}\ 11\text{ and }11\frac12 \qquad \text{(D)}\ 11\frac12 \text{ and }12 \qquad \text{(E)}\ 12\text{ and }12\frac12

10

1

1987 AJHSME Problem 10

4(299)+3(299)+2(299)+298=

\text{(A)}\ 2889 \qquad \text{(B)}\ 2989 \qquad \text{(C)}\ 2991 \qquad \text{(D)}\ 2999 \qquad \text{(E)}\ 3009

9

1

1987 AJHSME Problem 9

When finding the sum

\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}

, the least common denominator used is

\text{(A)}\ 120 \qquad \text{(B)}\ 210 \qquad \text{(C)}\ 420 \qquad \text{(D)}\ 840 \qquad \text{(E)}\ 5040

8

1

1987 AJHSME Problem 8

If

\text{A}

and

\text{B}

are nonzero digits, then the number of digits (not necessarily different) in the sum of the three whole numbers is
\begin{tabular}[t]{cccc} 9 & 8 & 7 & 6 \\ & A & 3 & 2 \\ & & B & 1 \\ \hline \end{tabular}

\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}

7

1

1987 AJHSME Problem 7

The large cube shown is made up of

27

\text{(A)}\ 10 \qquad \text{(B)}\ 16 \qquad \text{(C)}\ 20 \qquad \text{(D)}\ 22 \qquad \text{(E)}\ 24

6

1

1987 AJHSME Problem 6

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

\{ -7, -5, -1, 1, 3 \}

is

\text{(A)}\ -35 \qquad \text{(B)}\ -21 \qquad \text{(C)}\ -15 \qquad \text{(D)}\ -1 \qquad \text{(E)}\ 3

5

1

1987 AJHSME Problem 5

The area of the rectangular region is
[asy] draw((0,0)--(4,0)--(4,2.2)--(0,2.2)--cycle,linewidth(.5 mm)); label(".22 m",(4,1.1),E); label(".4 m",(2,0),S); [/asy]

\text{(A)}\ \text{.088 m}^2 \qquad \text{(B)}\ \text{.62 m}^2 \qquad \text{(C)}\ \text{.88 m}^2 \qquad \text{(D)}\ \text{1.24 m}^2 \qquad \text{(E)}\ \text{4.22 m}^2

4

1

1987 AJHSME Problem 4

Martians measure angles in clerts. There are

500

clerts in a full circle. How many clerts are there in a right angle?

\text{(A)}\ 90 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 125 \qquad \text{(D)}\ 180 \qquad \text{(E)}\ 250

3

1

1987 AJHSME Problem 3

2(81+83+85+87+89+91+93+95+97+99)=

\text{(A)}\ 1600 \qquad \text{(B)}\ 1650 \qquad \text{(C)}\ 1700 \qquad \text{(D)}\ 1750 \qquad \text{(E)}\ 1800

2

1

1987 AJHSME Problem 2

\frac{2}{25}=

\text{(A)}\ .008 \qquad \text{(B)}\ .08 \qquad \text{(C)}\ .8 \qquad \text{(D)} 1.25 \qquad \text{(E)}\ 12.5

1

1987 AJHSME Problem 1

.4+.02+.006=

\text{(A)}\ .012 \qquad \text{(B)}\ .066 \qquad \text{(C)}\ .12 \qquad \text{(D)}\ .24 \qquad \text{(E)} .426

1987 AMC 8

Subcontests

1987 AJHSME Problem 25

1987 AJHSME Problem 24

1987 AJHSME Problem 23

1987 AJHSME Problem 22

1987 AJHSME Problem 21

1987 AJHSME Problem 20

1987 AJHSME Problem 19

1987 AJHSME Problem 18

1987 AJHSME Problem 17

1987 AJHSME Problem 16

1987 AJHSME Problem 15

1987 AJHSME Problem 14

1987 AJHSME Problem 13

1987 AJHSME Problem 12

1987 AJHSME Problem 11

1987 AJHSME Problem 10

1987 AJHSME Problem 9

1987 AJHSME Problem 8

1987 AJHSME Problem 7

1987 AJHSME Problem 6

1987 AJHSME Problem 5

1987 AJHSME Problem 4

1987 AJHSME Problem 3

1987 AJHSME Problem 2

1987 AJHSME Problem 1