1987 AMC 8

Question 1

What is $0.4 + 0.02 + 0.006?$

$0.012$
$0.066$
$0.12$
$0.24$
$0.426$

Question 2

What is $\dfrac{2}{25}$ written as a decimal?

$0.008$
$0.08$
$0.8$
$1.25$
$12.5$

Question 3

What is the value of

$$
\begin{gathered} 2(81 + 83 + 85 + 87 + 89 \\ {}+ 91 + 93 + 95 + 97 + 99)? \end{gathered}
$$

$1600$
$1650$
$1700$
$1750$
$1800$

Question 4

Martians measure angles in clerts. There are $500$ clerts in a full circle. How many clerts are there in a right angle?

$90$
$100$
$125$
$180$
$250$

Question 5

What is the area, in square meters, of the rectangular region shown?

Question illustration

$0.088 \text{ m}^2$
$0.62 \text{ m}^2$
$0.88 \text{ m}^2$
$1.24 \text{ m}^2$
$4.22 \text{ m}^2$

Question 6

The smallest product one could obtain by multiplying two numbers in the set $\{ -7, -5, -1, 1, 3 \}$ is

$-35$
$-21$
$-15$
$-1$
$3$

The large cube shown is made up of $27$ identical sized smaller cubes. For each face of the large cube, the opposite face is shaded the same way. The total number of smaller cubes that must have at least one face shaded is

Question illustration

$10$
$16$
$20$
$22$
$24$

Question 8

In the addition problem below, $A$ and $B$ are nonzero digits:

$$
\begin{array}{r} 9876 \\ A32 \\ +B1 \\ \hline \end{array}
$$

How many digits (not necessarily different) are in the sum of the three whole numbers?

$4$
$5$
$6$
$9$
depends on the values of $A$ and $B$

Question 9

When finding the sum

$$
\dfrac12 + \dfrac13 + \dfrac14 + \dfrac15 + \dfrac16 + \dfrac17,
$$

what is the least common denominator used?

$120$
$210$
$420$
$840$
$5040$

Question 10

What is the value of

$$
4(299) + 3(299) + 2(299) + 298?
$$

$2889$
$2989$
$2991$
$2999$
$3009$

Question 11

The sum $2\dfrac17 + 3\dfrac12 + 5\dfrac{1}{19}$ is between which two values?

$10$ and $10\dfrac12$
$10\dfrac12$ and $11$
$11$ and $11\dfrac12$
$11\dfrac12$ and $12$
$12$ and $12\dfrac12$

Question 12

What fraction of the large $12$ by $18$ rectangular region is shaded?

Question illustration

$\dfrac{1}{108}$
$\dfrac{1}{18}$
$\dfrac{1}{12}$
$\dfrac{2}{9}$
$\dfrac{1}{3}$

Question 13

Which of the following fractions has the largest value?

$\dfrac{3}{7}$
$\dfrac{4}{9}$
$\dfrac{17}{35}$
$\dfrac{100}{201}$
$\dfrac{151}{301}$

Question 14

A computer can do $10{,}000$ additions per second. How many additions can it do in one hour?

$6$ million
$36$ million
$60$ million
$216$ million
$360$ million

Question 15

A 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?

$\$59.25$
$\$60$
$\$70$
$\$79$
$\$80$

Question 16

Joyce made $12$ of her first $30$ shots in the first three games of the basketball season, 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?

Question 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 $2?$

Abby
Bret
Carl
Dana
There is not enough information to be sure

Question 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. What was the original number of people in the room?

$24$
$30$
$36$
$42$
$72$

Question 19

A calculator has a squaring key $\boxed{x^2}$ that replaces the number currently displayed with its square. For example, if the display reads $\boxed{\phantom{00}3}$ and $\boxed{x^2}$ is pressed, the display becomes $\boxed{\phantom{00}9}.$ If the display reads $\boxed{\phantom{00}2},$ how many times must $\boxed{x^2}$ be pressed to produce a displayed number greater than $500?$

$4$
$5$
$8$
$9$
$250$

Question 20

Consider the statement: “If a whole number $n$ is not prime, then the whole number $n - 2$ is not prime.” Which of the following values of $n$ shows this statement to be false?

$9$
$12$
$13$
$16$
$23$