1990 AMC 8

What is the smallest sum of two $3$-digit numbers that can be obtained by placing each of the six digits $4,$ $5,$ $6,$ $7,$ $8,$ $9$ into one of the six boxes of a sum of two $3$-digit numbers?

Which digit of $0.12345,$ when changed to $9,$ gives the largest number?

What fraction of the square is shaded?

Which of the following could **not** be the units digit [one’s digit] of the square of a whole number?

Which of the following is closest to the product $(0.48017)(0.48017)(0.48017)?$

Which of these five numbers is the largest?

When three different numbers from the set $\{ -3, -2, -1, 4, 5 \}$ are multiplied, the largest possible product is

A dress originally priced at $\$80$ was put on sale at $25\%$ off. If $10\%$ tax was added to the sale price, then the total selling price of the dress was

The grading scale shown is used at Jones Junior High. The fifteen scores in Mr. Freeman’s class were: $89,$ $72,$ $54,$ $97,$ $77,$ $92,$ $85,$ $74,$ $75,$ $63,$ $84,$ $78,$ $71,$ $80,$ $90.$

A $93\text{--}100$ B $85\text{--}92$ C $75\text{--}84$ D $70\text{--}74$ F $0\text{--}69$

In Mr. Freeman’s class, what percent of the students received a grade of C?

On this monthly calendar, the date behind one of the letters is added to the date behind $C$. If this sum equals the sum of the dates behind $A$ and $B$, then the letter is

The numbers on the faces of this cube are consecutive whole numbers. The sums of the two numbers on each of the three pairs of opposite faces are equal. The sum of the six numbers on this cube is

There are twenty-four $4$-digit whole numbers that use each of the four digits $2,$ $4,$ $5,$ and $7$ exactly once. Listed in numerical order from smallest to largest, the number in the $17$th position in the list is

One proposal for new postage rates for a letter was $30$¢ for the first ounce and $22$¢ for each additional ounce (or fraction of an ounce). The postage for a letter weighing $4.5$ ounces was

A bag contains only blue balls and green balls. There are $6$ blue balls. If the probability of drawing a blue ball at random from this bag is $\dfrac14,$ then the number of green balls in the bag is

The area of this figure is $100 \text{ cm}^2.$ Its perimeter is

(The figure consists of four identical squares.)

What is the value of the following expression?

$$
\begin{aligned} &1990 - 1980 + 1970 - 1960 \\ &\quad {}+ \cdots - 20 + 10 \end{aligned}
$$

A straight concrete sidewalk is to be $3$ feet wide, $60$ feet long, and $3$ **inches** thick. How many cubic yards of concrete must a contractor order for the sidewalk if concrete must be ordered in a whole number of cubic yards?

Every corner of a rectangular prism is cut off by a straight slice through the three edges meeting at that corner, removing a small triangular piece at each of the eight corners. How many edges does the new figure have?

There are $120$ seats in a row. What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone?

The annual incomes of $1{,}000$ families range from $\$8200$ to $\$98{,}000.$ In error, the largest income was entered on the computer as $\$980{,}000.$ The difference between the mean of the incorrect data and the mean of the actual data is