Question bank AMC8 1993

Which pair of numbers does **not** have a product equal to $36?$

When the fraction $\dfrac{49}{84}$ is expressed in simplest form, then the sum of the numerator and the denominator will be

Which of the following numbers has the largest prime factor?

$1000 \times 1993 \times 0.1993 \times 10 =$

Which one of the following bar graphs could represent the data from the circle graph shown?



**(A)**

**(B)**

**(C)**

**(D)**

**(E)**

A can of soup can feed $3$ adults or $5$ children. If there are $5$ cans of soup and $15$ children are fed, then how many adults would the remaining soup feed?

$3^3 + 3^3 + 3^3 =$

To control her blood pressure, Jill’s grandmother takes one half of a pill every other day. If one supply of medicine contains $60$ pills, then the supply of medicine will last approximately

Consider the operation $*$ defined by the following table:

$$
\begin{array}{c|cccc} * & 1 & 2 & 3 & 4 \\ \hline 1 & 1 & 2 & 3 & 4 \\ 2 & 2 & 4 & 1 & 3 \\ 3 & 3 & 1 & 4 & 2 \\ 4 & 4 & 3 & 2 & 1 \end{array}
$$

For example, $3 * 2 = 1.$ Then $(2 * 4) * (1 * 3) =$

This line graph represents the price of a trading card during the first $6$ months of $1993.$ The greatest monthly drop in price occurred during which month?

Consider this histogram of the scores for $81$ students taking a test. The median is in the interval labeled which value?

If each of the three operation signs, $+,$ $-,$ $\times,$ is used exactly **once** in one of the blanks in the expression

$$
5 \, \underline{\phantom{x}} \, 4 \, \underline{\phantom{x}} \, 6 \, \underline{\phantom{x}} \, 3
$$

then the value of the result could equal

The word “**HELP**” in block letters is painted as a shaded region with strokes $1$ unit wide on a $5$ by $15$ rectangular sign. Each letter is $3$ units wide with a $1$-unit gap between letters, as shown. The area of the unshaded portion of the sign, in square units, is

The nine squares in the table shown are to be filled so that every row and every column contains each of the numbers $1,$ $2,$ $3.$ Then $A + B =$

$$
\begin{array}{|c|c|c|} \hline 1 & \phantom{X} & \phantom{X} \\ \hline \phantom{X} & 2 & A \\ \hline \phantom{X} & \phantom{X} & B \\ \hline \end{array}
$$

The arithmetic mean (average) of four numbers is $85.$ If the largest of these numbers is $97,$ then the mean of the remaining three numbers is

What is the value of the following expression?

$$
\cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{3}}}
$$

Square corners, $5$ units on a side, are removed from a $20$ unit by $30$ unit rectangular sheet of cardboard. The sides are then folded to form an open box. The surface area, in square units, of the interior of the box is

The rectangle shown has length $AC = 32,$ width $AE = 20,$ and $B$ and $F$ are midpoints of $\overline{AC}$ and $\overline{AE},$ respectively. The area of the quadrilateral $ABDF$ is

What is the value of the following expression?

$$
\begin{gathered} \small (1901 + 1902 + 1903 + \cdots + 1993) \\ \small {}- (101 + 102 + 103 + \cdots + 193) \end{gathered}
$$

When $10^{93} - 93$ is expressed as a single whole number, the sum of the digits is