AMC 8 1993

Which pair of numbers does NOT have a product equal to $36$? $\text{(A)}\ \{-4,-9\} \text{(B)}\ \{-3,-12\} \text{(C)}\ \left\{\frac{1}{2},-72\right\} \text{(D)}\ \{ 1,36\} \text{(E)}\ \left\{\frac{3}{2},24\right\}$

When the fraction $\dfrac{49}{84}$ is expressed in simplest form, then the sum of the numerator and the denominator will be $\text{(A)}\ 11 \text{(B)}\ 17 \text{(C)}\ 19 \text{(D)}\ 33 \text{(E)}\ 133$

Which of the following numbers has the largest prime factor? $\text{(A)}\ 39 \text{(B)}\ 51 \text{(C)}\ 77 \text{(D)}\ 91 \text{(E)}\ 121$

$1000\times 1993 \times 0.1993 \times 10 =$ $\text{(A)}\ 1.993\times 10^3 \text{(B)}\ 1993.1993 \text{(C)}\ (199.3)^2 \text{(D)}\ 1,993,001.993 \text{(E)}\ (1993)^2$

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? $\text{(A)}\ 5 \text{(B)}\ 6 \text{(C)}\ 7 \text{(D)}\ 8 \text{(E)}\ 10$

$3^3+3^3+3^3 =$ $\text{(A)}\ 3^4 \text{(B)}\ 9^3 \text{(C)}\ 3^9 \text{(D)}\ 27^3 \text{(E)}\ 3^{27}$

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 would last approximately $\text{(A)}\ 1\text{ month} \text{(B)}\ 4\text{ months} \text{(C)}\ 6\text{ months} \text{(D)}\ 8\text{ months} \text{(E)}\ 1\text{ year}$

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 $\text{(A)}\ \text{January} \text{(B)}\ \text{March} \text{(C)}\ \text{April} \text{(D)}\ \text{May} \text{(E)}\ \text{June}$

Consider this histogram of the scores for $81$ students taking a test:

The median is in the interval labeled $\text{(A)}\ 60 \text{(B)}\ 65 \text{(C)}\ 70 \text{(D)}\ 75 \text{(E)}\ 80$

If each of the three operation signs, $+$, $\text{--}$, $\times$, is used exactly ONCE in one of the blanks in the expression $$5\hspace{1 mm}\underline{\hspace{4 mm}}\hspace{1 mm}4\hspace{1 mm}\underline{\hspace{4 mm}}\hspace{1 mm}6\hspace{1 mm}\underline{\hspace{4 mm}}\hspace{1 mm}3$$ then the value of the result could equal $\text{(A)}\ 9 \text{(B)}\ 10 \text{(C)}\ 15 \text{(D)}\ 16 \text{(E)}\ 19$

The word "HELP" in block letters is painted in black with strokes $1$ unit wide on a $5$ by $15$ rectangular white sign with dimensions as shown. The area of the white portion of the sign, in square units, is

$\text{(A)}\ 30 \text{(B)}\ 32 \text{(C)}\ 34 \text{(D)}\ 36 \text{(E)}\ 38$

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 $\text{(A)}\ 81.0 \text{(B)}\ 82.7 \text{(C)}\ 83.0 \text{(D)}\ 84.0 \text{(E)}\ 84.3$

$\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=$ $\text{(A)}\ \dfrac{1}{6} \text{(B)}\ \dfrac{3}{10} \text{(C)}\ \dfrac{7}{10} \text{(D)}\ \dfrac{5}{6} \text{(E)}\ \dfrac{10}{3}$

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

$\text{(A)}\ 300 \text{(B)}\ 500 \text{(C)}\ 550 \text{(D)}\ 600 \text{(E)}\ 1000$

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 quadrilateral $ABDF$ is

$\text{(A)}\ 320 \text{(B)}\ 325 \text{(C)}\ 330 \text{(D)}\ 335 \text{(E)}\ 340$

$(1901+1902+1903+\cdots + 1993) - (101+102+103+\cdots + 193) =$ $\text{(A)}\ 167,400 \text{(B)}\ 172,050 \text{(C)}\ 181,071 \text{(D)}\ 199,300 \text{(E)}\ 362,142$

When $10^{93}-93$ is expressed as a single whole number, the sum of the digits is $\text{(A)}\ 10 \text{(B)}\ 93 \text{(C)}\ 819 \text{(D)}\ 826 \text{(E)}\ 833$

If the length of a rectangle is increased by $20\%$ and its width is increased by $50\%$, then the area is increased by $\text{(A)}\ 10\% \text{(B)}\ 30\% \text{(C)}\ 70\% \text{(D)}\ 80\% \text{(E)}\ 100\%$

Pat Peano has plenty of 0's, 1's, 3's, 4's, 5's, 6's, 7's, 8's and 9's, but he has only twenty-two 2's. How far can he number the pages of his scrapbook with these digits? $\text{(A)}\ 22 \text{(B)}\ 99 \text{(C)}\ 112 \text{(D)}\ 119 \text{(E)}\ 199$

Five runners, $P$, $Q$, $R$, $S$, $T$, have a race, and $P$ beats $Q$, $P$ beats $R$, $Q$ beats $S$, and $T$ finishes after $P$ and before $Q$. Who could NOT have finished third in the race? $\text{(A)}\ P\text{ and }Q \text{(B)}\ P\text{ and }R \text{(C)}\ P\text{ and }S \text{(D)}\ P\text{ and }T \text{(E)}\ P,S\text{ and }T$

What number is directly above $142$ in this array of numbers? $$\begin{array}{cccccc}& & & 1 & &\\ & & 2 & 3 & 4 &\\ & 5 & 6 & 7 & 8 & 9\\ 10 & 11 & 12 &\cdots & &\\ \end{array}$$ $\text{(A)}\ 99 \text{(B)}\ 119 \text{(C)}\ 120 \text{(D)}\ 121 \text{(E)}\ 122$

A checkerboard consists of one-inch squares. A square card, $1.5$ inches on a side, is placed on the board so that it covers part or all of the area of each of $n$ squares. The maximum possible value of $n$ is $\text{(A)}\ 4\text{ or }5 \text{(B)}\ 6\text{ or }7 \text{(C)}\ 8\text{ or }9 \text{(D)}\ 10\text{ or }11 \text{(E)}\ 12\text{ or more}$