## Problem 1 Which pair of numbers does NOT have a product equal to $36$? $\text{(A)}\ \{ -4,-9\} \qquad \text{(B)}\ \{ -3,-12\} \qquad \text{(C)}\ \left\{ \dfrac{1}{2},-72\right\} \qquad \text{(D)}\ \{ 1,36\} \qquad \text{(E)}\ \left\{\dfrac{3}{2},24\right\}$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 2 When the fraction $\dfrac{49}{84}$ is expressed in simplest form, then the sum of the numerator and the denominator will be $\text{(A)}\ 11 \qquad \text{(B)}\ 17 \qquad \text{(C)}\ 19 \qquad \text{(D)}\ 33 \qquad \text{(E)}\ 133$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 3 Which of the following numbers has the largest prime factor? $\text{(A)}\ 39 \qquad \text{(B)}\ 51 \qquad \text{(C)}\ 77 \qquad \text{(D)}\ 91 \qquad \text{(E)}\ 121$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 4 $1000\times 1993 \times 0.1993 \times 10 =$ $\text{(A)}\ 1.993\times 10^3 \qquad \text{(B)}\ 1993.1993 \qquad \text{(C)}\ (199.3)^2 \qquad \text{(D)}\ 1,993,001.993 \qquad \text{(E)}\ (1993)^2$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 5 Which one of the following bar graphs could represent the data from the circle graph? ![[1993_AJHSME_Problems_Problem5.svg]] ![[1993_AJHSME_Problems_Problem5_figure1.svg]] > [!sol]- Click Here for Solution! (Coming soon) ## Problem 6 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? $\text{(A)}\ 5 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 7 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 25$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 7 $3^3+3^3+3^3 =$ $\text{(A)}\ 3^4 \qquad \text{(B)}\ 9^3 \qquad \text{(C)}\ 3^9 \qquad \text{(D)}\ 27^3 \qquad \text{(E)}\ 3^{27}$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 8 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 $\text{(A)}\ 1\text{ month} \qquad \text{(B)}\ 4\text{ months} \qquad \text{(C)}\ 6\text{ months} \qquad \text{(D)}\ 8\text{ months} \qquad \text{(E)}\ 1\text{ year}$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 9 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 $(2*4)*(1*3)=$ $\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 5$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 10 This line graph represents the price of a trading card during the first $6$ months of $1993$. ![[1993_AJHSME_Problems_Problem10.svg]] The greatest monthly drop in price occurred during $\text{(A)}\ \text{January} \qquad \text{(B)}\ \text{March} \qquad \text{(C)}\ \text{April} \qquad \text{(D)}\ \text{May} \qquad \text{(E)}\ \text{June}$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 11 Consider this histogram of the scores for $81$ students taking a test: ![[1993_AJHSME_Problems_Problem11.svg]] The median is in the interval labeled $\text{(A)}\ 60 \qquad \text{(B)}\ 65 \qquad \text{(C)}\ 70 \qquad \text{(D)}\ 75 \qquad \text{(E)}\ 80$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 12 If each of the three operation signs, $+$, $-$, $\times$, 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 $\text{(A)}\ 9 \qquad \text{(B)}\ 10 \qquad \text{(C)}\ 15 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 19$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 13 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 ![[1993_AJHSME_Problems_Problem13.svg|test -noinv -wb]] $\text{(A)}\ 30 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 34 \qquad \text{(D)}\ 36 \qquad \text{(E)}\ 38$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 14 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 $A+B=$ $\begin{array}{|c|c|c|} \hline 1 & & \\ \hline & 2 & A \\ \hline & & B \\ \hline \end{array}$ $\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 6$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 15 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 $\text{(A)}\ 81.0 \qquad \text{(B)}\ 82.7 \qquad \text{(C)}\ 83.0 \qquad \text{(D)}\ 84.0 \qquad \text{(E)}\ 84.3$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 16 $\dfrac{1}{1+\dfrac{1}{2+\dfrac{1}{3}}} =$ $\text{(A)}\ \dfrac{1}{6} \qquad \text{(B)}\ \dfrac{3}{10} \qquad \text{(C)}\ \dfrac{7}{10} \qquad \text{(D)}\ \dfrac{5}{6} \qquad \text{(E)}\ \dfrac{10}{3}$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 17 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 ![[1993_AJHSME_Problems_Problem17.svg]] $\text{(A)}\ 300 \qquad \text{(B)}\ 500 \qquad \text{(C)}\ 550 \qquad \text{(D)}\ 600 \qquad \text{(E)}\ 1000$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 18 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 ![[1993_AJHSME_Problems_Problem18.svg]] $\text{(A)}\ 320 \qquad \text{(B)}\ 325 \qquad \text{(C)}\ 330 \qquad \text{(D)}\ 335 \qquad \text{(E)}\ 340$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 19 $(1901+1902+1903+\cdots + 1993) - (101+102+103+\cdots + 193) =$ $\text{(A)}\ 167,400 \qquad \text{(B)}\ 172,050 \qquad \text{(C)}\ 181,071 \qquad \text{(D)}\ 199,300 \qquad \text{(E)}\ 362,142$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 20 When $10^{93}-93$ is expressed as a single whole number, the sum of the digits is $\text{(A)}\ 10 \qquad \text{(B)}\ 93 \qquad \text{(C)}\ 819 \qquad \text{(D)}\ 826 \qquad \text{(E)}\ 833$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 21 If the length of a rectangle is increased by $20\%$ and its width is increased by $50\%$, then the area is increased by $\text{(A)}\ 10\% \qquad \text{(B)}\ 30\% \qquad \text{(C)}\ 70\% \qquad \text{(D)}\ 80\% \qquad \text{(E)}\ 100\%$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 22 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? $\text{(A)}\ 22 \qquad \text{(B)}\ 99 \qquad \text{(C)}\ 112 \qquad \text{(D)}\ 119 \qquad \text{(E)}\ 199$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 23 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? $\text{(A)}\ P\text{ and }Q \qquad \text{(B)}\ P\text{ and }R \qquad \text{(C)}\ P\text{ and }S \qquad \text{(D)}\ P\text{ and }T \qquad \text{(E)}\ P,S\text{ and }T$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 24 What number is directly above $142$ in this array of numbers? $\begin{array}{cccccc} & & & 1 & & \\ & & 2 & 3 & 4 & \\ & 5 & 6 & 7 & 8 & 9 \\ 10 & 11 & 12 & \cdots & & \\ \end{array}$ $\text{(A)}\ 99 \qquad \text{(B)}\ 119 \qquad \text{(C)}\ 120 \qquad \text{(D)}\ 121 \qquad \text{(E)}\ 122$ > [!sol]- Click Here for Solution! (Coming soon) ## Problem 25 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 $\text{(A)}\ 4\text{ or }5 \qquad \text{(B)}\ 6\text{ or }7\qquad \text{(C)}\ 8\text{ or }9 \qquad \text{(D)}\ 10\text{ or }11 \qquad \text{(E)}\ 12\text{ or more}$ > [!sol]- Click Here for Solution! (Coming soon)