1991 AJHSME Problems/Problem 8

Problem

What is the largest quotient that can be formed using two numbers chosen from the set $\{ -24, -3, -2, 1, 2, 8 \}$?

$\text{(A)}\ -24 \qquad \text{(B)}\ -3 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 12 \qquad \text{(E)}\ 24$

Solution

Let the two chosen numbers be $a$ and $b$. To maximize the quotient, we first have either $a,b>0$ or $a,b<0$, and from there we maximize $|a|$ and minimize $|b|$.

For the case $a,b<0$, we have $a=-24$ and $b=-2$, which gives us $(-24)/(-2)=12$. For the case $a,b>0$, we have $a=8$ and $b=1$, which gives us $8/1=8$.

Since $12>8$, our answer is $\boxed{\text{D}}$.

See Also

1991 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
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All AJHSME/AMC 8 Problems and Solutions

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