1993 AJHSME Problems/Problem 1

Problem

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

Solution 1

Let's calculate each of the answer choices and see which one DOES NOT equal $36$.

$A$ comes out to be $-4 \times -9= 36$,

$B$ equals $-3 \times -12= 36$,

$C$ is $\frac{1}{2} \times -72= -36$,

$D$ simplifies to $1 \times 36= 36$,

and $E$ equals $\frac{3}{2} \times 24= 3 \times 12= 36$.

Thus, our answer is $\boxed{C}$.

Solution 2

In order for a product to be positive ($36$), the numbers should either be both positive or both negative. Looking at our answer choices, the only option that does not fit this description is $\boxed{C}$.

See Also

1993 AJHSME (ProblemsAnswer KeyResources)
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First
Question
Followed by
Problem 2
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