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 $\boxed{C}$ .

1993 AJHSME (Problems • Answer Key • Resources)
Preceded by First Question	Followed by Problem 2
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1993 AJHSME Problems/Problem 1

Solution 1

Solution 2

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