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 x -9= 36

B equals -3 x -12= 36

C is 1/2 x -72= -36

D simplifies to 1 x 36= 36

and E equals 3/2 x 24= 3 x 12= 36

Thus, our answer is C. It is the only negative result.

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, this description matches with C since one number is positive and the other is negative.

See Also

1993 AJHSME (ProblemsAnswer KeyResources)
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Problem 2
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All AJHSME/AMC 8 Problems and Solutions

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