Difference between revisions of "1993 AJHSME Problems/Problem 1"

(Solution 1)
(Solution 2)
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Thus, our answer is C. It is the only negative result.
 
Thus, our answer is C. It is the only negative result.
  
==Solution 2==
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Solution 2
We know that if we want a product of 36, both numbers have to be positive or negative. Scanning the number pairs, the only choice with one negative number and one positive number is <math>\boxed{\text{(C)}}</math>
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~fn106068
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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==
 
==See Also==
 
{{AJHSME box|year=1993|before=First<br />Question|num-a=2}}
 
{{AJHSME box|year=1993|before=First<br />Question|num-a=2}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 18:31, 28 January 2022

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)
Preceded by
First
Question
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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