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1993 AJHSME Problems/Problem 1: Difference between revisions

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==Solution 1==
==Solution 1==
A. The ordered pair <math>{-4,-9}</math> has a product of <math>-4\cdot-9=36</math>


B. The ordered pair <math>{-3,-12}</math> has a product of <math>-3\cdot-12=36</math>
Let's calculate each of the answer choices and see which one DOES NOT equal <math>36</math>.


C. The ordered pair <math>{1/12, -72}</math> has a product of <math>-36</math>
<math>A</math> comes out to be <math>-4 \times -9= 36</math>,


D. The ordered pair <math>{1, 36}</math> has a product of <math>1\cdot36=36</math>
<math>B</math> equals <math>-3 \times -12= 36</math>,


E. The ordered pair <math>{3/2, 24}</math> has a product of <math>3/2\cdot24=36</math>
<math>C</math> is <math>\frac{1}{2} \times -72= -36</math>,


Since C is the only ordered pair which doesn't equal 36, <math>\boxed{\text{(C)}}</math> is the answer.
<math>D</math> simplifies to <math>1 \times 36= 36</math>,
 
and <math>E</math> equals <math>\frac{3}{2} \times 24= 3 \times 12= 36</math>.
 
Thus, our answer is <math>\boxed{C}</math>.


==Solution 2==
==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>
 
~fn106068
In order for a product to be positive (<math>36</math>), 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 <math>\boxed{C}</math>.


==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}}

Latest revision as of 11:05, 27 June 2023

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 (Problems • Answer Key • Resources)
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First
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Problem 2
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All AJHSME/AMC 8 Problems and Solutions

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