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

(See Also)
(Solution 2)
 
(4 intermediate revisions by 3 users not shown)
Line 3: Line 3:
 
<math> \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\} </math>
 
<math> \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\} </math>
  
==Solution==
+
==Solution 1==
A.The ordered pair <math>{-4,-9}</math> has a product of <math>-4*-9=36</math>
+
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*-12=36</math>
+
B. The ordered pair <math>{-3,-12}</math> has a product of <math>-3\cdot-12=36</math>
  
 
C. The ordered pair <math>{1/12, -72}</math> has a product of <math>-36</math>
 
C. The ordered pair <math>{1/12, -72}</math> has a product of <math>-36</math>
  
D. The ordered pair <math>{1, 36}</math> has a product of <math>1*36=36</math>
+
D. The ordered pair <math>{1, 36}</math> has a product of <math>1\cdot36=36</math>
  
E. The ordered pair <math>{3/2, 24}</math> has a product of <math>3/2*24=36</math>
+
E. The ordered pair <math>{3/2, 24}</math> has a product of <math>3/2\cdot24=36</math>
  
Since C is the only ordered pair which doesn't equal 36, <math>\boxed{C}</math> is the answer.
+
Since C is the only ordered pair which doesn't equal 36, <math>\boxed{\text{(C)}}</math> is the answer.
 +
 
 +
==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
  
 
==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}}

Latest revision as of 19:55, 23 July 2021

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

A. The ordered pair ${-4,-9}$ has a product of $-4\cdot-9=36$

B. The ordered pair ${-3,-12}$ has a product of $-3\cdot-12=36$

C. The ordered pair ${1/12, -72}$ has a product of $-36$

D. The ordered pair ${1, 36}$ has a product of $1\cdot36=36$

E. The ordered pair ${3/2, 24}$ has a product of $3/2\cdot24=36$

Since C is the only ordered pair which doesn't equal 36, $\boxed{\text{(C)}}$ is the answer.

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 $\boxed{\text{(C)}}$ ~fn106068

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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS