Difference between revisions of "1988 AJHSME Problems/Problem 14"

(New page: ==Problem== <math>\diamondsuit </math> and <math>\Delta </math> are whole numbers and <math>\diamondsuit \times \Delta =36</math>. The largest possible value of <math>\diamondsuit + \Del...)
 
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==Problem==
 
==Problem==
  
<math>\diamondsuit </math> and <math>\Delta </math> are whole numbers and <math>\diamondsuit \times \Delta =36</math>.  The largest possible value of <math>\diamondsuit + \Delta </math> is  
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<math>\diamondsuit </math> and <math>\Delta </math> are [[whole number|whole numbers]] and <math>\diamondsuit \times \Delta =36</math>.  The largest possible value of <math>\diamondsuit + \Delta </math> is  
  
 
<math>\text{(A)}\ 12 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 15 \qquad \text{(D)}\ 20\ \qquad \text{(E)}\ 37</math>
 
<math>\text{(A)}\ 12 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 15 \qquad \text{(D)}\ 20\ \qquad \text{(E)}\ 37</math>
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==Solution==
 
==Solution==
  
Since it doesn't take too long, we can just make a table with all the possible values of the sum:  
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Since it doesn't take too long, we can just make a table with all the possible values of the [[sum]]:  
 
<cmath>\begin{tabular}[t]{|c|c|c|}
 
<cmath>\begin{tabular}[t]{|c|c|c|}
 
\multicolumn{3}{t}{} \\ \hline
 
\multicolumn{3}{t}{} \\ \hline
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==See Also==
 
==See Also==
  
[[1988 AJHSME Problems]]
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{{AJHSME box|year=1988|num-b=13|num-a=15}}
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]

Revision as of 07:23, 3 June 2009

Problem

$\diamondsuit$ and $\Delta$ are whole numbers and $\diamondsuit \times \Delta =36$. The largest possible value of $\diamondsuit + \Delta$ is

$\text{(A)}\ 12 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 15 \qquad \text{(D)}\ 20\ \qquad \text{(E)}\ 37$

Solution

Since it doesn't take too long, we can just make a table with all the possible values of the sum:

\[\begin{tabular}[t]{|c|c|c|}
\multicolumn{3}{t}{} \\ \hline
\diamondsuit & \Delta & \diamondsuit + \Delta \\ \hline
36 & 1 & 37 \\ \hline
18 & 2 & 20 \\ \hline
12 & 3 & 15 \\ \hline
9 & 4 & 13 \\ \hline
6 & 6 & 12 \\ \hline
\end{tabular}\] (Error compiling LaTeX. Unknown error_msg)

Clearly $37\rightarrow \boxed{\text{E}}$ is the largest.

See Also

1988 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
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