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

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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]]:  
 
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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<cmath>\begin{tabular}[t]{|c|c|c|}
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<cmath>\begin{array}{|c|c|c|}
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\multicolumn{3}{t}{} \\ \hline
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\multicolumn{3}{}{} \\ \hline
 
\diamondsuit & \Delta & \diamondsuit + \Delta \\ \hline
 
\diamondsuit & \Delta & \diamondsuit + \Delta \\ \hline
 
36 & 1 & 37 \\ \hline
 
36 & 1 & 37 \\ \hline
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9 & 4 & 13 \\ \hline
 
9 & 4 & 13 \\ \hline
 
6 & 6 & 12 \\ \hline
 
6 & 6 & 12 \\ \hline
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\end{tabular}</cmath>
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\end{array}</cmath>
  
 
Clearly <math>37\rightarrow \boxed{\text{E}}</math> is the largest.
 
Clearly <math>37\rightarrow \boxed{\text{E}}</math> is the largest.
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{{AJHSME box|year=1988|num-b=13|num-a=15}}
 
{{AJHSME box|year=1988|num-b=13|num-a=15}}
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 18:37, 10 March 2015

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: \[\begin{array}{|c|c|c|} \multicolumn{3}{}{} \\ \hline \diamondsuit & \Delta & \diamondsuit + \Delta \\ \hline 36 & 1 & 37 \\ \hline 18 & 2 & 20 \\ \hline 12 & 3 & 15 \\ \hline 9 & 4 & 13 \\ \hline 6 & 6 & 12 \\ \hline \end{array}\]

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

See Also

1988 AJHSME (Problems • Answer Key • Resources)
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

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