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

m (Solution)
 
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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]]:  
<cmath>\begin{tabular}[t]{|c|c|c|}
+
<cmath>\begin{array}{|c|c|c|}
\multicolumn{3}{t}{} \\ \hline
+
\multicolumn{3}{}{} \\ \hline
 
\diamondsuit & \Delta & \diamondsuit + \Delta \\ \hline
 
\diamondsuit & \Delta & \diamondsuit + \Delta \\ \hline
 
36 & 1 & 37 \\ \hline
 
36 & 1 & 37 \\ \hline
Line 16: Line 16:
 
9 & 4 & 13 \\ \hline
 
9 & 4 & 13 \\ \hline
 
6 & 6 & 12 \\ \hline
 
6 & 6 & 12 \\ \hline
\end{tabular}</cmath>
+
\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.

Latest revision as of 19:37, 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 (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

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