Difference between revisions of "1988 AJHSME Problems/Problem 14"
5849206328x (talk | contribs) (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 | + | <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: | + | Since it doesn't take too long, we can just make a table with all the possible values of the [[sum]]: |
| − | <cmath>\begin{ | + | <cmath>\begin{array}{|c|c|c|} |
| − | \multicolumn{3}{ | + | \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 | ||
| − | \end{ | + | \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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==See Also== | ==See Also== | ||
| − | + | {{AJHSME box|year=1988|num-b=13|num-a=15}} | |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 18:37, 10 March 2015
Problem
and 
are whole numbers and 
. The largest possible value of 
is
Solution
Since it doesn't take too long, we can just make a table with all the possible values of the sum:
![\[\begin{array}{|c|c|c|} \multicolumn{3}{}{} \\ \hline \diamondsuit & \Delta & \diamondsuit + \Delta \\ \hline 36 & 1 & 37 \\ \hline 18 & 2 & 20 \\ \hline 12 & 3 & 15 \\ \hline 9 & 4 & 13 \\ \hline 6 & 6 & 12 \\ \hline \end{array}\]](http://latex.artofproblemsolving.com/3/d/4/3d4b845dfe3ac5e8b23b734971756edf7d61e360.png)
Clearly 
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
