1952 AHSME Problems/Problem 28
Problem
In the table shown, the formula relating x and y is:
![\[\begin{array}{|c|c|c|c|c|c|}\hline x & 1 & 2 & 3 & 4 & 5\\ \hline y & 3 & 7 & 13 & 21 & 31\\ \hline\end{array}\]](http://latex.artofproblemsolving.com/a/f/f/aff8c0c2bd3960b9c54ff61ff338bd697fa84bcd.png)
Solution
A simple method of solving the problem is trying each of the answer choices. One can plug in values of x and y for each, because many x-values and their single corresponding y-values are given.
- Choice A works for (1,3) and (2,7) but fails to work on (3,13) because 3*4=12 and 12-1=11, not 13.
- Choice B doesn't work for (2,7) because it would be 8-4+2+2=8, not 7.
- Choice C actually works for all five pairs, being 1+1+1=3, 4+2+1=7, 9+3+1=13, 16+4+1=21, and 25+5+1=31.
Thus, the answer is 
.
See also
| 1952 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 27 |
Followed by Problem 29 | |
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| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
