2005 AMC 12B Problems/Problem 19

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Problem

Let $x$ and $y$ be two-digit integers such that $y$ is obtained by reversing the digits of $x$. The integers $x$ and $y$ satisfy $x^{2}-y^{2}=m^{2}$ for some positive integer $m$. What is $x+y+m$?

$\mathrm{(A)}\ 88    \qquad \mathrm{(B)}\ 112   \qquad \mathrm{(C)}\ 116   \qquad \mathrm{(D)}\ 144   \qquad \mathrm{(E)}\ 154   \qquad$

Solution

See also