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Difference between revisions of "2005 AMC 12B Problems/Problem 19"
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== Problem ==
 
== Problem ==
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Let <math>x</math> and <math>y</math> be two-digit integers such that <math>y</math> is obtained by reversing the digits of <math>x</math>. The integers <math>x</math> and <math>y</math> satisfy <math>x^{2}-y^{2}=m^{2}</math> for some positive integer <math>m</math>. What is <math>x+y+m</math>?
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<math>
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\mathrm{(A)}\ 88    \qquad
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\mathrm{(B)}\ 112  \qquad
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\mathrm{(C)}\ 116  \qquad
 +
\mathrm{(D)}\ 144  \qquad
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\mathrm{(E)}\ 154  \qquad
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</math>
  
 
== Solution ==
 
== Solution ==

Revision as of 00:14, 4 February 2011

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

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