If $496=2^{m}-2^{n}$, where $m$ and $n$ are integers, then $m+n$ is equal to
(A) 13
(B) 9
(C) 4
(D) 14
(E) 5
Since 496 is less than $2^{m}$, we might think to look for a power of 2 bigger than, but close to $496.2^{9}=512$ works and in fact $496=512-16=2^{9}-2^{4}$ and so $m+n=9+4=13$. (This can also be done using an algebraic approach.)