Pick two consecutive positive integers whose sum is less than $100$. Square both
of those integers and then find the difference of the squares. Which of the
following could be the difference?
$\mathrm{(A)}\ 2 \qquad \mathrm{(B)}\ 64 \qquad \mathrm{(C)}\ 79 \qquad \mathrm{(D)}\ 96 \qquad \mathrm{(E)}\ 131$
Let the smaller of the two numbers be $x$. Then, the problem states that $(x+1)+x<100$. $(x+1)^2-x^2=x^2+2x+1-x^2=2x+1$. $2x+1$ is obviously odd, so only answer choices C and E need to be considered.
$2x+1=131$ contradicts the fact that $2x+1<100$, so the answer is $\boxed{\mathrm{(C)} 79}$