Marvin had a birthday on Tuesday, May 27 in the leap year $2008$. In what year will his birthday next fall on a Saturday?
$\mathrm{(A)}\ 2011 \qquad \mathrm{(B)}\ 2012 \qquad \mathrm{(C)}\ 2013 \qquad \mathrm{(D)}\ 2015 \qquad \mathrm{(E)}\ 2017$
$\boxed{(E)}$ $2017$
There are $365$ days in a non-leap year. There are $7$ days in a week. Since $365 = 52 \cdot 7 + 1$ (or $365\equiv 1 \pmod{ 7}$), the same date (after February) moves "forward" one day in the subsequent year, if that year is not a leap year.
For example:
$5/27/08$	Tue
$5/27/09$	Wed
However, a leap year has $366$ days, and $366 = 52 \cdot 7 + 2$ . So the same date (after February) moves "forward" two days in the subsequent year, if that year is a leap year.
For example:
$5/27/11$	Fri
$5/27/12$	Sun
You can keep counting forward to find that the first time this date falls on a Saturday is in $2017$:
$5/27/13$	Mon
$5/27/14$	Tue
$5/27/15$	Wed
$5/27/16$	Fri
$5/27/17$	Sat