Question

Marvin had a birthday on Tuesday, May 27 in the leap year $2008.$ In what year will his birthday next fall on a Saturday?

$2011$

$2012$

$2013$

$2015$

$2017$

Note that on a normal year, we have that $365 = 52 \cdot 7 + 1,$ which means that for a specific day, it moves to the day after the next year.

On a leap year, the day of the week moves forward two since there is an extra day.

Then in $2009,$ this day falls on a Wednesday. In $2010,$ it falls on a Thursday.

Similarly, in $2011,$ it falls on a Friday. In $2012,$ however, since it is a leap year, it falls on a Sunday.

Now, for the next three years, the day moves forward one. Then in $2016,$ it moves forward two, landing on a Friday.

Finally, in $2017,$ the day of the week is a Saturday.

Thus, E is the correct answer.