2010 AMC 10A Problem 10

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

Each non-leap year shifts the weekday forward by

1

Since May

27

is after leap day, leap years shift it forward by

2

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.

Problem 10 in other years