IMAT 2011 Q28 [Cousins]

I have two cousins. One was born the year before me, on June 3rd. The other was born the year after me, on April 28th.

My birthday is May 15th.

For how many days each year am I the same age as one or other of my cousins?

A. 35

B. 36

C. 37

D. 38

E. 39

Some Quick Questions to ask yourself when doing this type of problem solving:

  • What is being asked? Underline the specifics in the question.
  • Analyse the data, is there anything we can eliminate immediately?
  • What information do I need to solve the question? Where can I find it?
  • How can I draw or use the graph to help me?

The trickiest thing in this question is knowing how many days each month has. I know it can be trivial, but especially on the exam day, you will doubt yourself. Here is an easy trick to remember which months have 30 or 31 days.

(credit: modification of work by Cory Zanker)

We can break the question into two pieces, how long you are the same age with the older cousin (cousin 1) and how old you are with the second cousin (cousin 2).

Cousin 1

Interval between May 15th and June 3rd. From our knuckle trick, we know that May has 31 days. Therefore there are 19 days between both birthdays here when they will be the same age. Remember to include May 15 in your count.

Cousin 2

Interval between April 28th and May 15th. April has 30 days, therefore there is 17 days between both birthdays.

19 + 17 = 36

Therefore the answer is B.