### CAT Calendar Questions

**Question**

How many of the following
statements have to be true?

- No year can have 5 Sundays in the month of May and 5 Thursdays in the month of June
- If Feb 14
^{th}of a certain year is a Friday, May 14^{th}of the same year cannot be a Thursday - If a year has 53 Sundays, it can have 5 Mondays in the month of May

A. 0

B. 1

C. 2

D. 3

**Answer: Choice (B)**

**Explanation**

I.
No year can have 5 Sundays in the month of May
and 5 Thursdays in the month of June

A year has 5 Sundays in the month
of May => it can have 5 each of Sundays, Mondays and Tuesdays, or 5 each of
Saturdays, Sundays and Mondays, or 5 each of Fridays, Saturdays and Sundays.
Or, the last day of the Month can be Sunday, Monday or Tuesday.

Or, the 1

^{st}of June could be Monday, Tuesday or Wednesday. If the first of June were a Wednesday, June would have 5 Wednesdays and 5 Thursdays. So, statement I need not be true.
II.
If Feb 14

^{th}of a certain year is a Friday, May 14^{th}of the same year cannot be a Thursday
From Feb 14 to Mar 14, there are
28 or 29 days, 0 or 1 odd day

Mar 14 to Apr 14, there are 31
days, or 3 odd datys

Apr 14 to May 14 there are 30 days
or 2 odd days

So, Feb 14 to May 14, there are
either 5 or 6 odd days

So, if Feb 14 is Friday, May 14
can be either Thursday or Wednesday. So, statement 2 need not be true.

III.
If a year has 53 Sundays, it can have 5 Mondays
in the month of May

Year has 53 Sundays => It is
either a non-leap year that starts on Sunday, or leap year that starts on
Sunday or Saturday.

Non-leap year starting on Sunday:
Jan 1

^{st}= Sunday, jan 29^{th}= Sunday. Feb 5^{th}is Sunday. Mar 5^{th}is Sunday, Mar 26 is Sunday. Apr 2^{nd}is Sunday. Apr 30^{th}is Sunday, May 1^{st}is Monday. May will have 5 Mondays.
So, statement C can be true.

Only one of the
three statements needs to be true.

**Answer Choice (B)**Labels: 2IIM, 2iim Chennai, CAT 2013, CAT 2013 questions, CAT Calendars, CAT Coaching classes, CAT Coaching classes Chennai

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