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 nonleap year that starts on Sunday, or leap year that starts on Sunday or Saturday.
Nonleap 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)