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 14th of
a certain year is a Friday, May 14th of the same year cannot
be a Thursday
- If a year has 53 Sundays,
it can have 5 Mondays in the month of May
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 1st 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.
If Feb 14th of a certain year is a
Friday, May 14th 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.
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 1st = Sunday, jan 29th = Sunday. Feb 5th
is Sunday. Mar 5th is Sunday, Mar 26 is Sunday. Apr 2nd
is Sunday. Apr 30th is Sunday, May 1st is Monday. May
will have 5 Mondays.
So, statement C can be true.
Only one of the
three statements needs to be true. Answer