Question

How many of the following statements have to be true?
i. No year can have 5 Sundays in the month of May and 5 Thursdays in the month of June.
ii. If Feb 14th of a certain year is a Friday, May 14th of the same year cannot be a Thursday
iii. If a year has 53 Sundays, it can have 5 Mondays in the month of May.
0
1
2
3

Answer 1

Answer:

Nothing is true

Step-by-step explanation:

Answer 2

The correct answer is 1

GIVEN

1. No year can have 5 Sundays in the month of May and 5 Thursdays in the month of June.
2. If Feb 14th of a certain year is a Friday, May 14th of the same year cannot be a Thursday
3. If a year has 53 Sundays, it can have 5 Mondays in the month of May.

TO FIND

How many sentences are true.

SOLUTION

We can simply solve the above problem as follows -

(1) If an year has 5 sundays in the month of june then,

It can have - 5 sundays, 5 mondays and 5 tuesdays.

or,

5 saturdays, 5 sundays and 5 mondays.

or,

5 fridays, 5 saturdays and 5 sundays.

or,

31st of may can be Sunday, Monday or Tuesday.

So, First day of june can be Monday, Tuesday or Wednesday.

June will have 5 Wednesdays and Thursday.

Hence, Statement 1 is not true.

(ii) If Feb 14th of a certain year is a Friday, May 14th of the same year cannot be a Thursday.

Feb 14th = Thursday

March 14 can be either Thursday or Friday (February has 28 days, 1 leap day in a leap year)

March 14th can either be Friday or saturday.

Then,

May 14th can be either Wednesday or Thursday.

Hence, Statement 2 is incorrect.

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

If a year has 53 mondays - It can be either a leap year starting on sundays or saturdays.

Or a non-leap year starting on sundays.

Therefore,

1st Jan = sunday.

29th Jan = Sunday.

Feb 5th = sunday

March 5th = Sunday

March 26th = Sunday

April 2nd = Sunday

April 30th = Sunday

May 1st = Monday

Therefore, Mondays can have 5 Sundays.

Hence, statement 3 is correct.

Therefore, The correct answer is 1

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