1. Which two months in a year have the same calendar?

a) October, December

b) April, November

c) June, October

d) April, July

Explanation: If the period between the two months is divisible by 7, then that two months will have the same calendar.

(a) Oct + Nov = 31 + 30 = 61 (not divisible by 7)

(b) Apr + May + Jun + Jul + Aug + Sep + Oct = 30 + 31 + 30 + 31 + 31 + 30 + 31 = 214 (not divisible by 7)

(c) Jun + July + Aug + Sep = 30 + 31 + 31 + 30 = 122 (not divisible by 7)

(d) Apr + May + June = 30 + 31 + 30 = 91 (divisible by 7)

Hence, April and July months will have the same calendar.

2. How many leap years do 300 years have?

a) 75

b) 74

c) 72

d) 73

Explanation: Given year is divided by 4, and the quotient gives the number of leap years.

Here, 300 ÷ 4 = 75

But, as 100, 200 and 300 are not leap years ⇒ 75 - 3 = 72 leap years.

3. On what dates of July. 2004 did Monday fall?

a) 6^{th}, 10^{th}, 21^{th}, 30^{th}

b) 12^{th}, 7^{th}, 19^{th}, 28^{th}

c) 5^{th}, 10^{th}, 24^{th}, 17^{th}

d) 5^{th}, 12^{th}, 19^{th}, 26^{th}

Explanation: Let us find the day on 1

^{st}July, 2004.

2000 years have 0 odd day. 3 ordinary years have 3 odd days.

Jan. Feb. March April May June July

31 + 29 + 31 + 30 + 31 + 30 + 1

= 183 days

= (26 weeks + 1 day)

Total number of odd days = (0 + 3 + 1) odd days = 4 odd days.

1

^{st}July 2004 was 'Thursday'

Thus, 1

^{st}Monday in July 2004 as on 5

^{th}July. Hence, during July 2004, Monday fell on 5th, 12th, 19th and 26th.

4. The year next to 2005 will have the same calendar as that of the year 2005?

a) 2016

b) 2022

c) 2011

d) None

Explanation: Repetition of leap year ⇒ Add + 28 to the Given Year.

Repetition of non leap year

Step 1 : Add + 11 to the Given Year. If Result is a leap year, Go to step 2.

Step 2: Add + 6 to the Given Year.

Given Year is 2005, Which is a non leap year.

Step 1 : Add + 11 to the given year (i.e 2005 + 11) = 2016, Which is a leap year.

Step 2 : Add + 6 to the given year (i.e 2005 + 6) = 2011

Therefore, The calendar for the year 2005 will be same for the year 2011

5. If Feb 12^{th},1986 falls on Wednesday then Jan 1^{st},1987 falls on which day?

a) Wednesday

b) Tuesday

c) Thursday

d) Friday

Explanation: First,we count the number of odd days for the left over days in the given period.

Here,given period is 12.2.1986 to 1.1.1987

Feb Mar Apr May June July Aug Sept Oct Nov Dec Jan

16 31 30 31 30 31 31 30 31 30 31 1 (left days)

2 + 3 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 2 + 3 + 1(odd days)

= 1 odd day

So, given day Wednesday + 1 = Thursday is the required result.

6. What was the day of the week on 16^{th} August, 1947?

a) Sunday

b) Monday

c) Saturday

d) Thursday

Explanation: 15

^{th}August, 1947 = (1946 years + Period from 1

^{st}Jan., 1947 to 15th )

Counting of odd days:

1600 years have 0 odd day. 300 years have 1 odd day.

47 years = (11 leap years + 36 ordinary years)

= [(11 x 2) + (36 x 1) ] odd days

= 58 odd days

= 2 odd days

Jan Feb Mar Apr May Jun Jul Aug

= 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15

= 227 days

= (32 weeks + 3 days)

= 3

Total number of odd days

= (0 + 1 + 2 + 3) odd days

= 6 odd days

Hence, the required day was 'Saturday'.

7. Prove that any date in March of a year is the same day of the week corresponding date in November that year.

a) Same day

b) Not same day

c) Next day

d) Previous day

Explanation: We will show that the number of odd days between last day of February and last day of October is zero.

March April May June July Aug. Sept. Oct.

31 + 30 + 31 + 30 + 31 + 31 + 30 + 31

= 241 days

= 35 weeks

= 0 odd day

Number of odd days during this period = 0.

Thus, 1

^{st}March of an year will be the same day as 1

^{st}November of that year. Hence, the result follows.

8. If today is Saturday, what will be the day 350 days from now ?

a) Saturday

b) Friday

c) Sunday

d) Monday

Explanation: 350 days = $$\frac{{350}}{7}$$ = 50 weeks, i.e No odd days,

So it will be a Saturday.

9. The calendar for the year 1988 is same as which upcoming year ?

a) 2012

b) 2014

c) 2016

d) 2010

Explanation: We already know that the calendar after a leap year repeats again after 28 years.

Here 1988 is a Leap year, then the same calendar will be in the year = 1988 + 28 = 2016.

10. Given that on 9^{th} August 2016 is Saturday. What was the day on 9^{t}h August 1616 ?

a) Saturday

b) Sunday

c) Friday

d) Monday

Explanation: We know that, After every 400 years, the same day occurs.

If 9

^{th}August 2016 is Saturday, before 400 years

i.e., on 9

^{th}August 1616 has to be Saturday.