## Calendar Questions and Answers Part-1

1. On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?
a) Thursday
b) Sunday
c) Tuesday
d) Friday

Explanation:
The year 2006 is an ordinary year. So, it has 1 odd day.
So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.
But, 8th Dec, 2007 is Saturday.
∴ 8th Dec, 2006 is Friday.

2. It was Thursday on 12th January 2006. What day of the week it will be on January 12th 2007 ?
a) Thursday
b) Saturday
c) Friday
d) Wednesday

Explanation:
There is exactly 1 year, (365 days) between two dates.
2006 is an ordinary year. It has one odd day.
The day of the week on January 12th 2007 is one day beyond Thursday ⇒ Friday

3. If 1st October is Sunday, then 1st November will be
a) Thursday
b) Wednesday
c) Monday
d) Tuesday

Explanation:
Given that 1st October is Sunday
Number of days in October = 31
31 days = 3 odd days
(As we can reduce multiples of 7 from odd days which will not change anything)
Hence 1st November = (Sunday + 3 odd days) = Wednesday

4. What day of the week was 20th June 1837?
a) Wednesday
b) Tuesday
c) Monday
d) Thursday

Explanation:
20th June, 1837 means 1836 complete years + first 5 months of the year 1837 + 20 days of June
1600 years give no odd days
200 years give 3 odd days
36 years give (36 + 9 ) or 3 odd days
Thus 1836 years give 6 odd days
From 1st January to 20th June there are 3 odd days
Odd days: January 3, February 0, March 3, April 2, May 3, June 6 = 17
Thus the total number of odd days = 6 + 3 or 2 odd days
This means that the 20th of June fell on 2nd day commencing from Monday.
The required day was Tuesday.

5. If today is Monday, what will be the day 350 days from now?
a) Monday
b) Thursday
c) Tuesday
d) Wednesday

Explanation:
350 days, $$\frac{{350}}{7}$$ = 50, no odd days, so it will be a Monday.

6. What was the day on 25th January, 1975?
a) Friday
b) Sunday
c) Saturday
d) Monday

Explanation:
Counting the years 1600 + 300 + 74
In 1600 years, there are zero odd days
In 300 years, there is one odd day
In 74 years, there are 18 leap years and 56 normal years, so the odd days are:
18(2) + 56(1) = 36 + 56 = 92,
Which is 13 weeks and 1 odd day
In 25 days of January, 1975, there are 3 weeks and 4 odd days
Total odd days = 0 + 1 + 1 + 4
six odd days, so it was a Saturday.

7. January 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?
a) Sunday
b) Wednesday
c) Monday
d) Thursday

Explanation:
The year 2008 is a leap year. So, it has 2 odd days.
1st day of the year 2008 is Tuesday (Given)
So, 1st day of the year 2009 is 2 days beyond Tuesday.
Hence, it will be Thursday.

8. On 2007, What was the date of last Saturday in May month?
a) 24th May
b) 28th May
c) 26th May
d) 22th May

Explanation:
1 - May - 2007
\eqalign{ & = \frac{{1 + 2 + 7 + 1 + 6}}{7} \cr & = \frac{{17}}{7} \cr & = 3 \cr & = {\text{Tuesday}} \cr}
= May 1st → Tuesday + 5 days = Saturday = 5th may
5th may + 7 days = Saturday = 12th may
12th may + 7 days = Saturday = 19th may
19th may + 7 days = Saturday = 26th may

9. What was the day of the week on 10th March 1996?
a) Friday
b) Saturday
c) Thursday
d) Sunday

Explanation:
\eqalign{ & \frac{{10 + 4 + 96 + 24 + 0}}{7} \cr & = \frac{{134}}{7} \cr & = 1 \cr & = {\text{Sunday}} \cr}

10. What day of the week will 22 Apr 2222 be?
a) Monday
b) Wednesday
c) Tuesday
d) Thursday

Explanation:
22 Apr 2222 = (2221 years + period from 1-Jan-2222 to 22-Apr-2222)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2200
= Number of odd days in 200 years
= 5 x 2 = 10 = 3
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
Number of odd days in the period 2201-2221
= 16 normal years + 5 leap years
= 16 x 1 + 5 x 2 = 16 + 10 = 26 = 5 odd days
Number of days from 1-Jan-2222 to 22 Apr 2222
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 22(Apr) = 112
112 days = 0 odd day
Total number of odd days = (0 + 3 + 5 + 0) = 8 = 1 odd day
1 odd days = Monday
Hence 22 Apr 2222 is Monday