Sol : Option C
100 years contain 5 odd days.
Therefore, Last day of 1st century is Friday
200 years contain (5 x2) is 3 odd days (approx.)
Last day of 2nd century is Wednesday
300 years contain ( 5x3) = 15 i.e. 1 odd day( approx.)
Last day of 3rd century is Monday
400 years contain 0 odd day
Last day of 4th century is Sunday.
Thus, the cycle is repeated.
Last day of a century cannot be Tuesday or Thursday or Saturday.

Sol : Option D
16th July, 1776 = (1775 years + time period from Jan 1, 1776 to July 16, 1776)
Counting of odd days:

1600 years: 0 odd day.

100 years: 5 odd days.

75 years = (57 ordinary years + 18 leap years) = [((57 × 1) + (18 × 2)] = 93 days (13 weeks + 2 days) = 2 odd days.
1775 years have (0 + 5 + 2) odd days or 7 odd days = 0 odd day.
January February March April May June July
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (2 days + 28 weeks)
∴Total number of odd days = 2
So, the required day was 'Tuesday'.

Q.3. If it was Tuesday on 3rd Jan, 2006. What was the day on Jan 3, 2010?

A. Saturday

B. Tuesday

C. Wednesday

D. Sunday

Sol : Option D
It was Saturday on 31st December, 2005.
Number of odd days from 2006 to 2009 = (1 + 1 + 2 + 1) = 5 days.
∴On December 31, 2009, it was Thursday. Thus, on Jan 3, 2010 it was Sunday.

Q.4. What was the day on 15th August, 2010?

A. Saturday

B. Sunday

C. Monday

D. Tuesday

Sol : Option B
15th August, 2010 = (2009 years + time period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = 7 normal years + 2 leap years = (7 × 1 + 2 × 2) = 11 = 4 odd days.
January February March April May June July August
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days that is 3 odd days
Total number of odd days = (0 + 0 + 4 + 3) = 7 = 0 odd days.
Given day is Sunday.

Q.5. If 13th March, 2005 was Wednesday, what was the day of the week on 13th March, 2004?

A. Rs. Monday

B. Rs. Wednesday

C. Rs. Friday

D. Rs. Tuesday

Sol : Option D
We know year 2004 is a leap year. Therefore, it has 2 odd days.
Feb 2004 was not included as we are calculating from March 2004 to March 2005.
So it has 1 odd day.
The day on March 13, 2005 will be 1 day ahead of the day on March 13, 2004.
Given that, March 13, 2005 is Wednesday.
So March 13, 2004 is Tuesday (1 day before to 13th March, 2005).

Q.6. January 1, 2007 was Monday. What was the day on Jan. 1, 2008?

A. Saturday

B. Friday

C. Tuesday

D. Monday

Sol : Option C
The year 2007 is an ordinary year. So, it has 1 odd day.
1st day of the year 2007 was Monday
1st day of the year 2008 will be 1 day beyond Monday
Hence, it will be Tuesday.

Q.7. If 7th Dec, 2007 was Friday. What day of the week was on 7th Dec, 2006?

A. Saturday

B. Thursday

C. Monday

D. Sunday

Sol : Option B
The year 2006 was an ordinary year. So, it has 1 odd day.
The day on 7th Dec, 2007 will be 1 day beyond the day on 7th Dec, 2006.
But, 7th Dec, 2007 is Friday
So, 7th Dec, 2006 is Thursday.

Q8. The calendar for the year 2007 is the same for the year

A. 2018

B. 2019

C. 2022

D. 2025

Sol : Option A
Count the number of odd days from the year 2007 onwards to get the sum equal to 0 odd day.
Sum = 14 odd days 0 odd days
Calendar for the year 2018 will be the same as for the year 2007

Sol : Option C
15th August, 1947 = (1946 years + time period from 1st 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 × 2) + (36 × 1)] odd days = 58 odd days
= 2 odd days.
Jan. Feb. March April May June July August
31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 = 227 days » 3 odd days,
Total number of odd days = (0 + 1 + 2 + 3) odd days = 6 odd days.
Hence, the required day was 'Saturday'.

Q10. On what dates of July 2003 did Sunday fall?

A. 5th,10th,24th,17th

B. 6th,13th,20th,27th

C. 5th, 12th, 19th, 26th

D. 12th,7th,19th,28th

Sol : Option B
Let us find the day on 1st July, 2003.
2000 years have 0 odd day. 2 ordinary years have 2 odd days.
Jan Feb March April May June July
31 + 28 + 31 + 30 + 31 + 30 + 1 = 182 days = 0 odd day.
Total number of odd days = (0 + 0 + 2) odd days = 2 odd days.'
:. 1st July 2003 was 'Tuesday',-,-
Thus, 1st Sunday in July 2003 is 6th July.
So, during July 2003, Monday fell on 6th, 13th, 20th and 27th.