# Calender - Aptitude Questions and Answers - RejinpaulPlacement

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1.
What was the day of the week on 16th July, 1776 ?
Solution:   16th July 1776 = (1775 years + Period from 1.1.1776 to 16.7.1776)

Counting of odd days :
Number of odd days in 1600 years = 0
Number of odd days in 100 years = 5

75 years = 18 leap years + 57 ordinary years
= (18 * 2 + 57 * 1) odd days = 93 odd days
= (13 weeks + 2 days) = 2 odd days

1775 years have = (0 + 5 + 2) odd days = 7 odd days = 0 odd days

Jan. + Feb. + March + April + May + June + July
(31 + 29 + 31 + 30 +31 + 30 +16) = 198 days

198 days = (28 weeks + 2 days) = 2 odd days
Total number of odd days = (0 + 2) = 2

Hence, the required day is Tuesday
2.
What was the day of the week on 15th August 1947?
Solution:   15th August 1947 = (1946 years + Period from 1.1.1947 to 15.8.1947)

Counting of odd days:
Odd days in 1600 years = 0
Odd days in 300 years = (5 * 3) = 15 = 1

46 years = (11 leap years + 35 ordinary years)
= (11 * 2 + 35 * 1) odd days = 57 odd days
= (8 weeks + 1 day) = 1 odd day
Odd days in 1946 years = (0 + 1 + 1) = 2 days

Jan. + Fab. + March + April + May + June + July + Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days

227 days = (32 weeks + 3 days) = 3 odd days
Total number of odd days = (2 + 3) = 5

Hence, the required day is Friday.
3.
What was the day of the week on 4th June, 2002?
Solution:   4th June, 2002 = (2001 years + Period from 1.1.2002 to 4.6.2002)

Counting of odd days:
Odd days in 1600 years = 0
Odd days in 1 ordinary year = 1
Odd days in 2001 years = (0 + 0 + 1) = 1

Jan. + Feb. + March + April + May + June
(31 + 28 + 31 + 30 + 31 + 4) = 155 days
= 22 weeks + 1 day = 1 odd day

Total number of odd days = (1 + 1) = 2
Required day is Tuesday.
4.
On what dates of March 2005 did Friday fall?
Answer: (D) 4th, 11th, 18th, 25th
Solution:   First we find the day on 1.3.2005

1.3.2005 = (2004 years + Period from 1.1.2005 to 1.3.2005

Odd days in 1600 years = 0
Odd days in 400 years = 0

4 years = ( 1 leap year + 3 ordinary years)
= (1 * 2 + 3 * 1) odd days = 5 odd days

Jan. + Feb. + March
(31 + 28 + 1) = 60 days = (8 weeks + 4 days) = 4 odd days.

Total number of odd days = (0 + 0 + 5 + 4) = 9 = 2 odd day
1.3.2005 was Tuesday.
So, Friday lies on 4.3.2005

Hence, Friday lies on 4th, 11th, 18th, 25th of March, 2005.
5.
Prove that the Calendar for the year 2003 will serve for the year 2014.
Solution:   We must have same day on 1.1.2003 and 1.1.2014
So, number of odd days between 31.12.2002 and 31.12.2013 must be 0.
This period has 3 leap years and 8 ordinary years.
Number of odd days = (3 * 2 + 8 * 1) = 14 ≡ 0 odd day.

Calendar for the year2003 will serve for the year 2014
6.
January 1, 2007 was Monday. What day of the week lies on January, 2008?
Solution:   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.
7.
January1, 2008 is Tuesday. What day of the week lies on January 1, 2009 ?