Introduction
Calendar deals with odd days, leap year, ordinary year, counting of odd days, and day of the week related to odd days. To find the day of the week on a given date concept of odd days is used. The article Calendar Quiz 3 lists important Calendar practice questions for competitive exams like RRB ALP/Technical Exams/Junior Engineer Recruitment Exams, SSC, IBPS PO Exams and etc.
Concepts
Odd days:
Extra days, apart from the complete weeks in given periods are called odd days.
Note: An ordinary year has one day while a leap year has two odd days.
Leap year:
A leap year is divisible by 4 except for a century. For a century to be a leap year, it must be divisible by 400.
Examples:
- Years like 1988, 2008 are leap year (divisible by 4).
Centuries like 2000, 2400 are leap year ( divisible by 400).
Years like 1999, 2003 are not leap year (not divisible by 4).
Centuries like 1700, 1800 are not leap year ( not divisible by 400).
In a century, there is 76 ordinary year and 24 leap year.
Note: A leap year has 366 days(52 complete weeks + 2 extra days = 366 days).
Ordinary year:
Ordinary year is other than leap years. A ordinary year has 365 days.
Counting of odd days:
(i) 1 ordinary year = 365 days = (52 weeks + 1 day).
An ordinary year has one odd day.
(ii) 1 leap year = 366 days = (52 weeks + 2 days).
A leap year has 2 odd days.
Day of the week related to odd days:
Let the number of days be 0, 1, 2, 3, 4, 5 , 6 and their days are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday respectively.
Q1
What was the day of the week on, 16th July, 1776?
- A. Tuesday
B. Wednesday
C. Monday
D. Saturday
16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days:
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 2 days)
Total number of odd days = (0 + 2) = 2.
Required day was 'Tuesday'.
Q2
If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
- A. Sunday
B. Saturday
C. Tuesday
D. Wednesday
The year 2004 is a leap year. So, it has 2 odd days.
But, Feb 2004 not included because we are calculating from March 2004 to March 2005.
So it has 1 odd day only.
The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.
Given that, 6th March, 2005 is Monday.
6th March, 2004 is Sunday (1 day before to 6th March, 2005).
Q3
On what dates of April, 2001 did Wednesday fall?
- A. 2nd, 9th, 16th, 23rd
B. 12th, 18th, 27th, 6th
C. 4th, 11th, 18th, 25th
D. 1st, 8th, 15th, 22nd
We shall find the day on 1st April, 2001.
1st April, 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001)
Odd days in 1600 years = 0
Odd days in 400 years = 0
Jan. Feb. March April
(31 + 28 + 31 + 1) = 91 days 0 odd days.
Total number of odd days = (0 + 0 + 0) = 0
On 1st April, 2001 it was Sunday.
In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th.
Q4
On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?
- A. Saturday
B. Friday
C. Monday
D. Tuesday
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
So, 8th Dec, 2006 is Friday.
Q5
On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
- A. Tuesday
B. Saturday
C. Friday
D. Sunday
The year 2004 is a leap year. It has 2 odd days.
The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005.
Hence, this day is Sunday