Aptitude ➤ Calendar ➤ Set 1

#### Calendar : Important Facts and Formulae

Under this heading we mainly deal with finding the day of the week on a particular given date the process of finding it lies on obtaining the number of odd days.

1. Odd Days:
In a given period, the number of days more than the complete weeks are called odd days.

2. Leap Year:
(i). Every year divisible by 4 is a leap year, if it is not a century.
(ii). Every 4th century is a leap year and no other century is a leap year.
Note: A leap year has 366 days.
Examples:
i. Each of the years 1948, 2004, 1676 etc. is a leap year.
ii. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
iii. None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.

3. Ordinary Year:
The year which is not a leap year is called an ordinary years. An ordinary year has 365 days.

4. Counting of Odd Days:
i) 1 ordinary year = 365 days = (52 weeks + 1 day.)
∴ 1 ordinary year has 1 odd day.
ii) 1 leap year = 366 days = (52 weeks + 2 days)
∴ 1 leap year has 2 odd days.
iii) 100 years = 76 ordinary years + 24 leap years
= (76 × 1 + 24 × 2) odd days = 124 odd days.
= (17 weeks + days) ≡ 5 odd days.

∴ Number of odd days in 100 years = 5.
Number of odd days in 200 years = (5 x 2) ≡ 3 odd days.
Number of odd days in 300 years = (5 x 3) ≡ 1 odd day.
Number of odd days in 400 years = (5 x 4 + 1) ≡ 0 odd day.
Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.

5. Day of the Week Related to Odd Days:

No. of Days 0123456
DaySunMonTueWedThursFriSat

Question 1
Q1.  January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
Question 2
Q2.  January 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?
Question 3
Q3.  On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?
Question 4
Q4.  If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
Question 5
Q5.  The calendar for the year 2007 will be the same for the year: 