Aptitude - Calendar

Odd Days :

In calendar questions we are supposed to find the day of the week on a given date. For this, we use the concept of 'odd days'.
In a given period, the number of days more than the complete weeks are called odd days.

Leap Year :

Every year divisible by 4 is a leap year, if it is not a century.

Every 4^th century is a leap year and no other century is a leap year.

Leap year has 366 days.

Each of the years 1952, 2012, 1680 etc. is a leap year.

Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.

None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.

Ordinary year :

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

Counting Odd Days :

1 ordinary year = 365 days = (52 weeks + 1 day.)
∴ 1 ordinary year has 1 odd day.

1 leap year = 366 days = (52 weeks + 2 days.)
∴ 1 leap year has 2 odd days.

100 years = 76 ordinary years + 24 leap years
= (76 x 1 + 24 x 2) odd days = 124 odd days.
= (17 weeks + 5 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.

Day of the Week Related to Odd Days :