Calendar, Odd days, Leap years – Important Formulas & Notes
Numerical Aptitude Notes for APSC Prelims CSAT Paper, SSC and Competitive Exams
Go to Aptitude, Reasoning and Quants Formulas & Notes
Odd Days
To find the day of the week on a given date, use the concept of ‘odd days’.
Number of days more than the complete weeks are called odd days in a given period.
Finding No. of odd Days
1 ordinary year = 365 days = (52 weeks + 1 day.) i.e. 1 ordinary year has 1 odd day.
1 leap year = 366 days = (52 weeks + 2 days) i.e. 1 leap year has 2 odd days.
1 Century = 100 years = 76 ordinary years + 24 leap years = (76 x 1 + 24 x 2) odd days = 124 odd days. = (17 weeks + days) 5 odd days = 5 odd days in 100 years
Odd days in 200 years = (5 x 2) %7 =3 odd days.
Number of odd days in 300 years = (5 x 3) %7 = 1 odd day.
Number of odd days in 400 years = (5 x 4 + 1) %7 = 0 odd day.
Similarly, 800 years, 1200 years, 1600 years, 2000 years has 0 odd days.
Last day of a century cannot be Tuesday or Thursday or Saturday as odd days of any century can be one 0, 1, 3 and 5 days.
For the calendars of two different years to be the same, the conditions to be satisfied are
- Both years must be of the same type. i.e., both years must be ordinary years or both years must be leap years.
- 1st January of both the years must be the same day of the week.