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Calendar - Important Formulas | Aptitude

  1. Odd Days:
    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.
  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:
    1. Each of the years 1948, 2004, 1676 etc. is a leap year.
    2. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
    3. 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:
    1. 1 ordinary year = 365 days = (52 weeks + 1 day.)
       1 ordinary year has 1 odd day.
    2. 1 leap year = 366 days = (52 weeks + 2 days)
       1 leap year has 2 odd days.
    3. 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.
       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
    Day:Sun.Mon.Tues.Wed.Thurs.Fri.Sat.

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