Aptitude::Calendar
Important Formulas |
(I). 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.
(II). Leap Year:
(i). Every year divisible by 4 is a leap year, if it is not a century.
(ii). Every 4^{th} century is a leap year and no other century is a leap year.
Note: A leap year has 366 days.
Examples:
- Each of the years 1948, 2004, 1676 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.
(III). Ordinary Year:
The year which is not a leap year is called an ordinary year. An ordinary year has 365 days.
(IV). 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 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 * 2) = 3 odd days.
Number of odd days in 300 years = (5 * 3) = 1 odd day.
Number of odd days in 400 years = (5 * 4 + 1) = 0 odd day.
Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.
(V). Day of the Week Related to Odd Days:
No. of days: |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
Day: |
Sun. |
Mon. |
Tues. |
Wed. |
Thurs. |
Fri. |
Sat. |