Important Formulas - Calendar

Aptitude Important Formulas, shortcuts and tricks on Calendar:

(I). Odd Days Number of days more than the complete weeks are called odd days in a given period

(II). Leap Year A leap year has 366 days.

1. In a leap year, the month of February has 29 days
2. Every year divisible by 4 is a leap year, if it is not a century. Examples: 1952, 2008, 1680 etc. are leap years. 1991, 2003 etc. are not leap years
3. Every 4th century is a leap year and no other century is a leap year. Examples: 400, 800, and 1200 etc. are leap years. 100, 200, 1900 etc. are not leap years

(III). Ordinary Year The year which is not a leap year is an ordinary year. An ordinary year has 365 days

(IV). Counting odd days and Calculating the day of any particular date

1. 1 ordinary year ≡ 365 days ≡ (52 weeks + 1 day). Hence number of odd days in 1 ordinary year= 1.
2. 1 leap year ≡ 366 days ≡ (52 weeks + 2 days). Hence number of odd days in 1 leap year= 2.
3. 100 years ≡ (76 ordinary years + 24 leap years ) ≡ (76 × 1 + 24 × 2) odd days ≡ 124 odd days. = (17 weeks + 5 days) ≡ 5 odd days. Hence number of odd days in 100 years = 5.
4. Number of odd days in 200 years = (5 × 2) = 10 ≡ 3 odd days
5. Number of odd days in 300 years = (5 × 3) = 15 ≡ 1 odd days
6. Number of odd days in 400 years = (5 × 4 + 1) = 21 ≡ 0 odd days. Similarly, the number of odd days in all 4th centuries (400, 800, 1200 etc.) = 0
7. Mapping of the number of odd day to the day of the week

Number of Odd Days	0	1	2	3	4	5	6
Day of the week	Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday

Last day of a century cannot be Tuesday or Thursday or Saturday.

(V). For the calendars of two different years to be the same, the following conditions must be satisfied.

1. Both years must be of the same type. i.e., both years must be ordinary years or both years must be leap years.
2. 1st January of both the years must be the same day of the week. 

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Example: 01

Which of the following is not a leap year?

A. 1200

B. 800

C. 700

D. 2000

Answer: Option C

Solution:

We know that, 

1. Every year divisible by 4 is a leap year. If it is not a century.

2. Every 4th century is a leap year, but no other century is a leap year.

∴ 800, 1200 and 2000 comes in the category of 4th century, such as 400,800, 1200, 1600, 2000 etc.

Hence, 800, 1200 and 2000 are leap years.

700 is not a 4th century, but it is a century. Hence it is not a leap year.

Example: 02

8th February 2005, it was Tuesday, what was the day of the week on 8th February 2004?

A. Sunday

B. Friday

C. Saturday

D. Monday

Answer: Option A

Solution:

Given that, 8th Feb 2005 was Tuesday

Number of days from 8th Feb 2004 to 7th Feb 2005 = 366 days

(Since Feb 2004 has 29 days, as it is a leap year)

Now, 366 days = 2 odd days

Hence, 8th Feb 2004 = (Tuesday - 2 odd days) = Sunday.

Example: 03

Today is Thursday. The day after 59 days will be?

A. Monday

B. Tuesday

C. Saturday

D. Sunday

Answer: Option D

Solution:

59 days = 8 weeks and 3 days = 3 odd days

Hence, if today is Thursday, after 59 days, it will be = (Thursday + 3 odd days) = Sunday.