Aptitude ➤ Calendar ➤ 1

Under this heading we mainly deal with finding the day
of the week on a particular given date the process of finding it lies on obtaining the number of odd days.

**1. 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:**

i. Each of the years 1948, 2004, 1676 etc. is a leap year.

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

iii. 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:**

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 × 1 + 24 × 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:**

In a given period, the number of days more than the complete weeks are called odd days.

(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.

i. Each of the years 1948, 2004, 1676 etc. is a leap year.

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

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

The year which is not a leap year is called an ordinary years. An ordinary year has 365 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 × 1 + 24 × 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.

No. of Days | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|

Day | Sun | Mon | Tue | Wed | Thurs | Fri | Sat |

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