# Logical reasoning - Learn Calendars - CSEET

**Introduction**

Suppose you are asked to find the day of the week on 30th June, 1974. It would be a tough job to find it if you do not know the method. The method of finding the day of the week likes in the number of “odd days”

Note: Every 7th day count wise, i.e. if today is Monday, then the 7th day counting from Tuesday onwards will once again be Monday. Odd days is the days remaining after completion of an exact number of weeks. Odd days is the remainder obtained on dividing the total number of days with seven.

Example: 52 days ÷ 7 = 3 odd days.

**Leap and Non-leap Year**

A Non-leap year has 365 days whereas a leap year has one extra day because of 29 days in the months of February. Every year which is divisible by 4 is called a leap year. Leap year consists of 366 days. (52 complete weeks + 2 days), the extra two days are the odd days. So, a leap year has two odd days.

A non-leap year consist of 365 days (52 complete weeks + 1 day). The extra one day is the odd day.

Note: Every century, year which is a multiple of 400, is a leap year. A century year which is not divisible by 400 is non-leap year.

Example: 400, 800, 1200, 1600 ….. are leap years.

500, 700, 900, 1900 ….. are non-leap years.

Counting the number of Odd Days

100 years consist of 24 leap years + 76 ordinary years.

(100 years when divided by 4, we get 25. But at the 100th year is not a leap year, hence only 24 leap years).

= (2 × 24 odd days) + (1 × 76 odd days)

= 124 days

= 17 weeks + 5 days

The extra 5 days are the odd days. So, 100 years contain 5 odd days,

Similarly, for 200 year we have 10 extra days (1 week + 3 days). 200 years contains 3 odd days.

Similarly, 300 year contain 1 odd day and 400 years contain 0 odd days. Any month which has 31 days has 3 odd days.

(∵ 31 ÷ 7 leaves 3 as remainder] and any month which has 30 days has 2 odd days (30 ÷ 7 leaves 2 as reminder).

Then, the total number of odd days are calculated by adding the odd days for each month. The value so obtained is again divided by 7 to get the final number of odd days. The day of the week of the second date is obtained by adding the odd days to the day of the week of the earlier date.

**Solved Examples:**

1. If you were born on 14th April, 1992, which was a Sunday, then on which day of the week does your birthday fall in 1993?

1) Monday 4) Friday

2) Tuesday 5) Cannot be determined

3) Wednesday

Sol: 14th April 1992 to 14th April 1993 is a complete year, which has 365 days. Hence, the number of odd days from 14th April 1992 to 14th April 1993 is 1. Hence, 14th April 1993 one day after Sunday i.e., Monday. (Choice 1)

2. If 1st Jan, 1992 is a Tuesday then on which day of the week will 1st jan, 1993 fall?

1) Wednesday 4) Friday

2) Wednesday 5) Sunday

3) Thursday

Sol: Since 1992 is a leap year there are 2 odd days.

Hence, 1st January 1992 is two days after Tuesday i.e., Thursday (Choice 2)

3. If 1st April, 2003 was Monday, then which day of the week will 25th December of the same year be?

1) Tuesday 4) Friday

2) Wednesday 5) Sunday

3) Thursday

Sol: The number of days from 1st April to 25th December (29+31+30+31+31+30+31+30+25) days

= 268 = 38 + 2 odd days.

7

Hence, 25th December is two days after Monday, i.e., Wednesday, (choice 2)

4. What day of the week was 18th April 1901?

1) Monday 4) Tuesday

2) Tuesday 5) Thursday

3) Wednesday

Sol: 18th April 1901 = (1600+300) years + 1st January to 18th April 1901 1600 years have - 0 odd days

300 years have - 1 odd day

The number of days from 1st January, 1901 to 18th April 1901 is (31+28+31 + 18) days 108 days = 3 odd days

∴ Total number of odd days = 3 + 1 = 4 Hence, 18th April 1901 is Thursday, (choice 4)