Concept of Odd days

Concept of odd days emerges from the concept of a week.
Concept of a week - The day gets repeated after every seventh day.

Ex - If today is Monday, then 28th day from now will also be a Monday as it a multiple of 7 (28/7 = 4, so four weeks).

Ex - If today is Monday, then 30th day = 28 + 2 (4 weeks and 2 days), i.e. 30/7 will give a remainder of 2.
These two days are odd days. With starting day as Monday and two odd days, the 30th day will be Wednesday.

So, Number of odd days in a given period = Remainder {Period/7}
That is, Remainder left will be the number of odd days.

Extra days, apart from complete weeks in a given period are called odd days, e.g.:
A period of 7 days = 7 + 0 extra day = 0 odd day
A period of 8 days = 7 + 1 extra day = 1 odd day
A period of 9 days = 7 + 2 extra days = 2 odd days
A period of 10 days = 7 + 3 extra days = 3 odd days
A period of 11 days = 7 + 4 extra days = 4 odd days
A period of 12 days = 7 + 5 extra days = 5 odd days
A period of 13 days = 7 + 6 extra days = 6 odd days
But a period of 14 days = 7 + 7 = 2 complete weeks = 0 odd days

Odd days in a Month

Number of odd days in different months:

Number of odd days in different quarters:

Jan + Feb + Mar = 6 OR 7 (i.e. 0)
Apr + May + June = 7 (i.e. 0)
July + Aug + Sep = 8 (i.e. 1)
Oct + Nov + Dec = 8 (i.e. 1)

Q. Today is Tuesday. What day will it be a day after 72 days?

(a) Sunday     (b) Friday    (c) Thursday    (d) Saturday

Explanation:

Tuesday will be repeated after each 7 days, so after 70 days it will again be Tuesday.
The day after 72th day, i.e. 73rd day = 70 + 3, i.e. 3 odd days
The required day is Tuesday + 3 = Friday.
Answer: (b)

Odd days in a Year

Number of odd days in an ordinary year

Number of days in an ordinary year = 365 = 364 + 1
Number of odd days in an ordinary year = Remainder {365/7} = 1 odd day

Number of odd days in a leap year

Number of days in a leap year = 366 = 364 + 2
Number of odd days in a leap year = Remainder {366/7} = 2 odd days

Number of odd days in a 100 years

Number of odd days in 100 years = 76 ordinary years + 24 leap years
= 76 odd days of 76 ordinary years + (24 × 2) odd days of 24 leap years
= 76 odd days + 48 odd days = 124 odd days
= (7 × 17 + 5) odd days = 5 odd days

Note: This will be the case if the century year divisible by 400 (e.g. 1600, 2000) is not there in the 100 years counted, or else 1 more odd day has to be added.

Q. If 1st Jan 1901 is a Tuesday, what is the day on 1st Jan 2001?

(a) Sunday     (b) Tuesday    (c) Monday    (d) Saturday

Explanation:

Number of odd days in 100 years = 5 odd days
However, it’s true only when the century year divisible by 400 is not there, or else 1 more odd day has to be added.

Here, we are counting from 1st January, 1901 to 31st December, 2000. So, 2000 is also getting counted.

Hence, number of odd days between 1st January, 1901 and 1st January, 2001 = 5 + 1 = 6

So, 1st January, 2001 = Tuesday + 6 = Monday

Answer: (c)

Number of odd days in a 200 years

Odd days in 200 yrs = (Odd days in 100 yrs) × 2 = 5 × 2 = 10 days = 1 week + 3 days = 3 odd days

Note: This will be the case if the century year divisible by 400 (e.g. 1600, 2000) is not there in the 200 years counted, or else 1 more odd day has to be added.

Number of odd days in a 300 years

Odd days in 300 yrs = (Odd days in 100 yrs) × 3 = 5 × 3 = 15 days = 2 weeks + 1 day = 1 odd day

Note: This will be the case if the century year divisible by 400 (e.g. 1600, 2000) is not there in the 300 years counted, or else 1 more odd day has to be added.

Number of odd days in a 400 years

Odd days for 400 yrs = (Odd days in 100 yrs) × 4 + 1 day = (5 × 4 + 1) days = 21 days = 3 weeks = 0 odd day

Note: If we count any consecutive 400 years, the century year divisible by 400 (e.g. 1600, 2000) will always get counted.

Finding day on the same date

If today is Monday, then can you tell what day will it be on the same date next year or previous year?

Well, it is easy. Just remember this:

If 29th February falls in between the two given dates of consecutive years, then there will be 2 odd days between the two dates.
If there’s no 29th February between the two given dates of consecutive years, then there will only be 1 odd day between them.

Let’s see some examples:

Q. March 6, 1992 was Thursday. What day of the week will it be on March 6, 1993?

(a) Friday     (b) Thursday    (c) Monday    (d) Saturday

Explanation:

1992 – leap year
1993 – non-leap year

But our period is March 6, 1992 to March 6, 1993. 29th February, 1992 does not fall in this period.

So, there will only be 1 odd day between the two given dates. Hence, March 6, 1993 will be 1 day ahead of March 6, 1992.

So, March 6, 1993 will be Thursday + 1 = Friday

Answer: (a)

Q. January 6, 1992 was Thursday. What day of the week will it be on January 6, 1993?

(a) Friday     (b) Thursday    (c) Monday    (d) Saturday

Explanation:

1992 – leap year
1993 – non-leap year

Our period is January 6, 1992 to January 6, 1993. 29th February, 1992 does fall in this period.

So, there will be 2 odd days between the two given dates. Hence, January 6, 1993 will be 2 days ahead of January 6, 1992.

So, January 6, 1993 will be Thursday + 2 = Saturday

Answer: (d)

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Last updated on Oct 24, 2020