Calendar Aptitude

Calendar problems in aptitude tests often involve understanding and calculating days of the week, leap years, and date relationships. These problems require knowledge of the Gregorian calendar system, including how leap years are determined, the number of days in each month, and basic arithmetic calculations related to days and years.

1. What day of the week was it on 15th August 1947?

Calculation method: [Year's code + Month's code + Date number + Century code] mod 7.
1947's year code = (47 + (47 div 4)) mod 7 = (47 + 11) mod 7 = 58 mod 7 = 2.
August's month code = 2.
Century code for 1900s = 0.
15th's date number = 15.
Total = 2 + 2 + 15 + 0 = 19 mod 7 = 5.
5 corresponds to Friday.

2. If 4th July 2001 is a Wednesday, what was the day on 4th July 2000?

Year 2000 is a leap year. So, it has two odd days.
Day of the week goes 2 days back from 2001.
Since 4th July 2001 is Wednesday, 4th July 2000 is Monday.

3. How many times does the 29th day of the month occur in 400 consecutive years?

In 400 years, there are 97 leap years + 303 normal years.
In a leap year, 29th February occurs once and in all years, 29th of other months occur 12 times.
Total = 97 * 1 + 400 * 12 = 4852 times.

4. If 1st January 1995 was a Sunday, what was the day of the week on 1st January 2000?

Number of odd days from 1995 to 2000 = 1 (for 1996, leap year) + 4 (for 1997, 1998, 1999, 2000) = 5 odd days.
So, the day on 1st January 2000 is 5 days after Sunday, which is Saturday.

5. The last day of a century cannot be

100 years have 5 odd days. So, the last day of a century cannot be Tuesday (which corresponds to 2 odd days).

6. What day of the week was on 28th May 2006?

Calculation method involves determining the number of odd days.
2006 is a normal year. So, the number of odd days from 2000 to 2005 is 5 (1 for each normal year) + 2 (for the two leap years 2000 and 2004) = 7 odd days = 0 odd days.
For the year 2006, up to 28th May, the total days are (31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28 (May)) = 148 days = 21 weeks + 1 odd day.
Total odd days = 0 (from years) + 1 (from days) = 1.
1 odd day corresponds to Sunday.

7. If 15th August 2010 is a Sunday, what was the day on 15th August 2008?

2008 is a leap year, so it has two odd days.
The number of odd days from 2008 to 2010 is 2 (for 2008) + 1 (for 2009) = 3 odd days.
Going back 3 days from Sunday in 2010 lands on Friday in 2008.

8. If 20th April 2001 is a Friday, what day of the week will be on 20th April 2002?

2001 is a normal year. So, it has 1 odd day.
The day of the week advances by 1 day after a normal year.
Since 20th April 2001 is Friday, 20th April 2002 will be Saturday.

9. How many days are there from 2nd January 1995 to 15th March 1995?

From 2nd January to 15th March = 30 (Jan) - 2 + 28 (Feb) + 15 (Mar) = 71 days.

10. If 1st November 1999 is a Monday, what was the day on 1st November 2000?

Year 2000 is a leap year. It has two odd days.
So, the day of the week advances by 2 days from 1999 to 2000.
Since 1st November 1999 is Monday, 1st November 2000 will be Wednesday.

11. What day of the week was on 17th June 1998?

Calculation method involves determining the number of odd days from the reference year.
1998 is a normal year. So, the number of odd days from 1992 to 1997 is 5 (1 for each normal year) + 3 (for the three leap years 1992, 1996) = 8 odd days = 1 odd day.
For the year 1998, up to 17th June, the total days are (31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31 (May) + 17 (Jun)) = 168 days = 24 weeks + 0 odd day.
Total odd days = 1 (from years) + 0 (from days) = 1.
1 odd day corresponds to Wednesday.

12. If 4th July 2004 is a Sunday, what was the day on 4th July 2003?

2004 is a leap year, so it has two odd days.
The day of the week goes 2 days back from 2004 to 2003.
Since 4th July 2004 is Sunday, 4th July 2003 is Saturday.

13. On what day of the week will 15th August 2025 be?

Calculation method involves determining the number of odd days.
2025 is a normal year. So, the number of odd days from 2020 to 2024 is 5 (1 for each normal year) + 1 (for the one leap year 2024) = 6 odd days.
For the year 2025, up to 15th August, the total days are (31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31 (May) + 30 (Jun) + 31 (Jul) + 15 (Aug)) = 227 days = 32 weeks + 3 odd days.
Total odd days = 6 (from years) + 3 (from days) = 9 odd days = 2 odd days after removing multiples of 7.
2 odd days correspond to Friday.

14. If 1st January 1995 was a Sunday, what was the day of the week on 31st December 1995?

1995 is a normal year, so it has 1 odd day.
Since the year starts on Sunday, it will end on Sunday.

15. A year that is a multiple of 4 is not a leap year if it is a multiple of

According to leap year rules, a year is a leap year if it is divisible by 4. However, if the year is a multiple of 100, it must also be a multiple of 400 to be a leap year.

16. If 1st January 2000 was a Saturday, what day of the week was 1st January 2001?

Year 2000 is a leap year, so it has two odd days.
The day of the week advances by 2 days from 2000 to 2001.
Since 1st January 2000 is Saturday, 1st January 2001 will be Monday.

17. What day of the week was on 15th April 2010?

The number of odd days from 2000 to 2009 is 10 (2 for each leap year and 1 for each normal year) = 10 odd days = 3 odd days.
For the year 2010, up to 15th April, total days are (31 (Jan) + 28 (Feb) + 31 (Mar) + 15 (Apr)) = 105 days = 15 weeks + 0 odd day.
Total odd days = 3 (from years) + 0 (from days) = 3.
3 odd days correspond to Thursday.

18. If 25th June 2003 falls on a Wednesday, what day of the week will 25th June 2004 be?

2004 is a leap year. So, it has two odd days.
The day of the week advances by 1 day from 2003 to 2004.
Since 25th June 2003 is Wednesday, 25th June 2004 will be Friday.

19. How many times does the 29th day of February occur in 100 years?

In 100 years, there are 24 leap years (including 2000 but excluding 1900, 2100, etc.).
The 29th day of February occurs once in each leap year. Hence, it occurs 24 times.

20. If 8th May 2006 is a Monday, what was the day on 8th May 2002?

The number of odd days from 2002 to 2006 is 4 (1 for each normal year) + 1 (for the one leap year 2004) = 5 odd days.
The day of the week goes back by 5 days from 2006 to 2002.
Since 8th May 2006 is Monday, 8th May 2002 will be Wednesday.