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11. The calendar for the year 2007 will be the same for the year:
Sum = 14 odd days ≡ 0 odd days.
∴ Calendar for the year 2018 will be the same as for the year 2007.
Solution:
Count the number of odd days from the year 2007 onwards to get the sum equal to 0 odd day.| Year | Odd Day |
| 2007 | 1 |
| 2008 | 2 |
| 2009 | 1 |
| 2010 | 1 |
| 2011 | 1 |
| 2012 | 2 |
| 2013 | 1 |
| 2014 | 1 |
| 2015 | 1 |
| 2016 | 2 |
| 2017 | 1 |
Sum = 14 odd days ≡ 0 odd days.
∴ Calendar for the year 2018 will be the same as for the year 2007.
12. Which of the following is not a leap year?
∴ The year 700 is not a leap year.
Solution:
The century divisible by 400 is a leap year.∴ The year 700 is not a leap year.
13. On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?
So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.
But, 8th Dec, 2007 is Saturday.
∴ 8th Dec, 2006 is Friday.
Solution:
The year 2006 is an ordinary year. So, it has 1 odd day.So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.
But, 8th Dec, 2007 is Saturday.
∴ 8th Dec, 2006 is Friday.
14. January 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?
1st day of the year 2008 is Tuesday (Given)
So, 1st day of the year 2009 is 2 days beyond Tuesday.
Hence, it will be Thursday.
Solution:
The year 2008 is a leap year. So, it has 2 odd days.1st day of the year 2008 is Tuesday (Given)
So, 1st day of the year 2009 is 2 days beyond Tuesday.
Hence, it will be Thursday.
15. January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
1st day of the year 2007 was Monday.
1st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday.
Solution:
The year 2007 is an ordinary year. So, it has 1 odd day. 1st day of the year 2007 was Monday.
1st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday.
16. It was Thursday on 12th January 2006. What day of the week it will be on January 12th 2007 ?
2006 is an ordinary year. It has one odd day.
The day of the week on January 12th 2007 is one day beyond Thursday ⇒ Friday
Solution:
There is exactly 1 year, (365 days) between two dates.2006 is an ordinary year. It has one odd day.
The day of the week on January 12th 2007 is one day beyond Thursday ⇒ Friday
17. What day of the week will 22 Apr 2222 be?
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2200
= Number of odd days in 200 years
= 5 x 2 = 10 = 3
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
Number of odd days in the period 2201-2221
= 16 normal years + 5 leap years
= 16 x 1 + 5 x 2 = 16 + 10 = 26 = 5 odd days
Number of days from 1-Jan-2222 to 22 Apr 2222
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 22(Apr) = 112
112 days = 0 odd day
Total number of odd days = (0 + 3 + 5 + 0) = 8 = 1 odd day
1 odd days = Monday
Hence 22 Apr 2222 is Monday
Solution:
22 Apr 2222 = (2221 years + period from 1-Jan-2222 to 22-Apr-2222)We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2200
= Number of odd days in 200 years
= 5 x 2 = 10 = 3
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
Number of odd days in the period 2201-2221
= 16 normal years + 5 leap years
= 16 x 1 + 5 x 2 = 16 + 10 = 26 = 5 odd days
Number of days from 1-Jan-2222 to 22 Apr 2222
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 22(Apr) = 112
112 days = 0 odd day
Total number of odd days = (0 + 3 + 5 + 0) = 8 = 1 odd day
1 odd days = Monday
Hence 22 Apr 2222 is Monday
18. If today is Monday, what will be the day 350 days from now?
Solution:
350 days, = 50, no odd days, so it will be a Monday.
19. What was the day of the week on 24th July 2011?
Formula : (Date + Month code + No.of years + No.of leap year + Century code)/7
Solution:
| Day Codes | |
|---|---|
| Saturday | 0 |
| Sunday | 1 |
| Monday | 2 |
| Tuesday | 3 |
| Wednesday | 4 |
| Thursday | 5 |
| Friday | 6 |
| Month Codes | |
|---|---|
| January | 1 |
| February | 4 |
| March | 4 |
| April | 0 |
| May | 2 |
| June | 5 |
| July | 0 |
| August | 3 |
| September | 6 |
| October | 1 |
| November | 4 |
| December | 6 |
| Century Codes | |
|---|---|
| 1500 - 1599 | 0 |
| 1600 - 1699 | 6 |
| 1700 - 1799 | 4 |
| 1800 - 1899 | 2 |
| 1900 - 1999 | 0 |
| 2000 - 2099 | 6 |
| 2100 - 2199 | 4 |
| 2200 - 2299 | 2 |
| 2300 - 2399 | 0 |
Formula : (Date + Month code + No.of years + No.of leap year + Century code)/7
20. If the first day of a year (other than leap year) was Friday, then which was the last day of that year?
Odd days of the mentioned year = 1 (Since it is an ordinary year)
Hence First day of the next year = (Friday + 1 Odd day) = Saturday
Therefore, last day of the mentioned year = Friday
Solution:
Given that first day of a normal year was FridayOdd days of the mentioned year = 1 (Since it is an ordinary year)
Hence First day of the next year = (Friday + 1 Odd day) = Saturday
Therefore, last day of the mentioned year = Friday