The calendar for the year 2013 was the same as the year :
Answer: D
Count the odd days backwards from 2013 until they total a multiple of seven.
\[ 2012:2,\ 2011:1,\ 2010:1,\ 2009:1,\ 2008:2,\ 2007:1,\ 2006:1,\ 2005:1,\ 2004:2,\ 2003:1,\ 2002:1 \]
\[ \text{total} = 14 \quad\Longrightarrow\quad 0 \text{ odd days} \]
So 2013 repeats the calendar of 2002.
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The calendar for the year 1988 is same as which upcoming year ?
Answer: C
1988 is a leap year, and leap-year calendars repeat every 28 years:
\[ 1988 + 28 = 2016 \]
Both years must be leap years starting on the same weekday for every date to line up, which the 28-year cycle guarantees here.
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What will be the day of the week on fifteenth 2010?
Answer: A
fifteenth August,2010 =(2009 years+ Period from 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0.
Odd days in 400 years = 0.
9 year = (2 jump year +7 conventional years)
= (2*2+7*1) = 11 odd days= 4 odd days
Jan + feb + March + April + May + June + July + august
31+28+31+30+31+30+31+15 = 227 days =(32 weeks +3 days )
= 3 odd days
Aggregate no. of odd days = (0+0+4+3) =7
= 0 odd day
Given day is Sunday.
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The calendar of the year 2024 can be used again in the year?
Answer: B
A calendar repeats when the accumulated odd days return to zero. 2024 is a leap year, and leap-year calendars repeat on a 28-year cycle:
\[ 2024 + 28 = 2052 \]
The cycle holds as long as no skipped century year intervenes, and none does between 2024 and 2052.
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What was the day of the week on 28th May, 2006?
Answer: D
28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 
6 odd days
Jan. Feb. March April May (31 + 28 + 31 + 30 + 28 ) = 148 days
148 days = (21 weeks + 1 day) 1 odd day.
Total number of odd days = (0 + 0 + 6 + 1) = 7 0 odd day.
Given day is Sunday.
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Which of the following year is a leap year?
Answer: D
A year is a leap year if it is divisible by 4, except that a century year must also be divisible by 400.
All four are century years, so each must be divisible by 400.
\[ 2500 \div 400 = 6.25 \ \times, \quad 1700 \div 400 = 4.25 \ \times, \quad 1900 \div 400 = 4.75 \ \times \]
\[ 2400 \div 400 = 6 \ \checkmark \]
So 2400 is the leap year.
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The calendar for the year 2007 will be the same for the year
Answer: D
A calendar repeats once the accumulated odd days come back to zero. 2007 is an ordinary year, so count forward, giving each ordinary year 1 odd day and each leap year 2:
| Year | Odd days | Running total (mod 7) |
|---|---|---|
| 2007 | 1 | 1 |
| 2008 (leap) | 2 | 3 |
| 2009 | 1 | 4 |
| 2010 | 1 | 5 |
| 2011 | 1 | 6 |
| 2012 (leap) | 2 | 1 |
| 2013 | 1 | 2 |
| 2014 | 1 | 3 |
| 2015 | 1 | 4 |
| 2016 (leap) | 2 | 6 |
| 2017 | 1 | 0 |
The total returns to 0 after 2017, so the first year whose calendar matches 2007 is 2018. Both must also be non-leap for the match to hold, and 2018 is.
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On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?
Answer: B
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
S0, 8th Dec, 2006 is Friday.
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How many leap years do 300 years have?
Answer: C
Each century contributes 24 leap years, since the century year itself is skipped unless divisible by 400.
\[ 24 \times 3 = 72 \]
Only in a 400-year block does one century year qualify, giving 97 leap years in 400 rather than 96.
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The calendar for the year 2018 will be the same for the year
Answer: C
Now, the given year is 2018
We know that 2016 is a Leap year.
2016 2017 2018 2019 2020
LY 1st 2nd 3rd LY
Here 2018 is at 2 nd position after the Leap year.
According to rule ( b) the calendar of 2018 is repeated for the year is 2018 + 11 = 2029.
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