1. What day of the week does May 28 2006 fall on
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A. Saturday
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B. Monday
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C. Sunday
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D. Thursday
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Answer : Option C
Explanation :
28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)
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 2001-2005
= 4 normal years + 1 leap year
= 4 x 1 + 1 x 2 = 6
Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)
= 148
148 days = 21 weeks + 1 day = 1 odd day
Total number of odd days = (0 + 6 + 1) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence May 28 2006 is Sunday
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 2001-2005
= 4 normal years + 1 leap year
= 4 x 1 + 1 x 2 = 6
Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)
= 148
148 days = 21 weeks + 1 day = 1 odd day
Total number of odd days = (0 + 6 + 1) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence May 28 2006 is Sunday
2. What will be the day of the week 15th August, 2010?
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A. Thursday
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B. Sunday
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C. Monday
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D. Saturday
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Answer : Option B
Explanation :
15th Aug 2010 = (2009 years + period from 1-Jan-2010 to 15-Aug-2010)
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 2001-2009
= 7 normal years + 2 leap year
= 7 x 1 + 2 x 2 = 11 = (11 - 7x1) odd day = 4 odd day
Days from 1-Jan-2010 to 15-Aug-2010
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 30(Jun) + 31(Jul) + 15(Aug)
= 227
227 days = 32 weeks + 3 day = 3 odd day
Total number of odd days = (0 + 4 + 3) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence 15th August, 2010 is Sunday
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 2001-2009
= 7 normal years + 2 leap year
= 7 x 1 + 2 x 2 = 11 = (11 - 7x1) odd day = 4 odd day
Days from 1-Jan-2010 to 15-Aug-2010
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 30(Jun) + 31(Jul) + 15(Aug)
= 227
227 days = 32 weeks + 3 day = 3 odd day
Total number of odd days = (0 + 4 + 3) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence 15th August, 2010 is Sunday
3. Today is Monday. After 61 days, it will be
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A. Thursday
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B. Sunday
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C. Monday
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D. Saturday
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Answer : Option D
Explanation :
61 days = 8 weeks 5 days = 5 odd days
Hence if today is Monday, After 61 days, it will be = (Monday + 5 odd days)
= Saturday
Hence if today is Monday, After 61 days, it will be = (Monday + 5 odd days)
= Saturday
4. On what dates of April, 2001 did Wednesday fall?
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A. 2nd, 9th, 16th, 23rd
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B. 4th, 11th, 18th, 25th
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C. 3rd, 10th, 17th, 24th
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D. 1st, 8th, 15th, 22nd, 29th
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Answer : Option B
Explanation :
We need to find out the day of 01-Apr-2001
01-Apr-2001 = (2000 years + period from 1-Jan-2001 to 01-Apr-2001)
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)
Days from 1-Jan-2001 to 01-Apr-2001 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 1(Apr) = 91
91 days = 13 weeks = 0 odd day
Total number of odd days = (0 + 0) = 0 odd days
0 odd day = Sunday. Hence 01-Apr-2001 is Sunday.
Hence first Wednesday of Apr 2011 comes in 04th and successive Wednesdays
come in 11th, 18th and 25th
01-Apr-2001 = (2000 years + period from 1-Jan-2001 to 01-Apr-2001)
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)
Days from 1-Jan-2001 to 01-Apr-2001 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 1(Apr) = 91
91 days = 13 weeks = 0 odd day
Total number of odd days = (0 + 0) = 0 odd days
0 odd day = Sunday. Hence 01-Apr-2001 is Sunday.
Hence first Wednesday of Apr 2011 comes in 04th and successive Wednesdays
come in 11th, 18th and 25th
5. The calendar for the year 2007 will be the same for the year
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A. 2017
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B. 2018
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C. 2014
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D. 2016
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Answer : Option B
Explanation :
For a year to have the same calendar with 2007 ,the total odd days from 2007 should be 0.
| Year | : | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 |
| Odd Days | : | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 1 |
Take the year 2014 given in the choice.
Total odd days in the period 2007-2013 = 5 normal years + 2 leap year
= 5 x 1 + 2 x 2 = 9 odd days
= 2 odd day (As we can reduce multiples of 7 from odd days which will not change
anything)
Take the year 2016 given in the choice.
Number of odd days in the period 2007-2015 = 7 normal years + 2 leap year
= 7 x 1 + 2 x 2 = 11 odd days
= 4 odd days
(Even if the odd days were 0, calendar of 2007 will not be same as the calendar of 2016 because 2007 is not a leap year whereas 2016 is a leap year. In fact, you can straight away ignore this choice due to this fact without even bothering to check the odd days)
Take the year 2017 given in the choice.
Number of odd days in the period 2007-2016 = 7 normal years + 3 leap year
= 7 x 1 + 3 x 2 = 13 odd days
= 6 odd days
Take the year 2018 given in the choice.
Number of odd days in the period 2007-2017 = 8 normal years + 3 leap year
= 8 x 1 + 3 x 2 = 14 odd days
= 0 odd day (As we can reduce multiples of 7 from odd days which will not change
anything)
Also, both 2007 and 2018 are not leap years.
Since total odd days in the period 2007-2017 = 0 and both 2007 and 2018 are of same type, 2018 will have the same calendar as that of 2007
Total odd days in the period 2007-2013 = 5 normal years + 2 leap year
= 5 x 1 + 2 x 2 = 9 odd days
= 2 odd day (As we can reduce multiples of 7 from odd days which will not change
anything)
Take the year 2016 given in the choice.
Number of odd days in the period 2007-2015 = 7 normal years + 2 leap year
= 7 x 1 + 2 x 2 = 11 odd days
= 4 odd days
(Even if the odd days were 0, calendar of 2007 will not be same as the calendar of 2016 because 2007 is not a leap year whereas 2016 is a leap year. In fact, you can straight away ignore this choice due to this fact without even bothering to check the odd days)
Take the year 2017 given in the choice.
Number of odd days in the period 2007-2016 = 7 normal years + 3 leap year
= 7 x 1 + 3 x 2 = 13 odd days
= 6 odd days
Take the year 2018 given in the choice.
Number of odd days in the period 2007-2017 = 8 normal years + 3 leap year
= 8 x 1 + 3 x 2 = 14 odd days
= 0 odd day (As we can reduce multiples of 7 from odd days which will not change
anything)
Also, both 2007 and 2018 are not leap years.
Since total odd days in the period 2007-2017 = 0 and both 2007 and 2018 are of same type, 2018 will have the same calendar as that of 2007
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