Aptitude Questions and Answers

Answer: Option C

Explanation:

Since each day of the week is repeated after 7 days.

After 133 days,it will be thursday.

So one day before that would be Wednesday.

As per the question 9^th of the Month=Saturday. (Day preceding Sunday)

Day name repeats after 7 days.

Therefore 9 minus 7=2^nd of the given month is also Saturday.

Then 1^st of the given month= Saturday Minus one day = Friday

Normal year jump +1 gain; Leap year jump +2 gain.

Sunday plus five days

1. Monday
2. Tue
3. Wed
4. Thursday
5. Friday

Each day of the week is repeated after 7 days.

`63/7`=`9`, Remainder:0

So, after 63 days, it will be Monday.

The year 2004 is a leap year. So, it has 2 odd days.

But, Feb 2004 not included because we are calculating from March 2004 to March 2005.

So it has 1 odd day only.

The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.

Given that, 6th March, 2005 is Monday.

6th March, 2004 is Sunday (1 day before to 6th March, 2005).

This can be illustrated with an example.

Ex: 1896 is a leap year.The next leap year comes in 1904 (1900 is not a leap year).

To eliminate this error, the Gregorian calendar stipulates that a year that is evenly divisible by 100 (for example, 1900) is a leap year only if it is also evenly divisible by 400. This is because they are evenly divisible by 100 but not by 400.

Here Number of odd days in 1600 years = 0

Number of odd days in 300 years from 1600 to 1900 = 5*3 = 2 week + 1 odd day= 1 odd day

Number of odd days in 84 years= 21 leap year + 63 days = 21*2 + 63*1 = 105 days = 0 odd days

Number of odd days in 20 may = 31 days of Jan. + 28 days of feb + 31 days of mar. + 30 days in april + 20 days in may = 140 days = 0 odd day

So total number of odd days = 0+1+0+0=1 = Monday

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.

x weeks x days = (7×x)+x=7x+x= 8x days

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