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Calendar
1.It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

Explanation:

Solution:
On 31st December, 2005 it was Saturday.
Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.
∴ On 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday.

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

Explanation:

Solution:
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.

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

Explanation:

Solution:
17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)
Odd days in 1600 years = 0
Odd days in 300 years = (5 x 3) ≡ 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.

Jan.         Feb.       March       April         May         June
(31     +     28     +     31     +     30     +     31     +     17) = 168 days

Therefore 168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.

4.Today is Monday. After 61 days, it will be:

Explanation:

Solution:
Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
∴ After 61 days, it will be Saturday.

5.If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?

Explanation:

Solution:
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).

6.On what dates of April, 2001 did Wednesday fall?

Explanation:

Solution:
We shall find the day on 1st April, 2001.
1st April, 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001)
Odd days in 1600 years = 0
Odd days in 400 years = 0
Jan. Feb. March April
(31 + 28 + 31 + 1)     = 91 days ≡ 0 odd days.
Total number of odd days = (0 + 0 + 0) = 0
On 1st April, 2001 it was Sunday.
In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th.

7.How many days are there in x weeks x days?

Explanation:

Solution:
x weeks x days = (7x + x) days = 8x days.

8.On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?

Explanation:

Solution:
The year 2004 is a leap year. It has 2 odd days.
∴ The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005.
Hence, this day is Sunday.

9.The calendar for the year 2007 will be the same for the year:

Explanation:

Solution:
Count the number of odd days from the year 2007 onwards to get the sum equal to 0 odd day.

Sum = 14 odd days ≡ 0 odd days.
∴ Calendar for the year 2018 will be the same as for the year 2007.

10.Which of the following is not a leap year?

Explanation:

Solution:
The century divisible by 400 is a leap year.
∴ The year 700 is not a leap year.

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