1.
It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
A.Sunday B.Saturday
C.Friday D.Wednesday
Answer & Explanation
Answer: Option C
Explanation:
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?
A.Thursday B.Friday
C.Saturday D.Sunday
Answer & Explanation
Answer: Option D
Explanation:
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?
A.Monday B.Tuesday
C.Wednesday D.Thursday
Answer & Explanation
Answer: Option C
Explanation:
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
168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.
4.
What will be the day of the week 15th August, 2010?
A.Sunday B.Monday
C.Tuesday D.Friday
Answer & Explanation
Answer: Option A
Explanation:
15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days 4 odd days.
Jan. Feb. March April May June July Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
227 days = (32 weeks + 3 days) 3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 0 odd days.
Given day is Sunday.
Odd Days:
We are supposed to find the day of the week on a given date.
For this, we use the concept of 'odd days'.
In a given period, the number of days more than the complete weeks are called odd days.
Leap Year:
(i). Every year divisible by 4 is a leap year, if it is not a century.
(ii). Every 4th century is a leap year and no other century is a leap year.
Note: A leap year has 366 days.
Examples:
i. Each of the years 1948, 2004, 1676 etc. is a leap year.
ii. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
iii. None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.
Ordinary Year:
The year which is not a leap year is called an ordinary years. An ordinary year has 365
days.
Counting of Odd Days:
1. 1 ordinary year = 365 days = (52 weeks + 1 day.)
1 ordinary year has 1 odd day.
2. 1 leap year = 366 days = (52 weeks + 2 days)
1 leap year has 2 odd days.
3. 100 years = 76 ordinary years + 24 leap years
= (76 x 1 + 24 x 2) odd days = 124 odd days.
= (17 weeks + days) 5 odd days.
Number of odd days in 100 years = 5.
Number of odd days in 200 years = (5 x 2) 3 odd days.
Number of odd days in 300 years = (5 x 3) 1 odd day.
Number of odd days in 400 years = (5 x 4 + 1) 0 odd day.
Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0
odd days.
Day of the Week Related to Odd Days:
No. of
0 1 2 3 4 5 6
days:
Su Mon Tue We Thur Fri Sa
Day:
n. . s. d. s. . t.
