Q 1-Prove that any date in March of a year is the same day of the week corresponding date in November that year

A - Same day

B - Not same day

C - Next day

D - Previous day

Answer - A

Explanation

"We will show that the number of odd days between last day of February and last day of October is zero. .
March April May June July Aug. Sept. Oct.
31 + 30 + 31 + 30 + 31 + 31 + 30 + 31
= 241 days = 35 weeks = 0 odd day. ,Number of odd days during this period = 0.
Thus, 1st March of an year will be the same day as 1st November of that year. Hence, the result follows"

Q 2-What was the day of the week on 16th August, 1947?

A - Sunday

B - Monday

C - Saturday

D - Thursday

Answer - C

Explanation

"15th August, 1947 = (1946 years + Period from 1st Jan., 1947 to 15th
Counting of odd days:
1600 years have 0 odd day. 300 years have 1 odd day.
47 years = (11 leap years + 36 ordinary years)
= [(11 x 2) + (36 x 1ยป) odd days = 58 odd days = 2 odd days.
Jan. Feb. March April May June July Aug.
31 + 28 + 31 + 30 + 31 + 30 + 31 + 15
= 227 days = (32 weeks + 3 days) = 3,
Total number of odd days = (0 + 1 + 2 + 3) odd days = 6 odd days.
Hence, the required day was 'Saturday'."

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

A - Sunday

B - Tuesday

C - Friday

D - Wednesday

Answer - D

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"

Q 4-What will be the day of the week 15th August, 2010?

A - Sunday

B - Saturday

C - Wednesday

D - Monday

Answer - 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 = 4 odd days.
Jan. Feb. Mar.  Apr.  May.  Jun.  Jul.  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 Sunda"

Q 5-1.12.91 is the first Sunday. Which is the fourth Tuesday of December 91?

A - 20.12.91

B - 22.12.91

C - 24.12.91

D - 25.12.91

Answer - B

Explanation

"Explanation :

Day before yesterday was Thursday

=>Yesterday was a Friday

=> Today is a Saturday

=> Tomorrow is a Sunday"

Q 6-The maximum gap between two successive leap year is?

A - 4

B - 8

C - 2

D - 1

Answer - B

Explanation

"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)."

Q 7-If Aug 15th,2012 falls on Thursday then June 11th,2013 falls on which day ?

A - Wednesday

B - Saturday

C - Monday

D - Tuesday

Answer - A

Explanation

"First,we count the number of odd days for the left over days in the given period.
Here,given period is 15.8.2012 to 11.6.2013
Aug Sept Oct Nov Dec Jan Feb Mar Apr May Jun
16   30   31  30   31   31   28  31   30   31   11(left days)
2 + 2 + 3 + 2 + 3 + 3 + 0 + 3 + 2 + 3 + 4 (odd days) = 6 odd days
So,given day Thursday + 6 = Wednesday is the required result."

Q 8-How many days are there in x weeks x days?

A - 7x * x

B - 8x

C - 14x

D - 7

Answer - B

Explanation

"x weeks x days = (7x + x) days = 8x days.
"

Q 9-What was the day of the week on 28th May, 2006?

A - Sunday

B - Friday

C - Wednesday

D - Tuesday

Answer - A

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
(31[jan] + 28 [Feb]+ 31[Mar] + 30[April] + 28[May] ) = 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"

Q 10-January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?

A - Monday

B - Tuesday

C - Wednesday

D - Sunday

Answer - B

Explanation

"The year 2007 is an ordinary year. So, it has 1 odd day.
 day of the year 2007 was Monday
 day of the year 2008 will be 1 day beyond Monday
Hence, It will be Tuesday."

Q 11-What was the day on 15th august 1947 ?

A - Friday

B - Saturday

C - Sunday

D - Thursday

Answer - A

Explanation

"15 Aug, 1947 = (1946 years + Period from 1.1.1947 to 15.8.1947)
 
Odd days in 1600 years = 0
 
Odd days in 300 years = 1
 
46 years = (35 ordinary years + 11 leap years) = (35 x 1 + 11 x 2)= 57 (8 weeks + 1 day) = 1 odd day
 
Jan. Feb. Mar. Apr. May. Jun. Jul. Aug
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 1 ) = 213 days = (30 weeks + 3 days) = 3 odd days.
 
Total number of odd days = (0 + 1 + 1 + 3) = 5 odd days.
 
Given day is Friday."

Q 12-What was the day of the week on, 16th July, 1776?

A - Tuesday

B - Wednesday

C - Monday

D - Saturday

Answer - A

Explanation

"16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776) 
Counting of odd days : 1600 years have 0 odd day. 
100 years have 5 odd days.
 75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] 
= 93 (13 weeks + 2 days) = 2 odd days.
 1775 years have (0 + 5 + 2) odd days = 7 odd days 
= 0 odd day. Jan Feb Mar Apr May Jun Jul 31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days
= (28 weeks + 2 days) 
Total number of odd days = (0 + 2) = 2. 
Required day was 'Tuesday'.
"

Q 13-It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

A - Monday

B - Friday

C - Sunday

D - Tuesday

Answer - B

Explanation

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

Q 14-If the first day of a year (other than leap year) was Friday, then which was the last day of that year?

A - Saturday

B - Friday

C - Tuesday

D - Monday

Answer - C

Explanation

"Given that 1st October is Sunday


Number of days in October = 31

31 days = 3 odd days 

(As we can reduce multiples of 7 from odd days which will not change anything)


Hence 1st November = (Sunday + 3 odd days) = Wednesday"

Q 15-What was the day of the week on 16th April, 2000 ?

A - sunday

B - tuesday

C - wednesday

D - friday

Answer - A

Explanation

"16th April, 2000 = (1999 years + Period from 1st Jan., 2000 to 16th April)
Counting of odd days:
1600 years have 0 odd day. 300 years have 1 odd day.
99 years = (24 leap years + 75 ordinary years)
= [(24 x 2) + (75 x 1)] odd days = 123 odd days = (17 weeks + 4 days) = 4 odd days.
Jan. Feb. March April
31 + 29 + 31 + 16 = 107 days = (15 weeks + 2 days) = 2 odd
Total number of odd days = (0 + 1 + 4 + 2) odd days = 7 odd days = 0 odd day.
Hence, the required day was 'Sunday'."

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