Explanation / Important formulas:
Ordinary Year: The year which is not a leap year is called an ordinary years. An ordinary year has 365 days
Leap Year: Every year divisible by 4 is a leap year, if it is not a century. Every 4^{th} century is a leap year and no other century is a leap year
 A leap year has 366 days
Examples: Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year
Odd Days: To find the day of the week on a given date. we use the concept of ‘odd days’
In a given period, the number of days more than the complete weeks are called odd days
Counting of Odd Days:
 1 ordinary year = 365 days = (52 weeks + 1 day)
 1 ordinary year has 1 odd day
 1 leap year = 366 days = (52 weeks + 2 days)
 1 leap year has 2 odd days.
 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 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
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Question 1

A

Sunday

B

Monday

C

Tuesday

D

Wednesday

5 Days before Sunday is Tuesday
Question 2

A

16

B

17

C

18

D

19

44,48,52,56,60... 2004, 2008
17 leap years
Question 3

A

131

B

132

C

133

D

134

30 days in April
31 days in May
30 days in June
19 days in July [1st – 19th]
Total = 131 days
Question 4

A

17

B

18

C

19

D

20

From Jun ’90 to Feb ‘93
(4 in ‘90) + (7 in ‘91) + (7 in ‘92) + (1 in ‘93) = 19
Question 5

A

Wednesday

B

Friday

C

Monday

D

Tuesday

Number of odd days in a 10 day period = 3
Question 6

A

185

B

186

C

184

D

187

= 11+30+31+30+31+31+21
= 185
Question 7

A

2016

B

2017

C

2020

D

2022

= 1+2+1+1+1+2+1+1+1+2+1
= 14
Hence, 2022 will have a calendar similar to 2011
The number of odd days increases from 6 to 8 since 2016 is a leap year
Hence 14 odd days are calculated
Question 8

A

2000, 2006

B

2000, 2011

C

2014, 2019

D

2012, 2017

Between 2014 and 2019,
No. of odd days = 6
Hence they have a different calendar
Question 9

A

Tuesday

B

Wednesday

C

Thursday

D

Friday

Day after tomorrow will be Thursday
Question 10

A

Friday

B

Saturday

C

Sunday

D

Monday

No. of odd days in a 100 day period = 2
100 days after today (Thursday) will be Saturday
Question 11

A

Tuesday

B

Wednesday

C

Thursday

D

Friday

November 3, 2004  Wednesday
Question 12

A

45

B

45

C

16

D

15

Number of leap years between 1952 and 2013 = 15
Number of ordinary years = 60 – 16 = 45
Question 13

A

1

B

2

C

3

D

4

A leap year contains 366 days
i.e 52 weeks and 2 days
The number of odd days in a leap year is 2
Question 14

A

23

B

22

C

24

D

25

Sep 30 – Saturday
There are 4 Sundays in September
There are 25 working days in September
Question 15

A

today

B

Two days after today

C

Two days after tomorrow

D

Day after tomorrow

Hence, Sunday will be two days after tomorrow
Question 16

A

Monday

B

Sunday

C

Tuesday

D

Saturday

5th of the month is Sunday
Hence, twentieth of that month will be Monday (1 odd day from 5 to 20)
Question 17

A

July 3

B

July 7

C

July 1

D

July 4

Find using odd days concept
Question 18

A

Wednesday

B

Monday

C

Friday

D

Friday

No. of odd days from March ’00 to Mar ’12 = 15
So, 20th March 2000 was a Monday
Question 19

A

Sunday

B

Saturday

C

Friday

D

Thursday

Today is Sunday (27th dec)
New year falls on Friday
The difference between Christmas and new year is 7 days (0 odd days)
Hence, they fall on the same day
Question 20

A

0

B

2

C

5

D

6

No. of odd days = (76*1) + (24*2)
= 124
= (17*7) + 5
= 5 odd days
Question 21

A

Nov 25, 2011

B

Dec 5, 2011

C

Jan 5, 2012

D

Dec 10, 2011

Nov 25, 2011 – 10 years, 10 months
Dec 5, 2011 – 10 years, 10 months, 10 days
Question 22

A

Sunday

B

Friday

C

Friday

D

Thursday

Last day of third century is Monday
400 years (5*4) + 1 = 21 odd days = 0 odd days
1 is added since 400 is a leap year while 100,200,300 are not
Last day of fourth century is Sunday
The cycle starts repeating again
Last day of 5th century  Friday and so on
The last day of a century cannot be a Tuesday
Thursday or a Saturday
Question 23

A

25th November

B

25th July

C

25th October

D

25th August

April  2
May  3
June  2
July  3
August  3
September  2
October  3
The no. of odd days from March to October is 21(zero odd days)
Hence, 25th November falls on the same day as 25th march
Question 24

A

Mar, Sep

B

Feb, Nov

C

Jan, Apr

D

Aug, Dec

Jan and April begin on the same day
Question 25

A

25

B

24

C

75

D

74

Question 26

A

Friday

B

Monday

C

Saturday

D

Sunday

No. of odd days = (2*2) + 8 = 12
5 odd days
This date will fall on Saturday
Question 27

A

1,8,15,22,29

B

3,10,17,24,31

C

5,12,19,26

D

7,14,21,28

No. of odd days from Aug 2005 to Aug 2012 = 9
2 odd days
August 1, 2005 was a Monday
7,14,21,28 were Sundays
Question 28

A

76

B

75

C

65

D

24

So, there are 75 ordinary years in the 20th century
Question 29

A

Tuesday

B

Tuesday

C

Monday

D

Thursday

So, December 31, 20017 was a Monday
Hence Jan 1, 2008 was a Tuesday
Question 30

A

1975

B

1976

C

1977

D

1981

No. of odd days from 1970 – 1975
1+2+1+1+1 = 6
1970 – 1976 => 8
1970 – 1977 => 9
1970 – 1981 => 1+2+1+1+1+2+1+1+1+2+1 = 14
Her birthday falls on Sunday in the year 1981
Question 31

An application was received by inward clerk in the afternoon of a weekday. Next day he forwarded it to the table of the senior clerk, who was on leave that day. The next day evening, the senior clerk put up the application to the desk officer. Desk officer studied the application and disposed off the matter on the same day, i.e.., Friday.. Which day the application was received by the inward clerk?
A

Tuesday

B

Wednesday

C

Saturday

D

Monday

Question 32

A

110

B

111

C

112

D

113

Question 33

A

Thursday

B

Tuesday

C

Wednesday

D

Friday

= 1+1+2+1+1+1+2+1 = 10
1st Jan, 1998 was a Thursday
Question 34

Rajan remembers that his elder brother was born between 13th and 16th April while his mother remembers that he was born after 14th April and before 17th April. If the statements of both are considered correct then on which date of April he was born?
A

14

B

15

C

14 or 15

D

15 or 16

14 or 15
After 14th
So, 15 should be the answer
Question 35

A

Monday

B

Tuesday

C

Wednesday

D

Thursday

But there are only 4 Sundays
Hence, it started on a Monday. There would be 5
Mondays, Tuesdays and Wednesdays
If it started on any other day, then the number of either Thursday or Sundays would be 5
Question 36

A

69

B

70

C

71

D

72

Question 37

A

Thursday

B

Friday

C

Saturday

D

Wednesday

2011 = 1
2012 = 2
2013 = 1
Hence, October 10, 2013 falls on a Thursday
October 11, 2013 – Friday
Question 38

A

Wednesday

B

Thursday

C

Monday

D

Sunday

After 63 days, it will be Tuesday
After 62 days, it will be Monday
Question 39

A

Wednesday

B

Tuesday

C

Thursday

D

none of these

8th Feb, 1995 was Wednesday
8th Feb, 1994 was Tuesday
Question 40

A

Friday

B

Sunday

C

Tuesday

D

Wednesday

300 years contain 1 odd day
100 year contain 5 odd days
2000 years contain (0+1+5) odd days = 6 odd days
2001 has one odd day
Total number of odd days up to 1st Jan, 2001 = 7 odd days
Jan 1, 2001 will be Sunday
Question 41

A

71

B

73

C

72

D

74

Question 42

A

Thursday

B

Tuesday

C

Sunday

D

Saturday

= 27+31+31+28+20
= 137 days
= 19 weeks + 4 days
Number of odd days = 4
4 days before Monday is Thursday
Question 43

A

Monday

B

Tuesday

C

Wednesday

D

Sunday

1 day after Monday is Tuesday
Question 44

A

Monday

B

Wednesday

C

Thursday

D

Sunday

2 days after Tuesday is Wednesday
Question 45

A

700

B

800

C

1200

D

2000

The year 700 is not a leap year
Question 46

A

Sunday

B

Thursday

C

Tuesday

D

Friday

1 day before Saturday is Friday
Question 47

A

2014

B

2016

C

2017

D

2018

= 1+2+1+1+1+2+1 = 9
No. of odd days from 2007  2016
= 9+1+1 = 11
No. of odd days from 2007  2017
= 11+2 = 13
No. of odd days from 2007  2018
= 13+1 = 14
2018 and 2007 have the same calendar
So, the calendar for 2017
Question 48

A

Monday

B

Thursday

C

Tuesday

D

Friday

No. of odd days from 1950  2015
= (64*5) + 1
= 321 odd days
= 6 odd days
6 days before Monday is Tuesday
Question 49

A

Monday

B

Wednesday

C

Tuesday

D

Thursday

= 1+2+1+1+1+2+1
= 9 odd days
= 2 odd days
2 days after Tuesday is Thursday
Question 50

A

5th Aug

B

5th Nov

C

5th Oct

D

5th Dec

so the same day falls on 5th November
Question 51

A

Tuesday

B

Friday

C

Thursday

D

Monday

2 days after Wednesday i s Friday
Question 52

A

Saturday

B

Wednesday

C

Tuesday

D

Friday

One day before Thursday is Wednesday
Question 53

A

Sunday

B

Saturday

C

Monday

D

none of these

One day after Sunday is Monday
Question 54

A

Sunday

B

Saturday

C

Tuesday

D

Wednesday

One day before Monday is Sunday
Question 55

A

1,8,15,22,29

B

2,9,16,23,30

C

3,10,17,24

D

4,11,18,25

No. of odd days from April 2002 to April 2015 = 16
2 odd days
So, April 1, 2002 was a Monday
Hence, 3,10,17,24 of April ’02 are Wednesday
Question 56

A

7x2

B

8x

C

14x

D

7

= (7x+x) days
= 8x days
Question 57

A

Sunday

B

Monday

C

Tuesday

D

Friday

Odd days from Aug ’10 to Aug ’15 = 6
6 days before Saturday is Sunday
Question 58

A

Saturday

B

Friday

C

Sunday

D

Tuesday

3 odd days
3 days after Wednesday will be Saturday
Question 59

A

2,9,16,23,30

B

4,11,18,25

C

3,10,17,24

D

1, 8,15,22,29

4,11,18,25 were Sundays
Question 60

A

2003

B

2001

C

2002

D

2004

1996 2
1997 1
1998 1
1999 1
2000 2
2+1+1+1+2 = 7
Calendar for 2001 will be the same as that of 1996
Question 61

A

2 days ago

B

3 days ago

C

4 days ago

D

5 days ago

Friday was today
Hence, today is Wednesday
3 days after Sunday is Wednesday
Day after tomorrow should be Wednesday
Today should be Monday
Monday is 2 days before Wednesday
Question 62

A

Monday

B

Tuesday

C

Sunday

D

Thursday

We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0
Number of odd days in the period 2001  2200
= number of odd days in 200 years
= 5 x 2 = 10 = 3
Number of odd days in the period 2201 – 2221
= 16 normal years + 5 leap years
= 16x1 + 5x2 = 16+10 = 26 = 5 odd days
Number of days from 1jan2222 to 22 Apr 2222
= 31(Jan) +28(Feb) +31(Mar) +22(Apr ) = 112
112 days = 0 odd days
Total number of odd days = (0+3+5+0) = 8 = 1 odd day
1 odd days = Monday
Hence 22Apr 2222 is Monday
Question 63

A

Wednesday

B

Friday

C

Sunday

D

Saturday

Number of odd days in 9 days = 2
Hence today = (Thursday + 2 odd days) = Saturday
Question 64

He started work on Monday. Find the day of the week on which he gets his 12th rest day?
A

Wednesday

B

Tuesday

C

Monday

D

Friday

So on the 12th rest day, there are 9*12 = 108 days passed
Number of odd days = (108 1) /7 = 107 /7
Remainder = 2
So the 12th rest day is Wednesday
Question 65

A

Monday

B

Tuesday

C

Wednesday

D

Thursday

If the month starts with Monday, then Mondays, Tuesdays and Wednesdays are 5 and remaining days are 4 each for that month
According to the question, there are 4 Thursday and 4 sundays, so the 1st of the month starts with Monday
Question 66

A

Tuesday

B

Monday

C

Sunday

D

Saturday

= 3 odd days
Today is Thursday, After 59 days, it will be
= (Thursday + 3 odd days)
= Sunday
Question 67

A

Tuesday

B

Saturday

C

Sunday

D

None of these

So, the first day of 1996 will be one day beyond Sunday
i.e it will be Tuesday
Question 68

A

Wednesday

B

Sunday

C

Monday

D

Thursday

1st day of the year 2008 is Tuesday (Given)
So, 1st day of the year 2009 is 2 days beyond Tuesday
Hence, it will be Thursday
Question 69

A

Wednesday

B

Sunday

C

Monday

D

Tuesday

The day on 8th Feb, 2004 is 2 days before the day on 8th feb, 2005
Hence, this day is Sunday
Question 70

A

102

B

111

C

120

D

103

= 6 (Jan) + 29 (Feb) + 31(Mar) + 30(Apr) + 15(May) = 111
Question 71

A

22.12.91

B

22.12.91

C

24.12.91

D

20.12.91

Hence we can assume that 3.12.91 is the first Tuesday
If we add 7 days to 3.12.91, we will get second Tuesday
If we add 14 days to 3.12.91, we will get third Tuesday
If we add 21 days to 3.12.91, we will get Fourth Tuesday
Fourth Tuesday = (3.12.91 + 21 days) = 24.12.91
Question 72

A

Wednesday

B

Sunday

C

Friday

D

Saturday

Number of odd days in 9 days = 2(As 9  7 = 2, reduced perfect multiple of 7 from total days)
Hence today = (Thursday + 2 odd days) = Saturday
Question 73

A

Monday

B

Friday

C

Saturday

D

Tuesday

Odd days of the mentioned year = 1(Since it is an ordinary year)
Hence first day of the next year = (Friday + 1 odd day) = Saturday
Last day of the mentioned year = Friday
Question 74

A

Saturday

B

Monday

C

Sunday

D

Tuesday

We know that number of odd days in 400 years = 0
Hence the number of odd days in 1600 years = 0
Number of odd days in the period 1601 – 1900
= Number of odd days in 300 years
= 5 x 3 = 15 = 1
1st Jan 1901 = 1 odd day
Total number of odd days = (0+1+1) = 2
2 odd days = Tuesday
Hence 1 January 1901 is Tuesday
Question 75

A

Friday

B

Monday

C

Tuesday

D

Sunday

So, it has 1 odd day
So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec 2006
But 8th Dec, 2007 is Saturday
8th Dec, 2006 is Friday
Question 76

A

7

B

4

C

5

D

6

Hence 29th August = Monday
So 22nd, 15th and 8th and 1st of August also will be Monday
Number of Mondays in August = 5
Question 77

A

Sunday

B

Wednesday

C

Monday

D

Tuesday

Number of days in October = 31 days = 3 odd days
Hence 1st November = (Sunday + 3 odd days) = Wednesday
Question 78

A

45

B

44

C

16

D

15

Number of leap years between 1952 and 2013 = 15
Number of ordinary years = 60 – 16 = 45
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