**Campus Recruitment – Logical Reasoning – **Day Sequence/ Calendar

Contents

**Concepts**

In day sequence, questions will be asked on calendars to find a particular day of the week (or) a particular day of the given date. In order to solve these problems easily, you should have knowledge on calendar i.e. leap year, odd days etc.

**Leap year:** If the last two digits of a given year is perfectly divisible by 4 then that year is a leap year.

**Example:** 2016 is a leap year because last 2 digits

i.e. 16 is perfectly divisible by 4.

But a century year is not a leap year i.e. 100, 200,300,…. But every 4th century year is a leap year. i.e. 400, 800,1200,1600, 2000 etc.

A leap year has 366 days.

**Examples:**

(i) Each of the years 1764, 1028, 1948, 1676, 2004 etc is a leap year.

(ii) Each of the years 400, 800, 1200,1600, 2000, 2400 etc is a leap year.

(iii) The years 2001, 2002, 2003, 2005, 1900, 2100 are not leap years.

**Ordinary year:** The year that is not a leap year is called an ordinary year. An ordinary year has 365 days.

In order to solve the questions on calendars, we use a concept called ‘odd days’.

**Odd day:** The number of days more than a complete week are called odd days in a given period.

Lets discuss how to count the odd days in a given period.

**Counting of odd days:**

To find the number of odd days in a given period, we divide the total number of days with 7. The remainder obtained is the total number of odd days.

**Examples:**

1) How many odd days are there in 10 days.

2) How many odd days are there in 100 days.

3) How many odd days are there in an ordinary year? Explanation: An ordinary year has 365 days. So,

and 1 odd day. (365 days = 52 weeks + 1 day)

4) How many odd days are there in a leap year?

- Hence, in a leap year, there are 52 perfect week and 2 odd days. [366 days = 52 weeks + 2 days]

**Note:** Total number of odd days can be from 0 to 6 only.

**Counting odd days for century years:**

1) 100 years = 76 ordinary years + 24 leap years.

= (76 x1 + 24 x 2) odd days = 124 odd days

(Here 1 and 2 indicates number of odd days in an ordinary year and a leap year respectively)

124 odd days = 17 weeks + 5 days = 5 odd days.

Number of odd days in 100 years = 5

2) Number of odd days in 200 years = (5×2) = 3.

3) Number of odd days in 300 years =(5×3) = 1.

4) Number of odd days in 400 years = (5×4+1) = 0.

Similarly…, each one of 800, 1200, 1600, 2000 year etc has 0 (zero) odd days as they are multiples of 400.

**Some Important points to remember:**1) In every normal / ordinary year the first day (1st January) and the last day (31st December) are always same. For example, if January 1st is Monday then December 31st is also Monday.

2) In every leap year if the first day (January 1st) is Sunday, then last day (December 31st) will be it’s next day i.e. Monday.

3) In every year, tire calendar for the months April and July are always same.

4) For every’ 400 years, the day repeats. For example, it 14-Apri 1-1604 is Saturday, then 14-April- 2004 will also be Saturday.

5) The last day of a century’ cannot be either Tuesday or Thursday or Saturday.

Questions on day sequence/ calender are mainly 5 types.

1) Problems based on Total Day-Particular Day.

2) Problems based on Leap Year.

3) Problems based on Particular Date-Day.

4) Problems based on Same Calendar Year.

5) Problems based on Same Day-Date of the Month

**Type-(l): Problems on Total Days and Particular Day:**

In this type, particular day or date is given and you are required to find the day which will fall after/before some number of days or on particular other date which may be before/after the given day/date.

**Approach to solve:**

Step 1: Divide the given number of days by 7 and find the remainder, (or) If two dates are given, find the total number of days between them including the day of the second date and divide it by 7 to get the remainder.

Step 2: If the remainder obtained in the above step is 0 then the required day is same as the given day.

Step 3: If the remainder is 1 then the required day is the next day to the given day (or) if the remainder is 2 then the required day is two days after the given day and so on.

**Example:** If 15th August is Monday then on what day will come on 17th November?

**Explanation:** August month has 31 days. Number of days left over in August = 16.

September month has 30 days and October has 31 days.

So, the total number of days between 15th August and 17th November = 16 + 30 + 31 + 17 = 94. .

Odd days = 94/7 = 3 (remainder).

So, 17th November = 3 days after the given day

= Monday + 3 days = Thursday

**Shortcut Approach to solve:**

1) If you see the key words ‘after / later / hence’ in the question then use the below formula.

Required Day=Given Day + Total days/7 (remainder)

2) If you see the key words ‘ago! before’ in the question then use the below formula.

Required Day=Given Day + Total days/7 (remainder)

**Examples:** (1) If today is Tuesday, then what will be the day after 100 days?

**Explanation:** Here we have the keyword ‘after’.

So, Required day = Tuesday + 100/7 (remainder)

= Tuesday + 2 days = Thursday.

So, if today is Tuesday, then after 100 days it is Thursday.

2) If today is Sunday, then what day had fallen 200 days ago?

**Explanation:** Here we have the key word ’ago’.

So, Required day = Sunday-200/7(reminder)

=sunday-4days=wednesday

**Tvpe-(2): Problems based on leap year.**

In this type, a particular year is given and you are required to find its previous or next leap year.

**Approach to solve:**

1) To find the next leap year from the given year, add four (4) to the given year and check whether it is leap year. If not, then add ‘8’ to the given year to obtain it’s next leap year.

2) To find the previous leap year from the given year, subtract four (4) from the given year and check whether it is leap year. If it not leap year, then subtract 8 from the given year to obtain its previous leap year.

**Examples:**

1) What will be the next leap year after 2176?

**Explanation:** Here, we have to find leap year after 2176.

So, add 4 to the given year.

2180 is not a century year and divisible by 4. So, it is a leap year. Hence, the next leap year after 2176 is 2180.

2) What would be the previous leap year of 2176?

**Explanation:** We have to find previous leap year of 2176.

So, subtract 4 from the given year.

2172 is divisible by 4. So, it is a leap year.

.’. The previous leap year of the year 2176 is 2172.

**Type-(3): Problems based on particular date and day:** In this type of problem, a particular date is given, and you are required to find the day of the given date. To solve these kind of problems we use shortcut codes to years, months and days. They are as follows.

**Steps to Solve:** Example: 01-Jan-2016.

Step-1: Take the day number of the given date. i.e. 01.

Step-2: Take the month code of the given month from the above table i.e. January code is 1.

Step-3: Subtract 1 from the given year i.e. 16-1 = 15.

Step-4: Count how many leap years are there in 15. i.e. divide 15 by 4 and consider the quotient.

i.e.15/4=3( quotient)

Step-5: Take the year code of the given year. i.e. code for 2016 = 6 (Since, 2000 – 2099 = 6).

Step-6 : Add the values from step-1 to step-5 and dividethe result by 7 and find the remainder.

Based on the remainder obtained, the day of the given date can be determined from the below table.

(i.e Friday)

By combining all the above steps we can deduce a formula to find the day of a give date as shown below.

Where, D= Date

MC = Month code;

Last 2 digits = Last 2 digits of the year;

LP = Leap Years;

YC= Year Code;

**Note:** Leap Years (LP) = The quotient obtained when the (last two digits-1) of the year is divided by 4.

**Type****-(4): Problems on same calendar year:**

In this type of problems, particular year is given. You are required to find which year will have the same calendar as that of the given year.

There are two methods to solve this kind of problems.

**Method-1:**

**Example:** Which year will have the same calendar year as 2007?

Step-1: If the given vear is an ordinary/ non leap year, write the years up to leap year beture and alter the given year.

i .e.. 2004, 2005, 200b, 200“, 2006.

Step-2 : Now remove the leap years. You are left with 3 consecutive years, i.e. 2005, 2006, 2007.

Step-3: Add the code (6) (11) (11) to the corresponding years

The sum corresponding to the given year is the required answer.

i.e. year 2018 will have same calender as 2007.

• If the given year is a leap year, then add 28 to get the required answer.

**Example:** Which year will have the same calendar year as 2008?

**Explanation:** The given year is a leap year.

So, 2008 + 28 = 2036.

The year 2036 will have the same calendar as 2008.

**Method-2:**

We can also find the answer using ‘odd days’ concept. Count the number of odd days from the given year onward till the sum of all odd days is an exact multiple of 7. Then take the next year (after the sum equals to multiples of 7) which will have the same calendar as that of the given year.

**Example:** Which year will have the same calendar as 2007?

**Explanation:** As we know leap year has 2 odd days and ordinary year has 1 odd day.

Sum = 14 = multiple of 7. So, consider the next year.

The next year of 2017 is 2018.

.’. 2018 will have the same year as that of 2007.

**Type- (5): Problems on same day – dates of the month:**

In this type, particular month and year along with a week day (i.e. Sunday to Saturday) is given. You are required to find the dates of the given month which will fall on the given week days.

For example, what dates of March 2011 is Saturday?

**Approach to solve:**

Step-1: Find the day of the first date of the month using

Type-(3) approach, i.e. The day of 01-March-2011.

Step-2: 01-March-2011 is Tuesday. Then Saturday will be on 05-March-2011. Next Saturday will be after 7 days. i.e. 12-March-2011,19-March-2011 and 26-March-2011.

**Conceptual Examples**

1) If today is Sunday, what was the day 150 days ago?

a) Monday b) Tuesday c) Sunday

d) Thursday e) Friday

**Explanation:** Here keyword ‘ago’.

So, Required day=Sunday-150/7 (remainder)

Required day = Sunday – 3 = Thursday, i.e. counting 3rd day from Sunday in reverse.

2) If 25-December-2013 is Wednesday, then what is the

day on 15-January-2016?

a) Friday b) Saturday c) Sunday

d) Wednesday e) Monday

3) Which year will have the same calendar as 2013?

a) 2020 b) 2019 c) 2018 d) 2017 e) 2016

**Explanation:** Write till leap years before and after the given year.

i.e. 2012, 2013, 2014, 2015, 2016.

Eliminate the leap years and add code (6) (11) (11). i.e. 2013 2014 2015 6 11 11 2019

The sum corresponding to the given year is the required answer, i.e. 2013 + 6 = 2019.

4) What is the next leap year after 2096?

a) 2100 b) 2098 c) 2144 d) 2099 e) 2104

**Explanation:** The year 2096 is a leap year. So, add 4 to 2096 to get the next leap year. i.e. 2096 + 4 = 2100 year. But 2100 is a century year. We know that a century year should be divisible by 400 to be a leap year. But 2100 is not exactly divisible by 400. So, it is not a leap year.

So, add 4 to 2100 i.e. 2100 + 4 = 2104.

The last two digits of the year 2104 is divisible by 4. So, it is a leap year. The next leap year after 2096 is 2104.

5) What week day was on 15-August-1947?

a) Sunday b) Monday c) Thursday

d) Friday e) Wednesday

**Note:** LP = Leap Years = 46/4 = 11

**Exercise**

1) If 15-March-2003 is Saturday, then find the day of the week on 23-January-2005?

a) Sunday b) Saturday c) Monday

d) Tuesday e) Wednesday

2) If 18-Februarv-l 996 is Wednesday, then 15-July-2000 is on which day of the v eek?

a) Friday b) Monday c) Tuesday

d) Wednesday e) Thursday

3) If 29-December-1972 is Friday then 22-April-1975 is on which day of the week?

a) Sunday b) Saturday c) Monday

d) Tuesday e) Wednesday

4) If 14-April-1984 is Monday, then 16-March-1987 is on which day of the week?

a) Monday b) Wednesday c) Saturday

d) Sunday e) Friday

5) If 18-May-2001 is Friday, then 05-March 2005 is?

a) Sunday b) Monday c) Wednesday

d) Thursday e) Saturday

6) A boy says his birthday is on 05-March. His brother’s birthday is on 28-September. If his birthday comes on Monday, find the day of the week on his brother’s birthday?

a) Tuesday b) Wednesday c) Thursday

d) Friday e) Saturday

7) Mary’s daughter birthday is on June-29, Sunday. Her husband’s birthday is on x-mass day. Find the day of the week on her husband’s birthday?

a) Wednesday b) Thursday c) Friday

d) Saturday e) Sunday

8) Swapna’s birthday was on Friday, 16-April-1986. Find the day of the week when her age is 15 years 4 months 5 days?

a) Sunday b) Thursday c) Monday

d) Wednesday e) Saturday

9) If 14-May-1978 is Thursday, then find the day of the week on 16-July-1980?

a) Wednesday b) Tuesday c) Sunday

d) Saturday e) Monday

10) If Santosh’s birthday is Wednesday, 18-Feb-2000. He started going to school on 27-March-20G5. Then find the day of the week on when he started going to school, a) Tuesday b) Thursday c) Saturday

d) Friday e) Saturday

11) Lai’s father’s retirement is on 16-January of a leap year. He started a business on 24-November of the same year. If his father’s retirement is on Friday. Find the day of the week on his business start up?

a) Sunday b) Thursday c) Saturday

d) Wednesday e) Friday

12) If Raju’s date of birth is 18-March-2002. How old is he by 17-April-2007?

a) 5 years 29 days b) 5 years 1 month 29 days

c) 5 years 30 days d) 5 years 2 months

e) 5 years 1 month 30 days

13) Amala bom on 27-July-1985. How old is she by 24-October-2007?

a) 22 years 4 months 5 days

b) 22 years 2 months 27 days

c) 22 years 3 months 3 days

d) 21 years 2 months 3 days

e) 22 years 2 months 25 days

14) Vimala bom on Monday, 26-April-1979. Find the day of week of her 24th birthday?

a) Saturday b) Sunday c) Tuesday

d) Wednesday e) Thursday

15) Ram Gopal celebrates his 25th birthday on Saturday, 15-May-2006. Asha is 4 years 2 months 6 days younger to Ram Gopal. Find the day of the week Asha born?

a) Wednesday b) Tuesday c) Monday

d) Sunday e) Friday

16) If in a calendar year, there are 541 days and 10 days a week. Then how many odd days will be there in that year?

a) 2 b) 4 c) 1 d) 6 e) 0

17) How many odd days are there in x weeks and x days and a week has 7 days.

a) 2 odd days b) x odd days c) 3 odd days

d) 3x odd days e) Cannot be determined

18) If on 01-January-2024 is Tuesday, what week day will become on 01-January-2030?

a) Tuesday b) Wednesday c) Thursday

d) Friday e) Saturday

19) Which of the following year is not a leap year?

a) 600 b) 2076 c)2000 d) 2084 e) All are leap

20) If My birthday was 08-May-1986. Find the week day of my birthday ?

a)Tuesday b) Wednesday c) Friday

d) Thursday e) Monday

21) If Sahithya bom exactly 2 years 2 months 2 days later than her sister Alekhya. If Alekhya’s birth date is 03-August-1992, then find the week day of Sahithya’s birth date.

a) Monday b) Tuesday c) Wednesday

d) Friday e) Thursday

22) On what dates of Jan 2014 becomes Sunday?

a) 5th, 12th, 19th, 26th b) 6th, 13th, 20th, 27th

c) 8th, 15th, 22nd, 29th d) 10th, 17th, 24th, 31th

e) Cannot be determined

23) If Sudha Jennifer bom on Sunday. What week day will become after 100 years of her birthday?

a) Saturday b) Sunday c) Friday

d) Wednesday e) Monday

24) Which year will have the same calendar as 2020?

a) 2048 b)2082 c)2042 d) 2043

e) Cannot be determined

25) Which year will have the same calendar as 1998?

a) 2014 b) 2010 c)2008 d)2009 e)2013

26) If on 5th April 2015 is Sunday, then what day will becomes on 5th April 2016?

a) Tuesday b) Wednesday c) Thursday

d) Friday e) Same day

27) If 26th March 2013 is Tuesday, then what day will become on 14th October 2013?

a) Sunday b) Monday c) Tuesday

d) Wednesday e) Thursday

28) If today is Monday, what day it was 126 days ago from day after tomorrow?

a) Monday b) Sunday c) Wednesday

d) Thursday e) Saturday

**Explanations**

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