What is Calendar?
A Calendar is a chart or series of pages showing the days, weeks and months of a particular year, or giving particular seasonal information.
Given below is the list of topics under the CLAT logical reasoning Calendar topic:
- A basic structure of a calendar and a concept of an odd day.
- Decoded days of the weeks.
- Evaluation of a leap year.
- Evaluation of odd days in a century.
- Type 1 problems: Finding the day when another day is given.
- Type 2 problems: Finding the day when another day is not given.
- Type 3 problems: Matching the calendars of a month.
Basic Structure of a Calendar
- Ordinary year: Any year which 365 days is called an ordinary year.Ex: 1879, 2009, 2019, etc.
- Leap year: Any year with 366 days is called a leap year.Ex: 2012, 2016 2020 etc.
- The division of the number 365 by 7 gives the quotient 52 and the remainder 1, indicating that an ordinary year has 52 weeks and one extra day. This extra day is referred to as an “odd day” throughout the calendar topics.
- A leap year has 366 days, the division of the number 366 by 7 gives the quotient 52 and the remainder 2. This indicates that a leap year has 52 weeks and 2 extra days. These two extra days are also referred to as “odd days”.
An ordinary year has one odd day, whereas a leap year has two odd days.
Concept of an Odd Day
A number of odd days in a month
January has 31 days, irrespective of whether it’s an ordinary year or leap year. The division of the number 31 by 7 provides the remainder of 3 hence January has 3 odd days. In generalizing, any month which has 31 days has 3 odd days and any month which has 30 days has 2 odd days.
The only exception that happens is in the case of February. The February month of an ordinary year has 28 days, division of 28 by 7 provides zero as the remainder. Hence, the number of odd days in February of an ordinary year will have 0 odd days and that of leap year will have 1 odd day as February in a leap year has 29 days.
The below table depicts the number of odd days in different months of a calendar year:
Decoded day of the week
The week always begins on Monday and hence Saturday and Sunday are referred to as weekends. In order to make the calculation easier and reduce its time during the exams.
The days of the week are coded as follows:
Table 2: The corresponding codes of the day of the week.
Practice 2 to 3 clat mock test every week for better preparations.
This table helps in decoding the answers obtained at the end of the problem-solving process in the calendar topics.
Q.1. If it was Wednesday on 2 March, then which day would come on 26 March?
(A) Friday
(B) Saturday
(C) Sunday
(D) Tuesday
Solution
Difference between 2 March to 26 March is (26-2) = 24 days. When 24 is divided by 7, we find 3 as a remainder. So, the third day after Wednesday is Saturday. So, it will be Saturday on 26 March.
Q.2. If it is Friday on 10 March 2003, then which day would come on 25 June, 2003 ?
(A) Monday
(B) Tuesday
(C) Sunday
(D) Wednesday
Solution
Difference from 10 March, 2003 to 25 June, 2003 = March+April+May+June = 21+30+31+25=107
Keep in mind ! Only one date from 10 March & 25 June will be accounted, so, for the convenience, we consider 25 June. So, days in March will be (31-10)=21 is written.
Now, we divide the difference obtained by 7, which is :
= 15 & 2 is the remainder.
So, the day on 25 June will be 2nd next day after Friday, which is Sunday.
Second Method:
Here, we can solve this by writing the odd days only ( the remainder found after dividing by 7) as below :
March + April + May +June
0 + 2 + 3 + 4 = 9
So, = 1, remainder = 2
So, the day after 2 days will be Sunday.
Note: Here we have already divided the days of months by 7. The month of 30 days will give the remainder 2 & similarly, for 31 day’s month, we get remainder 3. In the month o March, we have 21 days as 10 days are not be accounted. So, here we’ll get remainder 0. So, for March, we’ve written 0 here. Similarly, we’ll get remainder 4 for June as we’ve to consider 25 days in June.
Q.3. If it is Wednesday on 17 March, 2005, then which day would come on 12 September, 2005?
(A) Monday
(B) Friday
(C) Sunday
(D) Saturday.
Solution
March+April+May+June+July+Aug+September = 0+2+3+2+3+3+5 = 18.
The remainder will be 4 when 18 is divided by 7.
So, the next 4th day from Wednesday is Sunday.
Note- In the given problem, 17 days of March are not considered, So the remaining days will be 31-17=14. Now, the remainder is 0 when 14 is divided by 7. So, we’ve written 0 for March. Similarly, we’ve to consider only 12 days in September. The remainder will be 5 when 12 is divided by 7, so we’ve written 5 for September.
Also read : Logical Reasoning: Blood Relations for CLAT
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