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Calendars

Kabir Singh
Nov 1, 2021

Introduction

Calendars are considered a small topic but are an essential part of the reasoning section.

A calendar can be defined as a series of pages that contains days, weeks, and months of a specific month and gives us information about the same.

Let's see some broad explanations of the years.

  1. Normal Year: The year which contains 365 days is called a Normal Year.
  2. Leap Year: The year which contains 366 days is called Leap Year.
  3. Odd Days: the number of specific days we can't complete a week are called odd days.

 

A normal year consists of 365 days. This consists of 52  weeks, and the last day would be an odd day for sure. It would shift the calendar ahead or behind by a specific day. 

Let’s now have a look at the number of odd days in different months of the year.

Odd Days

Months

Number Of Odd Days

JANUARY3
FEBRUARY(Normal/Leap)0/1
MARCH3
APRIL2
MAY3
JUNE2
JULY3
AUGUST3
SEPTEMBER2
OCTOBER3
NOVEMBER2
DECEMBER3

 

We still have a note to keep in mind, though,

Note : 

1. The number of odd days in the first 100 consecutive years is 5.

2. The number of odd days in the first 200 consecutive years is 3. 

3. The number of odd days in the first 300 consecutive years is 1. 

4. The number of odd days in the first 400 consecutive years is 0. 

Let’s finally have a look at some problems based on calendars:

Problems

Example 1: 11 August 2019 is a Sunday. What day was on 11 August 1983? 

Solution :

To find the day on 11 August 1983, you have to count the number of odd days. From 1983 to 2019, there are 36 years. This means 36 odd days and now count how many leap years or 29th Feb will appear.

 

So, 29th Feb would appear in 1984,1988,1992,1996,2000,2004,2008,2012,2016. So, 9 leap years means 9 further odd days. 

 

Hence, the total number of odd days = 36+9=45 days 

45 days have 6 complete weeks and 3 odd days left out. 

 

Going behind 3 odd days from Sunday. Hence, 11 August 1983 would be a Thursday. 

 

Example 2: What was the day of the week on 13th April 1723?

(a) Monday 

(b) Tuesday 

(c) Wednesday 

(d) Thursday 

Answer:

b) Solution: No. of odd days in 1700=5      (1700 = 1600 + 100, Odd days = 0 + 5 = 5) 

No of odd days in 22 years=5(leap years)*2+17(normal years)=27mod7=6

No. of odd days in Jan, Feb, and march=3+0(1723 is not a leap year)+3=6 

No. of odd days in 13 days=6 

Total odd days =23mod7=2 

Thus 13th April 1723 is Tuesday

 

OR

 

No. of odd days in 1700 = 5 (1600 = 0 + 100 =5) 

No of odd days in 22 year = 5(leap years) * 2 + 17 (normal years) = 27mod7 = 6 

No. of odd days in Jan, Feb, March and 13 days of April = 31 + 28(not leap year) + 31 + 13 = 103mod7 = 5 

Total odd days = 5+6+5 = 16mod7 = 2 

 

Thus 13th April 1723 is Tuesday.

 

Frequently Asked Questions

Question 1:

What is the logic behind 5 odd days in 100 years?

Answer : 

Odd days in a leap year = (52 weeks +2) days. 

So now we can say that odd days in 100 years will be (76 x 1 + 24 x 2) which sums up to 124 odd days

We can also say that 17 weeks + 5 days. So every 100 years will have 5 odd days.

Question 2:

What is a calendar?

Answer :

A calendar can be defined as a series of pages that contains days, weeks, and months of a specific month and gives us information about the same.

Question 3:

How do we check if a specific year is a leap year or not?

Answer :

To check if a given year is a leap year, divide the year by 4. If it is fully divisible by 4, it can be termed as a leap year. However, years like 300, 700, 1900, 2000 that are centuries need to be divided by 400 to see whether they are leap years or not.

 Key Takeaways

This blog takes you around how to find Calendars in detail. With this done, you may now switch towards aptitude preparation from our Guided Path.

As we all know, aptitude is a very easy way to score in interviews, so topics like this can help you clear aptitude rounds of many interviews.

If you wish to read more blogs on aptitude, you can find spectacular blogs here.

Happy learning!

 

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