 # Reasoning Concepts of Calendar

Calendar-based questions in logical reasoning are very important and easy to understand if we follow some basic concepts. Everything depends upon finding the odd days. We can use some quick tricks to find out the number of odd days and we can easily solve these calendar-based logical reasoning questions. These types of logical reasoning questions are frequently asked in various competitive exams. Let us understand some basic concepts and apply these in solving some examples.

This post includes some important terms such as types of years, ordinary year, leap year, odd day, etc.   Image by Amber Avalona from Pixabay

## Basic Concepts of Calendar

• A calendar is a collection of days, weeks, months, and years.
• There are two types of years.
(1) Ordinary year (365 days)
(2) Leap Year (366 days)
• A Decade is a period of 10 years.
• A Century is a period of 100 years.
• A Millennium is a period of 1000 years.

### How to find out the Leap Year?

A leap year occurs every 4th year except in some special cases. There are some cases where the difference between two leap years is 8. (for example, 1096 – 1104 because 1100 is not a leap year)

Two types of years:
(1) Normal Year
(2) Century year

100, 200, 300, 400, and so on are called the Century Years. All the other years are normal years.

We have different ways to find the leap years.

(1) For a Normal year, it should be divisible by 4.
(2) For a Century year, it should be divisible by 400.

#### Examples:

• 1999 ⇒ Not Divisible by 4. (Ordinary year)
• 2020 ⇒ Divisible by 4. (Leap year)
• 1600 ⇒ Divisible by 400. (Leap year)
• 1900 ⇒ Not Divisible by 400. (Ordinary Year)

## What is an Odd day?

• A week has 7 days. (Monday to Sunday)
• When we divide the total number of days of duration by 7 then the remainder is called the odd day or odd days.
• An ordinary year has 1 Odd Day as (365/7) gives remainder as 1.
• A leap year has 2 Odd Days as (366/7) gives remainder as 2.

The number of the odd day will point to a particular day of the week.

• If odd day = 0 ⇒ Sunday
• If odd day = 1 ⇒ Monday.
• If odd day = 2 ⇒ Tuesday.
• If odd day = 3 ⇒ Wednesday.
• If odd day = 4 ⇒ Thursday.
• If odd day = 5 ⇒ Friday.
• If odd day = 6 ⇒ Saturday.

### Number of Odd Days in a Month

• (Days of a month) divided by 7 ⇒ Remainder is equal to the number of odd days.
• Example: January has 31 days. If 31 is divided by 7 then we get 3 as the remainder. So there are 3 odd days in the month of January. Similarly, we can easily find out for other months.
• Number of odd days in an ordinary year ⇒ 1
• Number of odd days in a leap year ⇒ 2
If we have the year then we can easily calculate the number of odd years in that year.

### Number of Odd Days in a Century

A Century is a duration of 100 years. (24 leap years + 76 Ordinary years)
• 24 Leap Years ⇒ 24 x 2 = 48 odd days
• 76 Ordinary Years ⇒ 76 x 1 = 76 odd days
Total number of odd days = 48 + 76 = 124
(We can divide 124 by 7 and we will get the required number of odd days.)

⇒ The remainder of (124/7) is 5. So, we have 5 odd days in a century.

In a period of 200 years,
⇒ 200 = 100 +100
⇒ (5 + 5) odd days
⇒ 10/7
⇒ 3 odd days.

In a period of 300 years,
⇒ 300 = 200 + 100
⇒ (3 + 5) = 8 odd days
⇒ 8/7
⇒ 1 odd day.

In a period of 400 years, (We have one extra leap year as 400 is divisible by 400)
⇒ 400 = 300 + 100
⇒ (1 + 5) + 1 (An extra odd day due to the extra leap year)
⇒  7/7
⇒ 0 odd days.

Similarly, the number of odd days can be calculated for centuries.

#### Find out the day

Example 1: If today is Monday, then what day will be the day after 1000 days?
Example 2: If October 3, 1988, was Monday, then what day will be on 28 Feb 2001?
Example 3: What was the day on 26 January 1950?

#### Matching the Calendar of years

Example 1: Which year has the same calendar as 2020?