# Logical Reasoning Calendars notes – CSEET

**Logical Reasoning Calendars:**

**ICSI CSEET: **The Council of the ICSI has released a notice regarding CSEET on the day of the inauguration of ICSI Golden Jubilee Celebrations on 4th Oct 2017.

The Gazette Notification on the Company Secretaries (Amendment) Regulations, 2020 has been published on 3^{rd} February 2020 in the Official Gazette of India and the same shall be applicable from the said date of publication.

Now ICSI Published a notice regarding CSEET Test which going to start from 2020 May.

We are now going to discuss the details of CSEET Paper-2 Legal Aptitude and Logical Reasoning – **Logical Reasoning Calendars**** notes**.

**Logical Reasoning Calendars:**

- The time in which the earth travels round the sun is a solar year and is equal to 365 days 5 hrs. 48 minutes and 47 1/2 seconds
- Year is 365.2422 days approximately.
- The common year consists of 365 days.
- The difference between a common year and a solar year is therefore 0.2422 of a day and we consider it by adding a whole day to every fourth year.
- Consequently in every 4th year there are 366 days.
- The years which have the extra day are called leap years. The day is inserted at the end of February, The difference between 4 common years and 4 solar years is 0.969 of a day.
- If therefore, we add a whole day to every 4th year, we add too much by 0.0312 of a day. To take account of this, we omit the extra day three times every 400 years,
- The thing is to ensure that each season may fall at the same time of the year in all years.
- In course of time, without these corrections, we should have winter in July and summer in January also.

With the very small variation, the present divisions of the year are those given in B.C 46 by Julius Caesar. The omission of the extra day three times in 400 years is called the Gregorian Correction. This correction was adopted at once in 1582 in Roman Catholic Countries. But not in England until, 1752. The Gregorian mode* of reckoning is called the New Style, the former, the Old Style.

The New Style has not yet been adopted in Russia, so that they are now 13 days behind us. For example – ‘What we call October 26th, they call that 13 th October. They have Christmas day on 7th of January and we have on 25 th December every year.

- In an ordinary year there are 365 days i.e., 52 weeks + 1 day
- Therefore an ordinary year contains 1 odd day.

A leap year contains 2 odd days.

100 year = 76 ordinary years + 24 leap years.

= 76 odd days + 48 odd days

= 124 odd days = 17 weeks + 5 days. (in the consideration of weeks)

Therefore, 100 years contain 5 odd days.

200 years contains 3 odd days.

300 years contain 1 odd days

- Since there are 5 odd days in 100 years, there will be 20 days in 400 years. But every 4th century is a leap year.

* We have 1 possible answer for the clue as per the Mode of Reckoning dates according to Gregorian Calendar which appears 1 time in our database.

- Therefore, 400 years contain 21 days. Here 400 years contain no odd days.
- As First January 1 AD was Monday. One must count days from Sunday

i.e. Sunday for 0 odd days, Monday for 1 odd day, and Tuesday for 2 odd days and so on.

- Last day of a century cannot be either Tuesday. Thursday or Saturday.
- The first day of a century must either be Monday. Tuesday, Thursday or Saturday.
**Calendar: Examples**

We can clarify the concept of Calendars with following Examples

Example -1

How many times does the 29th days of the month occur in 400 consecutive years

(1) 97 Times

(2) 4400 times

(3) 4497 times

(4) None

Solution:

In 400 consecutive years there are 97 leap years. Hence in 400 consecutive years, February has the 29th Days – 97 times, and the remaining 11 months have the 29th Day400 x 11 or 4400 times.

Therefore, 29th Day of the month occurs (4400 + 97) or 4497 times.

Example – 2

Given that on 10th November 1981 is Tuesday, what was the day on 10th November 1581

(1) Monday

(2) Thursday

(3) Sunday

(4) Tuesday

Solution

After every400 years, the same day comes.

Thus if 10th November, 1981 was Tuesday, before 400 years i.e. on 10th November 1581, it has to be Tuesday.

**Sample Questions**

1) How many years have 29 days in February from 2001 to 2100?

(a) 26

(b) 25

(c) 23

**(d) 24**

Explanation : 100th year is not a leap year. So 24 February’s has 29 days

2) 2012 January 1st is Sunday, then which day is the Indian Independence Day of the same year.

(a) Saturday

**(b) Wednesday**

(c) Thursday

(d) Friday

Explanation : 30+ 29+ 31 + 30 + 31 + 30 + 31 + 15 = 227/7 = reminder = 3

So Independence Day is Wednesday

3) Which year has the same calendar as 1700?

(a) 1705

**(b) 1706**

(c) 1707

(d) 1708 Explanation

Year : | 1700 | 1701 | 1702 | 1703 | 1704 | 1705 |

Odd Days : | 1 | 1 | 1 | 1 | 2 | 1 |

4) If Arun’s birthday is on May 25 which is Monday and his sister’s birthday is on July 13. Which day of the week is his sister’s birthday?

**(a) Monday**

(b) Wednesday

(c) Thursday

(d) Friday

Explanation : Reference Day: May 25th is Monday

Days from May 25 to July 13 = 6 + 30 +13 = 49

No of Odd Days: 49/7 = 0

5) March 1 is Wednesday. Which month of the same year starts with the same day?

(a) October

**(b) November**

(c) December

(d) None of these

Explanation

Month : | Mar | April | May | June July | August | September October |

Odd Days : | 3 | 2 | 3 | 23 | 3 | 23 |

Total 21 odd days. 21/7 = 0. So November has start with the same day.

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