Calendars: Solved Examples | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

Question 1: If 15 March 1816 was Friday, what day of the week would 15th April 1916 be?
a) Monday
b) Wednesday
c) Thursday
d) Saturday
Answer: (d)
We are given that 15th March 1816 was a Friday.
Now we know that 100 years have 5 odd days. So till 15th March 1916, we will be having 5 odd days. So if we move from 15th March 1816 to 15th March 1916, we will encounter 5 odd days.
Now from 15th March 1916 to 15th April 1916 there would be 3 odd days.
So total number of odd days = 5+3 =8
8 mod 7 = 1
So 15th April 1916 would be Friday + 1= Saturday

Question 2: A leap year 1895 is having a same calendar as that of the year X. Which of the following is a possible value of X.
a) 1900
b) 1901
c) 1902
d) 1903
Answer: (b)
1895 is not a leap year. So it will have 1 odd day.
Since 1896 is a leap year, it will add 2 odd days.
Similarly 1987, 1898, 1899, 1900 will add 1,1,1,1 odd days.
Now the total number of odd days add up to 7.
So the next year 1901 will have the same calendar as 1895.

Question 3: If 28th August 1946 was a Wednesday, what day of the week was 31 August 1961?
a) Tuesday
b) Thursday
c) Monday
d) Wednesday
Answer: (b)
It is given that 28th August 1946 was Wednesday. From 28th August 1946 to 28th August 1961, we have 4 leap years and 11 normal years. So the number of odd days would be
11*1 + 4*2 = 19
Now the date which is asked is 31 Aug 1961. So if we move from 28th August to 31st August, we will have 3 more odd days.
So total number of odd days = 5 + 3 = 8
Now 8 mod 7 = 1 .
So 31st August 1961 would be Wednesday + 1 = Thursday.

Question 4: If 09/12/2001(DD/MM/YYYY) happens to be Sunday, then 09/12/1971 would have been a
a) Wednesday
b) Tuesday
c) Saturday
d) Thursday
Answer: (d)
30 years. The number of leap years is 8 (1972,1976,1980,1984,1988,1992,1996,2000).
So, the total number of days = 22*365 + 8*366 = 10958
10958 mod 7 = 3
Since 9/12/2001 is a Sunday, 9/12/1971 should be a Thursday.

Question 5: In 2016, Mohan celebrated his birthday on Friday. Which will be the first year after 2016 when Mohan will celebrate his birthday on a Wednesday? (He was not born in January or February)
a) 2021
b) 2023
c) 2020
d) 2025
Answer: (c)
Since it has been mentioned that Mohan was not born in February, so he can’t be born on 29th Feb. Hence He will celebrate his next birthday on a Wednesday in the year for which the sum of the odd days becomes 5 or a multiple of 5.
By his birthday in 2017, there will be 1 odd day.
By his birthday in 2018, there will be 2 odd days.
By his birthday in 2019, there will be 3 odd days.
By his birthday in 2020, there will be 5 odd days, as 2020 is a leap year.
So in 2020 He will celebrate his birthday on Wednesday.

6. What day of the week does May 28 2006 fall on

A. Saturday B. Monday C. Sunday D. Thursday

Answer: Option C

Explanation:

28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)

We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)

Number of odd days in the period 2001-2005
= 4 normal years + 1 leap year 
= 4 x 1 + 1 x 2 = 6

Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)
= 148

148 days = 21 weeks + 1 day = 1 odd day

Total number of odd days = (0 + 6 + 1) = 7 odd days = 0 odd day
0 odd day = Sunday

Hence May 28 2006 is Sunday.

7. What will be the day of the week 15th August, 2010?

A. Thursday B. Sunday C. Monday D. Saturday

Answer: Option B

Explanation:

15th Aug 2010 = (2009 years + period from 1-Jan-2010 to 15-Aug-2010)

We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)

Number of odd days in the period 2001-2009
= 7 normal years + 2 leap year 
= 7 x 1 + 2 x 2 = 11 = (11 - 7x1) odd day = 4 odd day

Days from 1-Jan-2010 to 15-Aug-2010 
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 30(Jun) + 31(Jul) + 15(Aug)
= 227

227 days = 32 weeks + 3 day = 3 odd day

Total number of odd days = (0 + 4 + 3) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence 15th August, 2010 is Sunday.

8. Today is Monday. After 61 days, it will be

A. Thursday B. Sunday C. Monday D. Saturday

Answer: Option D

Explanation:

61 days = 8 weeks 5 days = 5 odd days

Hence if today is Monday, After 61 days, it will be = (Monday + 5 odd days)
= Saturday

9. On what dates of April, 2001 did Wednesday fall?

A. 2^nd, 9^th, 16^th, 23^rd

B. 4^th, 11^th, 18^th, 25^th

C. 3^rd, 10^th, 17^th, 24^th

D. 1^st, 8^th, 15^th, 22^nd, 29^th

Answer: Option B

Explanation:

We need to find out the day of 01-Apr-2001

01-Apr-2001 = (2000 years + period from 1-Jan-2001 to 01-Apr-2001)

We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)

Days from 1-Jan-2001 to 01-Apr-2001 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 1(Apr) = 91
91 days = 13 weeks = 0 odd day

Total number of odd days = (0 + 0) = 0 odd days
0 odd day = Sunday. Hence 01-Apr-2001 is Sunday.

Hence first Wednesday of Apr 2011 comes in 04^th and successive Wednesdays come in 11^th, 18^th and 25^th

10. How many days are there in x weeks x days

A. 14x

B. 8x

C. 7x²

D. 7

Answer: Option B

Explanation:

x weeks x days =(7×x)+x=7x+x=8x=(7×x)+x=7x+x=8x days

11. The calendar for the year 2007 will be the same for the year

A. 2017

B. 2018

C. 2014

D. 2016

Answer: Option B

Explanation:

For a year to have the same calendar with 2007 ,the total odd days from 2007 should be 0.

12. Which of the following is not a leap year?

A. 1200

B. 800

C. 700

D. 2000

Answer: Option C

Explanation:

Remember the leap year rule (Given in the formulas)

1. Every year divisible by 4 is a leap year, if it is not a century.
2. Every 4th century is a leap year, but no other century is a leap year.

800,1200 and 2000 comes in the category of 4th century (such as 400,800,1200,1600,2000 etc). 
Hence 800,1200 and 2000 are leap years

700 is not a 4th century, but it is a century. Hence it is not a leap year

13. 01-Jan-2007 was Monday. What day of the week lies on 01-Jan-2008?

A. Wednesday

B. Sunday

C. Friday

D. Tuesday

Answer: Option D

Explanation:

Given that January 1, 2007 was Monday.

Odd days in 2007 = 1 (we have taken the complete year 2007 because we need to find out the odd days from 01-Jan-2007 to 31-Dec-2007, that is the whole year 2007)

Hence January 1, 2008 = (Monday + 1 Odd day) = Tuesday

14. 8th Dec 2007 was Saturday, what day of the week was it on 8th Dec, 2006?

A. Sunday

B. Tuesday

C. Friday

D. Tuesday

Answer: Option C

Explanation:

Given that 8th Dec 2007 was Saturday

Number of days from 8th Dec, 2006 to 7th Dec 2007 = 365 days
365 days = 1 odd day

Hence 8th Dec 2006 was = (Saturday - 1 odd day) = Friday

15. On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?

A. Sunday

B. Friday

C. Saturday

D. Monday

Answer: Option A

Explanation:

Given that 8th Feb, 2005 was Tuesday

Number of days from 8th Feb, 2004 to 7th Feb, 2005 = 366 (Since Feb 2004 has 29 days as it is a leap year)

366 days = 2 odd days
Hence 8th Feb, 2004 = (Tuesday - 2 odd days) = Sunday