Calendars: Solved Examples- 2 | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

1. 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.

2. 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.

3. 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

4. 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

5. 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

6. 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.

7. 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

8. 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

9. 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

10. 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