CRE 2 - Find the day of the week | LR - Calendar

Answer: Option C

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

For a year to be leap year there are 2 conditions
- If it is a non-century year, it should be divisible by 4.
- If it is a century year, it should be divisible by 400.

Here all the given years are century years, and only 2800 is divisible by 400.

Hence, 2800 is a leap year.

Hence, option (c).

Answer: Option C

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

Here we need to break days till 1^st Jan 1901.

Complete years = 1900

Odd days in first 1600 years = 0
Odd days in next 300 years = 1

∴ Odd days in complete years = 0 + 1 = 1.

Incomplete year (1901)

Just 1 day i.e., 1^st of January 1901.

∴ Odd days in incomplete year = 1

∴ Total odd days till 1^st Jan 1901 = 1 + 1 = 2.

∴ Day of the week on 1st Jan 1901 will be 2 days after Sunday i.e., Tuesday.

Hence, option (c).

Answer: Option D

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

Here we need to break days till 2^nd July 1184.

Complete years = 1183

Odd days in first 800 years = 0
Odd days in next 300 years = 1
Odd days in next 83 years (20 leap and 63 non-leap years) = 20 × 2 + 63 × 1 = 103.

∴ Odd days in complete years = 0 + 1 + 103 = 104 odd days.

∴ Odd days in complete years = Remainder (104 ÷ 7) = 6 odd days.

Incomplete year (1184, a leap year)

Jan + Feb + Mar = 0 odd days,
Apr + May + Jun = 0 = odd days,
Jul = 2

∴ Odd days in incomplete year = 0 + 0 + 2 = 2 odd days.

∴ Total odd days till 2^nd July 1184 = 6 + 2 = 8 = 1 odd day.

∴ Day of the week on 2^nd July 1184 will be 1 day after Sunday i.e., Monday.

Hence, option (d).

Answer: Option D

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

Here we need to break days till 31^st Oct 1984.

Complete years = 1983

Odd days in first 1600 years = 0
Odd days in next 300 years = 1
Odd days in next 83 years (20 leap and 63 non-leap years) = 20 × 2 + 63 × 1 = 103.

∴ Odd days in complete years = 0 + 1 + 103 = 104 odd days.

∴ Odd days in complete years = Remainder (104 ÷ 7) = 6 odd days.

Incomplete year (1984, a leap year)

Jan + Feb + Mar = 0 odd days,
Apr + May + Jun = 0 = odd days,
Jul + Aug + Sep = 1 odd day
Oct = 31

∴ Odd days in incomplete year = 0 + 0 + 1 + 31 = 32 odd days = 4 odd days.

∴ Total odd days till 31^st Oct 1984 = 6 + 4 = 10 odd days = 3 odd days.

∴ Day of the week on 31^st Oct 1984 will be 3 days after Sunday i.e., Wednesday.

Hence, option (d).

Answer: Option B

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

Here we need to break days till 14^th Mar 2393.

Complete years = 2392

Odd days in first 2000 years = 0
Odd days in next 300 years = 1
Odd days in next 92 years (23 leap and 69 non-leap years) = 23 × 2 + 69 × 1 = 115.

∴ Odd days in complete years = 0 + 1 + 115 = 116 odd days.

∴ Odd days in complete years = Remainder (116 ÷ 7) = 4 odd days.

Incomplete year (2393, a non-leap year)

Jan = 31,
Feb = 28
Mar = 14

∴ Odd days in incomplete year = 31 + 28 + 14 = 73 odd days = 3 odd days.

∴ Total odd days till 14^th Mar 2393 = 3 + 4 = 7 odd days = 0 odd days.

∴ Day of the week on 14^th Mar 2393 will be 0 days after Sunday i.e., Sunday.

Hence, option (b).

Answer: Option A

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

Let us first calculate the day of the week on 1^st August 1980.

Here we need to break days till 1^st August 1980.

Complete years = 1979

Odd days in first 1600 years = 0
Odd days in next 300 years = 1
Odd days in next 79 years (19 leap and 60 non-leap years) = 19 × 2 + 60 × 1 = 98.

∴ Odd days in complete years = 0 + 1 + 98 = 99 odd days.

∴ Odd days in complete years = Remainder (99 ÷ 7) = 1 odd days.

Incomplete year (1980, a leap year)

Jan + Feb + Mar = 0 odd days,
Apr + May + Jun = 0 odd days,
Jul = 31
Aug = 1

∴ Odd days in incomplete year = 0 + 0 + 31 + 1 = 32 odd days = 4 odd days.

∴ Total odd days till 1^st August 1980 = 1 + 4 = 5 odd days.

∴ Day of the week on 1^st August 1980 will be 5 days after Sunday i.e., Friday.

Since 1^st August 1980 is Friday, next Monday will be on 4^th August.

Hence Mondays in August 1980 will be on 4^th, 11^th, 18^th and 25^th. 

Hence, option (a).

Answer: Option C

Join our Telegram Group for CAT/MBA Preparation.

Explanation :

For the calendar to be same the year should be a non-leap year and the number of odd days should be 0.

Here, we will calculate the total odd days from 1st Jan of 2007 till 1^st Jan of the year.

2007 – 2008 = 1 odd day
2008 – 2009 = 2 odd days (Total 3 odd days)
2009 – 2010 = 1 odd day (Total 4 odd days)
2010 – 2011 = 1 odd day (Total 5 odd days)
2011 – 2012 = 1 odd day (Total 6 odd days)
2012 – 2013 = 2 odd day (Total 8 odd days)
2013 – 2014 = 1 odd day (Total 9 odd days)
2014 – 2015 = 1 odd day (Total 10 odd days)
2015 – 2016 = 1 odd day (Total 11 odd days)
2016 – 2017 = 2 odd day (Total 13 odd days)
2017 – 2018 = 1 odd day (Total 14 odd days = 0 odd days)

Now, 2018 is also a non-leap year like 2007 and odd days from 2007 till 2018 are 0.

∴ Calendar of 2018 will be same as calendar of 2007.

Hence, option (d).