Calendar - Aptitude Questions and Answers : The Infinity Mathematics

                        CALENDER-IQ SOLVE PROBLEM

·  Odd Days:

We are supposed to find the day of the week on a given date.

For this, we use the concept of 'odd days'.

In a given period, the number of days more than the complete weeks are called odd days.

·  Leap Year:

(i). Every year divisible by 4 is a leap year, if it is not a century.

(ii). Every 4^th century is a leap year and no other century is a leap year.

Note: A leap year has 366 days.

Examples:

1. Each of the years 1948, 2004, 1676 etc. is a leap year.
2. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
3. None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.

·  Ordinary Year:

The year which is not a leap year is called an ordinary years. An ordinary year has 365 days.

·  Counting of Odd Days:

1. 1 ordinary year = 365 days = (52 weeks + 1 day.)

1 ordinary year has 1 odd day.

2. 1 leap year = 366 days = (52 weeks + 2 days)

1 leap year has 2 odd days.

3. 100 years = 76 ordinary years + 24 leap years

  = (76 x 1 + 24 x 2) odd days = 124 odd days.

  = (17 weeks + days) 5 odd days.

Number of odd days in 100 years = 5.

Number of odd days in 200 years = (5 x 2) 3 odd days.

Number of odd days in 300 years = (5 x 3) 1 odd day.

Number of odd days in 400 years = (5 x 4 + 1) 0 odd day.

Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.

·  Day of the Week Related to Odd Days:

No. of days:	0	1	2	3	4	5	6
Day:	Sun.	Mon.	Tues.	Wed.	Thurs.	Fri.	Sat.
1.	It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
	A. Sunday B. Saturday C. Friday D. Wednesday Answer & Explanation Answer: Option C Explanation: On 31st December, 2005 it was Saturday. Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days. On 31st December 2009, it was Thursday. Thus, on 1st Jan, 2010 it is Friday.

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2.

What was the day of the week on 28th May, 2006?

A. Thursday B. Friday C. Saturday D. Sunday Answer & Explanation Answer: Option D Explanation: 28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006) Odd days in 1600 years = 0 Odd days in 400 years = 0 5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days Jan.  Feb.   March    April    May (31 +  28  +  31   +   30   +   28 ) = 148 days 148 days = (21 weeks + 1 day) 1 odd day. Total number of odd days = (0 + 0 + 6 + 1) = 7 0 odd day. Given day is Sunday.

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3.	What was the day of the week on 17th June, 1998?
	A. Monday B. Tuesday C. Wednesday D. Thursday View Answer Workspace Report Discuss in Forum

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4.

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

A. Sunday B. Monday C. Tuesday D. Friday Answer & Explanation Answer: Option A Explanation: 15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010) Odd days in 1600 years = 0 Odd days in 400 years = 0 9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days 4 odd days. Jan.  Feb.   March    April    May  June  July  Aug. (31 +  28  +  31   +   30   +  31  + 30  + 31  + 15) = 227 days 227 days = (32 weeks + 3 days) 3 odd days. Total number of odd days = (0 + 0 + 4 + 3) = 7 0 odd days. Given day is Sunday.

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5.	Today is Monday. After 61 days, it will be:
	A. Wednesday B. Saturday C. Tuesday D. Thursday Answer & Explanation Answer: Option B Explanation: Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday.
	If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
	A. Sunday B. Saturday C. Tuesday D. Wednesday Answer & Explanation Answer: Option A Explanation: The year 2004 is a leap year. So, it has 2 odd days. But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only. The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004. Given that, 6th March, 2005 is Monday. 6th March, 2004 is Sunday (1 day before to 6th March, 2005).

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7.

On what dates of April, 2001 did Wednesday fall?

A. 1st, 8th, 15th, 22nd, 29th B. 2nd, 9th, 16th, 23rd, 30th C. 3rd, 10th, 17th, 24th D. 4th, 11th, 18th, 25th Answer & Explanation Answer: Option D Explanation: We shall find the day on 1st April, 2001. 1st April, 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001) Odd days in 1600 years = 0 Odd days in 400 years = 0 Jan. Feb. March April (31 + 28 + 31 + 1)     = 91 days 0 odd days. Total number of odd days = (0 + 0 + 0) = 0 On 1st April, 2001 it was Sunday. In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th.

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8.	How many days are there in x weeks x days?
	A. 7x2 B. 8x C. 14x D. 7 Answer & Explanation Answer: Option B Explanation: x weeks x days = (7x + x) days = 8x days.

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9.

The last day of a century cannot be

A. Monday B. Wednesday C. Tuesday D. Friday Answer & Explanation Answer: Option C Explanation: 100 years contain 5 odd days. Last day of 1st century is Friday. 200 years contain (5 x 2) 3 odd days. Last day of 2nd century is Wednesday. 300 years contain (5 x 3) = 15 1 odd day. Last day of 3rd century is Monday. 400 years contain 0 odd day. Last day of 4th century is Sunday. This cycle is repeated. Last day of a century cannot be Tuesday or Thursday or Saturday.

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10.	On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
	A. Tuesday B. Monday C. Sunday D. Wednesday Answer & Explanation Answer: Option C Explanation: The year 2004 is a leap year. It has 2 odd days. The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005. Hence, this day is Sunday.
11.	The calendar for the year 2007 will be the same for the year:
	A. 2014 B. 2016 C. 2017 D. 2018 Answer & Explanation Answer: Option D Explanation: Count the number of odd days from the year 2007 onwards to get the sum equal to 0 odd day. Year    : 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Odd day : 1    2    1    1    1    2    1    1    1    2    1    Sum = 14 odd days 0 odd days. Calendar for the year 2018 will be the same as for the year 2007.

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12.	Which of the following is not a leap year?
	A. 700 B. 800 C. 1200 D. 2000 Answer & Explanation Answer: Option A Explanation: The century divisible by 400 is a leap year. The year 700 is not a leap year.

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13.	On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?
	A. Sunday B. Thursday C. Tuesday D. Friday Answer & Explanation Answer: Option D Explanation: The year 2006 is an ordinary year. So, it has 1 odd day. So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006. But, 8th Dec, 2007 is Saturday. 8th Dec, 2006 is Friday.

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14.	January 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?
	A. Monday B. Wednesday C. Thursday D. Sunday Answer & Explanation Answer: Option C Explanation: The year 2008 is a leap year. So, it has 2 odd days. 1st day of the year 2008 is Tuesday (Given) So, 1st day of the year 2009 is 2 days beyond Tuesday. Hence, it will be Thursday.

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15.	January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
	A. Monday B. Tuesday C. Wednesday D. Sunday Answer & Explanation Answer: Option B Explanation: The year 2007 is an ordinary year. So, it has 1 odd day. 1st day of the year 2007 was Monday. 1st day of the year 2008 will be 1 day beyond Monday. Hence, it will be Tuesday.