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Clock & Calendar 

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 4th century is a leap year and no other century is a leap year.
Note: A leap year has 366 days.
Examples:
Each of the years 1948, 2004, 1676 etc. is a leap year.
Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.
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 ordinary year = 365 days = (52 weeks + 1 day.)
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gif1 ordinary year has 1 odd day.
1 leap year = 366 days = (52 weeks + 2 days)
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gif1 leap year has 2 odd days.
100 years = 76 ordinary years + 24 leap years
= (76 x 1 + 24 x 2) odd days = 124 odd days.
= (17 weeks + days) http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif5 odd days.
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gifNumber of odd days in 100 years = 5.
Number of odd days in 200 years = (5 x 2) http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif3 odd days.
Number of odd days in 300 years = (5 x 3) http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif1 odd day.
Number of odd days in 400 years = (5 x 4 + 1) http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif0 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.


CLOCK

Minute Spaces:
The face or dial of watch is a circle whose circumference is divided into 60 equal parts, called minute spaces.
Hour Hand and Minute Hand:
A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called minute hand or long hand.


In 60 minutes, the minute hand gains 55 minutes on the hour on the hour hand.
In every hour, both the hands coincide once.
The hands are in the same straight line when they are coincident or opposite to each other.
When the two hands are at right angles, they are 15 minute spaces apart.
When the hands are in opposite directions, they are 30 minute spaces apart.
Angle traced by hour hand in 12 hrs = 360°
Angle traced by minute hand in 60 min. = 360°.
If a watch or a clock indicates 8.15, when the correct time is 8, it is said to be 15 minutes too fast.
On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.


SOLVED EXAMPLES
1. 
It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?


Sunday
Saturday
Friday
Wednesday
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.
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gifOn 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday.
2. 
What was the day of the week on 28th May, 2006?


Thursday
Friday
Saturday
Sunday
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) http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif6 odd days
Jan. Feb. March April May
(31 + 28 + 31 + 30 + 28 ) = 148 days
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gif148 days = (21 weeks + 1 day) http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif1 odd day.
Total number of odd days = (0 + 0 + 6 + 1) = 7 http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif0 odd day.
Given day is Sunday.
3. 
What was the day of the week on 17th June, 1998?


Monday
Tuesday
Wednesday
Thursday
Answer: Option C
Explanation:
17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)
Odd days in 1600 years = 0
Odd days in 300 years = (5 x 3) http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March April May June
(31 + 28 + 31 + 30 + 31 + 17) = 168 days
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gif168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.


4. 
What will be the day of the week 15th August, 2010?


Sunday
Monday
Tuesday
Friday
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 http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif4 odd days.
Jan. Feb. March April May June July Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gif227 days = (32 weeks + 3 days) http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif0 odd days.
Given day is Sunday.


5. 
Today is Monday. After 61 days, it will be:


Wednesday
Saturday
Tuesday
Thursday
Answer: Option B
Explanation:
Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gifAfter 61 days, it will be Saturday.


6. 
If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?


Sunday
Saturday
Tuesday
Wednesday
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.
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gifThe day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.
Given that, 6th March, 2005 is Monday.
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gif6th March, 2004 is Sunday (1 day before to 6th March, 2005).


7. 
On what dates of April, 2001 did Wednesday fall?


1st, 8th, 15th, 22nd, 29th
2nd, 9th, 16th, 23rd, 30th
3rd, 10th, 17th, 24th
4th, 11th, 18th, 25th
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 http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif0 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.


8. 
How many days are there in x weeks x days?


7x2
8x
14x
7
Answer: Option B
Explanation:
x weeks x days = (7x + x) days = 8x days.


9. 
The last day of a century cannot be


Monday
Wednesday
Tuesday
Friday
Answer: Option C
Explanation:
100 years contain 5 odd days.
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gifLast day of 1st century is Friday.
200 years contain (5 x 2) http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif3 odd days.
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gifLast day of 2nd century is Wednesday.
300 years contain (5 x 3) = 15 http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif1 odd day.
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gifLast day of 3rd century is Monday.
400 years contain 0 odd day.
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gifLast day of 4th century is Sunday.
This cycle is repeated.
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gifLast day of a century cannot be Tuesday or Thursday or Saturday.


10. 
On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?


Tuesday
Monday
Sunday
Wednesday
Answer: Option C
Explanation:
The year 2004 is a leap year. It has 2 odd days.
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gifThe 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:


2014
2016
2017
2018
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 http://www.indiabix.com/_files/images/aptitude/1-sym-deq.gif0 odd days.
Calendar for the year 2018 will be the same as for the year 2007.
12. 
Which of the following is not a leap year?


700
800
1200
2000
Answer: Option A
Explanation:
The century divisible by 400 is a leap year.
http://www.indiabix.com/_files/images/aptitude/1-sym-tfr.gifThe year 700 is not a leap year.


13. 
On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?


Sunday
Thursday
Tuesday
Friday


14. 
January 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?


Monday
Wednesday
Thursday
Sunday
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.


15. 
January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?


Monday
Tuesday
Wednesday
Sunday
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.
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