12-07-2021 Answers

1. Smitha's date of birth is 20-July-1980 which was a Sunday. Her daughter Akshaya was born on her 25th birthday. Which day was Akshaya born?

Answer: Wednesday

Solution: Number of days from 21-July-1980 to 31-Dec-1980 = 11 (Jul) + 31 (Aug) + 30 (Sep) + 31 (Oct) + 30 (Nov) + 31 (Dec) = 164 days which has 3 odd days

From 01-Jan-1981 to 31-Dec-2004 we have 6 leap years and 18 ordinary years. = 6*2 + 18*1 = 12+18 = 30 odd days = 2 odd days.

Number of days from 01-Jan-2005 to 20-July-2005 (Akshaya's birthday) = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31 (May) + 30 (Jun) + 20 = 201 days = 5 odd days. 

Hence over all there are 10 odd days = 3 odd days. Counting 3 days from Sunday, it is Wednesday.

2. Which of the following is a leap year?

Answer: 1200

Solution: A century should be divisible by 400 to be a leap year. Hence 1200 is a leap year.

3. If 14-Feb-2009 was a Saturday, what was the day of the week on 14th Feb, 2008?

Answer: Thursday

Solution: As 2008 is a leap year and 14-Feb is earlier than 29th feb (the additional day) it has 2 odd days. Hence the day on 14th Feb, 2008 will be Saturday minus 2 days = Thursday.

4.  Today is Thursday. The day after 59 days wil be?

Answer: Sunday

Solution: The answer is  Sunday. Every week has 7 days. So remainder when 59 is divided by 7 is 3. Hence 3 days after Thursday is Sunday.

5. January 2, 2007 was Tuesday. What day of the week was  Jan.1,  2008?

Answer: Tuesday

Solution: Jan 1st 2007 is a Monday. It is not a leap year so, there is only one odd day for the year 2007.

6. I met my friend 26 days ago. He then told me that he can meet me next after 10 days from today which is a wednesday. On which day of the week did I meet my friend?

Answer: Tuesday

Solution: 10 days from today is wednesday. Hence today is Sunday. Hence 28 days ago it will be sunday, which means 26 days ago it was Tuesday.

7. My grandfather said he was 84 years old but he was not counting the Tuesdays. How old my grandfather really was?

Answer: 98 years

Solution: 84 * 7/6 = 14*7 = 98

8. On which of the following dates of July 2004 did Tuesday fall?

Answer: 06.07.2004

Solution: As on 1st  July 2004 there are 4 odd days and  it was a thursday. 6th of July 2004 was Tuesday

9. If 15-Jan-2005 was a saturday, what was the day on 10-Jan-2003?

Answer: Friday

Solution: 2004 is a leap year. Hence it has 2 odd days.

Hence number of odd days between 15-Jan-2003 and 15-Jan-2005 = 3. So 15-Jan-2003 was saturday - 3 days = Wednesday. Hence 10-Jan-2003 was Wednesday - 5 days = Friday.

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

Answer: 700

Solution: A century is a leap year only when it is divisible by 400. Hence 700 is not a leap year.

11. On what dates of April, 1994 did Sunday fall? 

Answer: 24-April-1994

Solution: Let us find the day on 1-Apr-1994.

Number of odd days till 1900 = 1 days.

Number of odd days from 1901 to 1993 = 23 leap years * 2 + 70 ordinary years * 1 = 116 odd days = 4 odd days.

Number of odd days from 1-Jan-1994 to 31-Mar-1994 = 31+28+31 = 90 odd days = 6 odd days.

Total odd days = 1 + 4 + 6 = 11 odd days = 4 odd days. 

Hence 31-Mar-1994 was a Thursday. So 3rd April is a Sunday. Also 10th, 17th and 24th of April are sundays.

12. Today is Sunday. After 94 days, it will be

Answer: Wednesday

Solution: Dividing 94 by 7 and finding the remainder it is 3. Hence the day is Sunday + 3 days = Wednesday.

13. A man starts his work on a monday. He works for 10 days and takes rest on every 11th day, that is every 11th day as holiday. The 1233 rd holiday will fall on

Answer: Thursday

Solution: From day 1 to day 11 is considered one cycle. So for 1233 rd holiday it is 1233*11 = 13563. Excluding the starting Monday it is 13562 days.

13562 has 3 odd days.

So Monday+ 3 days = Thursday.

14. A girl is 18 years old on 28 feb 2009 (Saturday). What day it will be when she is 25 years old?

Answer: Sunday

Solution: On 28th Feb 2010 - 1 odd day and 19 years old and Sunday,

On 28th Feb 2011 - 1 odd day and 20 years old and Monday,

On 28th Feb 2012 - 1 odd day and 21 years old and Tuesday,

On 28th Feb 2013 - 2 odd days and 22 years old and Thursday (Previous 2012 is a leap year),

On 28th Feb 2014 - 1 odd day and 23 years old and Friday,

On 28th Feb 2015 - 1 odd day and 24 years old and Saturday,

On 28th Feb 2016 - 1 odd day and 25 years old and Sunday

15. A man starts his work on a monday. He works for 8 days and takes rest on every 9th day, that is every 9th day as holiday. The 12th holiday will fall on

Answer: Wednesday

Solution: From day1 to day 9 is considered one cycle. So for 12th holiday it is 12*9=108. Excluding the starting Monday it is 107 days.

107 has 2 odd days.

So Monday+2 days = wednesday.

16. A man starts work on a Monday and works for 8 days. Then on every ninth day he takes leave. His 12th leave will be on a 

Answer: Wednesday

Solution: So his 12th leave will be on 12*9 = 108th day. 108th day = remainder of 108 division 7 = 3 days. So the day will the third day from Monday (inclusive of Monday) which is Wednesday.

17. If 01-June-2009 was a Monday, what was the day of the week on 01-June-2008?

Answer: Sunday

Solution: Though 2008 is a leap year, 01-June-2008 is later than 29th feb (the additional day). Hence the difference is only 1 odd day. Hence the day on 01-June-2008 was Monday - 1 day = Sunday.

18. Assuming 2nd April 1983 is on Wednesday, then what day will be on 2nd April 1987?

Answer: Monday

Solution: Odd days in 4 years (The leap year has 2 odd days) = 5. Hence wednesday + 5 days = Monday.

19. Which day of week will come five times in Feb 2016?

Answer: Monday

Solution: 2016 = 2000 + 16. Hence odd days till 2000 = 0. Odd days  from 2001 to 2015 = 2 * 3 leap years + 1*12 ordinary years = 4 odd days. Odd days in Jan 2016 = 31 days = 3 days. Total odd days = 4+3 = 7 odd days = 0 odd days. Thus 31-Jan-2016 is a Sunday. Hence Monday which is the day on 01-feb-2016 will come five times.

20. How many days are there in z weeks and z days?

Answer: 8z days

Solution: z weeks and z days = (7z + z) = 8z days.

21. For which year the calendar used for the year 2003 can be used?

Answer: 2014

Solution: The number of odd days between the years 2003 and 2014 is zero. Hence they have the same calendar.

22. What was the day of the week on 15th august , 1947?

Answer: Friday

Solution: Number of odd days passed till 1900 = 5 days. Number of odd days from 1901 to 1946 = 11 leap years * 2 days + 45 ordinary years * 1 day = 67 days = 4 days (Remainder of 67 divided by 7). Number of odd days from 01-Jan-1947 to 31-July-1947 = Remainder of (31+28+31+30+31+30+31) divided by 7 = 2 days Number of odd days from 01-Aug-1947 to 15-Aug-1947 = 1 day (Remainder of 15 divided by 7). Total odd days = 5+4+2+1= 12 = 5 (Remainder of 12 divided by 7). 5 corresponds to Friday.

23. Rana started preserving calendars belonging to previous years. He found that the calendar for year 2013 was same as one of the previous year and hence decided not to buy a new calendar for 2013. Which year's calendar did he decide to re-use for 2013?

Answer: 2002

Solution: To reuse the calendar the difference in odd days should be zero. Counting backwards, the odd days in each of the year is 2012 - 2 (leap year), 2011 - 1, 2010 - 1, 2009 - 1, 2008 - 2, 2007 - 1, 2006 - 1, 2005 - 1, 2004 - 2, 2003 - 1, 2002 -1 , 2001 - 1, 2000 - 0. 

We find that the the sum of odd days from 2012 to 2008 is = 7 which is effectively 0 odd days. But as 2008 is a leap year and and 2013 is not a leap year (Feb having 29 days will disrupt) we find the next previous year having 14 odd days which turns out to be 2002. Hence 2002 is the answer.

24. In a particular year, the month of January had exactly four Thursdays and four Sundays. On which day of the week did 1st of January occur in that year?

Answer: Monday

Solution: January has 31 days. As Thursday to sunday occur only in four weeks (28 days), the remaining days of the month will fall on Monday to Wednesday. Hence 1st of Jan was on Monday.

25. What day of the week would be 26th March, 2023?

Answer: Sunday

Solution: Odd days in 2000 years = 0. In so from 2001 to 2023 it is 23 years. Leap year has 2 odd days and normal year has 1 odd day. 22 years = 5 leap year + 17 normal years. Hence odd days = 5 * 2 + 17 * 1 = 27 odd days.   27%7 = 6 odd days. From Jan 1 to March 26th it is 31 + 28 + 26 = 85 days. 85%7 = 1 odd day. Hence total odd days = 6+1 = 7 odd days. 7%7 = 0 and hence it is a sunday.