If 19 July 2000 is Wednesday, then what will be the day of the week on 17 March 2015?
Correct Answer :
Tuesday
Solution :
The correct option is Tuesday.
To find the day of the week on 17 March 2015 given that 19 July 2000 was Wednesday, we can calculate the total number of odd days between the two dates.
Step 1: Calculate odd days from 19 July 2000 to 19 July 2014
The number of years between 2000 and 2014 is:
2014 - 2000 = 14 years.
In these 14 years, we count the leap years (which have 2 odd days each) and normal years (which have 1 odd day each). Note that for year 2000, 19 July is after February 29, so its leap day does not fall in this interval. The leap years between July 2000 and July 2014 are 2004, 2008, and 2012 (3 leap years).
Number of ordinary years = 14 - 3 = 11 years.
Total odd days from years = (3 × 2) + (11 × 1) = 6 + 11 = 17 odd days.
17 odd days = 17 mod 7 = 3 odd days.
So, 19 July 2014 was 3 days after Wednesday, which is Saturday.
Step 2: Calculate odd days from 19 July 2014 to 17 March 2015
Now we count the remaining days month by month:
- July 2014: 31 - 19 = 12 days
- August 2014: 31 days
- September 2014: 30 days
- October 2014: 31 days
- November 2014: 30 days
- December 2014: 31 days
- January 2015: 31 days
- February 2015: 28 days (2015 is not a leap year)
- March 2015: 17 days
Total days = 12 + 31 + 30 + 31 + 30 + 31 + 31 + 28 + 17 = 241 days.
Step 3: Calculate total odd days and final day
Total days from 19 July 2000 to 17 March 2015 = (14 years odd days equivalent) + 241 days
= 17 + 241 = 258 days.
258 mod 7 = 6 odd days.
Adding 6 odd days to Wednesday:
Wednesday + 6 days = Tuesday.
Therefore, the day of the week on 17 March 2015 will be Tuesday.
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