Which year has the same calendar as that of 2009 ?
- (a) 2018
- (b) 2017
- (c) 2016
- (d) 2015 ✓ UPSC's answer
Why the answer is (d)
• A calendar repeats when the total number of odd days (remainder of days divided by 7) between the two years is zero.
• From 2009 to 2015, there are 6 intervening years: 2009, 2010, 2011, 2012, 2013, and 2014.
• Among these, 2012 is a leap year (366 days = 2 odd days), and the other five are common years (365 days = 1 odd day each).
• The total odd days are calculated as (5 × 1) + (1 × 2) = 7.
• Since 7 odd days equal exactly one full week (0 remainder), the days of the week align perfectly, making 2015 the same calendar as 2009.
Why the other options are wrong
- (a) 2018
- 2018 has 9 intervening years with 2 leap years, resulting in 11 odd days (4 remainder), so the calendar does not match.
- (b) 2017
- 2017 has 8 intervening years with 2 leap years, resulting in 10 odd days (3 remainder), so the calendar does not match.
- (c) 2016
- 2016 has 7 intervening years with 2 leap years, resulting in 9 odd days (2 remainder), so the calendar does not match.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.