The calendar for the year 2007 will be the same for the year:
20252025
The calendar for the year 2007 will be the same for the year:
- A.
2014
- B.
2016
- C.
2017
- D.
2018
Show answer & explanation
Correct answer: D
Two years have the same calendar exactly when two conditions hold together: (1) the cumulative count of "odd days" between them is a multiple of 7, so 1 January falls on the same weekday in both, and (2) both years share the same leap-year status. A common (non-leap) year contributes 1 odd day and a leap year contributes 2 odd days.
Starting from 2007, add each following year's odd days to a running total until it first becomes a multiple of 7 -- the very next year after that point repeats 2007's calendar.
Year | Odd days | Running total |
|---|---|---|
2007 | 1 | 1 |
2008 | 2 | 3 |
2009 | 1 | 4 |
2010 | 1 | 5 |
2011 | 1 | 6 |
2012 | 2 | 8 |
2013 | 1 | 9 |
2014 | 1 | 10 |
2015 | 1 | 11 |
2016 | 2 | 13 |
2017 | 1 | 14 |
The running total reaches 14 at the end of 2017, and 14 = 2 x 7 is a multiple of 7.
Independent check: 2007 is a common year (2007 divided by 4 leaves a remainder) and 2018 is also a common year (2018 divided by 4 leaves a remainder), so the leap-status condition is satisfied too -- confirming the full calendars align, not just 1 January.
Hence, the calendar for 2018 is identical to that of 2007.