In a leap year, which two months have the same calendar?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → January – July
Two months of the same year have the same calendar when the months from the first one up to the second one add up to 0 odd days, so that both months begin on the same day. A month of 31 days has 3 odd days, 30 days 2 odd days, and February 1 in a leap year (29 days).
January 3, February 1, March 3, April 2, May 3, June 2
Total from January to June \(=3+1+3+2+3+2=14\)
\(14=2\times7\), so there are 0 odd days and July begins on the same day as January; both months have 31 days
Why the other options are incorrect
Option (1) January – October — Incorrect. January to September give \(3+1+3+2+3+2+3+3+2=22\) odd days, which leaves 1. (This pair matches only in an ordinary year, when February gives 0.)
Option (2) March – December — Incorrect. March to November give \(3+2+3+2+3+3+2+3+2=23\) odd days, which leaves 2.
Option (4) May – August — Incorrect. May, June and July give \(3+2+3=8\) odd days, which leaves 1.