If today is Sunday, then which day is it exactly on 10¹⁰ th day ?
- (a) Wednesday ✓ UPSC's answer
- (b) Thursday
- (c) Friday
- (d) Saturday
Why the answer is (a)
• The key treats today (Sunday) as day 1, so the 10¹⁰th day falls 10¹⁰ − 1 days after today.
• Remainders of 10ⁿ on division by 7 repeat every 6 (10 → 3, 10² → 2, 10³ → 6, 10⁴ → 4, 10⁵ → 5, 10⁶ → 1); since 10 = 6 + 4, 10¹⁰ leaves the same remainder as 10⁴, which is 4.
• So 10¹⁰ − 1 leaves remainder 3: the day is 3 days after Sunday.
• Monday, Tuesday, Wednesday — option (a).
Why the other options are wrong
- (b) Thursday
- Thursday would follow only if the day were counted 10¹⁰ days after today; with today as day 1 the offset is 3 days.
- (c) Friday
- The offset from Sunday is 3 days, which gives Wednesday, not Friday.
- (d) Saturday
- The offset from Sunday is 3 days, which gives Wednesday, not Saturday.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.