If today is Sunday, then which day is it exactly on 10¹⁰ th day?
Answer & explanation
Answer: (a) Wednesday
Counting today (Sunday) as day 1, the 10^10th day comes 10^10 − 1 days later. Since 10 leaves remainder 3 on division by 7, 10^10 leaves the same remainder as 3^10, which is 4; so 10^10 − 1 leaves 3, and three days after Sunday is Wednesday.
- Take today, Sunday, as day 1. Then day N falls N − 1 days after Sunday.
- 10 leaves remainder 3 on division by 7, so 10^10 leaves the same remainder as 3^10.
- Remainders of powers of 3 by 7: 3, 2, 6, 4, 5, 1, then repeat (cycle of 6). 3^10 = 3^(6+4) leaves the same as 3^4, i.e. 4.
- So 10^10 − 1 leaves remainder 3: the day is 3 days after Sunday, i.e. Wednesday.
- Note: counting 10^10 days after today (not counting today) would give Sunday + 4 = Thursday; UPSC's key uses the reading in which today is the 1st day.
Remember · Day questions: reduce the count modulo 7 (powers via short cycles), and be clear whether today counts as day 1.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·