An 8-digit number 4252746B leaves remainder 0 when divided by 3. How many values of B are possible?
Answer & explanation
Answer: (c) 4
The known digits add to 30, already a multiple of 3, so B itself must be a multiple of 3: 0, 3, 6 or 9 — four values.
- 4 + 2 + 5 + 2 + 7 + 4 + 6 = 30.
- 30 + B is divisible by 3 exactly when B is divisible by 3.
- B can be 0, 3, 6 or 9 → 4 values.
Remember · Divisibility by 3 depends only on the digit sum; if the known digits already give a multiple of 3, the unknown digit must too.
Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·