Consider two Statements and a Question:
- Statement-1: Each of A and D is heavier than each of B, E and F, but none of them is the heaviest.
- Statement-2: A is heavier than D, but is lighter than C.
- Question: Who is the heaviest among A, B, C, D and E?
Which one of the following is correct in respect of the Statements and the Question?
Answer & explanation
Answer: (c) Both Statement-1 and Statement-2 are required to answer the Question — UPSC also accepted (d)
Statement-2 gives C > A > D, and Statement-1 adds that A and D are heavier than B and E; only together do they show that C is the heaviest of the five. UPSC's final key accepted both (c) and (d), because when both statements are required it is also true that neither alone is sufficient.
- Statement-1: A and D are heavier than B, E and F, but C is never compared with anyone, and 'the heaviest' may be someone outside the list — so it cannot name the heaviest of A, B, C, D, E.
- Statement-2: C > A > D, but B and E are not compared with C — not sufficient alone.
- Together: C > A > D, and A, D > B, E, so C is heavier than all the others — C is the heaviest.
- Both statements are required (c). That also makes 'neither statement alone is sufficient' (d) true, and UPSC accepted both.
- ✗ (a) Statement-1 never places C, so it cannot settle who is heaviest among the five.
- ✗ (b) Statement-2 says nothing about B and E relative to C.
- ✓ (c) Combining gives C > A > D, with A and D both heavier than B and E, so C is the heaviest.
- ✓ (d) Since both statements are needed, neither alone is sufficient — literally true, and accepted by UPSC.
Remember · In data sufficiency, 'both are required' also means 'neither alone suffices' — watch for overlapping options.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·