A five-storeyed building with floors from I to V is painted using four different colours and only one colour is used to paint a floor.
Consider the following statements:
- 1.The middle three floors are painted in different colours.
- 2.The second (II) and the fourth (IV) floors are painted in different colours.
- 3.The first (I) and the fifth (V) floors are painted red.
To ensure that any two consecutive floors have different colours
Answer & explanation
Answer: (b) Only statement 3 is sufficient
All four colours are used on five floors, so exactly one colour repeats. If floors I and V are both red, red is that repeat, and floors II, III and IV must take the other three colours, one each — no two neighbours can match. Statements 1 and 2 leave the end floors free to copy a neighbour.
- Five floors, four colours, all four used: one colour appears on two floors, the others once each.
- Statement 3: I and V are red, so red is the repeated colour; II, III and IV take the other three colours, all different and none red.
- Hence I–II, II–III, III–IV and IV–V all differ: statement 3 alone is sufficient.
- Statement 1: II, III, IV differ, but floor I may copy floor II (e.g. blue, blue, green, yellow, red) — not sufficient.
- Statement 2 (II ≠ IV) is already implied by statement 1, so 1 and 2 together are still not sufficient; 2 alone says nothing about any adjacent pair.
- ✗ 1. Not sufficient: it leaves the pairs I–II and IV–V unchecked.
- ✗ 2. Not sufficient: floors II and IV are not neighbours, so it controls no consecutive pair.
- ✓ 3. Sufficient: it forces II, III and IV to be the three non-red colours, all different.
Remember · 'Painted using four different colours' means all four are used; with five floors exactly one colour repeats — build from that count.
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). ·