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

The correct answer is (B) Only statement 3 is sufficient.

Explanation:

To find the correct sufficiency, let us analyze the constraints. We have a five-storeyed building (I to V) and 4 available colours. Consecutive floors must have different colours. Statement 3 gives floors I and V as red. Statement 2 states that floor II and floor IV are painted in different colours. Using Statement 3 alone, floors I and V are red, but we cannot determine II, III, and IV. Using Statement 3 along with Statement 2: If I is Red, II cannot be Red. Since there are 4 colours, II, III, IV, and V can be logically fitted without adjacent color conflicts. Specifically, statement 3 combined with statement 2 provides enough structural constraints to ensure any two consecutive floors have different colours. Thus, Statement 3 is not sufficient alone, but statement 3 along with statement 2 is sufficient.