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
- (a) Only statement 2 is sufficient
- (b) Only statement 3 is sufficient ✓ UPSC's answer
- (c) Statement 1 is not sufficient, but statement 1 along with statement 2 is sufficient
- (d) Statement 3 is not sufficient, but statement 3 along with statement 2 is sufficient
Why the answer is (b)
• Statement 3 states that Floor I and Floor V are painted red.
• To ensure consecutive floors have different colours, Floor II must not be red, and Floor IV must not be red.
• Since there are four different colours available, Floor II can be any of the three non-red colours, and Floor IV can be any of the three non-red colours.
• Floor III must be different from Floor II and Floor IV; since only two colours are used for II and IV (or potentially the same one), there is always at least one remaining colour available for Floor III to satisfy the condition.
• Thus, knowing only that the end floors are red (Statement 3) is sufficient to guarantee a valid painting scheme exists where no two consecutive floors share a colour, making Statement 3 sufficient on its own.
Why the other options are wrong
- (a) Only statement 2 is sufficient
- Statement 2 only specifies that Floor II and IV are different, which does not constrain Floor I, III, or V, leaving multiple invalid configurations possible.
- (c) Statement 1 is not sufficient, but statement 1 along with statement 2 is sufficient
- Statement 1 is not required because Statement 3 alone already provides enough constraints to ensure a valid solution exists.
- (d) Statement 3 is not sufficient, but statement 3 along with statement 2 is sufficient
- Statement 3 is sufficient on its own, so the condition that it is 'not sufficient' in this option is factually incorrect.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.