Six persons A, B, C, D, E and F are sitting equidistant from each other around a circular table (facing the centre of the table). Consider the Question and two Statements given below : Question : Who is sitting on the immediate left of A? Statement-1 : B is sitting opposite to C and D is sitting opposite to E. Statement-2 : F is sitting on the immediate left of B. Which one of the following is correct in respect of the Question and the Statements?
- (a) Statement-1 alone is sufficient to answer the Question
- (b) Statement-2 alone is sufficient to answer the Question
- (c) Both Statement-1 and Statement-2 are sufficient to answer the Question
- (d) Both Statement-1 and Statement-2 are not sufficient to answer the Question ✓ UPSC's answer
Why the answer is (d)
• With 6 persons, 'opposite' means 3 seats away, so Statement-1 fixes B and C as a pair and D and E as a pair, leaving A and F as the remaining pair.
• Statement-1 does not specify the relative order of these three pairs (B-C, D-E, A-F) around the circle, nor does it fix A's position relative to the others.
• Statement-2 states F is on the immediate left of B, but without knowing where A is located relative to B or F, we cannot determine who is on A's immediate left.
• Combining both statements, we know F is left of B, and A is opposite F (since A and F are the remaining pair after B-C and D-E are placed), but the specific arrangement of the D-E pair and the rotation of the entire setup leaves multiple valid configurations for A's neighbor.
• For example, if the order is B-F-A-E-D-C, A's left is E; if the order is B-F-C-A-D-E, A's left is D. Since multiple answers are possible, the data is insufficient.
Why the other options are wrong
- (a) Statement-1 alone is sufficient to answer the Question
- Statement-1 only establishes opposite pairs but does not fix the linear order or relative positions of A with respect to the others.
- (b) Statement-2 alone is sufficient to answer the Question
- Statement-2 links F and B but provides no information about the position of A relative to B or F.
- (c) Both Statement-1 and Statement-2 are sufficient to answer the Question
- Even with both statements, the position of the D-E pair relative to the B-F-A cluster allows for multiple valid arrangements of A's immediate left neighbor.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.