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 six seats, 'opposite' means three seats away. Statement-1 pairs B–C and D–E as opposites, so A and F must also be opposite each other; it does not fix who is next to A, so it is not sufficient.

• Statement-2 alone (F on B's immediate left) says nothing about A's neighbours, so it is not sufficient.

• Together: A and F are opposite, F is on B's immediate left and C is opposite B. This fixes A, B, C and F, but D and E can occupy the two remaining seats either way round.

• One of those two seats is A's immediate left, so it could be D or E (for example, going round in the direction of each person's left: A, D, B, F, E, C or A, E, B, F, D, C).

• The Question cannot be answered even with both statements, option (d).

Why the other options are wrong

(a) Statement-1 alone is sufficient to answer the Question: Statement-1 only fixes three opposite pairs; A's immediate left could be B, C, D or E.
(b) Statement-2 alone is sufficient to answer the Question: Statement-2 relates F and B only and says nothing about A's neighbours.
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question: Even together, D and E can swap the two unfixed seats, so A's immediate left could be D or E.

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.