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):

Correct Option:

D) Both Statement 1 and 2 are not sufficient to answer the question.

To uniquely identify the person sitting on the immediate left of A in a circular arrangement of six persons, the relative positions of all individuals must be definitively established.

• Statement 1 provides that B is opposite C and D is opposite E. In a six-person circular arrangement, this implies that A must be opposite F. However, this statement only defines the opposite pairs and does not fix the absolute or relative positions of any person's immediate neighbors. The specific individual to A's immediate left remains undetermined. Therefore, Statement 1 alone is insufficient.
• Statement 2 states that F is sitting on the immediate left of B. This establishes a direct relative order between F and B. However, it offers no information regarding A's position or its neighbors, nor does it involve C, D, or E. Therefore, Statement 2 alone is insufficient.
• Considering both Statement 1 and Statement 2 together:
  • From Statement 1, the opposite pairs are (A, F), (B, C), and (D, E).
  • From Statement 2, F is immediately to the left of B. This means if we consider a clockwise direction as 'left' for someone facing the center, the sequence B-F is established.
  • By placing B and F, and then their respective opposites C and A, the arrangement partially unfolds. For example, if B is at position 1, F is at position 2 (immediate left of B). Then C (opposite B) is at position 4, and A (opposite F) is at position 5.
  • The remaining two persons are D and E, and the remaining two seats are position 3 (between F and C) and position 6 (between A and B).
  • The person on A's immediate left (which is position 6 in this example, assuming clockwise is left) could be either D or E, as their specific placement in the remaining two seats is not determined by the statements.

Since the individual on A's immediate left cannot be uniquely identified even after combining both statements, the provided information is not sufficient to answer the question.

Incorrect Options:

A) Statement 1 alone is sufficient to answer the question.

Statement 1 only establishes the pairs of opposite persons (A-F, B-C, D-E). It does not provide any information to uniquely determine the immediate neighbors of A or any other person. Thus, it is insufficient.

B) Statement 2 alone is sufficient to answer the question.

Statement 2 only provides the relative position of F with respect to B (F is on the immediate left of B). It offers no information about A's position or its neighbors, making it insufficient to answer the question.

C) Both Statement 1 and 2 are sufficient to answer the question.

As detailed in the explanation for the correct option, even when both statements are combined, the specific positions of D and E relative to A (specifically, who is on A's immediate left) remain ambiguous. The person on A's immediate left could be D or E, preventing a unique answer. Therefore, both statements together are not sufficient.