Question

Questions 48 to 50 are followed by two statements labelled as (1) and (2). You have to decide if these statements are sufficient to conclusively answer the question. Give answer:

(A) If statement (1) alone or statement (2) alone is sufficient to answer the question
(B) If you can get the answer from (1) and (2) together but neither alone is sufficient
(C) If statement 1 alone is sufficient to answer the question and statement (2) alone is also sufficient
(D) If neither statement (1) nor statement (2) is sufficient to answer the question

Around a circular table six persons A, B, C, D, E and F are sitting. Who is on the immediate left to A?

Statement 1: B is opposite to C and D is opposite to E.
Statement 2: F is on the immediate left to B and D is to the left of B.

• A. If statement (1) alone or statement (2) alone is sufficient to answer the question
• B. If you can get the answer from (1) and (2) together but neither alone is sufficient
• C. If statement 1 alone is sufficient to answer the question and statement (2) alone is also sufficient
• D. If neither statement (1) nor statement (2) is sufficient to answer the question

Hint:

Statement 1 only fixes who sits opposite whom, and statement 2 only connects B, D and F; combine both to lock every seat and find A's left neighbour.

Answer 1

The Correct Option is B

Step 1: Understand the setup.
Six people, A, B, C, D, E and F, sit around a circular table. With 6 seats, there are exactly 3 pairs of seats that face each other directly (opposite pairs). We are asked to pin down exactly one person: whoever sits immediately to A's left.

Step 2: Check statement 1 alone.
Statement 1 says B is opposite C, and D is opposite E. Since there are only 3 opposite pairs among 6 seats, and two of them are now used up by B-C and D-E, the third opposite pair must be A and F, so A and F sit directly across from each other.
But this tells us nothing about which direction people are seated in, or which of the remaining seats each specific person occupies relative to A. We could rotate the whole seating, or flip B and C's seats, or flip D and E's seats, and statement 1 would still hold true, yet the person sitting immediately to A's left would change from one such seating to another. So statement 1 alone does not pin down a single answer.

Step 3: Check statement 2 alone.
Statement 2 says F is immediately to the left of B, and D is to the left of B. This only relates F, D and B to each other. It says nothing about where A, C or E sit, and does not even fix A's seat relative to B or F. Many different seatings satisfy this statement while placing a different person to A's immediate left each time, so statement 2 alone is not enough either.

Step 4: Combine both statements.
Now use both together. Fix B's seat as a reference point, seat 1, going clockwise as seats 1, 2, 3, 4, 5, 6, with a person's immediate left being the next seat clockwise from where they sit.
Since F is immediately to B's left, F takes seat 2. From statement 1, A is opposite F, and opposite seats are 3 apart, so A sits at seat 2 plus 3, which is seat 5.
Since B is opposite C, C sits at seat 1 plus 3, which is seat 4.
The two seats left over are seat 3 and seat 6, which must go to D and E, and indeed seats 3 and 6 are opposite each other, matching "D opposite E". Since D is said to be to the left of B, and seat 2, immediately left of B, is already F's, D must take the next seat further round in that same direction, seat 3, leaving E at seat 6.
So the full seating, going clockwise, is: B at seat 1, F at seat 2, D at seat 3, C at seat 4, A at seat 5, E at seat 6.
The seat immediately to A's left, seat 5's clockwise neighbour, seat 6, is occupied by E.

Step 5: Confirm neither statement alone was enough.
Statement 1 alone left the rotation and the B-C, D-E internal ordering free, so it could not fix who sits at A's left. Statement 2 alone never referenced A, C or E's seats at all. Only by combining the opposite-pair information from statement 1 with the adjacency information from statement 2 could we lock every seat down and find a single, definite person at A's left.

Final Answer:
The two statements together, but neither alone, let us work out exactly who sits to A's left.
\[ \boxed{\text{Both statements together are needed, neither alone is sufficient}} \]