There are 6 people sitting around a circular table: A, B, C, D, E, and F. All are facing either the centre or outside.

Statement I:
- B is second to the right of F and both are facing the centre.
- Only two people are sitting between A and E from either side.
- Both A and E are facing the same direction.
- A is not an immediate neighbor of B.

Statement II:
- C is facing the opposite direction of B.
- D is sitting to the second left of C.

Based on the above statements, which of the following is true?

1. Statement I alone is sufficient to answer the question while Statement II is not.
2. Statements I and II together are not sufficient to answer the question.
3. Statement II alone is sufficient to answer the question while Statement I is not.
4. Statements I and II together are sufficient to answer the question.

Question

There are 6 people sitting around a circular table: A, B, C, D, E, and F. All are facing either the centre or outside.

Statement I:
- B is second to the right of F and both are facing the centre.
- Only two people are sitting between A and E from either side.
- Both A and E are facing the same direction.
- A is not an immediate neighbor of B.

Statement II:
- C is facing the opposite direction of B.
- D is sitting to the second left of C.

Based on the above statements, which of the following is true?

1. Statement I alone is sufficient to answer the question while Statement II is not.
2. Statements I and II together are not sufficient to answer the question.
3. Statement II alone is sufficient to answer the question while Statement I is not.
4. Statements I and II together are sufficient to answer the question.

Accepted Answer

**Solution:**

1. From Statement I:
   - B is second to the right of F; both face the centre.
   - A and E have exactly two people between them on either side, so A and E are opposite each other.
   - A and E face the same direction.
   - A is not an immediate neighbor of B.

This fixes relative positions of B and F and the opposite positions of A and E, but leaves ambiguity about C and D's positions and directions.

2. From Statement II:
   - C faces opposite direction to B (B faces centre, so C faces outside).
   - D is second to the left of C.

This gives relative position and direction of C and D but no absolute positions.

3. Combining Statements I and II:
   - Place F facing centre.
   - B is second to the right of F, also facing centre.
   - A and E are opposite each other and face the same direction.
   - A is not neighbor of B, so A must be opposite F.
   - E is opposite A, so E is neighbor of B.
   - Remaining seats are for C and D.
   - From Statement II, D is second to the left of C.

By placing C and D accordingly, all conditions are satisfied with a unique arrangement.

**Answer:** Statements I and II together are sufficient to answer the question.

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