Five people A, B, C, D and E are seated about a round table. Every chair is spaced equidistant from adjacent chairs. (i) C is seated next to A (ii) A is seated two seats from D (iii) B is not seated next to A On the basis of above information, which of the following must be true ? 1. D is seated next to B 2. E is seated next to A 3. D and C are separated by two seats Select the correct answer using the code given below :

• Place A at a fixed position (Seat 1) on the round table with seats numbered 1 to 5 clockwise.

• From condition (ii), D is two seats away from A, so D must be at Seat 3 (since 1+2=3 and 1-2=4, but symmetry makes 3 the standard reference; let's test both: if D is at 3, seats 2 and 4 are adjacent to A; if D is at 4, seats 2 and 5 are adjacent to A).

• From condition (i), C is next to A. If D is at 3, C is at 2 or 4. If D is at 4, C is at 2 or 5.

• From condition (iii), B is not next to A. The seats next to A are 2 and 5 (if we consider A at 1, neighbors are 2 and 5). So B cannot be at 2 or 5.

• Let's analyze Case 1: D is at 3. Neighbors of A (1) are 2 and 5. B cannot be at 2 or 5. Remaining seats for B and E are 4 and... wait, seats are 1(A), 3(D). Left: 2, 4, 5. C is next to A, so C is 2 or 5. B is not next to A, so B is not 2 or 5. Thus B must be at 4. Then C is at 2 or 5, and E takes the other. In this case, D(3) is next to B(4). So Statement 1 is true. Is E next to A? E is at 2 or 5. Both 2 and 5 are next to A. So Statement 2 is true. Are D(3) and C(2 or 5) separated by two seats? If C is 2, distance is 1. If C is 5, distance is 2 (3->4->5). So Statement 3 is not necessarily true.

• Let's analyze Case 2: D is at 4. Neighbors of A (1) are 2 and 5. B cannot be at 2 or 5. Remaining seats: 2, 3, 5. C is next to A, so C is 2 or 5. B is not next to A, so B is not 2 or 5. Thus B must be at 3. Then C is at 2 or 5, and E takes the other. In this case, D(4) is next to B(3). So Statement 1 is true. Is E next to A? E is at 2 or 5. Both are next to A. So Statement 2 is true. Are D(4) and C(2 or 5) separated by two seats? If C is 2, distance is 2 (4->3->2). If C is 5, distance is 1. So Statement 3 is not necessarily true.

• In all valid arrangements, D is next to B and E is next to A. Therefore, statements 1 and 2 must be true.