A, B, C, D, and E are sitting in a single row of five chairs facing the same direction. B is seated between A and C. Who among them occupies the middle position in the row? Consider the following statements: I. A is to the left of B and to the right of D. II. C is seated at the right end of the row.

Introduction / Context:
This data sufficiency question concerns seating arrangement in a row. Five people A, B, C, D, and E sit in a straight line, and some relative positions are known. The goal is to identify who sits in the exact middle position of the row. Two statements provide partial information about the order, and we need to judge which of them, alone or together, fix the middle seat.

Given Data / Assumptions:

• B is between A and C in the row, which normally implies that A, B, and C occupy three consecutive seats in the order A B C or C B A.
• Statement I: A is to the left of B and to the right of D.
• Statement II: C is at the right end of the row.
• All five seats are in a single row with distinct positions from left to right, and no two people share a seat.

Concept / Approach:
We first understand the base constraint B between A and C, then apply each statement to see how the arrangement tightens. If a statement alone leaves multiple possible people in the middle, it is not sufficient. If combining the statements yields a single valid arrangement, then both are necessary and sufficient.

Step-by-Step Solution:
Step 1: Use the base condition. Since B is between A and C and they sit in a row, the possible patterns for A, B, and C on consecutive seats are A B C (from left to right) or C B A. No other arrangement keeps B strictly between A and C. Step 2: Interpret statement I. A is to the left of B and to the right of D. This implies the order D, A, B in that sequence from left to right. Combining this with the base pattern, A must be to the left of B, so the correct pattern among A, B, C is A B C, not C B A. Step 3: From the base condition and statement I, we get the partial sequence D, A, B, C as four consecutive positions in that order. The person E is still free to sit either at the extreme left or at the extreme right, as long as he does not break the constraints on A, B, C, and D. Step 4: Consider statement I alone. If E sits to the left of D, the row is E, D, A, B, C and the middle seat is A. If E sits to the right of C, the row is D, A, B, C, E and the middle seat is B. Since both arrangements satisfy statement I and the base condition but give different people in the middle, statement I alone is not sufficient. Step 5: Now consider statement II alone. C is at the right end. Knowing only that B is between A and C and that C is at the extreme right leaves many possibilities for the exact positions of A, B, and the other two persons. The middle position may be occupied by different people depending on the placement of D and E. Thus statement II alone is also not sufficient. Step 6: Combine statements I and II. From earlier, D, A, B, C must be in order, and now statement II requires C to be at the right end. Therefore the only possible arrangement is E, D, A, B, C, where E is at the left end, D next, then A, then B, and C at the right end. Step 7: In this unique arrangement, the third seat from the left is occupied by A, so A is in the middle position. Since no other arrangement fits all conditions, the combination of both statements is necessary and sufficient.

Verification / Alternative check:
To verify, try to place C at the right end while keeping B between A and C and A left of B but right of D. The sequence D, A, B, C is forced, leaving only one seat for E. Any attempt to swap E with another person violates either the base condition or one of the statements. Therefore, there is exactly one valid seating order, and it yields A as the middle person. This confirms sufficiency of the combined statements.

Why Other Options Are Wrong:
Option A is wrong because statement I alone admits at least two different middle occupants, A and B, depending on E position. Option B is wrong because statement II alone leaves the entire left side of the row underdetermined. Option C, which claims either statement alone is sufficient, fails for both reasons. Option E, saying that even both together are not sufficient, contradicts the unique arrangement we found. Only option D correctly states that both statements together are necessary and sufficient.

Common Pitfalls:
Learners sometimes misinterpret the phrase B is between A and C as allowing non consecutive seating, which leads to extra invalid patterns. Others may forget to check multiple placements of the unused person E when judging statement I alone. Drawing the row and trying all possibilities systematically is an effective way to avoid these mistakes in arrangement based data sufficiency questions.

Final Answer:
The data in both statements I and II together are necessary to answer the question, so the correct option is D.