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Data Sufficiency — Linear arrangement: Among A, B, C, D and E standing in a single row, who is in the middle? Statement I: C, who is third to the left of D, is to the immediate right of A and second to the left of E. Statement II: C is second to the left of E; E is not at an end and is third to the right of A. Also, D is at one of the ends. Decide which statement(s) are sufficient to identify the middle person. Choose the correct sufficiency option.

Difficulty: Medium

Statement I alone is sufficient, but Statement II alone is not sufficient.
Statement II alone is sufficient, but Statement I alone is not sufficient.
Either statement I or statement II alone is sufficient.
Both statements I and II together are sufficient, but neither alone is sufficient.
Even both statements I and II together are not sufficient.

Correct Answer: Either statement I or statement II alone is sufficient.

Explanation:

Using Statement I
Let positions be 1–5 (left→right). ‘‘C is 3 left of D’’ and ‘‘C is right of A’’ and ‘‘C is 2 left of E’’ give a unique order: A(1) – C(2) – B(3) – E(4) – D(5). Middle = B.

Using Statement II
E is 3 right of A and not at an end ⇒ A(1), E(4). ‘‘C is 2 left of E’’ ⇒ C(2). ‘‘D at an end’’ with A already at 1 ⇒ D(5). Remaining B(3). Middle = B.

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