Data sufficiency – ordering by height Among P, Q, R, S, and T: Q is the second tallest, and S is immediately taller than the shortest. Who stands in the middle (3rd) when arranged by height? Statements: (I) T is not the shortest. (II) R is taller than S but shorter than Q. (III) P ranks third in height above S when all are arranged by height.

Introduction / Context:This data-sufficiency problem combines fixed positions with comparative statements to find who is in the middle position (3rd tallest) among five people.

Given Data / Assumptions:

• From the stem: Q is 2nd tallest; S is 4th (immediately taller than the shortest at 5th).
• Positions (tallest to shortest): 1, 2(Q), 3(?), 4(S), 5(shortest).
• Statement I: T is not the shortest.
• Statement II: R taller than S but shorter than Q.
• Statement III: P is three ranks above S.

Concept / Approach:Translate each statement into a position constraint and see whether it, together with the stem, determines the middle person uniquely.

Step-by-Step Solution:

Verification / Alternative check:Try constructing a full order: with II, positions become 1(T or P), 2(Q), 3(R), 4(S), 5(the remaining). Multiple complete orders exist, but the identity at position 3 stays 'R', confirming sufficiency.

Why Other Options Are Wrong:

• Only I and II / Only II and III: More information than required; II alone suffices.
• Either II only or I and III only: I+III do not uniquely fix the 3rd place; II only does.
• None of these: Incorrect because 'Only II' is sufficient.

Common Pitfalls:Misreading 'immediately taller than the shortest' (which fixes S at 4th) and assuming extra constraints not given.

Final Answer:Only II