Heights of P, Q, R, S, T, U (all different): R is taller than only P and U. S is shorter than only T and Q (i.e., only T and Q are taller than S). Standing in descending order (tallest to shortest), who is at the third place?

Introduction / Context:
This problem mixes two relative statements to pin down specific ranks in a unique descending order. The language “shorter than only …” and “taller than only …” precisely indicates positions from the ends.

Given Data / Assumptions:

• All heights are distinct.
• “R taller than only P and U” ⇒ exactly two people are shorter than R (P and U). Therefore, in tallest→shortest order, R is 4th place.
• “S shorter than only T and Q” ⇒ only T and Q are taller than S. Therefore, S is 3rd place (after T and Q).

Concept / Approach:
Translate the exclusivity terms into fixed positions. With six people, being “taller than only two” means exactly the 4th position from the top. Being “shorter than only two” means exactly the 3rd position from the top.

Step-by-Step Solution:

Verification / Alternative check:
No other placement satisfies both exclusivity statements simultaneously. Any attempt to move S to 2nd would break “only T and Q taller,” and any attempt to move R would change the count of people below him.

Why Other Options Are Wrong:

• R: 4th, not 3rd.
• P: 5th or 6th.
• Q: 1st or 2nd.

Common Pitfalls:
Misreading “only” as “at least,” which would loosen constraints and lead to multiple answers.

Final Answer:
S