Data Sufficiency — Who Is Tallest? (P, Q, R, S, T) Who among P, Q, R, S, T is the tallest? I. P is taller than S and T but shorter than R. Q is taller than S. II. T is taller than S. P is not the tallest.
Correct Answer: Even both statements together are not sufficient.
Introduction / Context:We have partial height comparisons and must identify the tallest uniquely.
Given Data / Assumptions:
- I: R > P > {S,T}; and Q > S. No relation between Q and R or Q and P is fixed.
- II: T > S; and P is not the tallest.
Concept / Approach:From I, R or possibly Q could be tallest (since Q is only constrained above S). II only says P is not tallest and gives T > S, which does not settle R vs Q vs others.
Step-by-Step Solution:
1) Under I, construct two models: (a) R tallest; (b) Q tallest with Q > R (not prohibited). Both obey all inequalities.2) Adding II does not compare Q vs R, so both models remain feasible.Verification / Alternative check:Attempting to force a unique tallest fails without an explicit Q–R comparison.
Why Other Options Are Wrong:I alone or II alone insufficient; together also insufficient; “either alone sufficient” is false.
Common Pitfalls:Assuming transitivity where no link exists (e.g., inferring Q vs R).
Final Answer:Not sufficient even together.