Difficulty: Medium
Correct Answer: Both statements together are sufficient, but NEITHER alone is sufficient.
Explanation:
Introduction / Context:We must identify the unique tallest person among five, given partial comparisons. The question is about sufficiency, not computing relative heights numerically.
Given Data / Assumptions:
Concept / Approach:Translate statements into rank constraints. A statement is sufficient only if it determines the tallest uniquely in all consistent orders.
Step-by-Step Solution:
1) Using I alone: We know the local order B < A < C and D is not tallest. E is unconstrained, so the tallest could be C or E (since D is ruled out). Hence I alone is insufficient.2) Using II alone: If two people are taller than C, then the tallest is either of those two—but II does not tell us who they are; hence II alone is insufficient.3) Combine I + II: Since C is exactly 3rd, nobody below C can be tallest. From I, A < C and B < A, so both A and B are below C, therefore neither can be tallest. With C at rank 3, exactly two people (from {D, E}) are taller than C. But I says D is not tallest; hence the tallest must be E uniquely.Verification / Alternative check:Check consistency: A < C, B < A, C at 3rd, D at rank 2 and E at rank 1 is a valid arrangement satisfying all conditions.
Why Other Options Are Wrong:
Common Pitfalls:Overlooking that A and B being below C (from I) combined with C’s fixed rank (from II) forces the two-above set to {D, E}; then using “D not tallest” clinches E.
Final Answer:Both statements together are sufficient, but NEITHER alone is sufficient.
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