Who amongst A, B, C, D, and E is the tallest? I. A is taller than B but shorter than C. D is not the tallest. II. Exactly two people are taller than C.

Difficulty: Medium

Statement I alone is sufficient; Statement II alone is not.
Statement II alone is sufficient; Statement I alone is not.
Either Statement I alone or Statement II alone is sufficient.
Both statements together are NOT sufficient.
Both statements together are sufficient, but NEITHER alone is sufficient.

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:

I: A < C and A > B. Also, D is not the tallest.
II: Exactly two people are taller than C (so C is 3rd tallest).

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:

A/B: Each alone allows multiple tallest candidates.
C: Not “either alone”; both are needed.
D: Together they are sufficient; so “not sufficient” is false.

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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Who amongst A, B, C, D, and E is the tallest? I. A is taller than B but shorter than C. D is not the tallest. II. Exactly two people are taller than C.

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