Data Sufficiency — Ordering by height among five friends: Who is the tallest? Statements: I. D is taller than A and C. II. B is shorter than E but taller than D.

Introduction / Context:We have a ranking (taller/shorter) puzzle with five people: A, B, C, D, E. The objective is to determine the tallest person using the given pairwise relations. In data sufficiency, we judge whether each statement alone or together is enough to reach a unique conclusion.

Given Data / Assumptions:

• I: D > A and D > C (D is taller than A and C).
• II: E > B > D (E taller than B; B taller than D).
• All five friends are A, B, C, D, E; no ties unless implied (none implied here).

Concept / Approach:Combine inequalities to build a chain. If one person is shown to be taller than all others, the tallest is identified. Otherwise, insufficiency remains.

Step-by-Step Solution:From I: D is above A and C → D > A, D > C.From II: E > B > D; combined with I gives E > B > D > A and D > C.Thus E is taller than B, D, A, and C. No statement suggests anyone taller than E.Therefore, E is uniquely tallest.

Verification / Alternative check:Statement I alone mentions nothing about B and E, so tallest cannot be fixed. Statement II alone says nothing about A and C relative to E; one of them could exceed E. Together, the chain proves E is taller than all five.

Why Other Options Are Wrong:

• I alone: Insufficient—B and E unknown.
• II alone: Insufficient—A and C could be taller.
• Either alone: Not enough.
• Neither alone: Incorrect because together they work.

Common Pitfalls:

• Assuming transitivity without writing the chain; writing it out prevents overlooking someone.
• Assuming a person not mentioned is automatically shorter or taller—never assume beyond given relations.

Final Answer:Both I and II are sufficient