The question below consists of a question and two statements numbered I and II…

2024

The question below consists of a question and two statements numbered I and II are given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

Amongst A, B, C, D, E and F, each having a different height, who is the shortest?

I. C is shorter than only B.

II. A is taller than only D and F.

  1. A.

    if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.

  2. B.

    if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.

  3. C.

    if the data in Statement I alone or in Statement II alone are sufficient to answer the question.

  4. D.

    if the data in both the Statements I and II are not sufficient to answer the question.

Show answer & explanation

Correct answer: D

Concept: In a ranking-based data-sufficiency question, a statement only helps if it fixes the relative position of every entity needed to answer the specific query. The data is sufficient only when combining all the given statements produces one single, unambiguous order for the position asked about; if two entities remain interchangeable at that position even after combining everything given, the data is insufficient, no matter how much of the rest of the ranking is settled.

Application: Trace the two statements step by step and combine them:

  1. From Statement I (C is shorter than only B), the only person taller than C is B, so C ranks second overall and everyone else, A, D, E, and F, ranks below C: B > C > {A, D, E, F}.

  2. From Statement II (A is taller than only D and F), the only two people shorter than A are D and F, so exactly three people must rank above A; since D and F are already fixed below A, those three are B, C, and E: {B, C, E} > A > {D, F}.

  3. Combine the two chains: Statement I says only B is taller than C, so E (who is not B) must rank below C; Statement II says E must rank above A. Together this places E between C and A, giving the full order B > C > E > A > {D, F}.

  4. This order fixes every position except the last two, D and F remain interchangeable, so which of them is shorter is not settled by either statement or by combining them.

Cross-check: Swapping D and F does not violate either statement: C is still shorter than only B, and A is still taller than only D and F, which confirms the ambiguity between D and F is genuine, not an oversight.

Result: Since the shortest person cannot be pinned down even after using both statements together, the correct option is that the data in both Statements I and II, even combined, are not sufficient to answer the question.

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