Directions: The following consists of a question and two statements numbered I…

2024

Directions: The following consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. [WIPRO 2019]

Among five persons – A, B, C, D and E each one of different height, who is the tallest?

Statement I: B is taller than C and D but shorter than E who is not the tallest.

Statement II: E is taller than B and C but shorter than A.

  1. A.

    The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question

  2. B.

    The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question

  3. C.

    If the data in either in statement I alone or in statement II alone is sufficient to answer the question

  4. D.

    If the data in both the statements I and II together is not sufficient to answer the question

Show answer & explanation

Correct answer: A

Concept: In a data-sufficiency question asking who holds the extreme value (tallest, heaviest, first, etc.) among a group, a statement is sufficient only if the ordering clues it gives force a single, unique determination of that extreme person; if two different valid arrangements remain consistent with a statement, that statement alone is insufficient.

Applying Statement I:

  1. B is taller than C and D, and E is taller than B, so the partial order is E above B, with C and D somewhere below B.

  2. Statement I explicitly rules out E being the tallest, so at least one person must stand above E.

  3. Since B, C, and D have all already been placed below E, the only person left unplaced is A — so A must be the one taller than E.

  4. This forces a single arrangement: A above E, E above B, and B above C and D. Only one person — A — can be tallest, so Statement I alone is sufficient.

Applying Statement II:

  1. E is taller than B and C, and A is taller than E, so the partial order is A above E, above B and C.

  2. D's height is never compared with anyone else's in Statement II.

  3. D could slot in anywhere — below C, between the others, or even above A — without contradicting any comparison Statement II makes.

  4. Because more than one placement of D (and hence more than one candidate for tallest) stays consistent with Statement II, it alone cannot settle who is tallest.

Cross-check: Trying to build a valid height order from Statement I with anyone other than A as tallest fails immediately — E cannot be tallest (stated directly), and B, C, D are already fixed below E, leaving no other candidate but A. For Statement II, both an order with A tallest and D placed below E, and an order with D tallest and placed above A, satisfy every comparison given, confirming the ambiguity.

So exactly one of the two statements — the first — pins down a unique tallest person on its own, while the second does not.

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