Each of the questions below consists of a question and two statements numbered…

2024

Each of the questions below 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. Read both the statements.

Who amongst Shreya, Jyoti, Leena, Pia and Kajal is the shortest?

I. Leena is taller than Pia and Pia is taller only than Shreya.

II. Kajal is taller than Jyoti and Leena. Leena is taller than Pia. Shreya is not the tallest.

  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 either in statement I alone or in statement II alone are sufficient to answer the question.

  4. D.

    if the data even in both statements I and II together are not sufficient to answer the question.

Show answer & explanation

Correct answer: A

Concept: A statement in a data-sufficiency question is sufficient only if, used entirely on its own, it lets you uniquely answer the specific question asked - here, name one person as the shortest with no ambiguity left.

A clue of the form "X is taller than only Y" is a strong rank-fixing clue: among the group being compared, X is taller than exactly one person (Y) and shorter than everyone else. With five people total, this places X at the second-lowest rank and Y at the very lowest rank.

Applying Statement I:

  1. Leena is taller than Pia, so Leena > Pia.

  2. Pia is taller than only Shreya, so among the five people Pia is shorter than the other three (Leena, Jyoti, Kajal) and taller than exactly one - Shreya.

  3. This fixes Pia at the second-lowest height and Shreya at the lowest, no matter how Jyoti and Kajal are ordered between themselves.

Applying Statement II:

  1. Kajal is taller than Jyoti and Leena, and Leena is taller than Pia, giving Kajal > Leena > Pia and Kajal > Jyoti.

  2. "Shreya is not the tallest" is still informative: Jyoti, Leena, and Pia are already shown to rank below Kajal by the comparisons above, so only Kajal or Shreya could be the overall tallest; ruling out Shreya confirms Kajal is tallest, meaning Kajal is also taller than Shreya.

  3. Shreya's height relative to Jyoti and Pia is never fixed by any of these clues.

Cross-check: both Kajal > Leena > Jyoti > Pia > Shreya and Kajal > Leena > Shreya > Jyoti > Pia satisfy every clue in Statement II, yet they name different shortest people. So Statement II alone cannot fix a unique answer, while Statement I alone already does.

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