Govind is taller than Rajesh and Dinesh. Avinash is not as tall as Dinesh.…

2017

Govind is taller than Rajesh and Dinesh. Avinash is not as tall as Dinesh. Rajesh is taller than Avinash. Govind is not as tall as Sohan. Who is the second longest of all this?

  1. A.

    Govind

  2. B.

    Avinash

  3. C.

    Dinesh

  4. D.

    Sohan

Show answer & explanation

Correct answer: A

Concept:

In a comparison (ranking) problem, every statement of the form "X is taller than Y" gives one directed link X > Y. Combine all links into a single chain by transitivity: if X > Y and Y > Z then X > Z. The person who has nobody above them is 1st; the person who has exactly one person above them is 2nd, and so on. Note that "P is not as tall as Q" simply means Q > P.

Application:

Convert each statement into a height relation (use > for "taller than"):

  1. "Govind is taller than Rajesh and Dinesh" gives Govind > Rajesh and Govind > Dinesh.

  2. "Avinash is not as tall as Dinesh" gives Dinesh > Avinash.

  3. "Rajesh is taller than Avinash" gives Rajesh > Avinash.

  4. "Govind is not as tall as Sohan" gives Sohan > Govind.

Now chain them. Sohan is above Govind, and Govind is above Rajesh, Dinesh and (through them) Avinash. So the order from tallest to shortest is:

Sohan > Govind > {Rajesh, Dinesh} > Avinash

Rajesh and Dinesh both sit below Govind and above Avinash; their order relative to each other is not fixed, but that does not affect the top two places.

Cross-check:

Only Sohan stands above Govind, while Govind stands above all three of Rajesh, Dinesh and Avinash. Therefore exactly one person is taller than Govind, which makes Govind the second tallest. Sohan, having nobody above, is the tallest; the answer is the second position, so it is Govind.

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