The question consists of a problem question followed by two statements I and…

2023

The question consists of a problem question followed by two statements I and II.

Find out if the information given in the statement(s) is sufficient in finding the solution to the problem.

Problem Question:

In what proportion would Mukesh, Rakesh and Rajesh distribute profit among them?

Statements:

I) Rakesh gets one-third of the profit

II) Mukesh and Rajesh have invested 80% of the total investment.

  1. A.

    Statement I alone is sufficient in answering the problem question.

  2. B.

    Statement II alone is sufficient in answering the problem question.

  3. C.

    Both statements put together are sufficient in answering the problem question.

  4. D.

    Both statements put together are not sufficient in answering the problem question

Show answer & explanation

Correct answer: D

Concept: In a Data Sufficiency question, a statement (or combination of statements) is sufficient only when it lets you calculate one unique, fully-determined answer to the question asked. If, even after using every given statement, some quantity needed for the answer can still take more than one valid value, the statement(s) are not sufficient — a partial fact about one part of the problem does not automatically fix the rest.

  1. Statement I alone: it fixes only Rakesh's share of the profit at one-third. It says nothing about how the remaining two-thirds is divided between Mukesh and Rajesh, so the full three-way proportion cannot be found from Statement I alone.

  2. Statement II alone: it gives only the combined investment of Mukesh and Rajesh as 80% of the total (so Rakesh's investment share is 20%). This is investment data, not profit data, and it still does not tell us how that 80% splits between Mukesh and Rajesh individually, so Statement II alone cannot fix the profit proportion either.

  3. Statements I and II together: combining them gives Rakesh's profit share (one-third) and the combined investment share of Mukesh and Rajesh (80%). Neither statement establishes that profit is divided in the same ratio as investment, and even if it were, the 80% combined figure still does not separate Mukesh's individual share from Rajesh's. So the exact split between Mukesh and Rajesh — and hence the full three-way proportion — remains undetermined.

Cross-check: Try two different splits that both satisfy Statement II — for instance, Mukesh and Rajesh each investing 40% of the total, or Mukesh investing 60% and Rajesh 20%. Both fit "Mukesh and Rajesh together invest 80%", yet they can lead to different overall profit proportions. Since more than one distribution is consistent with both statements, no single proportion can be pinned down.

Because neither statement alone, nor both combined, fix a unique profit-sharing proportion among Mukesh, Rakesh and Rajesh, the data given is not sufficient to answer the problem question.

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