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

2023

The question consists of a problem question followed by two statements I & II. Find out if the information given in the statements is sufficient in finding the solution to the problem.

Problem question:

How old is Giya?

Statement:-

I) Giya's age is 3 times Amith's age + Bob's age.

II) Bob was of Amith's age 15 years ago.

  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

A Data Sufficiency statement (or a combination of statements) is sufficient only when it yields enough independent equations to solve for the required unknown to one single, unique value. If the target quantity can still take more than one value after using all the given information, the statements are insufficient, irrespective of how much algebraic manipulation is possible.

  1. Let Giya's age = G, Amith's age = A, and Bob's age = B.

  2. Statement I translates to G = 3A + B — one equation involving three unknowns, so G cannot be isolated from this alone.

  3. Statement II translates to B = A + 15 (Bob's age 15 years ago equalled Amith's present age) — this relates only A and B and never mentions G.

  4. Combining the statements: substitute B = A + 15 into G = 3A + B to get G = 3A + (A + 15) = 4A + 15.

  5. This combined equation still has two unknowns, G and A — Amith's actual age is never fixed by either statement, so G cannot be pinned to one number.

For example, A = 5 gives G = 35, while A = 10 gives G = 55 — both pairs satisfy both statements simultaneously, so Giya's age is not uniquely fixed even by the two statements together.

Since neither statement alone, nor both combined, pin Giya's age to a single value, both statements together are not sufficient to answer the problem question.

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