Given below is a question followed by two statements I and II. You have to…

2023

Given below is a question followed by two statements I and II. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Question: Find the cost of fencing a rectangle at the rate of ₹10 per metre. Statements: I. The length of the rectangle is 30 m. II. The breadth of the rectangle is twice of its length.

  1. A.

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

  2. B.

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

  3. C.

    If data in both statements I & II together are necessary to answer the question

  4. D.

    If data in both statements I & II together are not sufficient to answer the question

  5. E.

    Question not attempted

Attempted by 39 students.

Show answer & explanation

Correct answer: C

Concept: In a Data Sufficiency question, a statement (or combination of statements) is "sufficient" only when it pins the quantity asked for down to one exact value. Here, cost of fencing = Perimeter × rate, and for a rectangle, Perimeter = 2 × (Length + Breadth); so a definite cost needs BOTH Length and Breadth fixed as exact numbers. The rate “₹10 per metre” is a LINEAR rate along the boundary (fencing follows the perimeter, not the area), so no square-metre conversion applies.

Applying this to the two statements:

  1. Statement I alone ("Length = 30 m") fixes only one side; the breadth is still unknown, so the perimeter cannot be pinned to a single value — not sufficient by itself.

  2. Statement II alone ("Breadth = 2 × Length") fixes only the ratio between the sides, not either actual measurement, so again no single perimeter follows — not sufficient by itself.

  3. Statements I and II together: Length = 30 m (from I), so Breadth = 2 × 30 = 60 m (from II).

  4. Perimeter = 2 × (30 + 60) = 180 m, so Cost = 180 × ₹10 = ₹1,800 — one exact value, obtained only by using both statements together.

Cross-check: drop either statement and the answer reopens — with only the length, the breadth (and so the perimeter) could take any value; with only the ratio, both sides could scale up or down together — confirming that neither statement alone is sufficient, but both together are.

So the data in both statements I and II together is necessary (and sufficient) to answer the question, while neither statement alone is enough.

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