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Data Sufficiency: Value of X

CAT 1993 Slot 1 · Quantitative Ability · Easy · QA

This is an easy Quantitative Ability question from the CAT 1993 Slot 1 paper. It tests QA. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Given that XX and YY are non-negative. What is the value of XX?

I. 2X+2Y≤402X + 2Y \le 40 II. X−2Y≥20X - 2Y \ge 20

  1. A.

    If the question can be answered with the help of statement I alone

  2. B.

    If the question can be answered with the help of statement II alone

  3. C.

    If both statement I and statement II are needed to answer the question

  4. D.

    If the question cannot be answered even with the help of both statements

Answer

C

Explanation

From Statement I: X+Y≤20X + Y \le 20. Alone insufficient. From Statement II: X−2Y≥20X - 2Y \ge 20. Alone insufficient. Combining both: 2X+2Y≤402X + 2Y \le 40 and 2Y≤X−202Y \le X - 20. Since X,Y≥0X, Y \ge 0, adding X+Y≤20X + Y \le 20 and X−2Y≥20X - 2Y \ge 20 yields 3Y≤0  ⟹  Y=03Y \le 0 \implies Y = 0. Then X=20X = 20. Both statements together are sufficient.

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