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Sum of Absolute Values

CAT 2000 Slot 1 · Quantitative Ability · Medium · Algebra

This is a medium Quantitative Ability question from the CAT 2000 Slot 1 paper. It tests Algebra. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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If x2+y2=0.1x^2 + y^2 = 0.1 and ∣x−y∣=0.2|x - y| = 0.2, then ∣x∣+∣y∣|x| + |y| is equal to:

  1. A.

    0.3

  2. B.

    0.4

  3. C.

    0.2

  4. D.

    0.6

Answer

B

Explanation

∣x−y∣2=x2+y2−2xy=0.04|x - y|^2 = x^2 + y^2 - 2xy = 0.04. Given x2+y2=0.1  ⟹  2xy=0.1−0.04=0.06x^2 + y^2 = 0.1 \implies 2xy = 0.1 - 0.04 = 0.06. Now, (∣x∣+∣y∣)2=x2+y2+2∣xy∣=0.1+0.06=0.16(|x| + |y|)^2 = x^2 + y^2 + 2|xy| = 0.1 + 0.06 = 0.16. Therefore, ∣x∣+∣y∣=0.16=0.4|x| + |y| = \sqrt{0.16} = 0.4.

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