CAT 2023 Slot 1 QA Q2 Equations

Question 2 of the Quantitative Ability (QA) section, CAT 2023 Slot 1, with CAT's official answer and a worked solution.

If \(x\) and \(y\) are real numbers such that \(x^2+(x-2 y-1)^2=-4 y(x+y)\), then the value \(x-2 y\) is
  1. A
    0
  2. B
    1
  3. C
    2
  4. D
    -1

Answer: (B) 1 Equations MCQ

Solution

  1. Move everything to one side: \(x^2 + 4xy + 4y^2 + (x-2y-1)^2 = 0\).
  2. The first three terms are \((x+2y)^2\), so \((x+2y)^2 + (x-2y-1)^2 = 0\).
  3. A sum of two squares is zero only if both are zero, so \(x - 2y - 1 = 0\), i.e. \(x - 2y = 1\).

Same concept in other years

See every question on Rearrange into a sum of squares equal to zero, so each square is zero.

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