GMAT Challenging Question 12 | Algebra PS

GMAT Sample Questions | Absolute Value & Number Properties

This GMAT Problem Solving practice question tests basic concepts in solving algebraic expressions comprising absolute values and elementary concepts in number properties.

Question 12: If x and y are integers and |x - y| = 12, what is the minimum possible value of xy?

  1. -12
  2. -18
  3. -24
  4. -36
  5. -48

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Explanatory Answer | Algebra - Absolute Value

x and y are integers and |x - y| = 12

Approach: Square both sides and solve

Squaring both sides, we get (x - y)2 = 144
x2 + y2 - 2xy = 144
Add, 4xy to both sides of the equation.
x2 + y2 - 2xy + 4xy = 144 + 4xy
x2 + y2 + 2xy = 144 + 4xy
Or (x + y)2 = 144 + 4xy
(x + y)2 will NOT be negative for real values of x and y.
i.e., (x + y)2 ≥ 0
∴ 144 + 4xy ≥ 0
Or 4xy ≥ -144
So, xy ≥ -36

The least value that xy can take is -36.

Choice D is the correct answer.

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