GMAT Practice Question: Absolute Value

This question tests basics of solving algebraic expressions involving absolute values and elementary number properties.

Question

  • PS
  • If x and y are integers and |x - y| = 12, what is the minimum possible value of xy? A. -12
    B. -18
    C. -24
    D. -36
    E. -48

 

  • Correct Answer
    Choice D. -36 is the minimum possible value of xy.

Explanatory Answer

Detailed Solution

Given Data

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.