GMAT Challenging Question 12 | Algebra PS

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

Video Explanation

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.