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?

- -12
- -18
- -24
- -36
- -48

@ INR

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

Squaring both sides, we get (x - y)^{2} = 144

x^{2} + y^{2} - 2xy = 144

Add, 4xy to both sides of the equation.

x^{2} + y^{2} - 2xy + 4xy = 144 + 4xy

x^{2} + y^{2} + 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.

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