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

##

*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

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

Choice D is the correct answer.