Equation

[JeetGulia]

If xy = - 6, what is the value of xy ( x + y )?

(1) x - y = 5
(2)XY^2 = 18

[DanaJ]

You already know that xy = -6, so in order for you to find the value of xy (x + y), you'd need x + y OR some other value regarding x and y.

1. You know that x - y = 5, so you could rewrite this as x = y + 5. Remember that you also already know that xy = -6, so you can replace x to get:

y (y + 5) = -6
y^2 + 5y = -6
y^2 + 5y + 6 = 0

You may notice that the above equation could be written as (y + 3)(y + 2) = 0. In order for the product to be 0, at least one of the parentheses must be equal to 0. This means you have two cases:

a. y = -2 ---> x = y + 5 = 3
b. y = -3 ---> x = y + 5 = 2

You have two different pairs for x and y, which means that xy (x + y) cannot have an unique value.

So 1 is insufficient.

2 is slightly ambiguous, but I'll assume it means that only y is raised to the power of two. So you know now that x*(y^2) = 18 and since you know that xy = -6, it's easy to determine y: it will be 18/(-6) = -3. x can also be easily determined from the fact that xy = -6 - x will be 2. Knowing unique values for x and y means you can find xy (x + y) easily.

So 2 is sufficient.

The answer is B.