Bunuel wrote:

If xy = 3, what is the value of xy(x + y) ?

(1) x – y = 2

(2) x^2 + y^2 = 10

I took the conventional way.

We have x=3/y and we need the value of 3(x + y).

S1. x – y = 2

Substitute the equation \(x=3/y\) in the above equation to get \(y^2+2y-3=0\)

You will get y=1 and x=3 ; y=-3 and x=-1

Both the sets give you different value for 3(x+y)

Not sufficient

S2. \(x^2 + y^2 = 10\)

Again substitute \(x=3/y\) to obtain \(y^4 - 10y^2 + 9=0\)

The sets you obtain are:

x=3 and y=1

x=-3 and y=-1

x=1 and y=3

x=-1 and y=-3

The above values give you different answers for 3(x+y)

Not sufficient

S1 and S2 combined

Only value common to both condition is x=-1 and y=-3

This gives you -12 as the value of 3(x+y)

Sufficient

Answer : C

I know there has to be a faster way. Please suggest.