wizard wrote:

What is the value of x ?

(1) (x^2) + (y^2) = 25

(2) xy = 12

Required: x =?

Statement 1: \(x^2 + y^2 = 25\)

We have one equation and two unknowns. Hence we cannot solve this equaiton.

INSUFFICIENTStatement 2: xy = 12

Again, we have one equation and two unknowns. Hence we cannot solve this equaiton.

INSUFFICIENTStatement 1 and Statement 2 combined:

\(x^2 + y^2 = 25\) and xy = 12

Whenever we have something of the form \(x^2 +/- y^2\) , try to make it into perfect squares.We know that \((x+y)^2 = x^2 + y^2 +2xy\)

So, we need the value of xy to make statement 1 a perfect square and we have the value of xy from statement 2.

Adding 2xy = 24 on both sides in statement 1, we have

\(x^2 + y^2 +2xy = 49\)

or \((x+y)^2 = 7^2\)

Still we cannot solve for the value of x

INSUFFICIENTOption E is the correct answer