porvakanti wrote:

What is the value of x^2 – y^2?

(1) x + y = 66

(2) xy = 9

OA:E

What is the value of \(x^2 – y^2\) or \((x-y)(x+y)\)?

(1) \(x + y = 66\)

We are given the value of \(x + y\), and not given the value of \(x-y\)

So Statement 1 alone is not sufficient.

(2) \(xy = 9\)

The product of \(xy\) is given but we cannot find either individual value of \(x\) and \(y\) or value of expression of \(x^2 – y^2\) or \((x-y)(x+y)\)

So Statement 2 alone is not sufficient.

Combining 1 and 2, we get

\(x + y = 66\)

\((x-y)^2 =(x + y)^2-4xy\)

\((x-y)^2=(66)^2-4*9=(66)^2-(6)^2 =(66+6)(66-6)=72*60=2^1*3^1*5^1*12^2\)

\(x-y = ±12\sqrt{30}\)

So Expression \(x^2 – y^2\) can have 2 values : \(12*66*\sqrt{30}\) or \(-12*66*\sqrt{30}\)

Combining (1) and (2) will also not give unique value of expression \(x^2 – y^2\)