Data Sufficiency

Hi guys. Could you please explain how to solve ?

What is the value of xy ?

(1) (x + y)^2 = 37
(2) (x - y)^2 = 17

I can see that (1) and (2) alone are insufficient. If I solve (1) AND (2) I get following results (or numeric roots here):



Since it has more than one root I answered E.

Thanks!

IMO C.

Here is how I approached.

Stmts 1 and 2 independently are insufficient.

So could be C or E.
Lets look at them together.

expand both stmts.

x^2 +2xy +y^2 = 37 -------(1)
x^2 -2xy +y^2 = 17 ---------(2)

Multiply (2) by -1 and add to (1).
the square terms will cancel out giving us
4xy = 20
xy = 5.

So C.

Ht Helps

Well done Vittal!

(1) - (2) gives us the same

4xy = 20
xy=5

Thank you, vittalgmat! It's so simple!