VJesus12 wrote:If $$x+y^2=(x+y^2)^2,$$ what is the value of y?

(1) x = y ^2
(2) xy ^2 = 0

The OA is C.

I don't understand why is not sufficient the statement (1). Experts, may you give me some help here, please? Thanks.

If $$x+y^2=(x+y^2)^2,$$

then x+y^2 = 1 or 0

Question : y = ?

Statement 1: x = y ^2
@x+y^2 = 1, y ^2 = 1/2 i.e. y = 1/√2
@x+y^2 = 0, y ^2 = 0 i.e. y = 0
NOT SUFFICIENT

Statement 2: x*y ^2 = 0
@x+y^2 = 1, y ^2 = 0 or y^2=1 i.e. y = 0 or 1
NOT SUFFICIENT

Combining the two statements
x = y ^2 and x*y ^2 =
i.e. x = y = 0
SUFFICIENT

Answer: Option C