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**Quote:**

If y <> = 0 Does x = 0

(1) x^2 y = x^3 y

(2) x^2 / y = x^3 y

Very clear explanation, Bunuel. Thanks!

Initially, I had answer A and realised my mistake after reading Bunuel's solution. My error came from the fact that I cross-multiplied and eliminated as below:

**Quote:**

From Statement 1

--> x^2y=x^3y --> y/y = x^3/x^2 --> x = 1

Sufficient

Given y does not equal to zero, does x=0?

Statement 1x^2y = x^3y --> x^3=x^2 -->

0 = x^2(x-1)So, x=0 or x=1

Insufficient.

Statement 2x^2/y = x^3y -->

0 = x^2(xy^2-1)So, x=0 or xy^2=1 (i.e. x is not zero)

Insufficient.

Statement 1 + 2x^2(x-1) = x^2(xy^2-1)

x-1 = xy^2-1

x(1-y^2) = 0

So, x = 0 or x does not equals to zero (when y^2=1)

Insufficient.

Answer: E

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