VJesus12 wrote:Is xy< 0 ? $$\left(1\right)\ xy^2 < y^2$$ $$\left(2\right)\ y^2 < y$$ The OA is the option E.

Could someone give me some help here? I think that the first statement is sufficient. <i class="em em-confused"></i>

We are given that xy < 0.

If xy < 0, one of x and y must be postive and the other must be negative.

Let's see each statenment one by one.

(1) xy^2 < y^2

Since y^2 is a positive quantity, we can cancel it.

=> x < 1

=> x can be positive (for example, x = 1/2), 0, or negative (for example, x = -1). We are sure about the nature of x as well as y. Insufficient.

(2) y^2 < y

Since y^2 is a positive quantity and y is greater than y^2, y must be a positive quantity. However, we do not know about x. Insufficient.

(1) and (2) together

Even after combining the statements, we cannot be sure wether xy < 0 as x can be positive or negative.

The correct answer: E

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New Haven | Doha | Stockholm | Pretoria | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.