If $x,y \in R$ and $xy^2$ then: If $x,y \in R$ and $x&lt;y\implies x^2&gt;y^2$ then:

a). $x&gt;0$

b). $x&lt;0$

c). $y&gt;0$

d). $y&lt;0$

My Attempt:

Here, $x&lt;y \implies x^2&gt;y^2$ but How?
As for example: Let $x=0.001$ and $y=0.1$.
So, 
$$0.001&lt;0.1$$
Squaring Both Sides, We get:
$$0.000001&lt;0.01$$
??
As you noticed, the implication is false when x is positive. So x must be negative and the answer is (b).
Only possibility of holding inequality is that y must be negative. I.e option (d) is correct.
We check this by an example
-2&lt;-1 imply 4>1 (square of both sides)