1. is insufficient. Take some numeric examples to clear that out: \
x = 1 and y = -1. xy = -1 < 0 and x - y = 0 > -2
x = -2 and y = -1. xy = 2 > 0 and x - y = -1 > -2.

2. Again, it's the same case as above, so 2 is insufficient as well.

Now let's use the two inequalities.
x - y > -2. Subtract y from each side and you get that x - 2y > - 2 - y. But x - 2y < -6, so you get that -2 - y < x - 2y < -6. This means that - 2 - y < -6, or that - y < -4 or that y > 4.
Now, since x - y > - 2 and y > 4, this translates to x being greater than - 2 + 4 = 2. So in the end you get that y > 4 and x > 2, which means that xy > 0 (since both x and y are positive numbers).

Danaj rocks !!

Folks, this can be answered a bit faster.

We can straight away conclude that each statement alone is not sufficient to answer by just taking x = 0 and corresponding value for y in which case we get xy =0 and in all other cases xy may be greater or lesser than 0.

So each statement alone is not sufficient

Let's combine both the statements....

Let x-2y = k

So from statement 2 that k < -6
and from statement 1 k+y > -2

Now it is clear that y > 4 ( because by adding y to k, which is less than -6 now it has become greater than -2. Just imagine a number line and it would be more evident)

Since x-y > -2 i.e x > y-2 and y > 4, we get x > 2.

Thus xy>0.

Hence choice C

Folks, in fact you can combine both the statements in another quicker way as well.

Statement 1: x-y > -2

So x > y - 2

Statement 2: x-2y < -6

So x < 2y -6

Combining both we get y-2 < x < 2y -6

i.e y -2 < 2y -6

i.e -y < -4 . Hence y > 4 .

Since x> y-2 , we get x >2.

DanaJ good explanation!

Agree with SureshBala's approach!

x-y>-2 (I)
2x-3y<-6 or -6 > 2x-3y (II)

We can add inequalities facing same direction

So we get y>4 and x>2 so xy>0

Choose C