Hi,
From(1): x-y>-2
if x = 2, y=1 then xy=2 >0
if x = 2, y=0 then xy=0
Not sufficient
From(2): x-2y < -6
if x=2, y=5, xy =10>0
if x=-2, y=5, xy=-10<0
Not sufficient
Both(1)&(2):
x-y > -2 and 2y-x > 6
So, adding we get y>4
x>y-2
As y>4, y-2>2
So, x>y-2>2
i.e.x>2 and y>4
Product of xy is always positive
Sufficient

Hence, C

thanks Frank... this helps a lot

+1 for C.
x>2 and y>4 .
the above poster seals it .!

a x> y+2 where x =3,1 for y=1,-10. not sufficient.

b y> (x+6)/2 hence x and y can have positive and negative values. not sufficient.


a+b y>4 hence in x-y>-2 means for y=5, x= 3. thus x,y both >0/

sufficient. C it is.