1) y <0. Thus y can not be 0 and it will be a negative integer
Lets say x >0
Then x^2y+ 9 > 0
x^2y > -9
x^2 < -9/y
we know that y is negative ....the greatest value -9/y will have will be when y = -1
x^2 < -9/-1
x^2 < 9
-3 < x < 3 but x >0 so 0<x<3 is the greatest value of x
Now lets look at x <0
-x^2y+ 9 > 0
-x^2y > -9
x^2y < 9
x^2 < 9/y
Now this is not possible because y is negative so x can not be negative
Thus the only way this can be true is when 0<x<3 ...so x <6 ...Hence sufficient
2) |y| < 1
-1 < y < 1
We know that y is an integer. so the only possibility in this case is y = 0(Ok first of all this is not a GMAT question because GMAT questions choices never contradict each other whereas this does)
putting y =0
|x|×.0 + 9 > 0
This just cancels out the x's so wont help us in anyways ...Thus Insufficient
So IMO the answer should be A
