Data Sufficiency

never make the cardinal mistake of removing a variable from both sides of an inequality without knowing the sign. If y is negative than the sign will change. The only safe operation in inequality without knowing sign is add and subtract.

Anyways,

1. Clearly not enough as we don't know value of X
2. Not enough as we don't know Y

Both

still not enough as depending on the value of x eqn can be positive or negative

9*y-4*x^2*y > 0?
1. y>0
2. x> -3/2

First rewrigt the question.

9y-4x^2y>0 => y * (9-4x^2)>0

Now product of 2 factor is more than 0 is only possible if both are +ve or both are -Ve. it measn...

1) either y>0 and 9-4x^2>0=> 9/4>x^2
2) or y<0 and 9/4<x^2.


now check the answers..
1. y>0 but it cant say anything about x^ - NOT SUFF
2. x>-3/2 means x^2> 9/4 but it cant say ant thisng about y NOT SUFF
3. taking togather means 9/4<x^2 and y>0, so this is also not SUFF.

Answer is E.

9y-4(x^2)y >0

y(9-4x^2) >0

we have 2 possibilities:

y is positive and (9-4x^2) is positive
y is negative and (9-4x^2) is negative

now looking at the options
1) says y is positive

so (9-4x^2) > 0
9 > 4x^2
9/4 > x^2

so x lies between -3/2 and 3/2
ie

-3/2 < x < 3/2 --- (1)

if the above condition is satisfied 9y-4(x^2)y >0 is true
but we have no idea about x
so Insuff

2) says x> -3/2
but (1) requires that x is less than 3/2 too.
if x is greater than 3/2 the eqn will not be true
where as if x is greater than -3/2 and less than 3/2 the eqn will be true
so Insuff

so E