122 number comparison

ern5231 wrote:X,Y and Z are integers. X<YZ. Is XYZ<0?

(1) XY<0
(2) XZ<0

Statement 1: XY<0, means either X or Y is -ve. If Y is negative, X cannot be -ve as XY<0.
And for the given condition X<YZ, Z will also have to be -ve. Thus XYZ>0
But if X is -ve, Y will have to be +ve to satisfy XY<0. Now Z could be positive or negative and still satisfy X<YZ, e.g. X=-10, Y=2 and Z=-2 or 2. Thus this is not sufficient to tell whether XYZ is less than zero.

Similarly for second statement as well. It is insufficient.
Taking the two statements together, XZ<0 and XY<0, either Z and Y will both have to be -ve or X alone will have to be -ve.
If Y and Z are both -ve, XYZ>0 and if X is -ve, XYZ<0. So together also insufficient.
Thus E should be the answer.