Well here is the ans:
1. xyz < 0 suggests only one of them is -ve.
2. xy <0 suggests x and y lies on two sides of the origin or zero.

So lets draw the number line, and add both the constraints.

|-----------X--------------------------0-----------Y---------------------------------|
Now Z has to be positive. So Z can lie between 0 and Y or beyond Y. But it cannot be beyond Y as XY will be less than XZ. Even if you revert the picture the logic remains the same. So C.

Well here is the ans:
1. xyz < 0 suggests only one of them is -ve.
2. xy <0 suggests x and y lies on two sides of the origin or zero.

So lets draw the number line, and add both the constraints.

|-----------X--------------------------0-----------Y---------------------------------|
Now Z has to be positive. So Z can lie between 0 and Y or beyond Y. But it cannot be beyond Y as XY will be less than XZ. Even if you revert the picture the logic remains the same.

Till this point I agree with devp but ---

The answer should be E. coz in the above figure I can interchange the positions of X and Y

I also think the answer is E.
jaganbravo, Can you confirm?

I feel the answer is B

Ans should be E

From B we know that either X or Y is negative
From A Given that X or Y is negative we know that Z is +ve

X | Y | Z
-------------
+ | - | + Z can be between X and Y or it can be on the right of X so not between X and Y

- | + | + Z can only be between X and Y

hence insufficient.