Intuitive approaches are welcome:

First analyzing the information provided:

If zy < xy < 0, there are two possibilities: y is positive, or y is negative:

Case 1: If y is negative, then (dividing by y in the inequality above, and reversing it), we find that 0 < x < z

Case 2: If y is positive, then (dividing by y in the inequality above), we find that z < x < 0

Now to understand the question. Recall that |x - z| is just the distance from x to z on the number line, and |x| is the distance from x to zero. So the question "Is |x - z| + |x| = |z|?" is really just asking "Is the distance from x to z, plus the distance from x to zero, equal to the distance from z to zero?"

Let's draw a number line for Case 1 above:

------0------x--------z------

Here, if you add the distance from z to x and the distance from x to zero, you clearly get the entire distance from z to zero.

And the number line for Case 2:

----z------x--------0-------

Again, if you add the distance from z to x, and the distance from x to zero, you clearly get the entire distance from z to zero.

So in each possible case above, the answer to the question is 'yes'. We don't even need the Statements.

I suppose that makes the answer D, but it's the only real GMAT question I've ever encountered where you don't need either statement to answer the question. It's odd, to be sure, and makes me wonder if there was an error in the question design.

Ian superb explanation

Kudos to you

Wow, Have never seen such great explaination to a problem this challenging. +5

Ian, thanks for the great explanation!

Needless to say, OA D.