GMAT Prep Math zy < xy < 0 |x-z| + |x| = |z|

manjithmanohar wrote: 1. z < x (if it is considered with the inequality both z and x are negative and that y is positive.) so proves |z| > |x|, hence true.
2. y < 0 (when fit into the inequality proves that again |z| > |x|) so true.

Ian Stewart wrote:I posted a solution to this to another forum, so I'll just paste that here:

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This is one of the strangest questions in GMATPrep, since you don't need either of the statements to answer the question. That's not supposed to happen on a GMAT DS question, which makes me wonder whether there was an error in the question design. In any case, we're given:

zy < xy < 0

Rewrite this as three inequalities:

(1) xy < 0
(2) zy < 0
(3) zy < xy

From (1), we have two possibilities:

(A) x is positive, and y is negative. Then, from (2), z is positive, and from (3), dividing by y and reversing the inequality because y is negative, we have x < z. So it may be that y < 0 < x < z .

(B) x is negative and y is positive. Then, from (2), z is negative, and from (3), dividing by y, we have z < x. So it may be that z < x < 0 < y .

Those are the only two possibilities here. Draw the number line in each case:

(A)

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

(B)

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


In either case, we can see that the distance from z to zero is equal to the sum of the distance from x to zero and the distance from x to z. That is, in either case, |z| = |x| + |x - z|. So we don't need any additional information to be sure that the answer to the question is yes - neither of the statements is required here.

I suppose that makes the answer 'D', though it's the only question I know of in any official GMAT material (and I've seen pretty much every question) where the statements aren't needed to answer the question given.