Where is this question from? It seems that the stems are contradicting each other which is not possible in a GMAT question. I agree with your analysis of the question, but it is not a possible question.

It's from GMAT Prep. What is contradictory in the question?

z>x and y>0 is not possible given the stem. z and x can't take on different values (positive in 1, negative in 2) within the same question. Are you sure you didn't write the question down wrong?

You're right - it's z <x! I will edit it. Thanks for noting this.

But the idea is the same. Is there any other more straightforward way to solve this.

check out Ian's post
https://www.beatthegmat.com/gmat-prep-ma ... t5848.html

With that correction yes there is a quick way to solve this. As you can see x and z must be negative and so if we rearrange the equation to get

|x-z| = |z| - |x|

so with both x and z negative we get a positve z minus x on both sides.

-x--z=|z|- |x|

Note that this invalidates your explanation as the answer is yes |x-z| + |x| = |z|, and also that even without the correction your explanation to statement 2 was incorrect.

Hope this helps. For more help on ABS look for posts by Ian Stewart, he does a great job explaining ABS using a number line approach. It is usually very helpful, especially when you have integers and variables mixed with ABS, but on a problem like this the key is to break it down to something simple that will make the question easy.

Hi,


I solved the question and found that 2 was sufficient.

We dont know the sign of y.
We know that -

i) y>0, z<0 and x<0; z<x
ii) y<0, z>0 and x>0;z>x


For (i) the ans is Yes
For (i) ans is No.

From stmt 1:
z<x is true only if y>0

Hence disregard (ii) and stmt 1 is Suff

Ans D