gmat prep problem is |x| = y-z?

[i.ahmed111]

Is |x|= y-z?

1) x+y=z
2)x<0

So I know the answer to this question is C. I rephrased the statement as:
is y-x >0

1) we see that y-z =-x or -(y-z)=x. This of course doesn't tell us whether x is (-) or (+) so this is insufficient

2) gives us no information regarding y-z, so not helpful alone

Combined, we see that y-z is positive since -(y-z) is equal to x, which is (-)

My question: is this the correct way to solve this? Is there a more algebraic approach? I initially started by removing the abs value sign and treating x as either (neg) or (pos) but this complicated things....

Thanks!

[i.ahmed111]

sorry I just noticed a mistake in my post...the actual rephrasal is y-z >0

[esledge]

The only (minor) problem I have with rephrasing to "Is y-z > 0?" is that the absolute value of anything is positive. Your rephrase focuses only on sign, not on value.

The more accurate rephrase is "Is x = (y-z) or (z-y), and is y-z>0?" but I think you were doing so implicitly, based on what you wrote about (1). Your rephrase worked because (1) does relate x to y-z.

[imanemekouar]

I only rephrase the question as X=Y-z or X=Z-y but not Z-y should be >0.Also I did nt not understand Ahmed reasoning? Can somebody clarify the problem.
tks

[RonPurewal]

here is perhaps a faster way to approach statement (1):

if you move the "y" over to the other side, you get x = z - y.

therefore, in statement (1), the QUESTION becomes,
is |z - y| = y - z ?

if you are comfortable with the workings of absolute values, you will realize that this statement is only true when the quantity inside the absolute value bars -- i.e., (z - y) -- is 0 or negative. (if this makes no sense to you, then consult the sections in our EIV and/or number properties guides regarding absolute value.) therefore, for statement one, the question becomes:
is z - y < 0 ?

this question is unanswerable by statement (1) alone, but, the two statements together give a quick "yes".

[arturocb86]

here is perhaps a faster way to approach statement (1):

if you move the "y" over to the other side, you get x = z - y.

therefore, in statement (1), the QUESTION becomes,
is |z - y| = y - z ?

if you are comfortable with the workings of absolute values, you will realize that this statement is only true when the quantity inside the absolute value bars -- i.e., (z - y) -- is 0 or negative. (if this makes no sense to you, then consult the sections in our EIV and/or number properties guides regarding absolute value.) therefore, for statement one, the question becomes:
is z - y < 0 ?

this question is unanswerable by statement (1) alone, but, the two statements together give a quick "yes".

Ron,

First of all thank you because I am having a great experience with MGMAT as a whole!

I have a doubt in this problem:

|x| = y-z --> a. for x>0 x=y-z is it right?
--> b. for x<0 -x=y-z right?

then from (1) x+y=z --> -x=y-z since it matches b what do we conclude? that x<0?

[mschwrtz]

arturocb86, be careful. Remember that the statement you've labeled b is conditional. IF x< THEN -x=y-z (or IF x< THEN x=z-y). This does not necessarily mean that x=z-y, as your account would have it.