Uri wrote:
My logic:
St 1: x=z-y
Since |x| is always positive, we can modify statement (1) as -x=y-z
Thus, |x|=y-z
St 2: insufficient.
Please check my logic for statement (1).[/color]

You arrived at -x = y - z. You have also noted |x| cannot be negative. This is correct.

However, the mistake you are making is that you are assuming y-z to be positive (or x to be negative). You don't know this, hence you can't conclude anything here. Either you have to know the sign of (y-z), or you have know the sign of x, both of which is not known from this statement.

if x>0, then |x| = z - y
if x<0, then |x| = y - z

Statement 2 gives you the sign of x, so together with statement 1, you can conclude that |x| = y - z. Sufficient.

Choose C.

-BM-

Uri wrote:Is |x|= y-z?
(1) x + y = z
(2) x < 0

OA: [spoiler](C)[/spoiler] Not sure whether the OA is correct.

My logic:
St 1: x=z-y
Since |x| is always positive, we can modify statement (1) as -x=y-z
Thus, |x|=y-z
St 2: insufficient.
Please check my logic for statement (1).

Hi Uri, I have seen over the past few days that Absolute value seems to be your bugbear.
Here's a great rule to remember....Absolute Value of anything is >OR = Zero.
Thats the same as saying " Abs. Value is Not NEGATIVE"....but my restatement really helps in solving DS.

Let's restate the question now as:

Is y - z => Zero ?

Attack Statement II first, since it's easier to process:
X is NEGATIVE ........we cannot answer the question with this information

Eliminate B and D

Statement I
Rearrange to make it look like the question:

y - z = -x

Again we dont know what X is in this statement....eliminate A

Combining statements we get, y - z = - ( x)
Or ....................................... y - z = - ( Negative number)
Or ....................................... y - z = A POSITIVE NUMBER ALWAYS

ALWAYS is key, because this answers our DS question as "Always YES".
Therefore Sufficiency is obtained.

C is the correct answer.