absolute value confusion

[gmatmillenium]

Source - GMATPrep

Q. Is Absolute value x = y - z?

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

My doubt:

1 can be rearranged to read : x= -(y-z) and hence abs val x = y-z.....sufficient

answer however is C....why is 1 insufficient and why do we need 2 to answer this?

[jube]

Question is Is |x| = y-z?

St. 1: x+y = z implies x = z-y

Let's say z=0, and y=1, then x=-1 & |x|=1 i.e. |x|=y-z
However, if z=5 and y=2, then x=3 & |x| =3 which is not equal to y-z i.e. -3

-insuff ( I think in this one the key is considering z as 0 & taking a +ve value for y which shows that |x| can be equal to y-z)

St. 2: x<0 doesn't tell us anything - insuff.

Now, if we take 1 & 2 together:
x=z-y & x<0 implies |x| = y-z for all values of y & z, hence sufficient

Answer: C

[gmatmillenium]

Thanks makes sense...

Question is Is |x| = y-z?

St. 1: x+y = z implies x = z-y

Let's say z=0, and y=1, then x=-1 & |x|=1 i.e. |x|=y-z
However, if z=5 and y=2, then x=3 & |x| =3 which is not equal to y-z i.e. -3

-insuff ( I think in this one the key is considering z as 0 & taking a +ve value for y which shows that |x| can be equal to y-z)

St. 2: x<0 doesn't tell us anything - insuff.

Now, if we take 1 & 2 together:
x=z-y & x<0 implies |x| = y-z for all values of y & z, hence sufficient

Answer: C