mod X question from GMAT prep

[mohit.kant]

Is mod x = y - z

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


My approach

from the question step if x < 0 , mod x = x = z - y
if x >0 , mod x= x = y - z

1) x = z - y, which implies x < 0, and thus mod x is not equal to y-z - Suff

2) x<0, mod x = z-y Suff

OA is C, I know i am committing an error in assuming that x+y=z implies x <0 , I would appreciate if someone can throw some light on the theory and provide a "Takeaway" for this question.

[mohit.kant]

Ok thought about this..

From equation 1

X + Y = Z
X = Z - Y
taking mod on both sides

mod x = mod z - y

if x > 0, x = z -y

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

Two options so we can't decide, insuff.

2) says x<0. Which is exactly what we need so the correct answer should be C.

Is my approach to this question correct?

[gokul_nair1984]

One simpler approach:

Stem: Is |x| = y - z?
This means whether y-z is a positive number

1) x + y = z

This implies y-z=-x(Thus y-z will be positive only if if x is negative else y-z will be negative)...Not Sufficient

2) x < 0
This does not tell us anything about y or z. Thus insufficient again.

Combining the 2 statements,
y-z=-x
x<0

This implies that y-z has to be positive. Thus (C) is the answer

[gokul_nair1984]

X + Y = Z
X = Z - Y
taking mod on both sides

mod x = mod z - y

This is wrong... You cannot take modulus on both sides in such a manner

[mohit.kant]

I think we can !

[gokul_nair1984]

I think we can !

X + Y = Z
X = Z - Y
taking mod on both sides

mod x = mod z - y

Hi Mohit---So what you are trying to say is that both the equations mentioned underneath are the same:

y=z-x----(1)
y=|z|-|x|----(2)...

Do you think they are the same; if they are then both equations must satisfy common values for z and x. Let's check:

Let z=-1 and x=-2. this implies |z|=1 and |x|=2

Substituting these in (1), we get,
y=-1+2=1 =>y=1----(3)

Substituting the modulus values in (2),
y=1-2=-1 => y=-1---(4)

Are (3) and (4) the same? Surely not!!!

[RonPurewal]

X = Z - Y
taking mod on both sides

mod x = mod z - y

if x > 0, x = z -y

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

Two options so we can't decide, insuff.

whoa, whoa there.

it's true that you can take an absolute value of both sides (since you can always do any operation to both sides of an equation, if that operation is defined for those expressions). however, note that there is a loss of information if that operation is absolute value.
for instance,
IF i tell you that x = y, then, yes, you can take the absolute value of both sides, giving |x| = |y|, which is also a true statement. however, note that this new statement is LESS descriptive than the original statement; |x| = |y| would allow x and y to be either the same or opposite, but we can't forget our original information that they are the same.

here's an even simpler example:
if i tell you that x = 3, then, well, x = 3, and only 3.
if you square both sides, you get x^2 = 9, which is certainly a true statement.
however, you obviously can't "solve" this to get "x = 3 or -3", since we already know that x is only 3.

similarly, in your example above, you KNOW that x = z - y.
therefore, if you do a bunch of mathematical magic and somehow arrive at "either x = z - y or x = something else", then you can just ignore the "something else".