YAMT: Math madness!!

[luvya]

Is |x| = y - z?

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


A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient
B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient
C) Both statements together are sufficient, but neither statement alone is sufficient
D) Each statement alone is sufficient
E) Statements (1) and (2) together are not sufficient


I hate this kind of question, it always throws me off :| The answer is C though, but why?

 

[Legendary]

Edit: wait what I just said was wrong

Okay so if x < 0 and y - z = -x then y - z > 0 and y - z = |x|
So only if 1 and 2 are true is the original statement true.

 

[maziwanka]

if (1) is true only, then z>x, z>y, x or y can be pos/neg. x=z-y or -x=y-z. if x is neg then abs(x)=-x. if x is pos then this is not true (i.e. you need (1) and (2)).

 

[txxxx]

Statement 2 effectively states thats all values of x are positive, regardless. Or so I think, which is the only way it can work.

 

[dfi]

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

Three possible solutions, x < 0, and x >0, and x = 0. Ignoring x = 0...

If x > 0:

1*( |x| - y ) = 1*( -z )
x - y = - z

If x < 0:

-1*( |x| - y ) = -1*( -z )
x + y = z

dfi

 

[mobobuff]

You ruin the funness quality of math riddles when you throw in variables and absolute values and all that crap. Just give me +-/*!

 

[luvya]

Originally posted by: mobobuff
You ruin the funness quality of math riddles when you throw in variables and absolute values and all that crap. Just give me +-/*!

Hey, blame that to GMAT testmaker!

 

[DotheDamnTHing]

i detest math