Is |x| = y - z?

[victorgsiu]

GMAT Prep CD. Looks deceivingly easy.

Is |x| = y - z?

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

OA: C

Here is my work:
|x| means EITHER:
a) if x is positive, x = y - z OR
b) if x is negative, x = -y + z

(1) x + y = z
x = -y + z
Does not match a)
Matches b), answers yes to question prompt. Looks good to me.

(2) x <0
Does not match a)
Matches b), answers yes to question prompt. Looks good to me.

IMO:D, which is wrong. Where is my error in judgment here? How should I recalibrate my thinking?

[nitin_prakash_khanna]

I got it wrong as well, i thought answer should be A, but C is correct and here is why i feel C is correct.

Q is |x| = y-z

St1: x+y =z
x= -y+z
x= - (y-z)

if x>0 , |x| = -(y-z) i.e no need to reverse the sign
if x<0 , |x| = y-x i.e reverse the sign

So Cant decided and hence INSUFFICIENT

St2 : x<0 , no relationship with y & z given and hence INSUFFICIENT.

Combining both
x<0 so |x| = y-z

So Ans C.

[Ben Ku]

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


Here is my work:
|x| means EITHER:
a) if x is positive, x = y - z OR
b) if x is negative, x = -y + z

Your rephrase here is great!

(1) x + y = z
x = -y + z
Does not match a)
Matches b), answers yes to question prompt. Looks good to me.

Here, your reasoning is wrong; it matches b ONLY if we know that x is negative. However, from statement (1) alone, we don't know if x is positive or negative. This is why (1) is insufficient.

(2) x <0
Does not match a)
Matches b), answers yes to question prompt. Looks good to me.

Well, it tells us that x is negative, but doesn't tell us anything about y or z. We don't know if x = z - y. So this is why (2) is insufficient.

Once we know statement (2) (that x is negative), then statement (1) is correct. Therefore the answer is (C).

[jamieykim]

Ben, how is it that my logic is flawed.

If statement 2 is telling you outright that x<0,

then using the information from the question, doesn't

x = z - y?

Thus, isn't Statement 2 sufficient?

[gokul_nair1984]

Ben, how is it that my logic is flawed.

If statement 2 is telling you outright that x<0,

then using the information from the question, doesn't

x = z - y?

Thus, isn't Statement 2 sufficient?

@jamieykim-----------What are the values of y and z. You are not given anything about y and z apart from the fact that x is negative?

Let's plug in some values and disprove (B):
Let x=-1
Therefore |x|=1.
Substituting, this back in the stem,we can rephrase the question as Is 1=y-z?( Assume y= 3; z=2; The answer is YES; substitute y=100; z=1; The answer is No).

Hence (B) is out!!!

Hope it's clear

[RonPurewal]

Ben, how is it that my logic is flawed.

If statement 2 is telling you outright that x<0,

then using the information from the question, doesn't

x = z - y?

Thus, isn't Statement 2 sufficient?

no. no way.

statement 2 is ONLY telling you that x < 0.
this is it. this is absolutely the only thing that this statement is telling you.

in other words, in this statement, y and z could be literally any two numbers in the world.

--

it looks like you may benefit from a fundamental review of the first principles of data sufficiency, since you made a very basic mistake -- you took the QUESTION, and manipulated it as though it were a GIVEN FACT.
in other words, you actually assumed that |x| is equal to (y - z) in your analysis above!
since that's the question, you should not be in the least surprised that your (faulty) analysis gave answer (d): you were actually assuming that the answer to the question is "yes" before you even started analyzing the question!