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Is |x | = y - z ?

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Source: — Data Sufficiency |
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by uwhusky » Tue Aug 17, 2010 12:09 am
I want to lean toward E...

|x| = y - z could be either -x = y - z or x = y - z.

1) x + y = z confirms one of the two, but not both...insufficient.
2) x < 0 says pretty much the same thing as 1...insufficient.

I don't even know if I am on the right track.
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by kvcpk » Tue Aug 17, 2010 12:13 am
GMAT Hacker wrote:Is |x | = y - z ?

(1) x + y = z

(2) x < 0


I will post QA after some discussion.
(1) x + y = z
x= y-z
put y=2, z=1
x=2-1 = 1
now, |1|=2-1..TRUE
put y=1,z=2
x=1-2 = -1
now|-1| = 1 is not equal to 1-2..FALSE
INSUFF

(2) x < 0
no info about y,z..Hence INSUFF

combining:
x<0
means |x| = -x
so, -x= y-z??

x=y-z
x<0 -> y-z<0
hence y-z cannot equal z-y
-x = z-y is not equal to y-z.. always NO

SUFF

pick C
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by ymach3 » Fri Aug 20, 2010 4:33 am
one more for C
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by gig92 » Fri Aug 20, 2010 5:04 am
GMAT Hacker wrote:Is |x | = y - z ?

(1) x + y = z

(2) x < 0


I will post QA after some discussion.

|X| is always going to be +ve, so the question becomes is y-z > 0 ?

1) x = z - y, does not give any info abt y or z thus INSUFF

2) x < 0 but no idea about y OR z thus INSUFF

1) and 2) together give z - y = -ve thus y-z = +ve (chaging signs on both sides) thus we have an answer
thus

Ans:C
gig92
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by wdgolden » Fri Aug 20, 2010 7:09 am
Is |x | = y - z ?
(1) x + y = z
(2) x < 0

Absolute value creates two equations.

x = y-z (if x is positive)
x = z-y (if x is negative)

Statement (1) says
x + y = z or
x = z - y
so if x is negative the original statement is true, but we don't know if x is positive so insuff

Statement (2) gives us no information about y or z so insuff

Together
Statement (2) says x is negative which means we only need to find out if the "x is negative" equation (x = z-y) is correct. Statement (1) says that statement is correct so together they're sufficient.
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by missrochelle » Sun Aug 22, 2010 3:51 pm
This problem really confuses me....

I understand that the absolute value CREATES two equations, but I don't get what the DS question stem is asking us to do with that -- is it to confirm which one is true?

Yes |x| = y-z, if x is positive
or
No |x| does not equal y-z it actually equals z-y, if x is negative.

I'm just having trouble articulating what we are saying "yes/no" to on this D.S. question.
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by skprocks » Sun Aug 22, 2010 7:02 pm
GMAT Hacker wrote:Is |x | = y - z ?

(1) x + y = z

(2) x < 0
I will post QA after some discussion.
Basically we need to check if y-z > 0.From Stmt1: we do not have any info about the nature of x,y and Z.So, I is insufficient.
From Stmt 2: X is negative.This does not indicate anything about y and z.
Combining I and II , x=z-y and x<0 so, z-y < 0 i.e. y-z > 0 (multiplying both sides of inequality by -1)
Hence, IMO : C
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by Rahul@gurome » Sun Aug 22, 2010 7:24 pm
Solution:
l x l = x if x >= 0
= -x if x < 0.
So the question is asking that
is x = y - z if x > = 0?
Or is -x = y - z if x < 0?

First consider statement (1) alone.
It says x + y = z.
Or - x = y - z.
But we know nothing about x whether it is greater than or less than zero.
Or (1) alone is not sufficient.

Next consider just statement (2) alone.
x < 0.
But we know nothing about y and z.
So obviously statement (2) alone is not sufficient

Next combine both the statements and check.
On combining we have that - x = y - z and x < 0.
Since l x l = -x if x < 0.
We have l x l = y - z

So both statements together are sufficient.
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