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Is |x | = y - z ?

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GMAT Hacker: Senior | Next Rank: 100 Posts; Posts: 48; Joined: Sun May 30, 2010 12:35 am; Thanked: 1 times

by GMAT Hacker » Mon Aug 16, 2010 10:29 pm

Is |x | = y - z ?

(1) x + y = z

(2) x < 0

I will post QA after some discussion.

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Source: Beat The GMAT — Data Sufficiency | Mon Aug 16, 2010 10:29 pm

uwhusky: Legendary Member; Posts: 1172; Joined: Wed Apr 28, 2010 6:20 pmFollowed by: 4 members; Thanked: 74 times

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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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

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

"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)

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ymach3: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Mon Jul 13, 2009 4:25 pm; Thanked: 1 times

by ymach3 » Fri Aug 20, 2010 4:33 am

one more for C

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gig92: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Fri Jul 23, 2010 2:22 amFollowed by: 1 member; Thanked: 2 times

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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wdgolden: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Tue Aug 17, 2010 10:55 am; Thanked: 2 times

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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missrochelle: Master | Next Rank: 500 Posts; Posts: 117; Joined: Wed Jun 09, 2010 7:02 am

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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skprocks: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sun Dec 27, 2009 8:50 am; Thanked: 3 times; GMAT Score:710

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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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

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.

Rahul Lakhani
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Gurome, Inc.
https://www.GuroMe.com
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