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

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Is |x| = y - z ? 1) x + y = z 2) x < 0 [#permalink]

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30 Oct 2011, 10:34
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Difficulty:

45% (medium)

Question Stats:

64% (00:26) correct 36% (01:32) wrong based on 25 sessions

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Tried searching but couldnt find ...

Is |x| = y - z ?

1) x + y = z

2) x < 0

[Reveal] Spoiler: Please comment on my solution and say if its right or wrong
1) x = z-y

|x| = x or |x| = -x

Dont know if x is positive or negative .... Hence insufficient

2)X< 0

no info about x and y .... hence insufficient

taking 1 and 2 together

x< 0 thus |x| = -x

-x = -(z-y)

thus |x| = y-z

hence c ---- sufficient

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/is-x-y-z-1-x ... 84821.html
[Reveal] Spoiler: OA

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Re: Is |x| = y - z ? 1) x + y = z 2) x < 0 [#permalink]

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30 Oct 2011, 11:07
What is the source of the problem ?

imho OA should be C too. Here's my explanation :

Given,

Is |x| = y-z ?

Rephrase the Question :

x = y-z or -x = y-z ( => x = z-y ),

so the question could be re-phrased as : x = y-z or z-y . Is this True ?

Statement 1 :
x+y = z or
x = z-y => This statement says that x is only equal to z-y but not y-z , Hence insufficient

Statement 2 :
x < 0 => |x| = -x ( as per definition of absolute value ). It does not give info about y or z . Hence insufficient.

Taken Together :

From statement 1 , x = z - y
From statement 2, x < 0 => |x| = -x. But from above we have -x = - (z-y) = (y-z). Hence x can be both z-y or y-z. Sufficient

Hence Ans is C !
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Last edited by hoogly on 30 Oct 2011, 11:17, edited 2 times in total.

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Senior Manager
Joined: 29 Jan 2011
Posts: 336

Kudos [?]: 248 [0], given: 87

Re: Is |x| = y - z ? 1) x + y = z 2) x < 0 [#permalink]

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30 Oct 2011, 11:12
hoogly wrote:
What is the source of the problem ?

imho OA should be E. Here's my explanation :

Given,

Is |x| = y-z ?

Rephrase the Question :

x = y-z or -x = y-z ( => x = z-y ),

so the question could be re-phrased as : x = y-z or z-y . Is this True ?

Statement 1 :
x+y = z or
x = z-y => This statement says that x is only equal to z-y but not y-z , Hence insufficient

Statement 2 :
x < 0 => |x| = -x ( as per definition of absolute value ). This statement says, -x = y-z or x = z-y . Hence insufficient.

Taken Together :

X < 0 and |x| = -x. Both mean the same and imply -x = y-z or x = z-y . Hence insufficient.

Hence Ans is E !

Infact if statement 2 is x > 0 , Then C could be the answer.

First of all statement 2 doesnt tell us anything about y and z's relationship... I think you brought the equation from statement 1 ... when thinking about statement 2 you should leave statement 1 behind...

Now, getting back to your solution

1 gives x = z- y

2 gives x< 0 thus |x| = - x

1 and 2 combined

from 1 we know x = z-y

substitute this in 2 , we get

-x = -(z-y)

but -x = |x|

thus |x| = y-z or |x| = z-y (from 1)

hence c

Kudos [?]: 248 [0], given: 87

Manager
Status: Head Turner ! am I ?
Affiliations: RHCE , CCNA, MCSE and Now GMAT ;)
Joined: 29 Jul 2011
Posts: 138

Kudos [?]: 205 [0], given: 28

Location: India
WE: Operations (Computer Hardware)
Re: Is |x| = y - z ? 1) x + y = z 2) x < 0 [#permalink]

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30 Oct 2011, 11:15
Siddhans,
Even before you posted , I changed my thinking and edited my posted. Thanks. Yes i go with C.
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Re: Is |x| = y - z ? 1) x + y = z 2) x < 0 [#permalink]

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15 Nov 2011, 14:20
I agree with option C.

Stmt 1: x+y=z ---> x=z-y

not enough info, insuff

stmt 2: x<0 ---> x is negative but does not say anything about z or y.

stmt 1 and stmt 2: -x+y=z ---> -x=-y+z ---> x=y-z. and since it is an absolute value we know x is postive in the question.

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Re: Is |x| = y - z ? 1) x + y = z 2) x < 0 [#permalink]

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15 Nov 2011, 21:07
siddhans wrote:
Tried searching but couldnt find ...

Is |x| = y - z ?

1) x + y = z

2) x < 0

[Reveal] Spoiler: Please comment on my solution and say if its right or wrong
1) x = z-y

|x| = x or |x| = -x

Dont know if x is positive or negative .... Hence insufficient

2)X< 0

no info about x and y .... hence insufficient

taking 1 and 2 together

x< 0 thus |x| = -x

-x = -(z-y)

thus |x| = y-z

hence c ---- sufficient

Yes, your method is absolutely fine. I would do it in the same way too.
Stmnt 1: x + y = z
Rewrite: -x = y - z

Question: Is |x| = y-z?
So from statement 1, my question is: Is |x| = -x?
It is if x is negative. Stmnt 2 tells me that it is. Hence answer (C)
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Re: Is |x| = y - z ? 1) x + y = z 2) x < 0 [#permalink]

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23 Nov 2017, 06:30
siddhans wrote:
Tried searching but couldnt find ...

Is |x| = y - z ?

1) x + y = z

2) x < 0

[Reveal] Spoiler: Please comment on my solution and say if its right or wrong
1) x = z-y

|x| = x or |x| = -x

Dont know if x is positive or negative .... Hence insufficient

2)X< 0

no info about x and y .... hence insufficient

taking 1 and 2 together

x< 0 thus |x| = -x

-x = -(z-y)

thus |x| = y-z

hence c ---- sufficient

Is $$|x|=y-z$$?

Note that $$y-z$$ must be $$\geq{0}$$, because absolute value (in our case $$|x|$$) can not be negative.

Generally question asks whether $$y-z\geq{0}$$ and whether the difference between them equals to $$|x|$$.

(1) $$-x=y-z$$
if $$x>0$$ --> $$y-z$$ is negative --> no good for us;
if $$x\leq{0}$$ --> $$y-z$$ is positive --> good.
Two possible answers not sufficient;

(2) $$x<0$$
Not sufficient (we need to know value of y-z is equal or not to |x|)

(1)+(2) Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/is-x-y-z-1-x ... 84821.html
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Re: Is |x| = y - z ? 1) x + y = z 2) x < 0   [#permalink] 23 Nov 2017, 06:30
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