Is |x| = y - z ? (1) x + y = z (2) x < 0 : GMAT Data Sufficiency (DS)
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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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04 Oct 2009, 22:26
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Is |x| = y - z ?

(1) x + y = z
(2) x < 0
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Feb 2012, 12:04, edited 2 times in total.
Edited the question and added the OA
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Re: Abs equation from GMATPrep [#permalink]

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05 Oct 2009, 04:31
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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.

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

(1)+(2) Sufficient.

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Re: Is |X|= Y- Z? [#permalink]

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28 Jul 2012, 12:50
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sayak636 wrote:
Is |X|= Y- Z?

1. X+Y= Z
2. X< 0

(1) Can be rewritten as X = -Y + Z, so |X| = |-Y + Z|, which would be equal to Y - Z, if and only if $$-Y+Z\leq0$$. Obviously, we don't know that, so (1) insufficient.
(2) Cannot be sufficient, it doesn't say anything about Y and Z.
(1) and (2) together: X = -Y + Z < 0, therefore |X| = Y - Z, sufficient.

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Re: Abs equation from GMATPrep [#permalink]

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05 Oct 2009, 04:58
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Bunuel wrote:
y-z=|x|? --> y-z must be >=0...

Brilliant, thank you! :^)
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Re: Abs equation from GMATPrep [#permalink]

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17 Oct 2009, 14:04
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pm4553 wrote:
eresh wrote:
From 1, we get x= z-y => -x= y-z

Thus, |x| = y-z

Statement 2 does not give us anything more.

So, A.

For Abs Q's, you'll always have 2 solutions; A is insuff.

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01 Aug 2010, 13:15
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is |x|=y-z?

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

solving (1) first:

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

take x=1, z=2, y=1
1=1-2 (no)
take x=-1, z=2, y=3
|x|=y-z?
|-1|=3-2=1 YES

so what solving for |x|=-x meant was that x MUST be negative for the equation to be true, if it is positive then it is not true (since in that case, |x| would not equal -x).

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

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23 Apr 2012, 23:01
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Hey Bunuel I am not very sure of what the question is asking ...
Can you please explain the question....
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Re: Abs equation from GMATPrep [#permalink]

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25 Nov 2012, 17:17
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The question poses as x being the centerpiece variable but Bunuel turns it on its face and makes y-z the main subject. Which makes all the difference with data pt 1 when u look at it as y-z=-x. You immediately see that the right side has to be -ve for the LEft side to be +ve.
Brilliant approach.

Bunuel wrote:
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.

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

(1)+(2) Sufficient.

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Re: Abs equation from GMATPrep [#permalink]

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01 Oct 2013, 09:41
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Bunuel wrote:
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.

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

(1)+(2) Sufficient.

Bunuel, I was wondering if we can square the sides and then evaluate:

Is $$|x|=y-z$$
Is $$x^2= (y-z)^2$$

Statement 1:
$$x+y = z$$
$$x = z-y$$
squaring both sides...
$$x^2 = (z-y)^2 = (y-z)^2$$

Statement 1 alone seems to satisfy. Can you please point out my mistake?
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Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]

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20 Oct 2016, 10:29
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yashrakhiani wrote:
IS |x| = y -z??

1)x+ y = z

2)x<0

From the question,
if x>0, x = y-z
if x<0, x = -(y-z) = z-y

(2): Insufficient
x<0 doesn't give us any information about y and z. Eliminate B and D

(1): Insufficient
Statement 1 says that x = z - y
If x<0 , then the answer is yes since |x| will be equal to y-z
if x>0, then the answer is no since |x| = z-y
We have a Yes and a No. Eliminate A.

(1) and (2) together: Sufficient
We have x<0 and x = z - y. hence, |x| = y-z

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Re: Abs equation from GMATPrep [#permalink]

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05 Oct 2009, 01:49
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From 1, we get x= z-y => -x= y-z

Thus, |x| = y-z

Statement 2 does not give us anything more.

So, A.
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Re: Is IxI = y –z? [#permalink]

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05 Jun 2011, 04:37
(1)

x = z - y

So |x| = -x = -(z - y) = y -z only if x is negative

Here we don't know that.

Insufficient

(2)

Insufficient, no information about y and z

(1) + (2)

x is negative, Sufficient.

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Re: Is IxI = y –z? [#permalink]

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05 Jun 2011, 23:31
another way of looking at this numerical can be,
|x| = positive meaning is y>z being asked here.

a x= z-y means x can be <0 ,= 0 or >0. Hence not sufficient.

b gives no idea of y>z or y<z.

a+b clearly indicated y<z. Hence sufficient.

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

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24 Apr 2012, 11:11
shikhar wrote:
Hey Bunuel I am not very sure of what the question is asking ...
Can you please explain the question....

Question asks whether $$y-z$$ equals to some non-negative number $$|x|$$.
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Re: Abs equation from GMATPrep [#permalink]

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05 Oct 2012, 04:44
Bunuel wrote:
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.

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

(1)+(2) Sufficient.

Hi bunuel,
I am not able to understand the solution for this problem. Can you kindly explain the highlighted areas.
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.

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Re: Abs equation from GMATPrep [#permalink]

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05 Oct 2012, 05:12
fameatop wrote:
Bunuel wrote:
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.

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

(1)+(2) Sufficient.

Hi bunuel,
I am not able to understand the solution for this problem. Can you kindly explain the highlighted areas.
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.

Look at $$|x|=y-z$$: the left hand side is absolute value (|x|), which cannot be negative, hence the right hand side (y-z) also cannot be negative. Therefore must be true that $$y-z\geq{0}$$.

Next, for (1) given that $$-x=y-z$$. Now, if $$x>0$$, or if $$x$$ is positive, then we'll have that $$-positive =y-z$$ --> $$negative=y-z$$. But as we concluded above $$y-z$$ cannot be negative, hence this scenario is not good.

Hope it's clear.
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Re: Abs equation from GMATPrep [#permalink]

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02 Oct 2013, 01:28
emailmkarthik wrote:
Bunuel wrote:
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.

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

(1)+(2) Sufficient.

Bunuel, I was wondering if we can square the sides and then evaluate:

Is $$|x|=y-z$$
Is $$x^2= (y-z)^2$$

Statement 1:
$$x+y = z$$
$$x = z-y$$
squaring both sides...
$$x^2 = (z-y)^2 = (y-z)^2$$

Statement 1 alone seems to satisfy. Can you please point out my mistake?

The question asks whether |x|=y-z. This cannot be translated to is x^2=(y-z)^2. Consider this $$|2|\neq{1-3}$$ but 2^2=(1-3)^2.
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]

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

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12 Aug 2015, 10:04
DenisSh wrote:
Is |x| = y - z ?

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

Question : is |x| = y-z.

Rephrasing it : is x^2 = (y-z)^2.

Because root(x^2) = |x|.

Option 1 : x+y = z.

i.e x = (z-y).
x^2 = (z-y)^2 = (y-z)^2 .

Hence isn't 1 sufficient ?
Re: Is |x| = y - z ? (1) x + y = z (2) x < 0   [#permalink] 12 Aug 2015, 10:04

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