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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, 23:26
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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, 13:04, 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, 02:49
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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: Abs equation from GMATPrep [#permalink]

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05 Oct 2009, 05:31
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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: Abs equation from GMATPrep [#permalink]

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05 Oct 2009, 05:58
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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, 15:04
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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, 14:15
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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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Is IxI = y –z? [#permalink]

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05 Jun 2011, 05:20
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Re: Is IxI = y –z? [#permalink]

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05 Jun 2011, 05:37
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(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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06 Jun 2011, 00:31
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, 00:01
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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: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]

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24 Apr 2012, 12:11
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: Is |X|= Y- Z? [#permalink]

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28 Jul 2012, 13:50
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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 2012, 05:44
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, 06:12
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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25 Nov 2012, 18:17
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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, 10:41
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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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Re: Abs equation from GMATPrep [#permalink]

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02 Oct 2013, 02:28
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, 11:04
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 ?

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

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12 Aug 2015, 11:32
RPgolucky wrote:
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 ?

Be careful with squaring variables in PS or DS.

$$x^2 = (y-z)^2$$ , yes but this does not mean that x=y-z .

Example, x = 5, y = -2, z = -7, in this case $$x^2 = (y-z)^2$$ ---> x = y-z but if

x = - 5, y = -2, z = -7, in this case $$x^2 = (y-z)^2$$ ---> x = z-y

You are correct in saying that $$\sqrt{x^2}$$= |x| , thus $$\sqrt{(y-z)^2}$$ = |y-z|

In other words, |x| = |y-z| and this will have the following cases that will give you either a "yes" or a "no".

|x| = |y-z| ---> $$\pm$$ x = $$\pm$$ (y-z) and you will have the following cases:

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

Thus this statement is not sufficient.
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Is |x| = y - z ? (1) x + y = z (2) x < 0   [#permalink] 12 Aug 2015, 11:32

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