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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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Is |x| = y - z ?

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

Originally posted by DenisSh on 04 Oct 2009, 22:26.
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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Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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New post 05 Oct 2009, 04:31
25
17
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.

Answer: C.
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Re: Abs equation from GMATPrep  [#permalink]

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New post 05 Oct 2009, 01:49
1
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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New post 05 Oct 2009, 04:58
2
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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New post 17 Oct 2009, 14:04
1
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.



Oh...My bad...got that now :D
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Re: Inequality Problem  [#permalink]

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New post 01 Aug 2010, 13:15
2
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).

hence the answer is C.
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Is IxI = y –z?  [#permalink]

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Re: Is IxI = y –z?  [#permalink]

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New post 05 Jun 2011, 04:37
1
(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.

Answer - C
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Re: Is IxI = y –z?  [#permalink]

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New post 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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New post 23 Apr 2012, 23:01
1
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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New post 24 Apr 2012, 11:11
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Re: Is |X|= Y- Z?  [#permalink]

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New post 28 Jul 2012, 12:50
3
1
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.

Answer: C
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Re: Abs equation from GMATPrep  [#permalink]

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New post 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.
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.

Answer: C.



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.

Waiting for reply.
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Re: Abs equation from GMATPrep  [#permalink]

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New post 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.
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.

Answer: C.



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.

Waiting for reply.


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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New post 25 Nov 2012, 17:17
1
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.
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.

Answer: C.
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Re: Abs equation from GMATPrep  [#permalink]

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New post 01 Oct 2013, 09:41
1
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.
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.

Answer: C.


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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New post 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.
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.

Answer: C.


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

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New post 12 Aug 2015, 10:32
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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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0  [#permalink]

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New post 13 Dec 2015, 10:39
DenisSh wrote:
Is |x| = y - z ?

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


Question: x=y-z (when x is +ve) or x=z-y (when x is -ve)
(1) x=z-y, we don't know the sign of x
(2) clearly not sufficient
(1) + (2) from (2) we know that x<0 --> in this case |x| = y - z is equal to x=z-y and (1) gives us this expression
Answer C
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 &nbs [#permalink] 13 Dec 2015, 10:39

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