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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] New post 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] New post 05 Oct 2009, 01:49
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] New post 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.
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] New post 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] New post 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.



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

hence the answer is C.
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink] New post 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: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink] New post 24 Apr 2012, 11:11
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Re: Is |X|= Y- Z? [#permalink] New post 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.

Answer: C
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Re: Abs equation from GMATPrep [#permalink] 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] New post 05 Oct 2012, 05:12
Expert's post
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] New post 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.
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] New post 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.
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] New post 02 Oct 2013, 01:28
Expert's post
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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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DS question [#permalink] New post 06 Mar 2014, 08:16
Hi everyone!
As I was reviewing my GMAT material I run into this question:

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

Can sb help me?
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Re: DS question [#permalink] New post 06 Mar 2014, 08:21
Expert's post
Malolo355 wrote:
Hi everyone!
As I was reviewing my GMAT material I run into this question:

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

Can sb help me?


Merging similar topics. Please refer to the discussion above.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 3 and 5. Thank you.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: DS question   [#permalink] 06 Mar 2014, 08:21
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