Is |x| = y - z ? (1) x + y = z (2) x < 0 : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 09:25

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 12 Mar 2009
Posts: 192
Followers: 4

Kudos [?]: 330 [2] , given: 60

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

### Show Tags

04 Oct 2009, 22:26
2
KUDOS
34
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

55% (01:55) correct 45% (00:56) wrong based on 1192 sessions

### HideShow timer Statistics

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
Manager
Joined: 05 Jul 2009
Posts: 182
Followers: 1

Kudos [?]: 47 [0], given: 5

Re: Abs equation from GMATPrep [#permalink]

### Show Tags

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

Thus, |x| = y-z

Statement 2 does not give us anything more.

So, A.
Math Expert
Joined: 02 Sep 2009
Posts: 36566
Followers: 7079

Kudos [?]: 93180 [15] , given: 10553

Re: Abs equation from GMATPrep [#permalink]

### Show Tags

05 Oct 2009, 04:31
15
KUDOS
Expert's post
10
This post was
BOOKMARKED
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.

_________________
Manager
Joined: 12 Mar 2009
Posts: 192
Followers: 4

Kudos [?]: 330 [1] , given: 60

Re: Abs equation from GMATPrep [#permalink]

### Show Tags

05 Oct 2009, 04:58
1
KUDOS
Bunuel wrote:
y-z=|x|? --> y-z must be >=0...

Brilliant, thank you! :^)
Manager
Joined: 05 Jul 2009
Posts: 182
Followers: 1

Kudos [?]: 47 [1] , given: 5

Re: Abs equation from GMATPrep [#permalink]

### Show Tags

17 Oct 2009, 14:04
1
KUDOS
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.

Intern
Joined: 25 Jul 2010
Posts: 3
Followers: 0

Kudos [?]: 1 [1] , given: 0

### Show Tags

01 Aug 2010, 13:15
1
KUDOS
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).

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 651
Followers: 42

Kudos [?]: 861 [0], given: 39

Is IxI = y –z? [#permalink]

### Show Tags

05 Jun 2011, 04:20
1
This post was
BOOKMARKED
Attachment:

ineq..jpg [ 16.52 KiB | Viewed 4207 times ]

_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

SVP
Joined: 16 Nov 2010
Posts: 1672
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 514 [0], given: 36

Re: Is IxI = y –z? [#permalink]

### Show Tags

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.

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1353
Followers: 17

Kudos [?]: 240 [0], given: 10

Re: Is IxI = y –z? [#permalink]

### Show Tags

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.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Manager
Joined: 14 Feb 2012
Posts: 223
Followers: 2

Kudos [?]: 215 [1] , given: 7

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

### Show Tags

23 Apr 2012, 23:01
1
KUDOS
Hey Bunuel I am not very sure of what the question is asking ...
Can you please explain the question....
_________________

The Best Way to Keep me ON is to give Me KUDOS !!!
If you Like My posts please Consider giving Kudos

Shikhar

Math Expert
Joined: 02 Sep 2009
Posts: 36566
Followers: 7079

Kudos [?]: 93180 [0], given: 10553

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

### Show Tags

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 $$|x|$$.
_________________
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 100

Kudos [?]: 889 [3] , given: 43

Re: Is |X|= Y- Z? [#permalink]

### Show Tags

28 Jul 2012, 12:50
3
KUDOS
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.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Director
Joined: 24 Aug 2009
Posts: 507
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 17

Kudos [?]: 674 [0], given: 276

Re: Abs equation from GMATPrep [#permalink]

### Show Tags

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.

_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Math Expert
Joined: 02 Sep 2009
Posts: 36566
Followers: 7079

Kudos [?]: 93180 [0], given: 10553

Re: Abs equation from GMATPrep [#permalink]

### Show Tags

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.
_________________
Intern
Joined: 07 May 2011
Posts: 42
GMAT 1: Q V
GMAT 2: Q V
Followers: 0

Kudos [?]: 18 [1] , given: 11

Re: Abs equation from GMATPrep [#permalink]

### Show Tags

25 Nov 2012, 17:17
1
KUDOS
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.

Manager
Joined: 31 Mar 2013
Posts: 72
Location: United States
Followers: 0

Kudos [?]: 26 [1] , given: 109

Re: Abs equation from GMATPrep [#permalink]

### Show Tags

01 Oct 2013, 09:41
1
KUDOS
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?
Math Expert
Joined: 02 Sep 2009
Posts: 36566
Followers: 7079

Kudos [?]: 93180 [0], given: 10553

Re: Abs equation from GMATPrep [#permalink]

### Show Tags

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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13454
Followers: 575

Kudos [?]: 163 [0], given: 0

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

### Show Tags

29 Apr 2015, 12:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 29 Jul 2015
Posts: 5
Location: Saudi Arabia
GMAT 1: 720 Q49 V39
GPA: 3.5
Followers: 0

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

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

### Show Tags

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 ?
Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2654
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 116

Kudos [?]: 1339 [0], given: 789

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

### Show Tags

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.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

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

Go to page    1   2    Next  [ 29 posts ]

Similar topics Replies Last post
Similar
Topics:
1 If x, y and z are Integers and -2< z <2, z is not equal to 0, Is (x+y) 2 18 Oct 2016, 07:04
3 Is x^2y^3w^4z^1 < 0 ? 6 20 Apr 2016, 00:09
5 Is yz = x? (1) y > x/z (2) z < 0 5 10 Apr 2015, 04:15
Is |x| = y - z ? 1) x + y = z 2) x < 0 5 30 Oct 2011, 10:34
6 x+y)/Z>0 is x<0? (1) x<y (2) z<0 4 14 Jun 2011, 06:43
Display posts from previous: Sort by