Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 19:59 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # M23-17

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56277

### Show Tags 00:00

Difficulty:   35% (medium)

Question Stats: 65% (01:09) correct 35% (01:06) wrong based on 190 sessions

### HideShow timer Statistics If $$x$$, $$y$$, and $$z$$ are negative numbers, is $$x \lt y \lt z$$?

(1) $$x+z=2y$$.

(2) $$xz = yz$$.

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56277

### Show Tags

Official Solution:

(1) $$x+z=2y$$. If $$x=y=z=-1$$, then the answer is NO but if $$x=-3$$, $$y=-2$$ and $$z=-1$$, then the answer is YES. Not sufficient.

(2) $$xz = yz$$. Since $$z \ne 0$$, then we can reduce given equation by $$z$$ and we'll get $$x=y$$, so $$x \lt y \lt z$$ is not true. Sufficient.

_________________
Intern  Joined: 06 May 2016
Posts: 14

### Show Tags

Hi Bunuel,

x+z= 2y

or y = (x+z)/2
or we can say y is average of x and z. So y should be between x and z.

Am I missing anything here?

Kris
Math Expert V
Joined: 02 Sep 2009
Posts: 56277

### Show Tags

gmatravi wrote:
Hi Bunuel,

x+z= 2y

or y = (x+z)/2
or we can say y is average of x and z. So y should be between x and z.

Am I missing anything here?

Kris

The solution above gives an example which shows that this is not necessarily true: x = y = z = -1.
_________________
Intern  B
Joined: 28 May 2014
Posts: 30
Schools: ISB '17, NUS '17

### Show Tags

How all x, y and z numbers can have same value??? they are different negative numbers, right?
Math Expert V
Joined: 02 Sep 2009
Posts: 56277

### Show Tags

akashbolster wrote:
How all x, y and z numbers can have same value??? they are different negative numbers, right?

Unless it is explicitly stated otherwise, different variables CAN represent the same number.
_________________
Intern  B
Joined: 21 Jun 2016
Posts: 6

### Show Tags

1
If x, y, and z are negative numbers, is x<y<z?

(1) x+z=2y
from this equation we can say that y is the mean of x & z .
so there are two possibilities
x<y<z or z<y<x
statement 1 : insufficient . Option A and Option D gone
(2) xz=yz
from this statement we can find z=0 or x=y
Z=0 cant be as we have been told z is a negative intezer
so x=y must be valid . question whether x<y<z fails . Statement 2 is sufficient . Re: M23-17   [#permalink] 08 Mar 2018, 06:38
Display posts from previous: Sort by

# M23-17

Moderators: chetan2u, Bunuel  