Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 29 May 2015, 01:14

### 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

# If x and y are integers such that x<0<y, and z is non

Author Message
TAGS:
Director
Joined: 03 Sep 2006
Posts: 884
Followers: 6

Kudos [?]: 271 [1] , given: 33

If x and y are integers such that x<0<y, and z is non [#permalink]  24 Jan 2012, 08:49
1
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

66% (01:50) correct 34% (00:57) wrong based on 182 sessions
If x and y are integers such that x<0<y, and z is non negative integer then which of the following must be true?

A. $$x^2<y^2$$

B. $$x+y=0$$

C. $$xz<yz$$

D. $$xz=yz$$

E. $$\frac{x}{y}<z$$
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 27526
Followers: 4327

Kudos [?]: 42561 [0], given: 6038

Re: PS-which of the following must be true [#permalink]  24 Jan 2012, 08:59
Expert's post
LM wrote:
If x and y are integers such that $$x<0<y$$,and z is non negative integer then which of the following must be true?

A) $$x^2<y^2$$

B) $$x+y=0$$

C) $$xz<yz$$

D)$$xz=yz$$

E) $$\frac{x}{y}<z$$

Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

Given: $$x<0<y$$ and $${0}\leq{z}$$.

Evaluate each option:

A. $$x^2<y^2$$ --> not necessarily true, for example: $$x=-2$$ and $$y=1$$;

B. $$x+y=0$$ --> not necessarily true, for example: $$x=-2$$ and $$y=1$$;

C. $$xz<yz$$ --> not necessarily true, if $$z=0$$ then $$xz=yz=0$$;

D. $$xz=yz$$ --> not necessarily true, it's true only for $$z=0$$;

E. $$\frac{x}{y}<z$$ --> as $$x<0<y$$ then $$\frac{x}{y}=\frac{negative}{positive}=negative<0$$ and as $${0}\leq{z}$$ then $$\frac{x}{y}<0\leq{z}$$ --> always true.

_________________
Manager
Joined: 17 Oct 2010
Posts: 80
Followers: 1

Kudos [?]: 93 [0], given: 26

Re: PS-which of the following must be true [#permalink]  22 May 2012, 00:19
Bunuel wrote:
LM wrote:
If x and y are integers such that $$x<0<y$$,and z is non negative integer then which of the following must be true?

A) $$x^2<y^2$$

B) $$x+y=0$$

C) $$xz<yz$$

D)$$xz=yz$$

E) $$\frac{x}{y}<z$$

Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

Given: $$x<0<y$$ and $${0}\leq{z}$$.

Evaluate each option:
A) $$x^2<y^2$$ --> not necessarily true, for example: $$x=-2$$ and $$y=1$$;

B) $$x+y=0$$ --> not necessarily true, for example: $$x=-2$$ and $$y=1$$;

C) $$xz<yz$$ --> not necessarily true, if $$z=0$$ then $$xy=yz=0$$;

D)$$xz=yz$$ --> not necessarily true, it's true only for $$z=0$$;

E) $$\frac{x}{y}<z$$ --> as $$x<0<y$$ then $$\frac{x}{y}=\frac{negative}{positive}=negative<0$$ and as $${0}\leq{z}$$ then $$\frac{x}{y}<0\leq{z}$$ --> always true.

amazing ! couldn't figure out how option 3 was not necessarily true , forgot that non negative could mean that 0 is possible ,folks : non negative does not mean only positive integers , it could be 0 as well

Hypothetically speaking, Bunuel so if a question says, non positive numbers can we consider 0 as well , rather than only negative numbers.

Set of Non positive numbers { 0,-1,-5,-9 }
Set of Non negative numbers { 0,1, 4, 7, }

is this correct?
Math Expert
Joined: 02 Sep 2009
Posts: 27526
Followers: 4327

Kudos [?]: 42561 [0], given: 6038

Re: PS-which of the following must be true [#permalink]  22 May 2012, 00:23
Expert's post
Joy111 wrote:
Bunuel wrote:
LM wrote:
If x and y are integers such that $$x<0<y$$,and z is non negative integer then which of the following must be true?

A) $$x^2<y^2$$

B) $$x+y=0$$

C) $$xz<yz$$

D)$$xz=yz$$

E) $$\frac{x}{y}<z$$

Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

Given: $$x<0<y$$ and $${0}\leq{z}$$.

Evaluate each option:
A) $$x^2<y^2$$ --> not necessarily true, for example: $$x=-2$$ and $$y=1$$;

B) $$x+y=0$$ --> not necessarily true, for example: $$x=-2$$ and $$y=1$$;

C) $$xz<yz$$ --> not necessarily true, if $$z=0$$ then $$xy=yz=0$$;

D)$$xz=yz$$ --> not necessarily true, it's true only for $$z=0$$;

E) $$\frac{x}{y}<z$$ --> as $$x<0<y$$ then $$\frac{x}{y}=\frac{negative}{positive}=negative<0$$ and as $${0}\leq{z}$$ then $$\frac{x}{y}<0\leq{z}$$ --> always true.

amazing ! couldn't figure out how option 3 was not necessarily true , forgot that non negative could mean that 0 is possible ,folks : non negative does not mean only positive integers , it could be 0 as well

Hypothetically speaking, Bunuel so if a question says, non positive numbers can we consider 0 as well , rather than only negative numbers.

Set of Non positive numbers { 0,-1,-5,-9 }
Set of Non negative numbers { 0,1, 4, 7, }

is this correct?

Yes, a set of non-positive numbers consists of zero and negative numbers.
_________________
Intern
Joined: 30 Mar 2012
Posts: 36
Followers: 0

Kudos [?]: 2 [0], given: 11

Re: PS-which of the following must be true [#permalink]  24 May 2012, 01:08
Bunuel wrote:
Yes, a set of non-positive numbers consists of zero and negative numbers.

Isn't that one of the first few things one gets to learn when trying to read the number system. Thank you bunnel for reminding everyone about it
_________________

This time its personal..

Manager
Joined: 28 Jul 2011
Posts: 218
Followers: 0

Kudos [?]: 53 [0], given: 14

Re: If x and y are integers such that x<0<y, and z is non [#permalink]  25 May 2012, 21:34
So 0 "Zero" is even
and can be part of both a NON Postive set and a NON negative set
Set of Non positive numbers { 0,-1,-5,-9 }
Set of Non negative numbers { 0,1, 4, 7, }
Math Expert
Joined: 02 Sep 2009
Posts: 27526
Followers: 4327

Kudos [?]: 42561 [0], given: 6038

Re: If x and y are integers such that x<0<y, and z is non [#permalink]  04 Mar 2014, 09:42
Expert's post
Bumping for review and further discussion.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4959
Followers: 300

Kudos [?]: 55 [0], given: 0

Re: If x and y are integers such that x<0<y, and z is non [#permalink]  08 Apr 2015, 06:37
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.
_________________
Re: If x and y are integers such that x<0<y, and z is non   [#permalink] 08 Apr 2015, 06:37
Similar topics Replies Last post
Similar
Topics:
1 x+y)/Z>0 is x<0? (1) x<y (2) z<0 2 14 Jun 2011, 06:43
4 If (x + y) / z > 0, is x < 0? 1) x < y 2) z < 0 4 20 Apr 2008, 11:26
If X+Y/Z > 0, is X<0 ? 1. X<Y 2. Z<0 12 03 Feb 2008, 12:07
Is x>y? 1). x^2<y^2 2). y<0 10 27 May 2006, 22:36
If (x+y)/z >0, is x<0? 1.) x<y 2.) z<0 5 26 Feb 2006, 09:29
Display posts from previous: Sort by