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

 It is currently 20 Jul 2019, 17:20

### 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

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

Author Message
TAGS:

### Hide Tags

Director
Joined: 03 Sep 2006
Posts: 732
If x and y are integers such that x<0<y, and z is non  [#permalink]

### Show Tags

24 Jan 2012, 09:49
1
5
00:00

Difficulty:

35% (medium)

Question Stats:

61% (01:19) correct 39% (01:12) wrong based on 378 sessions

### HideShow timer Statistics

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. $$\frac{x}{y}<z$$
Math Expert
Joined: 02 Sep 2009
Posts: 56304
Re: PS-which of the following must be true  [#permalink]

### Show Tags

24 Jan 2012, 09:59
2
1
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: 18 Oct 2010
Posts: 73
Re: PS-which of the following must be true  [#permalink]

### Show Tags

22 May 2012, 01:19
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: 56304
Re: PS-which of the following must be true  [#permalink]

### Show Tags

22 May 2012, 01:23
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: 31
Re: PS-which of the following must be true  [#permalink]

### Show Tags

24 May 2012, 02:08
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: 173
Re: If x and y are integers such that x<0<y, and z is non  [#permalink]

### Show Tags

25 May 2012, 22:34
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: 56304
Re: If x and y are integers such that x<0<y, and z is non  [#permalink]

### Show Tags

04 Mar 2014, 10:42
Bumping for review and further discussion.
_________________
Board of Directors
Joined: 17 Jul 2014
Posts: 2539
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If x and y are integers such that x<0<y, and z is non  [#permalink]

### Show Tags

14 Sep 2016, 07:09
what a nice trap here!!!
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 11718
Re: If x and y are integers such that x<0<y, and z is non  [#permalink]

### Show Tags

02 Sep 2018, 11:25
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] 02 Sep 2018, 11:25
Display posts from previous: Sort by