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

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Director
Joined: 03 Sep 2006
Posts: 871
If x and y are integers such that x<0<y, and z is non [#permalink]

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24 Jan 2012, 09:49
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61% (01:49) correct 39% (00:53) wrong based on 344 sessions

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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: 39622
Re: PS-which of the following must be true [#permalink]

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24 Jan 2012, 09:59
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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.

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Joined: 18 Oct 2010
Posts: 79
Re: PS-which of the following must be true [#permalink]

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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: 39622
Re: PS-which of the following must be true [#permalink]

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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.
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Intern
Joined: 30 Mar 2012
Posts: 36
Re: PS-which of the following must be true [#permalink]

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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
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This time its personal..

Manager
Joined: 28 Jul 2011
Posts: 238
Re: If x and y are integers such that x<0<y, and z is non [#permalink]

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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: 39622
Re: If x and y are integers such that x<0<y, and z is non [#permalink]

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04 Mar 2014, 10:42
Bumping for review and further discussion.
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Joined: 09 Sep 2013
Posts: 15928
Re: If x and y are integers such that x<0<y, and z is non [#permalink]

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08 Apr 2015, 07:37
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).

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Re: If x and y are integers such that x<0<y, and z is non [#permalink]

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14 Sep 2016, 07:09
what a nice trap here!!!
Re: If x and y are integers such that x<0<y, and z is non   [#permalink] 14 Sep 2016, 07:09
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