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

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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 V
Joined: 02 Sep 2009
Posts: 56304
Re: PS-which of the following must be true  [#permalink]

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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]

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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 V
Joined: 02 Sep 2009
Posts: 56304
Re: PS-which of the following must be true  [#permalink]

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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]

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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]

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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 V
Joined: 02 Sep 2009
Posts: 56304
Re: If x and y are integers such that x<0<y, and z is non  [#permalink]

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Bumping for review and further discussion.
_________________
Board of Directors P
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]

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what a nice trap here!!!
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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]

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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] 02 Sep 2018, 11:25
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