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Intern Joined: 15 Sep 2017
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If x, y and z are non-zero integers [#permalink] 00:00

Question Stats: 19% (00:44) correct 80% (00:31) wrong based on 73 sessions
If x, y and z are non-zero integers, and if $$x > yz$$, then which of the following statements must be true?

Indicate all such statements.

A) $$\frac{x}{y} > z$$

B) $$\frac{x}{z} > y$$

C) $$\frac{x}{yz} > 1$$

D) $$yz < x$$
[Reveal] Spoiler: OA Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Re: If x, y and z are non-zero integers [#permalink]
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Expert's post
WRONG SOLUTION MY MISTAKE! IGNORE THIS AND SCROLL DOWN

AchyuthReddy wrote:
If x, y and z are non-zero integers, and if $$x > yz$$, then which of the following statements must be true?

Indicate all such statements.

A) $$\frac{x}{y} > z$$

B) $$\frac{x}{z} > y$$

C) $$\frac{x}{yz} > 1$$

d) $$yz < x$$

Since it is mentioned that x, y and z are positive you can divide them without flipping the inequality.

Given: $$x > yz$$

Dividing both sides with y

$$\frac{x}{y} > \frac{yz}{y}$$ or $$\frac{x}{y} > z$$... So A is true

Dividing both sides with z

$$\frac{x}{z} > \frac{yz}{z}$$ or $$\frac{x}{z} > y$$... So B is true

Dividing both sides with yy

$$\frac{x}{yz} > \frac{yz}{yz}$$ or $$\frac{x}{yz} > 1$$... So C is true

Option D cant be true as it is a direct contradiction of the stement given in problem.
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Sandy
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Intern Joined: 15 Sep 2017
Posts: 34
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Kudos [?]: 18 , given: 2

Re: If x, y and z are non-zero integers [#permalink]
sandy wrote:
AchyuthReddy wrote:
If x, y and z are non-zero integers, and if $$x > yz$$, then which of the following statements must be true?

Indicate all such statements.

A) $$\frac{x}{y} > z$$

B) $$\frac{x}{z} > y$$

C) $$\frac{x}{yz} > 1$$

d) $$yz < x$$

Since it is mentioned that x, y and z are positive you can divide them without flipping the inequality.

Given: $$x > yz$$

Dividing both sides with y

$$\frac{x}{y} > \frac{yz}{y}$$ or $$\frac{x}{y} > z$$... So A is true

Dividing both sides with z

$$\frac{x}{z} > \frac{yz}{z}$$ or $$\frac{x}{z} > y$$... So B is true

Dividing both sides with yy

$$\frac{x}{yz} > \frac{yz}{yz}$$ or $$\frac{x}{yz} > 1$$... So C is true

Option D cant be true as it is a direct contradiction of the stement given in problem.

Non-Zero integer means we must exclude only zero so option D is correct

Set of Non-Zero numbers{ ......-3,-2,-1,1,2,3,4....}
This reply is basing on my knowledge if I am wrong please correct me. Intern Joined: 27 Aug 2018
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Re: If x, y and z are non-zero integers [#permalink]
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We only know that the integers are non-negative. Hence, we don't know how the sign may change. Only D option is the correct one.

A: If y is negative, then it is false
B: If z is negative, then it is false
C: If x is positive and yz is negative, then it cannot be larger than 1. Manager Joined: 08 Dec 2018
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Re: If x, y and z are non-zero integers [#permalink]
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Non-zero integers are ( ...-3,-2,-1,123...)
How is the option D correct?
because, in the question stem x>yz
if we divide both sides by -1, then inequality flips i.e. x<yz
Aagin, if we divide both sides by 1, the inequality x>yz holds .
Founder  Joined: 18 Apr 2015
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GRE 1: Q160 V160 Followers: 317

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Re: If x, y and z are non-zero integers [#permalink]
Expert's post Manager Joined: 22 May 2019
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Re: If x, y and z are non-zero integers [#permalink]
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So far my realization, the stem is correct and the solution is d. x,y,z non zero integers it means it includes negative as well as positive. for option a,b,c there will be a change in sign direction if we consider negative numbers. But option d is correct. x> yz / yz<x same thing. Intern Joined: 14 Mar 2020
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Re: If x, y and z are non-zero integers [#permalink]
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Carcass wrote:

The stem should say: which of the following cannot be true.
All the answer choice are true but D

Regards

1: For option A if we say that y is a negative integer then x>(-y)(z)...... X/-y<z but for option A we have to find x/y relation with Z, not X/-y relation ,, so multiplying both side with negative 1 (in X/-y<z) again turn is like x/y>-z (here my question is ,, doing all these over and over is right or not )

2: how D can't be true ,, isn't x> yz or yz<x are the same things ? Founder  Joined: 18 Apr 2015
Posts: 13948
GRE 1: Q160 V160 Followers: 317

Kudos [?]: 3698  , given: 12956

Re: If x, y and z are non-zero integers [#permalink]
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Expert's post
The post is locked.

The question is bogus.

D is impossible.

Moreover, the question has ONLY the first three answer choices. D is NOT among those. It was added for errors to the original question by the student.

The discussion is located here https://greprepclub.com/forum/if-x-y-an ... tml#p47808

refer to it for the real question and solution provided.

regards
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