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# If x, y and z are non-zero integers

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If x, y and z are non-zero integers [#permalink]  09 Sep 2018, 01:41
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20% (00:44) correct 80% (00:30) wrong based on 70 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
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Re: If x, y and z are non-zero integers [#permalink]  09 Sep 2018, 16:05
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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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Intern
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Re: If x, y and z are non-zero integers [#permalink]  09 Sep 2018, 21:13
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.
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Re: If x, y and z are non-zero integers [#permalink]  10 Sep 2018, 08:46
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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.
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Re: If x, y and z are non-zero integers [#permalink]  11 Jun 2019, 07:01
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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 .
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Re: If x, y and z are non-zero integers [#permalink]  12 Jun 2019, 02:14
Expert's post

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

Regards
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Manager
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Re: If x, y and z are non-zero integers [#permalink]  03 Jul 2019, 17:58
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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.
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Re: If x, y and z are non-zero integers [#permalink]  10 Apr 2020, 12:14
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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 ?
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Re: If x, y and z are non-zero integers [#permalink]  10 Apr 2020, 13:20
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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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Re: If x, y and z are non-zero integers   [#permalink] 10 Apr 2020, 13:20
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