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If x, y and z are nonzero integers [#permalink]
09 Sep 2018, 01:41
Question Stats:
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80% (00:31) wrong based on 73 sessions
If x, y and z are nonzero 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) \(yz < x\)




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Re: If x, y and z are nonzero integers [#permalink]
09 Sep 2018, 16:05
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WRONG SOLUTION MY MISTAKE! IGNORE THIS AND SCROLL DOWNAchyuthReddy wrote: If x, y and z are nonzero 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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Re: If x, y and z are nonzero integers [#permalink]
09 Sep 2018, 21:13
sandy wrote: AchyuthReddy wrote: If x, y and z are nonzero 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. NonZero integer means we must exclude only zero so option D is correct Set of NonZero 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 nonzero integers [#permalink]
10 Sep 2018, 08:46
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We only know that the integers are nonnegative. 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 nonzero integers [#permalink]
11 Jun 2019, 07:01
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Nonzero 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 . Please help me out from this quagmire !



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Re: If x, y and z are nonzero integers [#permalink]
12 Jun 2019, 02:14



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Re: If x, y and z are nonzero 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 nonzero integers [#permalink]
10 Apr 2020, 12:14
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Carcass wrote: Do not scratch your head. You are right.
The stem should say: which of the following cannot be true. All the answer choice are true but D
Regards Carcass can you please help me about few things regarding this question 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 nonzero integers [#permalink]
10 Apr 2020, 13:20
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Re: If x, y and z are nonzero integers
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