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# If x and y are positive integers, is (x/y)^z > 1 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 51071
If x and y are positive integers, is (x/y)^z > 1 ?  [#permalink]

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20 Aug 2018, 00:11
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Difficulty:

45% (medium)

Question Stats:

68% (02:59) correct 32% (01:43) wrong based on 62 sessions

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If x and y are positive integers, is $$(\frac{x}{y})^z > 1$$ ?

(1) x - y = -5

(2) z ≠ 0

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Joined: 20 Jul 2018
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GPA: 2.87
If x and y are positive integers, is (x/y)^z > 1 ?  [#permalink]

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20 Aug 2018, 00:20
1
1) as $$x-y=-5$$, it means that y is greater than x, so $$x/y$$ is less than 1 but as z is unknown u can't determine whether $$(x/y)^z$$ is less than or greater than 1. e.g if z is positive then $$(x/y)^z$$ is less than 1, if z is negative then $$(x/y)^z$$ is greater than 1. INSUFFICIENT

2) still no clue whether z is positive or negative. INSUFFICIENT

by combining both provide no extra information either.

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Re: If x and y are positive integers, is (x/y)^z > 1 ?  [#permalink]

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20 Aug 2018, 00:23
From statement 1 we can conclude that X<Y. Means $$\frac{X}{Y}$$ is a fraction.
Since we don't know anything about Z. Statement 1 is insufficient.
From statement 2 we don't have any information about X and Y. So, 2 is insufficient.
Combining both gives two possibilities.
If X=1 and Y=6. and Z = $$\frac{{-1}}{2}$$ Then (X/Y)^Z Gives 36. which is greater than 1.
If Z is positive fraction then (X/Y)^Z is less than 1.
Hence combining also is insufficient.
E is the answer.
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Re: If x and y are positive integers, is (x/y)^z > 1 ?  [#permalink]

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21 Aug 2018, 07:57
Bunuel wrote:
If x and y are positive integers, is $$(\frac{x}{y})^z > 1$$ ?

(1) x - y = -5

(2) z ≠ 0

Here is my approach.

(1) x - y = -5 --> x < y --> $$\frac{x}{y}$$ < 1 . No info about z --> not sufficient.
(Number plugging: Let $$\frac{x}{y}$$ = $$\frac{1}{6}$$. If $$z = 1$$ --> Yes, If $$z=-1$$ --> No)

(2) z ≠ 0 --> No info about x, y --> not sufficient.

(1) + (2) We still have two different answers --> not sufficient.

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Re: If x and y are positive integers, is (x/y)^z > 1 ? &nbs [#permalink] 21 Aug 2018, 07:57
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# If x and y are positive integers, is (x/y)^z > 1 ?

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