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# If x, y, and n are positive integers, is (x/y)^n greater

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If x, y, and n are positive integers, is (x/y)^n greater [#permalink]

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01 Oct 2010, 09:01
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If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ?

(1) x=y^3 and n>y
(2) x>5y and n>x
[Reveal] Spoiler: OA
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If x, y, and n are positive integers, is (x/y)^n greater [#permalink]

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01 Oct 2010, 09:16
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If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ?

Question: is $$(\frac{x}{y})^n>1,00$$

(1) x=y^3 and n>y --> $$(\frac{x}{y})^n=(\frac{y^3}{y})^n=y^{2n}$$, so the question becomes is $$y^{2n}>1,000$$ --> y=1 and n=2 answer is NO but y=10 and n=11 answer is YES. Not sufficient.

(2) x>5y and n>x --> $$\frac{x}{y}>5$$ also as $$x$$, $$y$$, and $$n$$ are positive integers then the least value of $$x$$ is 6 (for $$y=1$$) and the least value of $$n$$ is 7 --> so we would have $$(# \ more \ than \ 5)^{(at \ least \ 7)}$$ which is more than 1,000 (5^7>1,000). Sufficient.

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06 Oct 2010, 23:40
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HI Bunuel,

I have a small doubt here....Do positive integers include zero too? If so, we have an undefined value as the answer right? Kinly clarify
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07 Oct 2010, 00:46
psychomath wrote:
HI Bunuel,

I have a small doubt here....Do positive integers include zero too? If so, we have an undefined value as the answer right? Kinly clarify

Nope .. 0 is neither positive nor negative
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07 Oct 2010, 01:15
OK so what i remember about zero being a positive integer is wrong...Thanks a ton!
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08 Oct 2010, 11:12
Bunuel wrote:

(2) x>5y and n>x --> $$\frac{x}{y}>5$$ also as $$x$$, $$y$$, and $$n$$ are positive integers then the least value of $$x$$ is 6 (for $$y=1$$) and the least value of $$n$$ is 7 --> so we would have $$(# \ more \ than \ 5)^{(at \ least \ 7)}$$ which is more than 1,000 (5^7>1,000). Sufficient.

Can you please explain the 2nd equation again.
I didn;t get this one.
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08 Oct 2010, 11:37
onedayill wrote:
Bunuel wrote:

(2) x>5y and n>x --> $$\frac{x}{y}>5$$ also as $$x$$, $$y$$, and $$n$$ are positive integers then the least value of $$x$$ is 6 (for $$y=1$$) and the least value of $$n$$ is 7 --> so we would have $$(# \ more \ than \ 5)^{(at \ least \ 7)}$$ which is more than 1,000 (5^7>1,000). Sufficient.

Can you please explain the 2nd equation again.
I didn;t get this one.

Question: is $$(\frac{x}{y})^n>1,00$$?

From (2):

$$x>5y$$ --> $$\frac{x}{y}>5$$, so $$base=\frac{x}{y}=(# \ more \ than \ 5)$$;

$$x>5y$$ and $$n>x$$ --> as $$x$$, $$y$$, and $$n$$ are positive integers then: the least value $$y$$ is 1 --> the least value of $$x$$ is 6 ($$x>5=5y_{min}$$) --> the least value of $$n$$ is 7 (as $$n>x$$);

Is $$(\frac{x}{y})^n>1,00$$ --> is $$(# \ more \ than \ 5)^{(at \ least \ 7)}$$? Answer is YES, as even $$5^7>1,000$$.

Hope it's clear.
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Re: If x, y, and n are positive integers, is (x/y)^n greater tha [#permalink]

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09 Mar 2012, 07:16
Let us substitute numbers to disprove/prove the choices :

We need to predict whether (x/y)^n > 1000

(1) x = y^3 and n > y.

if y = 1 and x = 1 , and n = 2, then it's false.

if y = 10, x = 1000 and n = 1001, it's true

Insufficient

(2) x > 5y and n > x.

Let us take lowest value of y = 1
Then x = 6 at least , and n = 7 at least

So 6^7 > 1000

Another way to look at this is :

x > 5y
=> x/y > 5 and n > 5x => n >= 5 (because these are all positive numbers)

So 5^5 > 1000

Sufficient.

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Re: If x, y, and n are positive integers, is (x/y)^n greater [#permalink]

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25 Jun 2013, 04:47
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Re: If x, y, and n are positive integers, is (x/y)^n greater [#permalink]

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25 Jun 2013, 12:34
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agnok wrote:
If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ?

(1) x=y^3 and n>y
(2) x>5y and n>x

Given x,y and n are positive integers

From st 1 we have x= y^3 and n>y so the given expression becomes

(y^2)^n > 1000

now if y = 2 and n = 5 we have 4^5>1000----> yes
but if y=1 and n=5 then we have 1^5>1000-----> no

Not sufficient

St 2 says x>5y and n>x

Let us assume x= 5y so we have 5^n > 1000

now also n> x so if x= 5 then n can be any value integer greater than 5 ----> 5^n>1000 is definitely true
now since x>5y then ----> value of x is more than 5 and since n>x it will always be greater than 1000

Hence ans B
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Re: If x, y, and n are positive integers, is (x/y)^n greater [#permalink]

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04 Dec 2014, 05:00
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Re: If x, y, and n are positive integers, is (x/y)^n greater [#permalink]

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05 Mar 2016, 19:48
Hello from the GMAT Club BumpBot!

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Re: If x, y, and n are positive integers, is (x/y)^n greater [#permalink]

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08 Mar 2016, 21:26
agnok wrote:
If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ?

(1) x=y^3 and n>y
(2) x>5y and n>x

Excellent Question,,
Here i just plugged in y=1 to calculate the least value of LHS as y increases x increases and so does n hence B is correct
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Re: If x, y, and n are positive integers, is (x/y)^n greater   [#permalink] 08 Mar 2016, 21:26
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