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If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ?

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agnok
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If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ? [#permalink] New post   01 Oct 2010, 09:01
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If x, y, and n are positive integers, is \((\frac{x}{y})^n\) greater than 1,000 ?


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

(2) \(x > 5y\) and \(n > x\).
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Re: If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ? [#permalink] New post   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 \((number \ more \ than \ 5)^{(at \ least \ 7)}\) which is more than 1,000 (5^7>1,000). Sufficient.

Answer: B.
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psychomath
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Re: If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ? [#permalink] New post   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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Re: If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ? [#permalink] New post   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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Re: If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ? [#permalink] New post   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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Re: If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ? [#permalink] New post   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.

Answer: B.


Can you please explain the 2nd equation again.
I didn;t get this one.
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Re: If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ? [#permalink] New post   08 Oct 2010, 11:37
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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.

Answer: B.


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 than 1,000 ? [#permalink] New post   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.

Answer - B
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Re: If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ? [#permalink] New post   25 Jun 2013, 04:47
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Re: If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ? [#permalink] New post   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 than 1,000 ? [#permalink] New post   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 than 1,000 ? [#permalink] New post   23 Sep 2023, 07:06
Hello from the GMAT Club BumpBot!

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Re: If x, y, and n are positive integers, is (x/y)^n greater than 1,000 ? [#permalink]
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