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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

Expert's post

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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.

(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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(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 \(5^7>1,000\).

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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This post received KUDOS

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

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