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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
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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
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. Answer: B.
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Re: Yes/ NO Question [#permalink]
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06 Oct 2010, 23:40
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: Yes/ NO Question [#permalink]
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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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Re: Yes/ NO Question [#permalink]
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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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Re: Yes/ NO Question [#permalink]
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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.
Answer: B.
Can you please explain the 2nd equation again. I didn;t get this one.
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Re: Yes/ NO Question [#permalink]
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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.
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 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. Answer  B
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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
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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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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