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# If n and y are positive integers

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Manager
Joined: 05 Aug 2008
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Schools: McCombs Class of 2012
If n and y are positive integers [#permalink]

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03 Jan 2009, 22:32
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Intern
Joined: 26 May 2008
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03 Jan 2009, 23:02
450y = n^3
or (2* 3^2 * 5^2) * (3 * 5 * 2^2) = n^3

So the smallest value of y can be 60 which is satisfied by I. So answer is B.
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Joined: 29 Aug 2007
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03 Jan 2009, 23:50
agree with B. I.
450y = n^3
(2* 3^2 * 5^2) y = n^3
y has to be at least (2^2) (3) (5) to have 450y = n^3.
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Manager
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04 Jan 2009, 00:13
That's what I had thought, but that is not the correct answer.
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04 Jan 2009, 13:43
smarinov wrote:
That's what I had thought, but that is not the correct answer.

What is the correct answer?

I donot think there is anything other than what is discussed above.

B should be it..
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Manager
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04 Jan 2009, 14:36
According to the GMATprep it is E.
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04 Jan 2009, 15:30
smarinov wrote:
According to the GMATprep it is E.

Uncover the OE as well.
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Senior Manager
Joined: 23 May 2008
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05 Jan 2009, 04:20
i am pretty sure there is something wrong with the GMAT prep software....
the answer has to be B
Intern
Joined: 03 Jan 2009
Posts: 2
Schools: u of chicago

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05 Jan 2009, 08:27
II: (n^3/(5 x5 x 3 x 3 x 2))/(5 x 3 x 3 x 2) => ((n^3)(5 x 3 x 3 x 2))/(5 x5 x 3 x 3 x 2) => (n^3)/5 if n = 3 then 9/5, which isn't an integer. similar results for I and III: none of them cancels completely out, right? unless there's a typo in the question stem or something. ???
Intern
Joined: 05 Jan 2009
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06 Jan 2009, 17:05
Correct me if I'm wrong. I think we are forgetting that the question is not asking for the smallest integer.

the smallest value of y would be 5 x 3 x 2^2 in order for 450y = n^3 to be true

but, y could also be 5^4 x 3^4 x 2^5 and that would still make choices I, II and II into integers

Hope that's correct.
Retired Moderator
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06 Jan 2009, 22:18
B is right and OE is wrong
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Joined: 29 Aug 2007
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06 Jan 2009, 22:45
ic3ncok3 wrote:
Correct me if I'm wrong. I think we are forgetting that the question is not asking for the smallest integer.

the smallest value of y would be 5 x 3 x 2^2 in order for 450y = n^3 to be true

but, y could also be 5^4 x 3^4 x 2^5 and that would still make choices I, II and II into integers

Hope that's correct.

Must implies that "at any case or worst case scenerios". Those (y's value other than 2^2*3*5) are not the worst case scenerios.
Aaccording to the question: y must be at least 60 (or 2^2*3*5). if y is none othe r than 60, II and III cannot be an integer.

So none other B is an OA. Hope everybody agrees.

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Re: Integers   [#permalink] 06 Jan 2009, 22:45
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# If n and y are positive integers

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