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# If x and y are positive integers and 180x=y^3...

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Intern
Joined: 30 Aug 2010
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If x and y are positive integers and 180x=y^3... [#permalink]

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04 Sep 2010, 11:34
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Difficulty:

45% (medium)

Question Stats:

63% (02:12) correct 37% (01:35) wrong based on 620 sessions

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If x and y are positive integers and 180x=y^3, which of the following must be an integer?

I. x/(2^2*3*5)
II. x/(2*3^2*5)
III. x/(2*3*5^2)

(A) None
(B) I only
(C) II only
(D) III only
(E) I and II
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 37691
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Kudos [?]: 99910 [7] , given: 11118

Re: If x and y are positive integers and 180x=y^3... [#permalink]

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04 Sep 2010, 12:01
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rraggio wrote:
If x and y are positive integers and 180x=y^3, which of the following must be an integer?

I. x/(2^2*3*5)
II. x/(2*3^2*5)
III. x/(2*3*5^2)

(A) None
(B) I only
(C) II only
(D) III only
(E) I and II

$$x$$ and $$y$$ are integers and $$180x=y^3$$ --> $$180x$$ equals to cube of an integer ($$y^3$$). $$180x=2^2*3^2*5*x=y^3$$. The smallest value of $$x$$ for which $$2^2*3^2*5*x$$ is a cube of an integer is when $$x=2*3*5^2$$ (to complete powers of 2, 3 and 5 to cubes). In this case $$180x=(2^2*3^2*5)*(2*3*5^2)=(2*3*5)^3=cube \ of \ an \ integer$$. So $$x$$ is definitely divisible by $$2*3*5^2$$.

Similar problems:
number-properties-92562.html?hilit=following%20must%20none#p712584
og-quantitative-91750.html#p704028
division-factor-88388.html#p666722

Hope it helps.
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Kudos [?]: 175 [0], given: 0

Re: If x and y are positive integers and 180x=y^3... [#permalink]

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11 Jan 2014, 23:06
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Kudos [?]: 175 [0], given: 0

Re: If x and y are positive integers and 180x=y^3... [#permalink]

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28 Jan 2015, 14:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Joined: 09 Sep 2013
Posts: 14547
Followers: 609

Kudos [?]: 175 [0], given: 0

Re: If x and y are positive integers and 180x=y^3... [#permalink]

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09 Feb 2016, 00:57
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Kudos [?]: 175 [0], given: 0

Re: If x and y are positive integers and 180x=y^3... [#permalink]

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12 Mar 2017, 10:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x and y are positive integers and 180x=y^3...   [#permalink] 12 Mar 2017, 10:00
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