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# If n and y are positive integers adn 450y=n^3 , which of the

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Manager
Joined: 17 Jan 2006
Posts: 92
If n and y are positive integers adn 450y=n^3 , which of the [#permalink]

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07 May 2006, 18:19
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If n and y are positive integers adn 450y=n^3 , which of the following must be an integer?
I y/(3*2^2*5)
II y/(3^2*2*5)
III y/(3*2*5^2)

None
I only
II only
III only
I,II,and III
VP
Joined: 29 Apr 2003
Posts: 1403

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07 May 2006, 20:03
Nope, I think its I

Cos u can get y = 3*2*2*5 Atleast!
VP
Joined: 29 Dec 2005
Posts: 1341

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08 May 2006, 09:30
sm176811 wrote:
Nope, I think its I

Cos u can get y = 3*2*2*5 Atleast!

n^3 = 450y
n^3 = 2x3x3x5x5 y

if n and y are +ve integers, y must, at least be, 2x2x3x5.

hmmm.... ok, it is only I.
Manager
Joined: 11 Oct 2005
Posts: 94

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08 May 2006, 20:17
I dont get it ??? Isnt 2*3^2*5 the same as 6^10 and if that is true how is 2.2.3.5 which is 60/6^10 an integer? please explain
Senior Manager
Joined: 29 Jun 2005
Posts: 403

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09 May 2006, 09:03
450=9*50=3*3*2*5*5=3^2*5^2*2. 3rd root of y must be integer, so y must be a number that is composed of 3^(n-2)^2^(n-1)^5^(n-1), where n is multiple of 3. from the choices 1 only satisfies this. So the answer is A.
09 May 2006, 09:03
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