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# If n and y are positive integers and 450y = n^3, which is

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Senior Manager
Joined: 06 Jul 2006
Posts: 295
Location: SFO Bay Area
Schools: Berkeley Haas
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If n and y are positive integers and 450y = n^3, which is [#permalink]  24 Feb 2008, 15:49
If n and y are positive integers and 450y = n^3, which is the following must be an integer ?

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

A. None
B. I only
C. II only
D. III only
E. I, II and III
Senior Manager
Joined: 26 Jan 2008
Posts: 267
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Re: Maths: Value of y [#permalink]  24 Feb 2008, 16:14
suntaurian wrote:
If n and y are positive integers and 450y = n^3, which is the following must be an integer ?

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

A. None
B. I only
C. II only
D. III only
E. I, II and III

(B)

Since n^3 = 450y = 2 * (3^2) * (5^2) * y
=> y is atleast 60 (2*2*3*5) in order to make a perfect cube

Substituting y=60 in the three equations, only I gives an integer
_________________
Senior Manager
Joined: 06 Jul 2006
Posts: 295
Location: SFO Bay Area
Schools: Berkeley Haas
Followers: 2

Kudos [?]: 38 [0], given: 0

Re: Maths: Value of y [#permalink]  24 Feb 2008, 16:27
OA is B.

For some lame reason i kept writing 450 as 5*3*5*2*5 and had three 5s instead of two.
Re: Maths: Value of y   [#permalink] 24 Feb 2008, 16:27
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# If n and y are positive integers and 450y = n^3, which is

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