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

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

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New post 17 Feb 2008, 08:49
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Anyone can help? I can't figure this out...

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If n and y are positive integers and 450y=n^3, which of the following must be an integer?

1. y/(3 x 2^2 x 5)

2. y/(3^2 x 2 x 5)

3. y/(3 x 2 x 5^2)


A. 1 only

B. 2 only

C. 3 only

D. 2 and 3

E. 1, 2 and 3
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Re: DS integers [#permalink]

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New post 18 Feb 2008, 02:00
n^3 must end in 0 to meet any integer multiplier of 450, so just need to test any number in multiples of 10.

n^3 must be divisible by 450.

The lowest number do-able is 30, so 30^3 = 27000

lowest of y = 27000/450 = 60

...so y must be at least divisible by 60, so y/60 must be an integer.

but if y is 60, then y/90 and y/150 are not integers...

A.
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Re: DS integers [#permalink]

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New post 18 Feb 2008, 09:45
Agree with A.

prime factors of 450 are 3^2, 5^2 and 2. in order to make y = n^3/450 an integer, since n is a power of 3 all primefactors of n should raise to 3. so 3*5*2^2 should be part of n^3.
Re: DS integers   [#permalink] 18 Feb 2008, 09:45
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If n and y are positive integers and 450y=n^3, which of the

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