GMAT practice test #1 question

[john_haddock]

In n and p are positive integers and 450n=n^3, which of following must be integer?

i y/(3 times 2^2 times 5)
ii. y/(3^2 times 2 times 5)
iii. y/(3 times 2 times 5^2)

[kevinmarmstrong]

If 450y is a perfect cube, when 450y is written as a product of prime numbers, the exponents on the prime factors must all be multiples of 3.

Since 450 = 2 * 3^2 * 5^2, y must be a multiple of 2^2 , 3 and 5.

Thus only i must be an integer

[RonPurewal]

here are some previous postings on this question.

if-n-and-y-are-positive-integers-and-450y-n-3-t4311.html

if-n-and-y-are-positive-integers-and-450y-n-3-which-of-t279.html