* Tough Math problem

[GMAT Eater]

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

Answer: Y/(3)(2^2)(5)

Can someone please explain this to me? Also, how come this particular concept is not fully explained in th "Number Properties" MGMAT book?

[Rustic Myth]

450Y = n^3

450 =( 2*3*3*5*5)

Y = n^3 / 2 * 3^2 * 5^2

Y = {(n/2*3*5) ^ 3} * (3* 5 * 2^2)


My reasoning

As N is a integer and 450Y is equal to the third power of N, Y should have the minimum remaining prime factors of 450 to make it into a power of three. that is Y should be equal to 2*2*3*5*x*x*x.

Thus Y / 3*5*2^2 is a integer.

[esledge]

Please cite the source (author) of this problem. We cannot reply unless a source is cited (and, if no source is cited, we will have to delete the post!). Thanks.

Please also make sure to read and follow the forum guidelines before posting. The subject heading should be the first 5-8 words of the problem.

BTW, the Number Properties strategy guide p.15-16 discusses factors, prime boxes, and prime products. The problem can be done with that info, but please post the author of the problem first.

[bhuwan]

The question appears to already have been answered:

http://www.manhattangmat.com/forums/if- ... -t279.html

[RonPurewal]

this is a gmatprep problem, so i'm going to move this thread over to the ::ahem:: CORRECT folder.

posters: please post your problems in the correct folder. gmatprep problems have their own special little folder, so, please use it.
thanks.

here's another link:
http://www.manhattangmat.com/forums/if- ... t4311.html