n & y are positive integers

GhassanMBA wrote:Hello everyone this is a question I encountered as i was going through GMAT Prep 1:

If n and y are positive integers and 450 * y = 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 )

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


The OA is B

Also, after i finished my practice test I noticed there are no explanations for the questions in the test. Are they somewhere and I just can't find them?

Thanks

Anything with integers, divisors, etc you can recognize as a factoring problem. Factor out 450 into its prime factors:

450 -> 2,3,3,5,5

n^3 must have ATLEAST these prime factors for the equality to be true. Note the pattern: you have one 2, two 3s and two 5s. What prime factors COULD n have that would make this relatively close? 2, 3 and 5 naturally!

n -> 2,3,5

looking at the factors...

(2,3,3,5,5) * (?) = (2,3,5) * (2,3,5) * (2,3,5) = (2,2,2,3,3,3,5,5,5)

therefore the prime factors of y must be AT MINIMUM

(2,2,3,5)

Therefore y will be divisible by 2*2*3*5. Choose (b)

GhassanMBA wrote: Also, after i finished my practice test I noticed there are no explanations for the questions in the test. Are they somewhere and I just can't find them?

Thanks

Gmat prep does not give explanations. It only shows the correct and incorrect answers that you marked. To learn the explanations, you need to look into forums or external sources.
However, almost all the gmat prep questions have been discussed in BTG. you can use the search option in the forum to locate your question.

GhassanMBA wrote:Hello everyone this is a question I encountered as i was going through GMAT Prep 1:

If n and y are positive integers and 450 * y = 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 )

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


The OA is B

Also, after i finished my practice test I noticed there are no explanations for the questions in the test. Are they somewhere and I just can't find them?

Thanks

Given is 2*3*3*5*5*y = n^3 and that y and n are positive integers. The least supply that makes 2*3*3*5*5*y a perfect cube of some positive integer, is 2*2*3*5 = 60, such that n^3 = (2*3*5) ^3 or the least n is 30 and the least y is 60.

I. 3 * 2^2 * 5 = 60, which is a definite multiple of y. So, it’s ok

II. 3^2 * 2 * 5 = 90, which is NOT a definite multiple of y. So, it’s out

III. Not sure whether it’s typo or what, either way 3 2 * 5^2 (taken as 150 or 225 or 800) is NOT a definite multiple of y. So, it’s out too

Hence, [spoiler]I only[/spoiler]

[spoiler]B[/spoiler]