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[sana.noor]

If n and y are positive integers and 450y = n^3

Which of the following is an integer?

I. y / 3 x 2^2 x 5

II. y / 3^2 x 2 x 5

III. y / 3 x 2 x 3^2

A. I
B. II
C. III
D. I and II
E. I and II and III

OA is B but why not A

[srcc25anu]

If n and y are positive integers and 450y = n^3

Which of the following is an integer?

I. y / 3 x 2^2 x 5
II. y / 3^2 x 2 x 5
III. y / 3 x 2 x 3^2

A. I
B. II
C. III
D. I and II
E. I and II and III

The correct question and correct answer choices are as follows:

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

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

[srcc25anu]

450 y = 2 * 3^2 * 5^2 y = n^3
hence y must atleast be 2^2 * 3 * 5
therefore I is clearly true.

II has 2 powers of 3 which y may or maynot have hence NOT necessarily an Integer
III has 2 powers of 5. Again Y for sure has 1 power of 5 but we cant say for sure whether it has 2 powers of 5 or not. It may or may not be true

Hence only statement I is true
Ans B

[ceilidh.erickson]

Where did you find this question? You're right, the given answer doesn't make sense. Furthermore, a real GMAT question would have said "which of the following MUST be an integer?" All 3 of the answer choices could potentially be integers, but only the first one must be.

If n^3 = 450y, then n^3 = (2)(3^2)(5^2)y

Since we know that in any cube, all of the prime factors must be in groups of 3, then we know that y must contain at least the extra factors to get us to (2^3)(3^3)(5^3). 450 on contains one 2, two 3's, and two 5's. So, y must contain at least (2^2)(3)(5) to get three of each factor. y might also contain other prime factors in groups of 3 - it might contain 7^3, or an extra 3^3, etc - but we don't know. All that we know it that it must contain at least (2^2)(3)(5) to make n^3 a cube.

If y contains (2^2)(3)(5), then it will be divisible by those things. So, statement I must be an integer. However, we can't prove that y is definitely divisible by 3^2 (unless it's also divisible by 3^4 - the extra 1, plus another set of 3). Statement II is actually wrong.

Beware of studying from sources that contain incorrect information!