GMAT Prep Question

[Khalid.B]

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

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

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

Correct answer is
B

[sam2304]

Given 450y = n^3. We need to find y first.

Factorize 450 = 3*3*5*5*2
This 450 * y = n^3, so y will have the remaining prime factors along with 450 will add up to cube of every prime factor

n^3 = (3*3*5*5*2) * (3*5*2*2).

So y = 3*5*2*2.

Now check for the options. Only I gives us an integer.

IMO B.

[Anurag@Gurome]

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

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

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

Correct answer is
B

450y=n^3 implies (3^2 * 5^2 * 2)y = n^3, which implies y should be 2^2 * 3 * 5 so that 450y=n^3
Then (I) will be an integer.
(II) and (III) will not be an integer always.

The correct answer is B.