Integers

[Atonio79]

If n and y are positive integers and 450y=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

[Retake_GMAT]

First Attack 450 by writing it in terms of powers of primes.

450= 45*10=9*5 *5*2=(3^2)*(5^2)*(2)
(3^2)*(5^2)*(2) * y = n^3.

If we take cube root, we must get both n and y as integers ( Question stem says that).

hence we need to have 3 as power on the primes 3,2,5.

We already have 3^2 , 5^2, hence y = 3*5*2^2.

If y=3*5*2^2. should be an integer.

Ans B

[Anson800]

I think all these questions are already discussed. Please search instead of starting new thread. It's just suggestion

[Atonio79]

B is the correct answer... Thanks Retake Gmat!