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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 x 5^2) a. None b. I only c. II only d. III only e. I, II, and III
and ask about relating it to the explanation on the following page.... you're quite right, the answer on the following page does not relate to the question!
The answer option 'B' is quite correct, but the way this is explained is as follows:
450 = 2 * 3^3 * 5^2
if (2* 3^3 * 5^2 )*y = n^3, what we really need for an integer answer is for the left hand side of this equation to all be powers of three.
we already have 2^1, so y needs to contain 2^2 as a factor... we also have 5^2, so y needs to contain 5^1 as a factor as well. The only answer that satisfies both requirements is answer I, making B the correct choice.