GMAT Prep Question

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GMAT Prep Question

by Khalid.B » Wed Apr 18, 2012 9:58 am
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
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by sam2304 » Wed Apr 18, 2012 10:43 am
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.
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by Anurag@Gurome » Wed Apr 18, 2012 5:10 pm
Khalid.B wrote: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.
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