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1575 × k is a perfect square

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by sanju09 » Tue Sep 14, 2010 4:35 am
What is the smallest positive integer k such that the product 1575 × k is a perfect square?
(A) 7
(B) 9
(C) 15
(D) 25
(E) 63



[spoiler]Source: https://readyforgmat.com[/spoiler]
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by Rahul@gurome » Tue Sep 14, 2010 4:42 am
1575 = 3^2 * 5^2 * 7
So, if k = 7 (which is the smallest positive integer), then 1575 × 7 = 3^2 * 5^2 * 7^2, which will be a perfect square.

The correct answer is [spoiler](A)[/spoiler].
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by sanju09 » Tue Sep 14, 2010 4:50 am
Rahul@gurome wrote:1575 = 3^2 * 5^2 * 7
So, if k = 7 (which is the smallest positive integer), then 1575 × 7 = 3^2 * 5^2 * 7^2, which will be a perfect square.

The correct answer is [spoiler](A)[/spoiler].
Good! Generally, on GMAT PS, the smallest hardly happens to be the smallest of all the choices, this question is just an EXCEPTION, isn't it, Rahul?
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by Rahul@gurome » Tue Sep 14, 2010 4:54 am
sanju09 wrote: Good! Generally, on GMAT PS, the smallest hardly happens to be the smallest of all the choices, this question is just an EXCEPTION, isn't it, Rahul?
Right Sanju, I agree with you.
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