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If Y is the smallest positive integer such that 3150

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Intern
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If Y is the smallest positive integer such that 3150 [#permalink] New post 14 Jun 2006, 18:26
If Y is the smallest positive integer such that 3150 mutlipled by Y is the square of an integer then Y must be?


A2
B5
C6
D7
E14

?????
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Re: GMAT MATH SET 15 P 25 [#permalink] New post 14 Jun 2006, 18:53
GMATCUBS21 wrote:
If Y is the smallest positive integer such that 3150 mutlipled by Y is the square of an integer then Y must be?


A2
B5
C6
D7
E14

?????


3150 = 3x3 x 5x5 x 7 x 2
Hence Y = 7x2 = 14
E
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 [#permalink] New post 14 Jun 2006, 23:07
Ans 14

3150 * 14 = 441 * 100
= 21* 21 * 10 * 10
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 [#permalink] New post 14 Jun 2006, 23:11
Factorize the number, and you'll find that only 2 and 7 are the non-squared factors. Answer E.
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 [#permalink] New post 15 Jun 2006, 00:04
3150Y
= 315 * 10 * Y
= 63 * 5 * 2 * 5 * Y
= 2 * 3^2 * 5^2 * 7 * Y = m^2

Y must be 2*7 = 14
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 [#permalink] New post 16 Jun 2006, 10:40
Yup, E..

Used the factoring technique.

3150 = 5*5*3*3*2*7

For this to be a perfect square, we need one more 2 and one more 7 = 14.
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 [#permalink] New post 16 Jun 2006, 12:08
E.

3150 = 3*3*5*5*7*2

To make it a perfect square we need 7*2 i.e 14
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  [#permalink] 16 Jun 2006, 12:08
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