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# If y is the smallest positive integer such that 3,150

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Manager
Joined: 03 Oct 2008
Posts: 61

Kudos [?]: 31 [0], given: 0

If y is the smallest positive integer such that 3,150 [#permalink]

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06 Oct 2008, 13:48
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

A. 2
B. 5
C. 6
D. 7
E. 14

Kudos [?]: 31 [0], given: 0

Director
Joined: 12 Jul 2008
Posts: 514

Kudos [?]: 162 [1], given: 0

Schools: Wharton

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06 Oct 2008, 13:50
1
KUDOS
albany09 wrote:
If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

A. 2
B. 5
C. 6
D. 7
E. 14

E

Prime factorize 3150:

3150 = 2*3*3*5*5*7
= 2*3^2*5^2*7
= 2*7*(3*5)^2
= 14*15^2

Need to multiply by 14 to make a perfect square

Kudos [?]: 162 [1], given: 0

Manager
Joined: 27 Sep 2008
Posts: 76

Kudos [?]: 9 [0], given: 0

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06 Oct 2008, 13:51
3150*y = x^2

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

y = 2*7 = 14

so (2*7)*(5*2*5*3*3*7) = (2*5*7*3)^2

x = 2*5*7*3

Kudos [?]: 9 [0], given: 0

Re: math problem   [#permalink] 06 Oct 2008, 13:51
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