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# If y is the smallest positive integer such that 3150

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Manager
Joined: 23 Mar 2008
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If y is the smallest positive integer such that 3150 [#permalink]  09 May 2008, 03:54
If y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be

a) 2
b) 5
c) 6
d) 7
e) 14
VP
Joined: 10 Jun 2007
Posts: 1465
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Re: smallest positive integer [#permalink]  09 May 2008, 05:45
puma wrote:
If y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be

a) 2
b) 5
c) 6
d) 7
e) 14

E.

3150 = 2*3^2*5^2*7
Missing a 2 and a 7
7*2 = 14
SVP
Joined: 28 Dec 2005
Posts: 1583
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Re: smallest positive integer [#permalink]  09 May 2008, 05:58
E for me as well. I dont know why, but im so excited that I was able to figure this out.

This is how I approached it:

3150*y = i^2 , where i is the integer in question. I took the square root of both sides, so:

root(3150*y) = i

Now, I broke 3150 up in its primes: 3150 = 2*3^2*5^2*7. That simplifies the above into:

3*5*root(14y) = i

The only thing stopping i from being an integer is the root(14y) piece ... so if y=14, then rwe have:

root(14*14) = 14, and then we will have an integer
Current Student
Joined: 28 Dec 2004
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Location: New York City
Schools: Wharton'11 HBS'12
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Re: smallest positive integer [#permalink]  09 May 2008, 06:07
i get 14 as well..

y*3150=N^2

now i know that prime^even=perfect square..

so lets see primes of 3150=315*10=5^2*3^2*7*2..ahh we need at least a 7 and 2 to make it a perfect sq...
Re: smallest positive integer   [#permalink] 09 May 2008, 06:07
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