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

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Manager
Joined: 25 Aug 2004
Posts: 169
Location: MONTREAL
If y is the smallest positive integer such that 3,150 [#permalink]

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01 Oct 2005, 16:15
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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
Senior Manager
Joined: 30 Oct 2004
Posts: 284

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01 Oct 2005, 16:32
E) 14

Find factors of 3150. You get 2^1*3^2*5^2*7^1.
If you multiply this number by 2*7 you will get a perfect square of an integer (2*3*5*7=210).
_________________

-Vikram

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Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

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01 Oct 2005, 17:09
first of all mbass...you are posting some really good questions..where are you getting them from? pls keep posting...math forum has been lil boring for sometime....

3150*y=X=perfect square....

well I know that (prime)^even power are perfect squares...so lets break 3150 into prime

315(5,63)*10 (5,2)

so lets break 63 down again...9*7...

so prime factors are 3^2, 5^2, 2 and 7....well if X is a perfect square then all its prime factors must be in equal power or should be perfect sqaures to...we see that so far 3150 has 3^2 and 5^2 prime factor...but we only have 2^1 and 7^1...in order to complete the perfect square we need one more 2 and 7...so that we have prime factors in the following way 2^2, 3^2, 5^2 and 7^2...

y has 7*2...14...E it is..
Current Student
Joined: 29 Jan 2005
Posts: 5218

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01 Oct 2005, 21:09
Thanx fresinha! You just made solving this problem crystal clear
Senior Manager
Joined: 15 Apr 2005
Posts: 415
Location: India, Chennai

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04 Oct 2005, 03:53
vikramm wrote:
E) 14

Find factors of 3150. You get 2^1*3^2*5^2*7^1.
If you multiply this number by 2*7 you will get a perfect square of an integer (2*3*5*7=210).

Vikramm, I did the hard way by mulitplying each answer choice by 3150 and taking the square root, to find the answer as 14. Follwed your post to realise that there is always a short cut. Thanks much for your post.

regards
04 Oct 2005, 03:53
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