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Re: If y is the smallest positive integer such that 3,150 [#permalink]
28 Jan 2012, 17:00

1

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Expert's post

mrwaxy 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

Detailed explanation would be appreciated.

3,150=2*3^2*5^2*7, now 3,150*y to be a perfect square y must complete the odd powers of 2 and 7 to even number (perfect square has even powers of its primes), so the least value of y is 2*7=14. In this case 3,150y=(2*3^2*5^2*7)*(2*7)=(2*3*5*7)^2=perfect \ square.

Re: If y is the smallest positive integer such that 3,150 [#permalink]
30 Jan 2012, 08:46

factorise 3150, to find out the missing doubles... 3150 = 5x5x3x3x2x7... so 2x7=14... when multiplied to 3150, will make it a perfect square... answere is E

Re: If y is the smallest positive integer such that 3,150 [#permalink]
13 Jun 2013, 01:07

1

This post received KUDOS

mrwaxy 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

In such questions we need to break the number into the smallest possible prime factors. So the smallest prime factors of 3150 are: 315*10=63*5*2*5=7*9*5*2*5=7*3*3*5*2*5. In order to get a square of an integer we have to have at least two identical primes. In our case we have 3*3 and 5*5 corresponding to this condition but not 2*7 so our smallest number should be 14.

Answer is E
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Re: if y is the smallest positive interger such that 3150 multip [#permalink]
29 Aug 2013, 00:35

kumar83 wrote:

if y is the smallest positive interger such that 3150 multiplied by y is the square of an interger, that Y must be

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

Kindly Explain.

3150 =2*3^2*5^2*7 For it to be perfect square all the prime number should be least raised to the power 2 in 3150 ...only 2 and 7 needs to be multiplied so that all prime will be raised power 2 hence least value of 4y = 2*7 = 14

hence E
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