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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

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]

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30 Jan 2012, 09:46

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]

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13 Jun 2013, 02:07

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]

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29 Aug 2013, 01:35

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

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22 Jul 2014, 04:18

Hello,

can anyone help me with this type of question? I don't get it why the remaining numbers, 7 and 2, are the smallest positive integer y. Which chapter in the MGMAT books should i restudy to deal with this kind of problem? I don't understand the explanation in the OG which says: "To be a perfect square, 3,150y must have an even number of each of its prime factors."

can anyone help me with this type of question? I don't get it why the remaining numbers, 7 and 2, are the smallest positive integer y. Which chapter in the MGMAT books should i restudy to deal with this kind of problem? I don't understand the explanation in the OG which says: "To be a perfect square, 3,150y must have an even number of each of its prime factors."

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

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01 Aug 2016, 02:08

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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

Key concept: The prime factorization of a perfect square (the square of an integer) will have an EVEN number of each prime. For example, 36 = (2)(2)(3)(3) And 400 = (2)(2)(2)(2)(5)(5)

Likewise, 3150y must have an EVEN number of each prime in its prime factorization. So, 3150y = (2)(3)(3)(5)(5)(7)y We have an EVEN number of 3's and 7's, but we have a single 2 and a single 7. If y = (2)(7), then we get a perfect square.