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Re: If y is the smallest Positive integer such that 3150 [#permalink]
23 Feb 2014, 15:59

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Re: If y is the smallest positive integer such that 3,150 multip [#permalink]
23 Feb 2014, 16:32

1

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Expert's post

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

\(3,150=2*3^2*5^2*7\), 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 multip [#permalink]
19 Apr 2014, 07:43

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3150*y = A^2

3 * 1050 * y = A^2

3*5*210*y = A^2

3*5*7*3*2*5*y = A^2

2*3^2*5^2*7*y = A^2

Concept: The factors of squared integer should occur in pair. So, the only numbers left are 2*7

Hence 14 _________________

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Re: If y is the smallest positive integer such that 3,150 multip
[#permalink]
19 Apr 2014, 07:43

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