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

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

12 Jun 2008, 05:00

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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.

[Reveal] Spoiler: OA

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Last edited by Bunuel on 28 Jan 2012, 18:01, edited 1 time in total.

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Re: PS - S26 q30 [#permalink]

13 Jun 2008, 04:35

IMO E should be the answer for this

i just tried plugging in the numbers and found out that

14*3150 = 44, 100, which is a square of 210

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

28 Jan 2012, 17:42

answer E. factor out the number and find any prime numbers that are not paired. 7 & 2.
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Re: If y is the smallest positive integer such that 3,150 [#permalink]

28 Jan 2012, 18:00

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.

Answer: E.

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

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] 30 Jan 2012, 09:46

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

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

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