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

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

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18 Feb 2004, 23:48
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-y-is-the-smallest-positive-integer-such-that-65323.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 23 Feb 2014, 17:31, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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19 Feb 2004, 00:00
I go with E.

B and C are out because they are odd.
A and D do not work. Just do the multiplication and you can see that there is not square.
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19 Feb 2004, 05:57
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E. 3150= 5*5*3*3*7*2, so we need one 7 and one 2 to make it a square of a number. so 7*2= 14
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Re: If y is the smallest Positive integer such that 3150 [#permalink]

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23 Feb 2014, 16:59
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Re: If y is the smallest positive integer such that 3,150 multip [#permalink]

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23 Feb 2014, 17:32
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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

$$3,150=2*3^2*5^2*7$$, 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 $$3,150y=(2*3^2*5^2*7)*(2*7)=(2*3*5*7)^2=perfect \ square$$.

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Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-y-is-the-smallest-positive-integer-such-that-65323.html
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Re: If y is the smallest positive integer such that 3,150 multip [#permalink]

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19 Apr 2014, 08:43
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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, 08:43
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