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Need help thanks [#permalink]

21 Mar 2010, 13:15

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hi please provide help

thanks in advance

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

[Reveal] Spoiler: OA

OA is E

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Re: Need help thanks [#permalink]

21 Mar 2010, 13:59

aljatar wrote:

hi please provide help

thanks in advance

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

[Reveal] Spoiler: OA

OA is E

Honestly I don't know exactly why this is right but this is what I did:

3150*y = x^2
y = \frac{x^2}{3150}

Next we do the prime factorization of 3150 and get 2*5^2*3^2*7

for x^2 to be divisible by 3150, x has to be at least 2*5*3*7. In that case, x^2 divided by 3150 will be 2*7=14

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Re: Need help thanks [#permalink]

21 Mar 2010, 15:57

Thanks a lot

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Re: Need help thanks [#permalink]

22 Mar 2010, 07:45

aljatar wrote:

hi please provide help

thanks in advance

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

[Reveal] Spoiler: OA

OA is E

We need y*3150 should be a perfect square
or, y*3*3*5*5*2*7
if we take sqrt of this number= 15 sqrt (y*2*7)
To make it perfect square y should be 2*7 or 14. hence answer is E
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Re: Need help thanks [#permalink]

22 Mar 2010, 08:55

aljatar wrote:

hi please provide help
thanks in advance
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

[Reveal] Spoiler: OA

OA is E

Prime Factors of 3150 = 2*3^2*5^2*7
for it to square of integer = 2*3^2*5^2*7 * 2 * 7
= 2*3^2*5^2*7 * 14
hence E.

Re: Need help thanks [#permalink] 22 Mar 2010, 08:55

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