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Intern
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Need help thanks [#permalink] New post 21 Mar 2010, 12:15
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

93% (02:08) correct 6% (01:34) wrong based on 16 sessions
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] New post 21 Mar 2010, 12:59
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] New post 21 Mar 2010, 14:57
Thanks a lot

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Senior Manager
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Re: Need help thanks [#permalink] New post 22 Mar 2010, 06:45
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] New post 22 Mar 2010, 07:55
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, 07:55
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