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# Need help thanks

Author Message
Intern
Joined: 08 Dec 2009
Posts: 29

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21 Mar 2010, 13:15
00:00

Difficulty:

(N/A)

Question Stats:

97% (01:48) correct 3% (01:34) wrong based on 49 sessions

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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

[Reveal] Spoiler: OA
OA is E
Manager
Joined: 10 Aug 2009
Posts: 123

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21 Mar 2010, 13:59
aljatar 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

[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 $$2*7=14$$
Intern
Joined: 08 Dec 2009
Posts: 29

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21 Mar 2010, 15:57
Thanks a lot

Posted from my mobile device
Senior Manager
Joined: 13 Dec 2009
Posts: 262

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22 Mar 2010, 07:45
aljatar 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

[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
_________________

My debrief: done-and-dusted-730-q49-v40

Senior Manager
Joined: 01 Feb 2010
Posts: 264

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22 Mar 2010, 08:55
aljatar 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
[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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