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# Is 30 a factor of n? (1) 30 is a factor of n^2 (2) 30 is a

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SVP
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Is 30 a factor of n? (1) 30 is a factor of n^2 (2) 30 is a [#permalink]  04 Sep 2006, 00:31
Is 30 a factor of n?

(1) 30 is a factor of n^2
(2) 30 is a factor of 2n
Current Student
Joined: 29 Jan 2005
Posts: 5244
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In statement 2: n could be 15. INSUFF

I'll take (A)
Intern
Joined: 11 May 2006
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It must be C..

A. Is insufficient as n can be sqrt(30)

B. Is insuficient as n can be 15.

A and B together satisfies the condition...
Director
Joined: 13 Nov 2003
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Agree with C. In A n=sqrt30
Current Student
Joined: 28 Dec 2004
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how can it be A?

we dont even know if N is an integer?

(1) N^2=30M,

so we know that N^2 has prime factors, 2,3 and 5..but we dont know if N is an integer or not...N cud sqrt(30)..Insuff

(2)..well everyone else explained why it isnt suff...

C..together..cause (2) tells us that N is an integer and has definetly prime factors 3 and 5...statemnet confirms that N has 2, 3 and 5 as prime factors...thus togehter they are sufficient..

C it is..
SVP
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OA IS C

Thanks folks
CEO
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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
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ps_dahiya wrote:
Straight A.

Silly mistake.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Manager
Joined: 04 Feb 2004
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another one -
VP
Joined: 21 Sep 2003
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This questions never gets old

Here is a detailed explanation from the expert - HongHu
http://www.gmatclub.com/phpbb/viewtopic.php?t=16160
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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

Manager
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how can it be C

if n= 15 , then from St2, 30 is factor of 30, but 30 is not a factor of n (15) or n^2 ( 225). Only if n = 30, 60, 90 then n is factor of n^2 and n and also satisy statement 2.

Since from both statements you can not get a clear yes/ no answer, it must be E
SVP
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Jainan 24 i will try to explain it to you in details

Is 30 a factor of n?

(1) 30 is a factor of n^2
(2) 30 is a factor of 2n

From one

n^2 = 30m ie n = sqrt of 30m if m = 1 n is not integer if m=30 therfore n=30......thus insuff

from 2

2n = 30k thus n = 15 k if k is odd thus 30 is not a factor of n only when k is even that this is true ( ie k = 2z).....insuff

C scinario

from one
n^2 is even (15*2m)

from two

n = 15k ie : n^2 = 15^2*k^2 and since from one n^2 is even

therfore 15^2*k^2 is even , we know that odd*even = even,

15^2 is odd ie:(odd*odd) therfore k^2 is even thus k is even ie = 2z

therfore both together are enough
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