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

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Is 30 a factor of N? 1) 30 is a factor of N^2? 2) 30 is [#permalink]  06 May 2005, 17:01
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299. Is 30 a factor of N?
1) 30 is a factor of N^2?
2) 30 is factor of 2N.
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[#permalink]  06 May 2005, 17:11
A it is.

30 = 2*3*5

A. if 30 is a factor N*N, it has to be a factor of N because every factor of N is repeated twice in the factor of N*N .
Sufficient.

B. 30 is a factor of 2N.

Let N=15, 30 is a factor of 2N and not a factor of N
Let N=30, 30 is a factor of 2N and is a factor of N
Insufficient.
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Re: DS [#permalink]  06 May 2005, 18:11
perezhan wrote:
299. Is 30 a factor of N?
1) 30 is a factor of N^2?
2) 30 is factor of 2N.

I may go with E as well

(1) N^2 =30, 30 is not a factor of N--> insufficient

(2) N =15, 30 is not a factor of N

but conbine 1 and 2, I couldn't find a counterexample.

Last edited by chunjuwu on 07 May 2005, 07:02, edited 2 times in total.
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Re: DS [#permalink]  06 May 2005, 18:12
MA wrote:
perezhan wrote:
299. Is 30 a factor of N?
1) 30 is a factor of N^2?
2) 30 is factor of 2N.

A is Ok.

It didn't consider N is non-integer
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[#permalink]  06 May 2005, 18:40
ashkg wrote:
A it is.

30 = 2*3*5

A. if 30 is a factor N*N, it has to be a factor of N because every factor of N is repeated twice in the factor of N*N .
Sufficient.

B. 30 is a factor of 2N.

Let N=15, 30 is a factor of 2N and not a factor of N
Let N=30, 30 is a factor of 2N and is a factor of N
Insufficient.

take N^2 = 60

So N=sqrt(60) which isnt divisible by 30.
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Re: DS [#permalink]  06 May 2005, 20:01
chunjuwu wrote:
(1) N^2 =30, 30 is not a factor of N

if you know 30 is not a factor of n, then this information is sufficiet to anseer the question.

Last edited by MA on 06 May 2005, 20:06, edited 1 time in total.
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Re: DS [#permalink]  06 May 2005, 20:03
MA wrote:
chunjuwu wrote:
(1) N^2 =30, 30 is not a factor of N

if you know 30 is not a factor of n, then this information is sufficiet to anseer the question. therefore A is ok.

MA: if N^2 = 60 then N is not divided by 30 right? I am stuck up there
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[#permalink]  06 May 2005, 20:04
gmat2me2 wrote:
take N^2 = 60
So N=sqrt(60) which isnt divisible by 30.

i am sorry guys, it's not A. i thought N is an integer, let me do it again:

from i, if 30 is a factor of N^2, N could be 30 or sqrt(30). so isuff.
from ii, if 30 is factor of 2N, N could be 15 or 30. so still insufficient.

combining i and ii is sufficient to answer the question. to satisfy i and ii, N must be a multiple of 30.

Last edited by MA on 06 May 2005, 20:17, edited 3 times in total.
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[#permalink]  06 May 2005, 20:39
MA wrote:
gmat2me2 wrote:
But where is it given??

yes, you are correct.

No issues MA....Thanks to you too for helping me with my inequalities problem.
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[#permalink]  07 May 2005, 07:01
MA wrote:
gmat2me2 wrote:
take N^2 = 60
So N=sqrt(60) which isnt divisible by 30.

i am sorry guys, it's not A. i thought N is an integer, let me do it again:

from i, if 30 is a factor of N^2, N could be 30 or sqrt(30). so isuff.
from ii, if 30 is factor of 2N, N could be 15 or 30. so still insufficient.

combining i and ii is sufficient to answer the question. to satisfy i and ii, N must be a multiple of 30.

Hi, where to get it?

what is the OA?
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[#permalink]  07 May 2005, 07:31
by reading all the posts, it seems like there were a lot of edits to this which makes it hard to follow.

I fell for the A trap initially, but I agree that if we don't know that N is an integer, we can't make an absolute judgement. I suppose, however, that we know in number 2 that N IS an integer, because there's no fraction that, times 2, will be a multiple of N. That said, it's not enough, because N could be 15.

So I'm going with C.
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[#permalink]  07 May 2005, 07:39
C)...

1) N could be 30 YES N could sqrt30 NO => insufficient

2) N could be 15 NO n could be 30 YES => insufficient

1+2) no prove why it shouldn`t be C), unless you correct me
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[#permalink]  07 May 2005, 08:18
Yes C looks fine. WHat's the OA?
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Re: DS [#permalink]  08 May 2005, 19:45
perezhan wrote:
299. Is 30 a factor of N?
1) 30 is a factor of N^2?
2) 30 is factor of 2N.

The case of combined:

1) N^2=30k
2) 2N=30s
Where k and s are integers.

2)=>
N=15s
N^2=15^2*s^2

From 1) we know that N^2 is even. => s is even
Say s=2m where m is integer
N=15s=30m
N is a multiple of 30.

Therefore C.

Another simpler approach, the only case where 1) is not sufficient is when N is not integers. From 2 we know that N IS an integer. Thus combine 1) and 2) is sufficient.
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[#permalink]  07 Sep 2005, 05:23
can somebody explain this in very easy terms please.
Thanks
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Re: DS [#permalink]  07 Sep 2005, 11:48
perezhan wrote:
299. Is 30 a factor of N?

1) 30 is a factor of N^2
30 may or may not be integers so it may or may not be a factor of N.
eg. If N=60, then 30 is a factors of both N and N^2. But if N=sqrt(30) then so is a factor of N^2, but not a factor of N.
Insufficient

2) 30 is factor of 2N.
This means 15 must be a factor of N. If we know N is even, in other words 2 is also a factor of N, then we are sure 30 is a factor of N. Without knowing whether N is even or odd, we don't know.
Insufficient

Combined:
From 2) N must be an integer. From 1) if N is an integer and 30 is a factor of N^2, then 30 must be a factor of N. This is because 30=2*3*5.

Something for more thought:
If the question is changed, instead of 30, the number is 24, for example, then we will not be able to say this, because 12=2*2*3.
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Re: DS   [#permalink] 07 Sep 2005, 11:48
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