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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, 18:01
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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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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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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, 08:02, edited 2 times in total.
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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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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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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, 21:06, edited 1 time in total.
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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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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, 21:17, edited 3 times in total.
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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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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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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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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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Yes C looks fine. WHat's the OA?
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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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can somebody explain this in very easy terms please.
Thanks
S
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Regards, S
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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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