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Is positive integer N divisible by 3?

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Is positive integer N divisible by 3? [#permalink] New post 05 Apr 2010, 08:26
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (02:01) correct 44% (00:59) wrong based on 50 sessions
Is positive integer N divisible by 3?

(1) N^2/36 is an integer

(2) 144/N^2 is an integer
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Aug 2014, 02:10, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Is positive integer N divisible by 3? [#permalink] New post 05 Apr 2010, 10:49
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silver870 wrote:
I don't understand why the answer is A, and not D. Can someone please explain?

Is positive integer N divisible by 3?

1.) N^2 / 36 is an integer

2.) 144 / N^2 is an integer


st 1) N^2 / 36 is an integer
36 = 2^2 * 3^3
For N^2 to be evenly divided by 36, N should have factors at a minimum, one 2 and one 3. Sufficient
st 2) 144 / N^2 is an integer
144 = 2^4 * 3^2
N could be either 2, 4, or 3. Not sufficient

A
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Re: Is positive integer N divisible by 3? [#permalink] New post 05 Apr 2010, 18:37
I agree with Chix47, with a little more detail...

S1. The prime factorization of 36 is
2^2 * 3^2
therefore to be divisible by 36, both N^2 and N must have 3 as a factor
S

S2. this statement is written differently from the first. notice that N^2 is in the denominator. Possible values for N^2 are 16, 9, 4. Therefore possible values for N are 4, 3, 2.

4/3 = not an integer
3/3 = an integer

therefore for S2 you get "sometimes yes, sometimes no" and it is insufficient.
Answer: A
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Re: Is positive integer N divisible by 3? [#permalink] New post 06 Apr 2010, 09:35
Now I get it.

Thanks for info. :-D
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Re: Is positive integer N divisible by 3? [#permalink] New post 04 Aug 2014, 20:37
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Re: Is positive integer N divisible by 3?   [#permalink] 04 Aug 2014, 20:37
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