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Is positive integer N divisible by 3?

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Is positive integer N divisible by 3? [#permalink]

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New post 05 Apr 2010, 09:26
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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, 03:10, 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]

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New post 05 Apr 2010, 11:49
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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]

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New post 05 Apr 2010, 19:37
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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Is positive integer N divisible by 3? [#permalink]

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New post 13 Jan 2016, 10:44
silver870 wrote:
Is positive integer N divisible by 3?

(1) N^2/36 is an integer

(2) 144/N^2 is an integer


From (1) \(n^2/36\)= INT
Therefore the values for \(n^2\) that fit the condition = 36, 144 and so on
n= 6, 12 (bcoz \(n\) is positive int) and so on. Fact (1) SUFF
From (2) \(144/n^2\)= INT
Therefore \(n^2\) could be 1, 4, 9....
and when n= 1 (No), 2 (No), 3 (Yes). Fact 2 INSUFF
Hence A :-D
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Last edited by Sash143 on 07 Feb 2017, 09:35, edited 1 time in total.

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Re: Is positive integer N divisible by 3? [#permalink]

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New post 14 Jan 2017, 23:26
A very useful property -> X and X^n always have the exact same prime factors.
For N to be divisible by 3 => 3 must be the prime factors of N.

Statement 1=>
N^2/36 is an integer.
N^2 has both 2 and 3 as it prime.
Thus N must have 3 as its prime too.
Hence Sufficient.
Statement 2=>
Lets use test Cases here.
N=1 => 144/1^2 =Integer => 1 is not divisible by 3.
N=3 => 144/N^2 =integer => 3 is divisible by 3.
Hence not sufficient.

Hence A

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Re: Is positive integer N divisible by 3? [#permalink]

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New post 06 Feb 2017, 07:14
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I did this problem with difference approach. Can some one please evaluate is my approach towards this problem correct?
Attachments

problem.jpg
problem.jpg [ 1.41 MiB | Viewed 790 times ]


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Re: Is positive integer N divisible by 3? [#permalink]

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New post 07 Oct 2017, 10:39
St 1: N sq/36 = integer. 36 is a multiple 3, so dvble by 3
St 2: 144/ N sq = integer. N = what? Not suff

Ans: A

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Re: Is positive integer N divisible by 3?   [#permalink] 07 Oct 2017, 10:39
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