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

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05 Apr 2010, 10:49

1

This post was BOOKMARKED

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

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

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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 _________________

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

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04 Aug 2014, 20:37

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

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13 Jan 2016, 09:44

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
_________________

Sortem sternit fortem!

Last edited by Sash143 on 07 Feb 2017, 08:35, edited 1 time in total.

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

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14 Jan 2017, 22:26

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.

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