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Re: Is positive integer N divisible by 3? [#permalink]
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]
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]
04 Aug 2014, 20:37

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