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If N is a positive integer, is 9 a factor of N

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If N is a positive integer, is 9 a factor of N

by arora007 » Tue Jul 06, 2010 4:39 am
If N is a positive integer, is 9 a factor of N ?

1. 18 is a factor of N^2
2. 27 is a factor of N^3



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post from GMAT club...pretty easy
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by kvcpk » Tue Jul 06, 2010 4:48 am
arora007 wrote:If N is a positive integer, is 9 a factor of N ?

1. 18 is a factor of N^2
2. 27 is a factor of N^3
18 is a factor of n^2
so n^2 = 18*X
we need to know if 9 is a factor of n
let n=6
n^2 = 36 =18*2
9 is not factor of 6 ..NO
let n=18
n^2 = 18*18
9 is a factor of 18....... YES

27 is a factor of N^3
so n^3 = 27 * X
let n=6
6^3 = 216 = 27 *8
9 is not a factor of 8..NO
let n=18
18^3=27*12*18
9 is a factor of this value...YES

pick E
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by sanju09 » Tue Jul 06, 2010 4:52 am
arora007 wrote:If N is a positive integer, is 9 a factor of N ?

1. 18 is a factor of N^2
2. 27 is a factor of N^3



OA - E

post from GMAT club...pretty easy

(1) if N^2 = 18 k, for some positive integer k, N could be a multiple of 9 only if k is a multiple of 3, otherwise 9 cannot be a factor of N. Insufficient

(2) if N^3 = 27 m, for some positive integer m, N could be a multiple of 9 only if m is a multiple of 27, otherwise 9 cannot be a factor of N. Insufficient

When taken together, we can get N^5 = 18 × 27 × k × m, for some positive integers k and m.

And still, N could be a multiple of 9 only if k × m is a multiple of 243, otherwise 9 cannot be a factor of N. [spoiler]Insufficient

E[/spoiler]
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