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If n and t are positive integers, is n a factor of t?

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If n and t are positive integers, is n a factor of t? [#permalink] New post 30 Jul 2009, 03:35
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68% (01:57) correct 32% (01:06) wrong based on 28 sessions
If n and t are positive integers, is n a factor of t ?

(1) n = 3^{n-2}
(2) t = 3^n
[Reveal] Spoiler: OA
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Re: is n a factor of t?? [#permalink] New post 30 Jul 2009, 03:40
1) n= 3^n-2 ... but no relationship with t defined .. so insuff

2) t=3^n =

for n = 1 t = 3 so 1 is a factor of 3 .. true
for n = 2 t = 9 so 2 is not a factor of 9 ... false

so insuff


combine both ..

we see that the only value of n that satisfies stmt1 condition is n = 1
and for n = 1 we see that stmt 2 is true ...

therefore C
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Re: is n a factor of t?? [#permalink] New post 30 Jul 2009, 05:13
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arvs212 wrote:
If n and t are positive integers, is n a factor of t?

1) n= 3^n-2

2) t=3^n

pllz give reasonings...or if discussed earlier do post the link..


The answer here really depends on how S1 is written. There's a question in GMATFocus where Statement 1 reads n = 3^{n-2}. Then, from S1 you can determine by inspection that n = 3, but we have no information about t, so this is not sufficient. Statement 2 is not sufficient either; n could be 3 and the answer is 'yes', or n could be 2 and the answer is 'no'. Using both together, the question 'is n a factor of t' becomes 'is 3^(n-2) a factor of 3^n', to which the answer is clearly yes, since n-2 is less than n (when you divide 3^n by 3^(n-2), you get 3^2 = 9). So the answer is C.

If, on the other hand, Statement 1 is written as in the original post above, so that the '-2' is not part of the exponent: n = 3^n - 2, then from S1 you can see by inspection that n = 1. Since 1 is a factor of every positive integer, Statement 1 would then be sufficient, and the answer would be A.
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Re: is n a factor of t?? [#permalink] New post 30 Jul 2009, 05:53
So true ... whats the OA ?
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Re: is n a factor of t?? [#permalink] New post 30 Jul 2009, 07:36
thnks everyone...the OA is C...and in the question it is...1) n = 3^(n-2)... :P
Re: is n a factor of t??   [#permalink] 30 Jul 2009, 07:36
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