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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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This question can be solved with a combination of arithmetic and TESTing VALUES.

We're told that N and T are POSITIVE INTEGERS. We're asked if N is a factor of T. This is a YES/NO question.

Fact 1: N = 3^(N−2)

Since this Fact tells us NOTHING about T, it's clearly insufficient. We can find the value of N without too much trouble though since we already know that it's a positive integer. With a little "brute force", we can find that N = 3 is the solution. Fact 1 is INSUFFICIENT

Fact 2: T = 3^N

IF.... N = 1 T = 3 1 IS a factor of 3 so the answer to the question is YES

IF.... N = 2 T = 9 2 is NOT a factor of 9 so the answer to the question is NO Fact 2 is INSUFFICIENT

Combined, we know... N = 3 T = 3^N = 3^3 = 27 3 IS a factor of 27 so the answer to the question is ALWAYS YES. Combined, SUFFICIENT

Re: If n and t are positive integers, is n a factor of t? [#permalink]

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22 Aug 2016, 13:34

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If n and t are positive integers, is n a factor of t? [#permalink]

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26 Aug 2016, 05:50

Statement 1 is insufficient as there is no relation mentioned between 'n' & 't' Statement 2 is also insufficient, consider n=0, then t=1 , n=1 then t=3 but if n=3, then t=27. Different cases can be obtained.

Combined: n=3^n.3^-2, n=t.3^-2, 9.n=t. Hence option C.

gmatclubot

If n and t are positive integers, is n a factor of t?
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26 Aug 2016, 05:50

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