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

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

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30 Jul 2009, 04:35
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If n and t are positive integers, is n a factor of t ?

(1) $$n = 3^{n-2}$$
(2) $$t = 3^n$$
[Reveal] Spoiler: OA

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Senior Manager
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Re: is n a factor of t?? [#permalink]

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30 Jul 2009, 04:40
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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GMAT Tutor
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Re: is n a factor of t?? [#permalink]

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30 Jul 2009, 06:13
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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]

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30 Jul 2009, 06:53
So true ... whats the OA ?

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Manager
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Re: is n a factor of t?? [#permalink]

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30 Jul 2009, 08:36
thnks everyone...the OA is C...and in the question it is...1) n = 3^(n-2)...

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

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07 May 2015, 11:46
1) n = 3^{n-2}=3^n/2
2) t = 3^n

From 1) and 2)

t = 2*n

arvs212 wrote:
If n and t are positive integers, is n a factor of t ?

(1) $$n = 3^{n-2}$$
(2) $$t = 3^n$$

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

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08 May 2015, 11:40
Hi All,

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

[Reveal] Spoiler:
C

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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.

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