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# If n and t are integers, is n a factor of t? (1) n = 3^(n-2)

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Manager
Joined: 09 Jul 2008
Posts: 111

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Location: Dallas, TX
Schools: McCombs 2011
If n and t are integers, is n a factor of t? (1) n = 3^(n-2) [#permalink]

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30 Nov 2008, 19:31
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If n and t are integers, is n a factor of t?

(1) n = 3^(n-2)

(2) $$t = 3^n$$

Kudos [?]: 42 [0], given: 1

Director
Joined: 14 Aug 2007
Posts: 726

Kudos [?]: 212 [0], given: 0

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30 Nov 2008, 19:58
Looks like something is wrong in 1), it does not tell us anything about t.

heres a try:

1) is clearly insuff.
2) consider n = 1 => t = 3 => n is a facotor of t
consider n = 2 => t =9 => n is NOT a factor of t

so insuff.

together

from 1)

n = 3^n/3^2 = n = 3^n/9
i.e 3^n = 9n
substituting this in 2)
t = 9*n

so t is a multiple of n and thus n is a factor of t

C

Kudos [?]: 212 [0], given: 0

Re: DS: exponents   [#permalink] 30 Nov 2008, 19:58
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