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# For all integers n, the function f is defined by f (n) =

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Manager
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For all integers n, the function f is defined by f (n) = [#permalink]

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22 Jul 2010, 10:45
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Question Stats:

72% (00:41) correct 28% (00:49) wrong based on 202 sessions

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For all integers n, the function f is defined by f (n) = a^n, where a is a constant. What is the value of f (1)?

(1) f (2) = 100
(2) f (3) = -1,000
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Jun 2013, 02:29, edited 2 times in total.
Edited the stem.

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22 Jul 2010, 11:13
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Expert's post
Edited the stem. It should be:

For all integers n, the function f is defined by f (n) = a^n, where a is a constant. What is the value of f (1)?

$$f(1)=a^1=a$$, so basically the question is: what is the value of $$a$$?

(1) f(2) = 100 --> $$f(2)=100=a^2$$ --> $$a=10$$ or $$a=-10$$. Two answers, not sufficient.

(2) f(3) = -1,000 --> --> $$f(3)=-1,000=a^3$$ --> only one solution: $$a=-10$$. Sufficient.

Hope it's clear.
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22 Jul 2010, 11:18
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KUDOS
Bunuel wrote:
Edited the stem. It should be:

For all integers n, the function f is defined by f (n) = a^n, where a is a constant. What is the value of f (1)?

$$f(1)=a^1=a$$, so basically the question is: what is the value of $$a$$?

(1) f(2) = 100 --> $$f(2)=100=a^2$$ --> $$a=10$$ or $$a=-10$$. Two answers, not sufficient.

(2) f(3) = -1,000 --> --> $$f(3)=-1,000=a^3$$ --> only one solution: $$a=-10$$. Sufficient.

Hope it's clear.

I apologize Bunuel for mistake in stem

Thanks a ton for correcting the mistake and the solution.

You really explain things very well
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Re: For all integers n, the function f is defined by f (n) = [#permalink]

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30 Aug 2014, 07:56
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Re: For all integers n, the function f is defined by f (n) = [#permalink]

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17 May 2016, 22:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: For all integers n, the function f is defined by f (n) = [#permalink]

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09 Aug 2017, 00:02
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: For all integers n, the function f is defined by f (n) =   [#permalink] 09 Aug 2017, 00:02
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