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

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

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17 Jan 2006, 18:20
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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

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VP
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17 Jan 2006, 18:28
B.

1. f(2) = a^2 = 100. a = 10,-10...INSUFF.
2. f(3) = a^3 = -1000. a = -10....Thus a(1) = (-10)^1 = -10..SUFF.

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17 Jan 2006, 19:17
B

From I We get +10 or -10
From II we get 1- so f(1) = -10.

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Director
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17 Jan 2006, 22:55
B is suffiecient

a) gives us a=+ or -10 so INSUFF
b) gives us a=-10 so sufficient

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18 Jan 2006, 02:44
B

f(1) = a we need to find a.

St1: f(2) = a^2 = 100. So a = -10 or 10 INSUFF

St2: f(3) = a^3 = -1000. So a = -10. SUFF
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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

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06 May 2013, 21:24
Can someone help me here, IF the question is a value question such as this one, statement one provides two values (+10) or (-10), I'm under the impression that the values are found,
but the gmat wants one value, is this true for all DS questions, the value cannot have two or more possibilities, correct?

Thanks,

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

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07 May 2013, 00:01
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Expert's post
laythesmack23 wrote:
Can someone help me here, IF the question is a value question such as this one, statement one provides two values (+10) or (-10), I'm under the impression that the values are found,
but the gmat wants one value, is this true for all DS questions, the value cannot have two or more possibilities, correct?

Thanks,

There are two kinds of data sufficient questions: YES/NO DS questions and DS questions which ask to find a value.

In a Yes/No Data Sufficiency questions, statement is sufficient if the answer is “always yes” or “always no” while a statement is insufficient if the answer is "sometimes yes" and "sometimes no".

When a DS question asks about the value of some variable, then the statement is sufficient ONLY if you can get the single numerical value of this variable.

BACK TO THE QUESTION.
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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Re: For all integers n, the function f is defined by f (n) = a^n [#permalink]

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07 May 2013, 06:12
Super clear explanation, thank you Banuel.

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

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29 Jan 2016, 14:11
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Re: For all integers n, the function f is defined by f (n) = a^n   [#permalink] 29 Jan 2016, 14:11
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# For all integers n, the function f is defined by f (n) = a^n

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