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

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

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New post 17 Jan 2006, 17:20
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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
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New post 17 Jan 2006, 17:28
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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New post 17 Jan 2006, 18:17
B

From I We get +10 or -10
From II we get 1- so f(1) = -10.
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New post 17 Jan 2006, 21:55
B is suffiecient

a) gives us a=+ or -10 so INSUFF
b) gives us a=-10 so sufficient
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New post 18 Jan 2006, 01:44
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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Re: For all integers n, the function f is defined by f (n) =  [#permalink]

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New post 06 May 2013, 20:24
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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New post 06 May 2013, 23:01
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1
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.

Answer: B.

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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New post 07 May 2013, 05:12
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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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New post 18 Nov 2018, 07:10
If \(f(n) = a^n\), what is the value of \(f(1)\)?

Statement 1:

\(f(2) = 100\)
\(a^2 = 100\)
\(\sqrt{a^2}=\sqrt{100}\)
\(a = 10, -10\)

2 answers: INSUFFICIENT.

Statement 2:

\(f(3) = 1,000\)
\(a^3 = 1,000\)
\(\sqrt{a^3}=\sqrt{1,000}\)
\(a = 10\)

1 answer: SUFFICIENT.

\(f(1) = 10^1 =10\)
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Re: For all integers n, the function f is defined by f (n) = a^n &nbs [#permalink] 18 Nov 2018, 07:10
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