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

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sperumba
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For all integers n, the function f is defined by f(n) = a^n, where a [#permalink] New post   Updated on: 15 Sep 2020, 03:08
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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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B

Originally posted by sperumba on 17 Jan 2006, 18:20.
Last edited by Bunuel on 15 Sep 2020, 03:08, edited 1 time in total.
Renamed the topic and edited the question.
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Re: For all integers n, the function f is defined by f(n) = a^n, where a [#permalink] New post   22 Jul 2010, 11:13
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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.

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, where a [#permalink] New post   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) = a^n, where a [#permalink] New post   07 May 2013, 00:01
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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, where a [#permalink] New post   07 May 2013, 06:12
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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, where a [#permalink] New post   10 Jun 2021, 00:24
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From Statement 1 the value of a can be +10 or -10 therefore INSUFFICIENT.
From Statement n2 it is clear that the value of a is -10 therefor SUFFICIENT.

Answer B
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Re: For all integers n, the function f is defined by f(n) = a^n, where a [#permalink] New post   02 Nov 2021, 02:58
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The function f is defined by f(n) = \(a^n\), where a is a constant. We need to find the value of f(1).

Statement 1:f(2) = 100

\(a^2 \)= 100
a=+10 or -10

Since there are 2 values possible for a , f(1) will also have 2 values i.e 10 ^1= 10 and -10^1 =-10
Statement 1 alone is not sufficient.

(2) f(3) = -1,000
\(a^3\) =-1000
a=-10
Here, there is only one possible value of a, so f(1) =-10^1 =-10.
Since we have only one definite value for f(1), Statement 2 alone is sufficient.

Option B is the answer.

Thanks,
Clifin J Francis,
GMAT SME
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For all integers n, the function f is defined by f(n) = a^n, where a [#permalink] New post   02 Nov 2021, 06:59
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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 , \(a^2 =100\) means a= 10 or -10, so f(1) can be 10 or -10, so Not sufficient

(2) f (3) = -1,000 , \(a^3 = -1000\), so \(a= -10\), so \(f(1)= -10\) Sufficient

Answer: B
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Re: For all integers n, the function f is defined by f(n) = a^n, where a [#permalink] New post   14 Apr 2022, 08:54
This might be a silly question, can anyone help explain here please? Why is 100^2 = +10 and -10 ? as a is not |a|. Thanks
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Re: For all integers n, the function f is defined by f(n) = a^n, where a [#permalink] New post   22 Oct 2023, 21:15
Hello from the GMAT Club BumpBot!

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