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

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Manager
Joined: 13 Jun 2005
Posts: 246
Location: Haverhill, MA
For all integers n, the function f is defined by f (n) = a^n  [#permalink]

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17 Jan 2006, 17:20
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00:00

Difficulty:

15% (low)

Question Stats:

71% (00:48) correct 29% (00:47) wrong based on 447 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
Director
Joined: 20 Sep 2005
Posts: 998

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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.
SVP
Joined: 16 Oct 2003
Posts: 1717

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17 Jan 2006, 18:17
B

From I We get +10 or -10
From II we get 1- so f(1) = -10.
Director
Joined: 04 Oct 2005
Posts: 554
Location: Chicago

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17 Jan 2006, 21:55
B is suffiecient

a) gives us a=+ or -10 so INSUFF
b) gives us a=-10 so sufficient
CEO
Joined: 20 Nov 2005
Posts: 2774
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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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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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Manager
Joined: 17 Jul 2010
Posts: 112
Re: For all integers n, the function f is defined by f (n) =  [#permalink]

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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,
Math Expert
Joined: 02 Sep 2009
Posts: 52296
Re: For all integers n, the function f is defined by f (n) =  [#permalink]

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06 May 2013, 23:01
2
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.

Hope it's clear.
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Manager
Joined: 17 Jul 2010
Posts: 112
Re: For all integers n, the function f is defined by f (n) = a^n  [#permalink]

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07 May 2013, 05:12
1
Super clear explanation, thank you Banuel.
Intern
Joined: 29 Sep 2018
Posts: 12
Re: For all integers n, the function f is defined by f (n) = a^n  [#permalink]

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18 Nov 2018, 07:10
If $$f(n) = a^n$$, what is the value of $$f(1)$$?

Statement 1:

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

Statement 2:

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

$$f(1) = 10^1 =10$$
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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# For all integers n, the function f is defined by f (n) = a^n

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