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

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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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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, where a [#permalink]
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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]
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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.

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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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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.

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

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