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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] New post 11 Jul 2009, 09:26
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-all-integers-n-the-function-f-is-defined-by-f-n-97735.html
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Re: For all integers n, the function f is defined by f(n)=a^n [#permalink] New post 11 Jul 2009, 10:12
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square root of any number can be either positive or negative, but cube root of any number will always have the same sign as the number itself.

stmt 1 only gives us the absolute value of a, but not the sign
Stmt 2 alone gives us both, the value and sign, ie a = -10

So B
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Re: For all integers n, the function f is defined by f(n)=a^n [#permalink] New post 11 Jul 2009, 12:46
nice and simple explanation right off the bat. thanks
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Re: For all integers n, the function f is defined by f(n)=a^n [#permalink] New post 01 Jan 2015, 11:14
AT FIRST I GOT IT ALL WRONG !!! :shock: square-root will yield two possible values
1) f(2)=100=a^2
so a=+/_ sqrt 50 , Insufficient because two values are possible.

2) a^3=-1000
a=-10 , Sufficient

Hence the answer is B

gmatraj wrote:
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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Re: For all integers n, the function f is defined by f(n)=a^n [#permalink] New post 01 Jan 2015, 16:33
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Hi All,

The concept of "squared terms" is something you'll see repeatedly in the Quant section of the GMAT. Since math rules don't change, part of your practice should be based on learning how to "respond" to a piece of information when it shows up in a question. When I see ANY exponents, I immediately think of the handful of exponent rules that they GMAT COULD test me on. When I see a squared term, I immediately think "there's MORE than one answer." In this way, before I start doing any of the *real* work that is required to answer the question, I have the idea in mind (and I can jot it down on my pad) so I won't miss that question for a silly reason.

During your studies, you're not just trying to answer an individual question correctly, you should also be trying to build up your memory, pattern-matching ability, etc. so that when those same patterns occur again, you'll be able to answer the question correctly (and likely faster).

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Re: For all integers n, the function f is defined by f(n)=a^n [#permalink] New post 02 Jan 2015, 04:42
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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)?

\(f(1)=a^1=a\), 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-all-integers-n-the-function-f-is-defined-by-f-n-97735.html
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Re: For all integers n, the function f is defined by f(n)=a^n   [#permalink] 02 Jan 2015, 04:42
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