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f is defined by f (n) = k a^n

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f is defined by f (n) = k a^n

by sanju09 » Tue Jul 30, 2013 11:51 pm
For all integers n, the function f is defined by f (n) = k a^n where k and a are constants. What is the value of f (3)?

(1) f (0) = 5.

(2) f (2) = 20.



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by gmatsid » Wed Jul 31, 2013 1:33 am
The answer should be E in my opinion.

From the statement: f(n)=ka^n which gives us f(3)=ka^3 So you would need k and a.

Statement 1: f(0)=5=ka^0=k(1)=k.

So k=5, inputting in question stem, f(3)=5a^3
Hence INSUFFICIENT. Cross out options A AND D.

Statement 2: f(2)=ka^2=20 => ka^2=20.

Inputting in question stem, f(3)=ka^3 => f(3) =ka^2.a=20a
Still no value of a. Hence cross out options B.

Checking together, k=5 =>5.a^2=20 =>a^2=4=>a=+2,-2

Inputting in question stem, f(3)=5(2)^3=40 OR f(3)=5(-2)^3=-40

Since two distinct solutions possible, so no unique solution for the question stem. Hence cross out option C. Select E
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by rajeshsinghgmat » Wed Jul 31, 2013 4:24 am
E

a^2-4=0

a=2,-2
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by Brent@GMATPrepNow » Wed Jul 31, 2013 6:24 am
sanju09 wrote:For all integers n, the function f is defined by f (n) = k a^n where k and a are constants. What is the value of f (3)?

(1) f (0) = 5.

(2) f (2) = 20.
Target question: What is the value of f(3)?

Given: f (n) = (k)(a^n)

Jump to . . .

Statements 1 and 2 combined:
So, f(0) = 5, and f(2) = 20
There are two sets of values that meet this condition. They are
Case a: a = 2, k = 5, in which case f(3) = (5)(2^3) = 40
Case b: a = -2, k = 5, in which case f(3) = (5)[(-2)^3] = -40
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = e

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