Data Sufficiency

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.



Source: The Princeton Review

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

E

a^2-4=0

a=2,-2