SajjadAhmad wrote:
If f(n) = xa^n, what is the value of f(5) ?
(1) f(0) = 3
(2) f(4) = 48
Target question: What is the value of f(5)? Given: f(n) = xa^n Statement 1: f(0) = 3 In other words, x(a^0) = 3
Since a^0 = 1, we can write: (x)(1) = 3
This tells us that x = 3
So, our function now looks like this: f(n) = 3a^n
Since we still don't know the value of a,
this is NOT enough information to determine the value of f(5)Since we cannot answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: f(4) = 48 In other words, x(a^4) = 48
There are several values of x and a that satisfy statement 2. Here are two:
Case a: x = 3 and a = 2. Notice that x(a^4) = 48 turns into 3(2^4) = 48, which works. In this case
f(5) = 3(2^5) = 96Case b: x = 3 and a = -2. Notice that x(a^4) = 48 turns into 3[(-2)^4] = 48, which works. In this case
f(5) = 3[(-2)^5] = -96Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that x = 3
Statement 2 tells us that, when x = 3, either a = 2 or a = -2
In other words, we still have 2 possible cases that satisfy BOTH statements:
Case a: x = 3 and a = 2. Notice that x(a^4) = 48 turns into 3(2^4) = 48, which works. In this case
f(5) = 3(2^5) = 96Case b: x = 3 and a = -2. Notice that x(a^4) = 48 turns into 3[(-2)^4] = 48, which works. In this case
f(5) = 3[(-2)^5] = -96Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E