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If f(n) = xa^n, what is the value of f(5) ? [#permalink]

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02 Apr 2017, 13:06

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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) = 96 Case 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] = -96 Since 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) = 96 Case 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] = -96 Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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If f(n) = xa^n, what is the value of f(5) ?
[#permalink]
02 Apr 2017, 13:06