Exponents question 2

[Troika]

If, for any integer n, a^n = a^(n + 4), what is the value of a?

1. a^2 - 1 = 0
2. a^(n - 4) = a^n

OA: E

[Brent@GMATPrepNow]

If, for any integer n, a^n = a^(n + 4), what is the value of a?

1. a^2 - 1 = 0
2. a^(n - 4) = a^n

OA: E

This one is a great candidate for summarizing the given information before checking the statements.

Given: a^n = a^(n + 4)
Divide both sides by a^n to get: 1 = [a^(n + 4)]/[a^n]
Simplify to get: 1 = a^4
From this, we can conclude that a = 1 or -1

So, a = 1 or -1 and we need to determine which value of a is THE value.

Statement 1: a^2 - 1 = 0
Add 1 to both sides: a^2 = 1
We can conclude that a = 1 or -1
So, statement 1 is NOT SUFFICIENT

Statement 2: a^(n - 4) = a^n
Divide both sides by a^(n-4) to get: 1 = [a^n]/[a^(n - 4)]
Simplify to get: 1 = a^4
From this, we can conclude that a = 1 or -1
So, statement 2 is NOT SUFFICIENT

Statements1 & 2:
Since each statement yields the conclusion that a = 1 or -1, combining them does not provide any extra information.
So, the statements combined are NOT SUFFICIENT, and the answer is E

Cheers,
Brent

[Troika]

Brent, thank you for the wonderful explanation! The steps in your solution make it very easy to understand.