Hey guys,
Yeah, I definitely wouldn't call this a simple question...this is one that isn't all that labor-intensive, but it definitely digs fairly deep into your knowledge of exponents, properties of numbers, etc.
I'd look at the given information this way:
x^n - x^-n = 0
To simplify, add x^-n to both sides to get:
x^n = x^-n
Or, to rephrase:
x^n = 1/(x^n)
Basically, x^n is the same as its own reciprocal.
Well, only two numbers are the same as their own reciprocal (remember, you can't divide by 0 so 0 doesn't count!). -1 = 1/-1 and 1 = 1/1. So either x is 1 or -1, or n is 0.
Statement 1 tells us that x is an integer, which isn't enough because as long as n is 0 x could be any integer.
Statement 2 tells us that n is not 0, but that still allows x to be 1 or -1.
Taken together, x could still be 1 or -1, so the answer is indeed E.
Keep in mind, though, that if statement 1 said that x is a positive integer, we'd be able to eliminate -1 from the mix, so this one is a lot closer to being sufficient than it might look at first glance! Definitely not a problem I'd call "simple"...
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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