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We know that:

x^n - x^(-n) = 0
or
x^n = x^(-n)

and we want to find the value for x.

Let's start by analyzing the question stem, something too many test takers fail to do.

A negative exponent is the same as 1 over that exponent. In other words:

x^(-n) = 1/(x^n)

So, we can rewrite the equation as:

x^n = 1/(x^n)

Now let's ask ourselves: when can a number equal its reciprocal? We answer ourselves: only if that number is 1 or -1.

So, we now know that x^n = 1 or -1

We ask ourselves another question: when will x^n = 1 or -1? Feeling particularly brilliant today, we have no trouble answering ourselves that could happen if:

1) n=0 (since anything raised to the exponent 0 = 1);
2) x = 1 (since 1 raised to any exponent is still 1); or
3) x = -1 (since -1 raised to any exponent is -1 or 1).

To the statements!

(1) x is an integer.

No help here at all; x could still be -1 or 1 (or anything else if n=0); insufficient, eliminate A and D.

(2) n doesn't equal 0

This statement eliminates one of the 3 possibilities (that n=0 and x could be anything), but x could still be 1 or -1; insufficient, eliminate B.

Since neither statement is sufficient alone, we have to look at the statements together:

(2) eliminates the n=0 possibility, but both -1 and 1 satisfy statements (1) and (2). Therefore, we don't have a specific value for x; still insufficient, eliminate C. Choose E!

_________________
Stuart Kovinsky, B.A. LL.B.
Kaplan Test Prep & Admissions
Toronto Office
1-800-KAP-TEST
www.kaptest.com

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