Data Sufficiency

beater wrote:What is the value of 3^-(x + y) / 3^-(x - y)?
(1) x = 2
(2) y = 3

There are a few ways to break this down. Three different approaches (there are surely others):

-recall that 3^a/3^b = 3^(a-b) (when you have the same base in a division, you subtract the powers). We can use that here:

3^-(x + y) / 3^-(x - y) = 3^[ -(x+y) - (-(x-y))] = 3^[-x-y+x-y] = 3^(-2y)

So we only need to find y.

Alternatively you could use the fact that 3^(a+b) = [3^a][3^b]. Note that we can do this with any powers, negative or positive. You can expand the brackets and apply this:

3^-(x + y) / 3^-(x - y) = [3^(-x-y)/3^(y-x)] = [3^(-x)*3^(-y)]/[(3^y)*(3^(-x)]

Since the 3^(-x) term cancels, we only need y.

Or, you could use the fact that 3^(-a) = 1/3^a, so

3^-(x + y) / 3^-(x - y) = [1/(3^(x+y)]/[1/3^(x-y)] = [3^(x-y)]/[3^(x+y)]

and now that the potentially confusing minus signs are gone, it's easier to continue the problem using either of the methods above.

Each of the exponent rules I've used above is tested extensively on the GMAT, so each is worth understanding thoroughly.