Complex GRE Problem Solving Practice

Recently, we posted a complex Problem Solving question on the KaplanGradPrep Facebook page. It intrigued a lot of people, so we decided it’s worth sharing here, too.

First, here are some strategy suggestions.  Unless you’re really adept with exponents, this is a good question to skip initially. Fractional exponents already designate this problem as a higher difficulty one, so you should make sure you get to other problems first.  When we say you should skip the question, we really mean you should make a guess (since there is no penalty for wrong answers on the GRE) and mark it for review. Then, return to the question only after you’ve answered all the questions that are faster for you.

There are two approaches to getting the right answer to this problem.  The first is to try out the answer choices until you find one that works. In this case, we’re solving for the variable x.

Trying answer choice (A):

Choice (A) doesn’t work, so try (B):

Choice (B) works, so it’s the right answer. With this approach, you need to know how to apply exponent rules, but you don’t have to understand how to use them in the context of solving for a variable.

Another approach is to use algebra.  To do this, follow the steps for isolating a variable. Here are the calculations, in test day scratch work format, with notes:

Which is the best way to solve this problem? Whichever way is fastest for you.