PS Step Method
Here are the four steps to Problem Solving success:
Step 1: Get the Specs.
Step 2: Plan the Attack.
Step 3: Mine the Math.
Step 4: Power Through.
Let’s have a closer look.
Step 1: Get the Specs. Step 1 puts you in the right frame of
mind to successfully work through a PS question. The main specifications that
should interest you include the following:
- What general subject area—arithmetic, algebra, geometry, or data
- What relevant features does the question contain? For example, is it
amenable to a straightforward standard application of one or more math
concepts? Is it a word problem that requires English-to-math translation?
Does it contain variables or manageable numbers in the answer choices that
suggest you may want to try an alternative approach? The answers to these
questions will help you to plan your attack in Step 2.
- What specific math concepts does the question concern? This will be
your catalyst for mining the math in Step 3 and doing the work in Step 4.
Step 2: Plan the Attack. While knowing math concepts cold is
necessary to succeed on GRE math, you still need to apply them effectively to
solve the problems. In Step 2, you’ll determine how you’ll use what you know to
answer the questions; that is, whether you’ll apply math concepts in a standard
way and then search the choices for the answer you get, or whether it’s better
to make up numbers or work backward. Use the information you discover as you
scope out the problem in Step 1 to help you decide how to proceed.
Step 3: Mine the Math. With a solid plan in mind, you’ll then
dig through your storehouse of Math 101 concepts to pick out the ones you’ll
need to solve the problem. If the question concerns a right triangle, for
example, then the Pythagorean theorem and rules for the length of the sides of
right triangles should pop into your head. If you’re up against exponents, or an
arithmetic mean situation, or a quadratic equation, then you’d pull concepts
related to those topics from your reservoir of math knowledge. Don’t think you
have to gather every single concept you’ll need at this stage; some necessary
concepts will emerge as you proceed through the problem in Step 4. In Step 3,
simply dig out the essential math concept or concepts you need to get started.
Note that for easy reference, we’ve bolded all these math concepts whenever they
appear in the explanations to our practice questions.
Step 4: Power Through. With relevant math concepts and a plan
for how to use them firmly in mind, you’ll now be able to power through the
question. “Power Through,” however, doesn’t necessarily imply using brute force,
since in many cases clever or elegant solutions may be possible. How you do the
work will depend on the method you choose in Step 2, and in many cases the
standard approach works fine (hence, we call it “standard”). But in other cases
you may settle on one of the alternative approaches we’ve shown you. Either way,
Step 4 is the time to solve the problem and make your selection.
It’s time to test drive the method, so when you feel you have a good
sense of the steps, sink your teeth into this:
||If a ≠ 0, then
Step 1: Get the Specs. The little raised 2s and 3s in the
equation tell you you’re dealing with exponents, an arithmetic concept, and
the huge powers that the as are raised to in the choices
suggest it would be insane to try to make up numbers in this case.
Step 2: Plan the Attack. Nothing particularly fancy
here—either you know the rules of exponents, or you don’t. (If you still
don’t after our lengthy Math 101 chapter, back to chapter 2 for you!) Our
analysis from Step 1 indicates that this problem is best approached via a
standard application of the rules of exponents—precisely our concern in the
Step 3: Mine the Math. The rule of negative exponents states
, something you need to know to
deal with the a–2
part of the
expression. Beyond that, when multiplying terms with exponents
containing the same base, we add the exponents, and something raised to
a power and then taken to another power requires multiplying those
These are the relevant math concepts you may need to
call upon to simplify the expression.
Step 4: Power Through.
Based on the concepts discussed
. That means we can rewrite
the expression as
, and cancel out
from the top and bottom,
3)3. Multiplying the exponents gives us our final