QC Step Method
We’ve provided many fundamentals to get you thinking the right way about
QCs. Now we’ll give you a method to employ your newfound knowledge. Here’s a
Step 1: Get the Specs.
Step 2: Plan the Attack.
Step 3: Mine the Math.
Step 4: Make the Comparison.
As you can see, the first three steps are identical to those of the
Problem Solving method: You’ll see what the problem presents (Get the Specs),
settle on an approach (Plan the Attack), and extract Math 101 concepts as
necessary from the extensive list in chapter 2 (Mine the Math). However, since
QCs differ in format from PS questions, Step 4 (Power Through, in the PS method)
must be changed accordingly. While in some cases you will
“power through” to arrive at quantities to compare, other questions are best
handled with alternative approaches, as you’ve seen. Step 4 will consist of
making the final comparison, no matter how you arrive at your determination.
Let’s take a closer look at how the steps play out before trying out the
method on QC practice problems.
Step 1: Get the Specs. Step 1 helps you to adopt the proper
mindset to attack the question. Here are the kinds of things you should notice
about each new QC that appears:
- Is the question a Problem Solving challenge in disguise?
- Is there additional information to take into account, or are you to
focus entirely on the quantities in Columns A and B?
- If there is additional information, does it place restrictions on any
variables appearing in the problem? If you’re planning on testing out
choices, check to see whether you’re free to try all four kinds of FONZ
numbers or whether the additional information limits the numbers you can
- Does the question contain only numbers, allowing you to chop choice
D right off the bat?
- What specific math concept or concepts does the question concern?
Recognizing the relevant concepts will help you mine the math in Step 3 and
make the comparison in Step 4.
- If a diagram is provided, do the test makers indicate that it’s drawn
to scale? If not, realize that elements of the figure may not be as they
Step 2: Plan the Attack. Here your main decision will be to
decide whether to treat the problem as a basic Problem Solving question, working
through the math as appropriate, or whether you may be able to use one of the
shortcuts discussed in the previous section. It takes practice to make this
determination, and we’ll give you that practice in the rest of this chapter and
in the practice test at the end of the book.
Step 3: Mine the Math. No matter which approach you settle
on, there are bound to be Math 101 concepts required to solve the problem. We’ll
continue to help you figure out which math concepts are required for each
question and will continue to put them in bold for easy reference.
Step 4: Make the Comparison. In the end, every QC comes down
to the same three questions:
- Is one column bigger?
- Are the two columns equal?
- Is it impossible to tell?
Everything you do in Steps 1–3 is geared to helping you close the deal and
make the proper determination in Step 4.
We’ve seen lots of QC questions already, but let’s do another one to
illustrate the step method. This will put you in the right frame of mind to
try a bunch of these on your own. Give this one a shot and then follow along
with the steps in the explanation that follows.
Film contains 24 frames per
second. Video contains 30 frames per second.
The number of
frames in 595 seconds of
The number of
frames in .2 hours of
||The quantity in Column A is greater.
||The quantity in Column B is greater.
||The two quantities are equal.
||The relationship cannot be determined from the
Step 1: Get the Specs. There’s additional information
concerning the precise number of frames per second for two different kinds
of movie, and we’re given precise times in columns A and B to work with. So,
there are no variables, and we do have enough information to figure out the
number of frames in each scenario. Therefore, we can eliminate
D from contention immediately. The other thing to notice is
that the times in the columns are in different units (seconds and hours) and
the numbers are not particularly simple ones to multiply, especially the 595
seconds of film.
Step 2: Plan the Attack. Since 595 × 24 isn’t the easiest
calculation without a calculator, we can assume there may be a cleverer way
to go about this, perhaps involving approximating. Because the units in
Columns A and B are different, some mirroring may also be in order, since
they’d be easier to compare if they better resembled one another.
Step 3: Mine the Math. The formula in play here is an
offshoot of our typical work formula: total = rate × time. In
this case, total frames = # of frames per second × # of seconds. But since
our plan of attack is to use some math logic to get us
through, don’t assume you’ll need to perform the actual calculations;
understanding the gist of how to calculate the number of
frames in each column may be enough.
Step 4: Make the Comparison. Column B is a bit easier to
work with, and there’s no reason why we can’t start there. The length of the
video is .2 hours, which multiplied by 60 minutes in an hour gives us 12
minutes. Not too tough. Now, you could convert that to seconds and then
multiply by 30 to arrive at the precise value of Column B, but we’re trying
to avoid lengthy calculations, so let’s leave it at 12 minutes for the video
and move on to Column A. But 595 seconds isn’t so easy to work with, while
600 seconds is: Dividing by 60 seconds per minute gives us 10 minutes, so
595 seconds is just under 10 minutes of film. Aha! The video is longer and
contains more frames per second as well, so without even figuring out the
exact number of frames in each, we can conclude with certainty that there
are more frames in Column B. Choice B is correct.
Sure, you could have multiplied it all out, but with a little
mirroring (expressing both movie times in minutes), a little approximating,
and a little general cleverness, we arrive at the same point—hopefully
faster, and with less risk.