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 preview:

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:

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:

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.

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.