So, how does this math question grab you?

1446 = ?

D’oh! Not fun, huh? It would take a heavy-duty calculator, something you have no access to on the GRE, to come up with the correct answer of just under 9 trillion. That’s trillion, with a tr, with the “just under” clocking in at around 100 billion—numbers you’ll thankfully never see on the GRE. But what about this question:

What is larger, 1446 or 1112?

Well, that’s more like it—something definitely GRE-worthy. But how, you may wonder, can you figure out which of these two quantities is bigger if you can’t even figure out the value of the first one? That’s the beauty of it—you don’t have to figure out the actual values; you just have to figure out how to compare them. We can make this much easier by using a technique called “mirroring,” which we’ll cover later in this chapter: Since 144 is the same as 12 × 12, 144 multiplied by itself 6 times (which is what 144⁶ means) is the same thing as 12 × 12 multiplied by itself 6 times, which is the same as 12 multiplied by itself 12 times, or 12¹². Now we can see that 12¹² is greater than 11¹², so 144⁶ must be greater than 11¹², and we have our answer. No fuss, no muss, and certainly no calculating into the trillions involved. (If the exponents in this example are making your head spin, go back and review that section in chapter 2 on pages 53–58).

As the name implies, Quantitative Comparison questions (QCs) ask you to compare the sizes of two given quantities. That’s not to say that some QCs won’t benefit from some actual computation—they do rely on the same basic concepts as other GRE math questions, and sometimes, when the calculations aren’t difficult, crunching the numbers will be the way to go. However, the QCs that usually throw people are the ones requiring math reasoning, not number-crunching, so we’ll show you how to find the shortcuts you need—such as the one described above—to cut these down to size.

QCs have an unusual format that you’ve probably never dealt with before, so let’s first clear up the mechanics of the question type. The following X-ray should do the trick.