Two GRE Math Terms to Banish from Your Lexicon
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There are a few math terms that are banned from my GRE classroom. “I’m not a math person” is a big one. So is “You either know it, or you don’t.” Both of those sentences are untrue—they don’t describe how the human brain really works—and they’re also dangerous.
The words that we choose are important. If we want to succeed on the GRE, we should talk about our learning in a way that reflects that. And if we want to do GRE Quant problems clearly and methodically, we should also talk about them clearly and methodically. That’s why, in addition to the “dangerous” math terms up there, there are a couple of other “dirty words” that I’ve banned from my classroom. If you cut these words and phrases out of your GRE Quant vocabulary, I promise that you’ll make fewer careless errors, understand problems more clearly, and feel more confident about your solutions.
Don’t say this: “Moved it to the other side of the equation”
Say this instead: “Added/subtracted it from both sides”
Here’s a little math problem where this comes into play:
If (x – 1)² = 256, which of the following could be the value of x?
(A) 24
(B) 15
(C) -15
(D) -16
(E) -17
Okay, take the square root first—that gives you x-1 = 16. Then, just move the -1 to the other side of the equation… aha! 15 is the right answer. Right? Nope.
The answer is actually -15, and here’s how you get there with confidence, 100% of the time. Say the following to yourself, and write the equations down on your paper.
Take the square root of both sides. x – 1 = 16
Add 1 to both sides. x = 17. Okay, that’s not an answer choice. Let’s try the negative square root.
x – 1 = -16. Add 1 to both sides. x = -16 + 1 = -15. There’s the right answer.
If you’re doing math in your head, or if you’re working quickly, or if you’re tired, it’s easy to mess this one up. (By the way, never do math in your head on the GRE. Doing math in your head is like eating a dozen donuts by yourself: it seems like a good idea, until you discover the consequences.) The problem is with the “move the -1 to the other side.” There’s no math operation called “move it to the other side.” There’s no “move it to the other side” button on your calculator! You aren’t moving anything: you’re either adding the same number to both sides, or subtracting the same number from both sides. In this case, you’re adding 1 to both sides.
Even if you don’t think you need to work on your arithmetic skills, try banning “move it to the other side” from your vocabulary. Instead, speak and think in terms of doing the same math to both sides. You’ll probably catch yourself almost making mistakes—every time that happens, it means this technique paid off.
Don’t say this: “Cross-multiplied”
Say this instead: “Multiplied both sides by…”
“Cross-multiplication” is among my ten least favorite phrases in the English language, right along with “pop quiz” and “boiled cabbage.” The problem isn’t with cross-multiplication itself. Rather, it’s with knowing when to use it. Cross-multiplication is for one very specific situation: when you have exactly two fractions with an equals sign between them, like this.
It’s not for problems like this:
Or this:
Or this:
Cross-multiplication isn’t anything special. It’s a combination of techniques that you can use on a lot of different types of problems. However, using a special name for it makes it less clear when you can use it, and what it actually does. That’s where careless errors come from: not clearly thinking through exactly what math you’re trying to do. Say and think through what you’re doing mathematically, instead.
To solve the first problem, you could multiply both sides by 7, then multiply both sides by 8. That’s not cross-multiplication—it’s just doing the same thing to both sides of the equation, twice.
For the second problem, you can’t do the same thing to both sides, because there’s nothing on the right side. You have to use a different technique. Multiply the top and bottom of the left fraction by 8, and multiply the top and bottom of the right fraction by 5. That gives you a common denominator, so you can add them together.
To do the third one, you could multiply the two fractions together first. Or, you could multiply both sides of the equation by 4 and then by 7. Take your pick! The fourth equation requires you to combine the techniques from the previous two. None of them involve “cross-multiplication.” If you think about the math you’re actually doing when you cross-multiply, instead of just applying the technique right away, you’ll be better equipped to handle fractions on the GRE.
This might seem like nit-picking. But I’ve worked with many students who are frustrated with careless mistakes on GRE Quant. Most or all of those careless mistakes, in my experience, are completely avoidable. Often, they come from thinking carelessly—for instance, from using a math technique in the wrong way, or on the wrong problem. Going back to the basics and thinking through the mathematical steps you’re taking will keep you from doing this, so please give it a try! ?
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Chelsey Cooley
is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.