This simple approach will help you avoid mistakes on GRE algebra

by Chelsey Cooley Nov 16, 2015

GRE high-scorers might not be smarter than everyone else, but they do think about the test differently. One key difference is in how high-scorers do algebra. They make far fewer algebraic mistakes, because, either consciously or subconsciously, they use mathematical rules to check their work as they simplify. Here’s how to develop that habit yourself.

Consider these two equations:

x – 6 = y + 6

a – 10 = b – 10

In the second one, you can ‘cancel out’ the two “-10” terms, leaving a and b equal. In the first, you can’t cancel at all. Instead, you might think about ‘moving over’ a 6, and combining it with the other one. Have you ever accidentally ‘canceled out’ an equation like the first one, though, leaving the equation below?

x = y

Or have you ever ‘moved over’ a term in an equation like the second one, leaving something like this?

a – 20 = b

If you have, you’re in excellent company. I’ve seen almost every one of my tutoring students make this mistake at least once. It’s an easy one to make, and even worse, the GRE is designed with it in mind. That means that making this particular mistake will lead you directly to a trap answer.

The situation is even worse when it comes to simplifying fractions. Suppose you have one equation that looks like this:

a / b = b / c

And another like this:

a / b = c / b

When do you ‘cancel out’ the matching b‘s on both sides, and when don’t you?

Even if you can cite the rule, you may still be vulnerable to making a mistake when under pressure. (By the way, you can ‘cancel’ in the second equation, but not the first.)

To avoid these mistakes and many other similar ones, start thinking about math instead of shortcuts. Forget everything except for the golden rule of simplifying equations, which is: you can do the same math to both sides. Decide what mathematical operation would simplify one side of the equation, then perform it on both sides.

In the first equation, add 6 to both sides:

x – 6 + 6 = y + 6 + 6

x = y + 12

In the second, add 10 to both sides:

a – 10 + 10 = b – 10 + 10

a = b

In the third, multiply both sides by b to simplify the left side, and then multiply by c to simplify the right side:

ab / b = b² / c

a = b² / c

ac = b²c / c

ac = b²

And in the fourth, multiply both sides by b:

ab / b = cb / b

a = c

You’ll get the same result you would with a well-executed shortcut, but writing out the mathematical steps reduces your risk of making careless simplification errors.

The two things to try in order to avoid careless algebra errors

You don’t have to write out every single step on your paper when you actually take the GRE — although I often do, and many of my highest-scoring students do as well! But I will ask you to try two things, if careless algebra errors have ever troubled you:

1. While you practice and review GRE problems, write out the math you’re doing on both sides of the equation every time you simplify. Forcing yourself to write out the math when you practice means you’ll get in the habit of thinking through it, even if you eventually stop writing as much down to save time.
2. Every time you simplify or reduce, think through exactly what you’re doing and why it works. Weak test-takers often say to themselves “I’m canceling out.” Stronger test-takers often say “I’m adding 10 to both sides, and here’s what happens.”

These are small changes to make, but they go a long way. Try them out as you practice GRE Quant problems, and watch your consistency improve. 📝

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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 170/170 on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.