### Combating Careless GRE Math Mistakes

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**Careless GRE Math Mistakes Cost Points**

If you scored a 158 on your GRE Quant, you likely missed around 10-15 of the 40 questions you saw. A few of those may have been ones you didn’t know how to do. A few may have been ones you didn’t have enough time to solve. How many do you think were “careless GRE math mistakes”? 1 or 2? 5 or 6?

I hear this come up more than any other issue when I discuss exam results with my students. Careless GRE math mistakes cost points, and fixing only a few of them could result in a large jump in your score. If you scored a 158 and made 6 careless mistakes, fixing them could be the difference between your current score and something more like a 164.

In this entry, I’ll share 5 ways of combating careless GRE math mistakes.

**I. Stop Writing Them Off as “Careless GRE Math Mistakes” (and Make an Error Log)**

I can remember getting a math test back in my 8th grade algebra class. I wasn’t exactly happy with my grade: it was a solid dip down from the scores I was used to getting. When I flipped through to see which red slashes of my teacher’s pen had cost me so many points, I noticed that my mistakes were mostly missing negative signs, failures to carry a digit in long multiplication, terms left out when I distributed through a set of parentheses. *Ah, it’s nothing but careless mistakes*, I thought. *No real issue here*. I knew how to do all the math, so it wasn’t really a big deal, right?

This thought might have provided some solace on a grade-school exam—as long as my teacher could see I knew how to do the math, there was no real worry—but it lulled me into thinking there was nothing worth reviewing. On a test like the GRE, the grading algorithm doesn’t know the difference between the slight fumble of a decimal place and a complete lack of understanding of a problem. There is no partial credit. This makes it doubly important to iron out the kinks in the way you do your math.

More importantly, when you call something “a careless mistake,” it may be tempting to think that the mistake is unimportant and not worth further attention. Often, “careless GRE math mistakes” mask a deeper sloppiness in one’s math and thinking—the kind of sloppiness that makes one susceptible to the tricks and traps set throughout the GRE. The first step toward combatting “careless GRE math mistakes” is to take them seriously.

And if you want to take them really seriously, try setting up an error log. One of the most tried-and-true weapons for combatting careless GRE math mistakes, error logs collect short anecdotes and takeaways from missed problems in a central location. An error log might look something like this:

I did one of these in my own GRE practice. I missed so many practice problems in the final few steps because I would “move something over” from one side of the equation to the other. I theoretically knew how to do the math, but I needed to direct a little more awareness to “adding something to both sides.” It would have been easy to write this off as a careless mistake and forget about it, but instead I noticed the trigger: solving simple algebraic equations like “x + 3 = 16” without writing the “-3” under each side of the equation. (Check out this article from Chelsey Cooley for more on tackling this particular type of careless mistake.) Being aware is half the battle. If you can train yourself to spot your mistake triggers, you can slow down, become more aware, and address them the way you know you should.

**II. Check Your Work**

Try this problem. Seriously. Think about it and come up with an answer before you read any further:

Now test your answer.

If you take the price of the ball (your answer) and add a dollar to it, you should get the price of a bat. Now add those two prices together. Do you have $1.10 spent in total? If you notice something funny about your answer, try to go back and fix it.

With a modicum of additional mental energy, you can run your answer back through each part of the problem, locate careless GRE math mistakes, and fix them. Make a habit of doing this—whether the problem is easy or hard, lengthy or short. It’s well worth the additional 5-10 second investment to make sure you’re getting the points for your work. And if you’ve already spent the time to solve the problem, it’s worth a little extra to make sure you’ve got it.

Don’t start thinking you don’t need to check your work, either, even if you had this one right to begin with. If you build a habit of **always** checking your work, you’ll remember to do so (and you’ll really save yourself) on a butt-kicker of a problem like this one:

**III. Focus on the Step You’re On, Not the Next One or the One Before**

As the name implies, “careless GRE math mistakes” result from a lack of sufficient *care* placed on the math at hand.

One of the most common answers to the bat-and-ball question above is 10 cents. It’s easy to jump straight there without putting pen to paper. This is an answer you’d get if you started piecing together an attractive answer before ever drawing out the relationships between your variables. If you test it out, you’ll find that a 10 cent ball and a $1.10 bat add up to $1.20. It doesn’t work. This question is discussed at length in Daniel Kahneman’s book *Thinking Fast and Slow*. When students at top schools like Harvard, Princeton, and MIT tried that same question as part of a psychological study, more than half of them got it wrong. You’ll learn way more about why this occurs if you read Kahneman’s book, but to ruthlessly summarize: human beings tend to think with two “brains”—one “brain” that wildly leaps ahead and makes connections and another “brain” that trudges along carefully, skeptically proving its answers. One of the keys to success on a test like the GRE is learning to activate that second way of thinking—the one that carefully puts pen to paper and tests its own work. If you can be present with the step you’re on rather than leaping toward answers that “seem” right, you’ll iron out a boatload of careless GRE math mistakes.

All of this is, of course, easier said than done. If you want to work on this element, it may be worth your time to focus on mindfulness: the practice of being fully present rather than letting your mind wander off. Aside from slowing down, deep breathing, and double-checking your work, you may consider trying an app like Headspace.

**IV. Mental Math is Dangerous, But Calculators Are Dangerous Too**

In my classes, I’ve noticed two major branches of arithmetic mistakes that my students make: mental math errors and calculator errors. These tend to occur when test-takers over-rely on one way of doing the math because they’re uncomfortable with the other. If you don’t feel confident with your mental math, you can get much better with practice. Try using a website like Mental Math Trainer. There are some great apps for working on mental math, like this one for Android. You can also check out this series by our very own Neil Thornton.

These apps and games give you practice questions like these with ~10 seconds to solve each one:

If you can learn how to do these in your head, you’ll be much better at using your calculator—you’ll know when you’ve cranked out an answer that makes no sense.

Likewise, even if you can do these quickly and easily in your head, you’ll likely benefit from writing out at least some of your math on paper and checking at least some of your steps on the calculator.

When you use both methods in tandem, you’re much more likely to self-correct before things get really bad. As we all know, one little mistake can lead to a whole slew of troubles later on.

**V. Neatness Counts**

Recently, I was working with a student who had studied extraordinarily hard, putting in well over 100 hours in preparing for his GRE. For the life of him, he couldn’t figure out why he was still getting so many questions wrong and why his score still wasn’t improving. When we sat down together and I looked over his work, I noticed something alarming: his plus signs, minus signs, and multiplication signs all looked identical. When I asked him to go back and check a prior step in his work, he realized his mistake, cursed under his breath, scribbled out the minus sign that should have been a plus sign, and turned it into something even less clear.

More than any particular content practice, he needed to work on the neatness of his math on paper. It’s worth a little extra time to write deliberately and to organize your work so you know which variable is which and how it all fits together.

A good rule of thumb: make your work on paper so clear that you could pick it up and give it to someone else with no explanation and they could figure out the reasoning behind your answer.

**Careless GRE Math Mistakes May Be the Bane of Your Existence, But There’s Hope!**

Careless mistakes have cost me so many points on GRE exams and elsewhere. And they never really go away. Just a couple months ago, I wrote a GRE blog entry on this very website and made a crucial careless mistake in my math (woops!). Even so, with a little more attention, we careless-mistake-makers can learn to catch them, iron them out, and minimize them on test day. Here, again, are the 5 things you can do to combat careless GRE math mistakes:

- Take them seriously (use an error log).
- Check your work by running your answer back through the problem.
- Be “present” with the step at hand. Don’t let your mind wander off to what’s next.
- Learn how to do mental math…and put some of that mental math on paper.
- Focus on neatness: do slow, deliberate, and organized math.

Got any other methods that helped you learn to do more careful math? Post them in the comments below. Happy studying! ?

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**Tom Anderson is a Manhattan Prep instructor based in New York, NY.** He has a B.A. in English and a master’s degree in education. Tom has long possessed an understanding of the power of standardized tests in propelling one’s education and career, and he hopes he can help his students see through the intimidating veneer of the GRE. Check out Tom’s upcoming GRE courses here.

Hi Emily,

Here’s Tom’s answer:

“Sure thing! This is actually a fairly tough word problem. If you find that you read the explanation below and want some more practice, note that we cover some like this in the 3rd and 4th sessions of the class. There are also many similar “2-variable word problems” in the 5 Pound Book and Word Problem Strategy Guide.

To solve it….

First, define variables and expressions:

Eric has x dollars

Suzie has 300 + x

Next define variables and expressions again after the $ exchange:

Suzie has 90 percent of her original money, or .9(300 + x)

Eric has his original amount (x) plus 10 percent of Suzie’s money. Altogether, that’s: x + .1(300 + x)

Finally, link the new expressions together into an equation.

Eric would have 2/3 of the amount Suzie would have, so:

x + .1(300 + x) = 2/3(.9(300 + x))

Combine terms and solve:

x + 30 + .1x = 2/3(270 + .9x)

1.1x + 30 = 180 + .6x

.5x = 150

x = 300

Now (of course) plug it back in and check that it all works.

Eric has 300 dollars

Suzie has 600 dollars.

If she gives him 10 percent, that’s 60 bucks. She now has 540 bucks. And he now has 360 bucks. 360/540 is in fact 2/3. It checks out. 300 is your answer.”

Can you solve the Suzie problem? Thanks!

Emily