Articles published in Algebra

Two GRE Math Terms to Banish from Your Lexicon

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Manhattan Prep GRE Blog - Two GRE Math Terms to Banish from Your Lexicon by Chelsey Cooley

You can attend the first session of any of our online or in-person GRE courses absolutely free. Crazy, right? Check out our upcoming courses here.


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. Read more

More Fun with GRE Variables

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Manhattan Prep GRE Blog - More Fun with GRE Variables by Chelsey Cooley

You can attend the first session of any of our online or in-person GRE courses absolutely free. Crazy, right? Check out our upcoming courses here.


In my last blog post, we practiced using variables to solve Quant word problems—and we solved some problems without using variables, too. The big takeaway: you don’t have to start every word problem with a tidy little list of variables and equations! It’s okay to focus on the numbers in the problem first. However, variables are sometimes the key ingredient to getting a GRE problem right. In this article, we’ll try using variables to solve some tougher GRE Quant word problems.

Here’s one of my favorite problems from the 5lb. Book of GRE Practice Problems. Give it a try before you keep reading: Read more

GRE Math for People Who Hate Math: Absolute Value

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Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Absolute Value by Chelsey Cooley

You can attend the first session of any of our online or in-person GRE courses absolutely free. Ready to take the plunge? Check out our upcoming courses here.


Think of an absolute value as a simple machine that looks like this: ||. You put a value into it, and the machine answers a single question for you: how far away from zero was the value that you put in?

The basic operation of the machine is simple. Take any number, put it into the machine, and find out how far from zero that number is. The absolute value of 12, |12|, is equal to 12. The absolute value of -10, |-10|, is equal to 10. That’s because -10 is 10 units away from zero.

It starts to get complicated when the GRE asks you to put things into the machine that are more complex than simple numbers. Imagine that somebody else is operating the machine. She puts values in, but she doesn’t tell you what those values are. All you can see is the answer that the machine gives when it receives those values. Read more

Solving GRE Problems in Multiple Ways to Build Flexibility

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Manhattan Prep GRE Blog - Solving GRE Problems in Multiple Ways to Build Flexibility by Cat Powell

Did you know that you can attend the first session of any of our online or in-person GRE courses absolutely free? We’re not kidding! Check out our upcoming courses here.


Recently, my colleague Tom and I decided that, since we were teaching in adjacent classrooms, it might be fun to combine our classes and co-teach a lesson. Tom and I have very different strengths, both as test-takers and teachers. I love algebra, and I’ll always seek out an algebraic solution to a problem (even when this might not be the most efficient method—my strength is also a weakness). Tom prefers non-algebraic methods, like drawing diagrams or picking numbers. And our strengths inform what we emphasize in class.

So, for our joint lesson, we chose a number of GRE problems that could be solved in more than one way, and then took turns demonstrating each method. First, we each used the method we preferred (algebra for me, picking numbers for Tom), and then we switched and demonstrated the method we were less comfortable with. Here’s one of the GRE problems we used: Read more

7 Ways to Avoid Careless GRE Math Errors

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Manhattan Prep GRE Blog - 7 Ways to Avoid Careless GRE Math Errors by Chelsey Cooley

Did you know that you can attend the first session of any of our online or in-person GRE courses absolutely free? We’re not kidding! Check out our upcoming courses here.


There’s nothing wrong with making GRE math errors because the problem is too hard. That’s just the way that the test is designed—there are Quant questions on the GRE that will challenge even the mathematical geniuses among us. However, it’s much more frustrating to miss a problem that you could’ve gotten right, just because you made a silly mistake. Try out the following tips to cut down on careless GRE math errors. Read more

GRE Percentage Problems – Part 2: Percent Increase and Percent Decrease

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Manhattan Prep GRE Blog - GRE Percentage Problems - Part 2: Percent Increase and Percent Decrease by Chelsey CooleyDid you know that you can attend the first session of any of our online or in-person GRE courses absolutely free? We’re not kidding! Check out our upcoming courses here.


If you’ve been following this blog for a while, you’ve probably read our article on how to handle GRE percentage problems. That article teaches you an ultra-simple approach for “percent of” Quant problems — that is, problems like the following:

xy is 20% of z. In terms of y, what percent of x is z? Read more

A Step-by-Step Guide to ‘Multiple Workers’ GRE Rates Problems

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Manhattan Prep GRE Blog - A Step-By-Step Guide to 'Multiple Workers' GRE Rates Problems by Chelsey CooleyDid you know that you can attend the first session of any of our online or in-person GRE courses absolutely free? We’re not kidding! Check out our upcoming courses here.


Nine identical machines, each working at the same constant rate, can stitch 27 jerseys in 4 minutes. How many minutes would it take 4 such machines to stitch 60 jerseys?

First, take a deep breath. In this article, you’ll learn a methodical approach that will work on GRE rates problems every single time. On test day, it’ll be tempting to throw away your new habits and go back to old ones. Try to do the opposite. You’ve done all of this studying for a reason!

On problems like this, don’t try anything fancy. A lot of GRE test-takers will try to logically reason their way through this problem, saying something like “well, if 9 machines stitch 27 jerseys in 4 minutes, then 3 machines stitch 9 jerseys in 12 minutes…” That approach is valid but dangerous. Whenever you choose not to write something down, you’re taking away your ability to check your work for mistakes. (By the way, where’s the mistake in the logic described above?)

To start the problem, make a table. Your scratch paper should look like this: Read more

Let’s Have Fun with GRE Exponents

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blog-exponentsYou may already know the basic rules of exponents for the GRE. These rules tell you what to do if you want to multiply or divide two exponential numbers, or raise an exponent to another power. Once you’ve memorized them, exponent problems become exponentially easier (I’m so sorry). But there are two types of exponent problems that many students find intimidating, because the basic rules just don’t seem useful. In this article, we’ll go over those two problem types, how to recognize them, and what to do if you see one. Read more

Here’s How to Create Your Own GRE Quant Cheat Sheet

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You can attend the first session of any of our online or in-person GRE courses absolutely free. Crazy, right? Check out our upcoming courses here.


Do you remember, when you took exams in high school or college, being allowed to bring a one-page ‘cheat sheet’? I always spent days putting those cheat sheets together in my tiniest handwriting, summarizing an entire semester’s notes on a single page. The funny thing is, by the time I took the exam, I almost never needed to look at the cheat sheet I’d created. After spending all of that time creating it, I had practically memorized my notes. So, even if you can’t bring a GRE Quant Cheat Sheet to the test, you can still benefit from creating one. Synthesizing your notes and thoughts on a single page will give you the ‘big picture’ view of a topic—and will teach you what you do and don’t know. Read more

Here’s How to Always Know What to Do on Any GRE Problem

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Blog-GREAnyQuestion

You can attend the first session of any of our online or in-person GRE courses absolutely free. Crazy, right? Check out our upcoming courses here.


“When I See This, I Will Do This”: A GRE Study Tool

“I know all of the rules, but I’m nowhere close to my goal score.”

“When I study, I understand everything right away. But when I took the actual GRE, I couldn’t make it happen.”

“I never know what to do when I see a Quant problem for the first time. If somebody tells me how to set the problem up, I can do it perfectly, but I can’t get started on my own.”

“I get overwhelmed by Verbal questions. I’ll think that my answer makes sense, but then I’ll review the problem and realize that there were a dozen different things I didn’t notice.” Read more