And what do they tell us about prepping for the GRE?

Students often ask me, “Where can I find the most difficult questions on the GRE?” In this blog entry, I’ll show you the top three hardest GRE Math problems, ranked by percent of students who got them wrong. Before we get there, I should say: you don’t need to correctly answer questions like these to get a very, very good score on the GRE. This is a test that favors accuracy and consistency on mid-range questions over the ability to get the very hard ones. One can nab a score in the 90th percentile or above without getting any of the very hardest GRE Math problems correct. In case you’re curious, though, this is what the hardest GRE Math problems look like. Each of these questions were correctly answered by fewer than 20 percent of GRE test takers.

Start the drum roll.

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Combinatorics—it’s a word none of us can say and none of us had ever heard of before we started studying for the GRE. It’s a fancy word that just means “the number of possibilities” or “all the ways something could go” (my definitions). 

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There’s a pretty complete list of GRE study topics available at the ETS’s website. Here’s the list for Quant, and here’s where to find the corresponding lists for Verbal. These lists can show you what content you definitely need to know for the GRE. But, in this article, I’d like to complement them by doing the opposite: show you what you may think you need to learn for the GRE, but really don’t.

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Mastering GRE math means challenging yourself to improve your executive reasoning, on top of re-learning math rules you may not have seen for years. It’s not always an easy process, but there are a few quick math tricks that might earn you some points!

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Quick: here’s an expression from a GRE math problem. How do you simplify it?

√2¹⁴+2¹⁷ 

As a long-time GRE teacher, I like collecting problems like these: ones that often reveal the math misconceptions we don’t even know we have! There are a lot of different wrong ways to simplify this expression. Try it out before you keep reading—then we’ll look at some other math myths and common mistakes, and how to avoid second-guessing on the GRE. 

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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

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.

Imagine a world where every conversation went like this:

Student: When is our final project due?

Professor: Three days after the first Wednesday after your rough draft is due.

Student: What?

Professor: The rough draft is due 15 days after the date 6 days before May 14.

Solving a GRE math word problem is a little bit like having this kind of conversation. That’s why word problems can be so infuriating. The problem isn’t lying to you. It’s just telling you the truth in a really annoying, backwards way. (Reading Comprehension problems do that too—it’s not just a Quant thing.)

In the conversation above, how would you work out the due date of the final project? Personally, I’d start by getting out my calendar. I’d start at May 14, then count 6 days backwards. Then, I’d count 15 days forwards, put a star on the calendar, and mark it ‘rough draft.’ Then I’d find the first Wednesday after that date, and finally, I’d count three days forward from there. That would give me my answer. Read more

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.

You know what I love about GRE Discrete Quant problems? Specifically, multiple-choice Discrete Quant? The answer choices. Think about it: out of the infinite number of numbers in the universe, the GRE has already narrowed it down to just five possibilities. They’ve done almost all of the work for you. And that makes Discrete Quant a huge opportunity for People Who Hate Math. Read more

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.

You know what’s really frustrating? Making a ridiculous math mistake on a GRE Quant problem, totally by accident, and never noticing it. Add a three-second sanity check to your GRE Quant routine, and you’ll be more likely to catch small mistakes before they turn into huge disasters. Read more

You 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