Articles published in Challenge Problems

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 GRE 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: What Is a Variable, Really?

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Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: What is a Variable, Really? 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.


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

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

GRE Percent Change Questions

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Manhattan Prep GRE Blog - GRE Percent Change Problems by Neil Thornton

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.


One of the most common mistakes many students make on the Quant section of the GRE is to misread percent questions, especially ones that ask you to calculate percent change (i.e. increase, decrease, more, less, greater, discount, or profit). You can fix this issue with a bit of practice, but it requires some careful reading on your part. Read more

How to Really Remember a GRE Vocabulary Word

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Manhattan Prep GRE Blog - How to Really Remember a GRE Vocabulary Word by Chelsey CooleyYou 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.


Think about your least favorite GRE vocabulary word. You know the one—every time you see it in your flashcards, you get that sinking feeling of dread. You always get this one wrong. You know it’s important, but for some reason, it just won’t stick in your head.

Okay, do you have a word in mind? Let’s conquer it—right here and now. Read more

GRE Prime Factorization and Divisibility Problems

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Manhattan Prep GRE Blog - GRE Prime Factors and Divisibility Problems 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.


Here’s a hard problem that I used to teach in session 1 of our GRE course (my poor students! This was a rough intro to GRE math.)

Manhattan Prep GRE Blog - GRE Prime Factorization and Divisibility Problems by Cat Powell

If you’d like to, give yourself a minute or two to try this (but don’t bang your head against it for too long). If you’re thinking wow, I have no idea what’s going on here—well, it’s a good thing you’re reading this. And even if you do feel comfortable with this problem, it might be worth reading further to see how the techniques used to solve this are more broadly applicable in GRE Quant. Read more

Tackling GRE Word Problems: One Thing at a Time

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Manhattan Prep GRE Blog - Tackling GRE Word Problems: One Thing at a Time by Neil Thornton

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.


“The man who moves a mountain begins by carrying away small stones.” -Confucius

Recently, one of my students emailed me the following question. I imagine at some point in your GRE practice you’ve run into the same issue: Read more

GRE Math for People Who Hate Math: Backsolving

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Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Backsolving 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.


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

GRE Vocab Words You Think You Know…But Don’t

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Manhattan Prep GRE Blog - GRE Vocab Words You Think You Know...But Don't 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.


Some researchers estimate that there are as many as a million words in the English language. However, you won’t see words like mylohyoid, ekphrasis, or cotyledon on the GRE. In fact, even though English has a huge number of extremely rare words, the GRE almost never tests them. Instead, it focuses on a set of words we’ll call rare but reasonable. Read more

Are GRE Verbal Questions Subjective?

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Manhattan Prep GRE Blog - Are GRE Verbal Questions Subjective? 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.


A lot of people think that GRE Verbal questions can have more than one right answer. The GRE itself doesn’t do anything to dispel this myth, since Verbal questions often include wording like which of the following is best supported? or with which statement would the author most likely agree?. These questions make it sound as if you’re supposed to read five pretty good answers and pick the best one, even if the other ones are okay, too. However, this mindset will hurt you on test day. Read more