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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A perfect score on the GRE would be a 170 on each the Quant and Verbal sections and a 6.0 on the Analytical Writing Measure. Perfect scores are incredibly rare—while getting a perfect score in just one of these sections would put you in or close to the 99th percentile for that section, getting a perfect score in all three makes you a unicorn. In other words, you absolutely don’t need to get a perfect score in order to get into your program. I feel confident making that blanket statement. But for all the would-be unicorns out there, below I break down what you can do to get a perfect score in all three sections.

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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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Can’t get enough of Neil’s GRE wisdom? Few can. Fortunately, you can join him twice monthly for a free hour and a half study session in Mondays with Neil.

As a long-time instructor of all things standardized testing (GRE, GMAT, LSAT, SAT), I love reading books about math, logic, learning, skill acquisition, neurology, and psychology. Is important to me to stay up-to-date with anything that will help my students use their study time effectively. In this blog series, I’ll be bringing you book reviews and recommendations, as well as excerpts and summaries you can put into practice right away on your GRE journey. 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

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. Read more

To see this week’s answer choices and to submit your pick, visit our Challenge Problem page.

To see this week’s answer choices and to submit your pick, visit our Challenge Problem page.

When it comes to quantitative comparison questions, zero is a pretty important number, because it’s a weird number. It reacts differently from other numbers when placed in some of the situations. And zero isn’t the only weirdo out there.

Most of us equate “number” with “positive integer”, and for good reason. Most of the numbers we think about and use in daily life are positive integers. Most of our math rules were learned, at least at first, with positive integers.

The GRE knows this, and takes advantage of our assumption. That’s why it’s important to remember all the “other” numbers out there. In particular, when testing numbers to determine the possible values of a variable, there are a few categories of numbers you want to keep in mind.

If I’m going to think about picking numbers, I want to pick numbers that are as different as possible. I try to choose my numbers from a mixture of seven categories, which can be remembered with the word FROZEN:

FR: fractions (both positive and negative)
O: one and negative none
ZE: zero
N: negatives

So we’ve got positive and negative integers (the bigger the absolute value, the better), positive and negative one, positive and negative fractions, and zero. Don’t forget, zero is an integer too!

There are other categories of numbers to think about, particularly if they are mentioned in the problem: odd versus even, prime versus non-prime, etc. But the seven groups listed above account for most of the different ways that numbers behave when you “do math” to them. Because of that fact, picking numbers from different categories can be a fast way to understand the limits of a problem.

To illustrate my point, let’s think about the value of x raised to the power of y. What happens to the value of that expression as y gets bigger? Let’s simplify our lives even further by stipulating that y is a positive integer.

What first comes to mind is the idea that as we increase the value of the exponent, we increase the value of the expression. Well, if x is a positive integer, that’s true: the expression gets exponentially bigger as y increases. Unless x is the positive integer 1, in which case the expression stays the same size, regardless of the value of y. The same is true if x is equal to 0. If x is a positive proper fraction, the expression gets smaller as the value of y increases.
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Each week, we post a new GRE Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.

See the answer choices and submit your pick over on our Challenge Problem page.