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.
Read more

Deciding whether to take a GRE prep course is tough. Prep courses can be expensive and take a lot of time. So the question is, is a GRE prep course worth it?

You might think that because I teach and GRE prep course and work for a GRE prep course company, my answer would be a certain “yes”. But in reality, it’s a resounding and certain “maybe”.

Helpful, right? Sorry. But I firmly believe that a prep course is incredibly valuable for some people but not for others. Here are the factors I usually encourage students to consider in deciding if a prep course will be worthwhile for them.

How much improvement do you really need?

It’s a good idea to take a reputable practice exam to see where your scores currently stand. Manhattan GRE offers a free practice test that you can use to see where you are right now. Then, check in with the programs to which you plan to apply and see what score would make you a competitive applicant there.

If you only need minimal improvement, or you only need improvement in one area, you might be able to do that on your own! Either way, you’ve got to know where you are starting and where you need to end up before you can make an informed plan.

How likely are you to stick to a schedule on your own? Read more

We all have a way of learning that works best for us. Most of us are able to learn by reading, writing, listening, speaking, and doing: the world pretty much requires that we do all five of these. But, just the same, most of us are better learners in some ways than in others.

Fortunately, when it comes to studying for the GRE, you can do a lot to design your own way of studying to take advantage of your strengths. First, you have to know what your strengths are. You may already know. If you don’t, think back to your time in high school or college. Which ways of studying were effective for you? Did you find homework to be pointless, but learn a lot in class? You might learn best by listening. On the other hand, if you found it very helpful to take notes while studying, you might learn best by writing. If you aren’t sure, you can take an online quiz such as this one to give yourself some guidance in the right direction.

I suggest that you try to combine more than one learning style in your studying – research has shown that this improves learning. I also suggest that you make sure to incorporate the learning style that works best for you.

So what are some ways to study in each learning style?

Learn by reading

• Obviously, the first piece here is to read the assigned reading in your homework.
• You might find that reading explanations of problem solutions really helps to cement things for you.
• Reading online forums can help you link concepts together.
• Doing a Google search for vocab words and reading them in context can help those who learn by reading to form strong connections for the words.
• Reading different solutions to a tough problem might bring you lots of insight.

Learn by writing Read more

Maybe by now, you all know that I hate vocab. It’s not my thing. It doesn’t come naturally to me at all. I have to make the flashcards, do the practice quizzes, and fight my way through it. One thing that really works for me is coming up with my own short, general description of a word. If I try to have just some idea of what it means, that’s probably what I’ll need for the test.

But sometimes, the reason a word is on the GRE is that we often us it wrong. Sometimes it’s just a common misunderstanding that’s caught on. Other times, it’s a word we’ve pretty much stopped using except in one context, where either one of the two meanings would make sense.

Want a couple examples?

1. Peruse. Peruse doesn’t mean “to browse or glance something over”. It means “to read or examine carefully.” If you start using it that way in conversation, everyone will think you’re an idiot. But you should know it come GRE test day.
2. Abscond. We usually only use this word in sentences like, “He absconded with the diamonds.” A lot of us think it means stealing, but it doesn’t. It means to sneak away, especially to avoid getting in trouble.
3. Refute. We’re used to this word, and know that when you “refute” someone’s argument, you shut it down. But not just by disagreeing, as is commonly thought. “Refute” means to completely disprove something.
4. Condone. We usually use this word in expressions like, “the school does not condone this behavior.” Well, the school might not approve of the behavior, but that’s not what “condone” means – it means “overlook” or “disregard”. If I condone what you’re doing, I don’t necessarily approve of it – I’m just not going to stop you.
5. Consent. This one’s kind of like condone. If I consent to your argument, that doesn’t necessarily mean I like it. It just means I agree, even in a passive way or with a negative attitude. Read more

I’m a terrible photographer because I don’t zoom in a reasonable manner. I try to zoom in on things that really can’t be appreciated without context. I try to zoom out and capture a whole panorama when the scene is too busy for any viewer to appreciate it. I suppose I could practice, but instead I’ve just stopped taking pictures and let other people do it for me.

But when it comes to the quantitative section of the GRE, I know exactly how to zoom, and I try to make sure my students know how to do the same. If you took all your photos with the camera on its factory setting, they would all be okay, but none of them would be really great. You want to get closer and more into the minutiae sometimes, and take a broader view other times, skipping all the details. The same is true when studying for (and taking) the GRE.

Zooming Out

Consider the following problem:

If x is the median of all the even multiples of 7 from 15 to 100, and y is the mean of all the even multiples of 7 from 16 to 104, what is the value of x –  y?

With your mental math camera on the regular setting, your approach might sound something like, “Okay, I know how to find the median. I’ll list out all the terms, and choose the middle one. After I’ve done that, I can find the mean by average out the first and last terms, because this is an evenly spaced set. Once I find both those numbers, I’ll subtract to find the difference.”

This approach is okay, and it will get you to the right answer. But zooming out a little allows you to look at the problem collectively, as a whole, and think something like, “Hey, both these sets of numbers are the same, since they both start at 21 and end at 98. And in an evenly spaced set, the mean and median are the same. So their difference is zero.”

Zooming out lets you pick up patterns in the exam and take advantage of the fact that you’ve studied them and notice them. It allows you to notice trends in the exam, which helps you know quickly what issues to consider and can also help you make an educated guess. Let’s take a look at another sample problem.

What is the average (arithmetic mean) of all the multiples of ten from 10 to 290 inclusive?

1. 140
2. 145
3. 150
4. 190
5. 200

On a regular setting, I’m looking at this and thinking, “Great, I know how to find the mean. I’ll list all the multiples of ten, add them up, and divide by the number of terms.” By zooming out, I can realize, “Hey, I know the GRE doesn’t want me to do that. This test rewards me for reasoning; is there a faster way? Yeah, this is an evenly spaced set of terms, so the middle one is the mean. And I can find that by just taking the mean of 10 and 290.

Making a Plan

The purpose of zooming out (or zooming in, as we’ll see in a second) is to make a plan. Each question should cause you to clarify what information you’re being given (“What are they telling me?”) and what you’re being asked to find from it (“What are they asking me?). Then, make a plan. Read more

When it comes to the GRE, your mindset can make a big difference. The test is long. The test is hard. The test is fast. The people who make the GRE are experts in creating the feeling of, “I know that I know how to do this, but I just can’t seem to figure it out.” There are people who say that one of the problems with tests such as this on is that they aren’t accurate because they have pressure and unpredictability. That would be right if the test just wanted to find your understanding of vocabulary and mathematics, but that’s not all they want to test. They want to test how you deal with pressure. They want to test how you deal with unpredictability. They want to test how you reason, above everything else. So all those added difficulties are fair game. They aren’t in the way of your test; they are your test.

That’s what makes your mindset so important. You might be able to convince me that mindset doesn’t have anything to do with your ability to do math (although I disagree) or to remember vocabulary (I still would disagree, but maybe not as strongly). But you won’t be able to convince me that mindset has nothing to do with how you handle pressure, unpredictability, and reasoning.

So what’s a good mindset? And how do you get it? Here are some tips.

Crisis mode versus panic mode

I hope you haven’t been in a lot of emergency situations, but I’m sure you’ve had at least one opportunity to see both crisis mode and panic mode demonstrated in real life. Picture a situation where John is preparing lunch and cuts his hand severely. He calls for his wife, Kelly. In panic mode, Kelly would see the blood and scream, “Are you okay? Are you okay? What happened?” She would go to find her keys to drive to the hospital, then decide to call the doctor, then get mad because she couldn’t find the keys, then start yelling. Now picture Kelly in crisis mode. She appears calm, although she talks rapidly and with direction. “John, sit down and put pressure on your hand with this towel. I’m going to drive you to the hospital. Hand me your keys.”

Both modes are normal responses to a problem, but the chief difference is that crisis mode works, and panic mode doesn’t. Not only does panic mode not help, but it also hurts.

You have to approach your test in crisis mode. Focus, take in the information you see, assess the situation, make a decision, and follow through. The good news is that crisis mode can be artificially created until it becomes a habit. In other words, fake it ‘til you make it. Read more

I definitely come from the procrastinate-and-then-cram-the-night-before-or-even-the-morning-of-the-test school of studying. It’s how I survived high school. And college. And law school. And grad school. And work. Okay, it’s how I do almost everything. But when it comes to preparing for a test like the GRE, studying in smaller sessions over a longer period of time IS better. You give your brain a chance to dredge up and sort and apply the information without any cues from the material before, which is what the real exam is like.

It’s pretty easy to think of ways to study vocab for five minutes. As long as you have the words with you, working on one or two for a couple minutes is no problem. (By the way, you should definitely start doing that if you aren’t already.) But how do you improve your math skills in five minutes?

Do One Problem

Students fight me on this, saying that it’s not worth getting started if you don’t have time to study a whole bunch. I’m sorry to say, they’re wrong. Keep a set of problems with you, whether you print them out or just tear them out of your books. (Sacrilege! I know! But the point of those books is to up your score, not to look beautiful on the shelf.) In five minutes, you can do a problem and look over the answer. But the benefits don’t stop there, because when you’ve done only one problem, your brain has time to process it and think about it. You’ll be working on it still, even when you aren’t trying to. It sticks with you in a different way. Because you’ve done only one problem, you don’t get to rely on anything that came before it to prop you up – you have to really know what you’re doing.

Review One Problem

Sometimes during a study session there will be a few problems that really bug you. Maybe that’s because you thought you should have gotten them right. Maybe it’s because you still don’t understand the explanation. Maybe they seem to contradict something you thought you learned in another problem.

These are the problems that are perfect for their own five-minute review session. Look them up on a forum and read some explanations and conversation. Discuss them with a friend. Give them a try on your own again. Try to explain the problem to yourself (or someone else). Whatever you do, coming back to the problem on its own with a fresh pair of eyes may help really cement something into place that was loose before.

Practice Your Arithmetic

Maybe your days are more exciting than mine, but I bet you still find yourself sitting around sometimes. Whether you’re waiting for a meeting to start, waiting for a meeting to end, waiting for your dinner to cook, or just watching TV, there is probably a five-minute period in the day where your mind wanders. (Think of how many times you check your phone in a day. What if you spent all that time doing math?)

Just practicing your arithmetic really pays off. I’m not a phone person, but I’m sure there are apps for your phone that let you do just that. Or, get out the old paper and pen. Filling in your multiplication tables, listing out prime numbers, practicing division and multiplication shortcuts, and manipulating fractions can all help you get more comfortable and faster with numbers. I know the exam has a calculator, but a comfort and facility with numbers will help you recognize patterns and shortcuts.

Drill Your Rules

No calculator can overcome a lack of knowing the mathematical rules. Knowing the rules doesn’t take genius abilities or even great reasoning powers; it just takes practice. So if you aren’t rock solid comfortable on the rules of fractions, exponents, triangles, and the like, five minutes is a great time to practice them in drill form. Memorizing the exponent rules is nice, but using them enough that you know how to use them when they show up is even better.

Estimate

Read more

I thought I might share my GRE experience and the lessons it taught me about the GRE prep process.

I’ve always been a test girl. My favorite two days of first grade were taking the IOWA exams, which I used to try to write at home to administer to my class of stuffed animals. I wish that were a joke. I got into a car crash on the way to the LSAT, pulled myself out a ditch, hitchhiked to the exam, and still scored in the 98^th percentile. I left the bar exam for a few hours in the middle to go shopping for a sweater because I was cold. I love tests. I own them. That is, until I took the GRE.

I was pretty cocky rolling into the GRE. I bought a pack of vocab flashcards and looked them over for a few weeks. I took a few practice tests. I read over the math. I showed up feeling like a boss. And then I got my score. And then I cried.

I did badly. What the heck? Tests are basically the one thing I can do!

Lesson one: The GRE must be studied.

The GRE really benefits from familiarity with the test. If you want to max out your score, you can’t just know the underlying material “ you have to be familiar with how it shows up and the best methods for handling it when it does.

I was daunted for a while, but I decided the GRE wouldn’t beat me. So after hiding from the exam for a few months, I got some study materials and got back on the horse.

Lesson two: The vocab must be learned.
Read more

Some song writers really like their vocab! While you probably won’t pick up a lot of GRE words listening to Justin Beiber, here are just a couple suggestions where you might actually enjoy picking up some new vocab.

1. Tidal, Fiona Apple. A 90s classic, if you were a teenage girl in the 90s. Pop in a copy of Tidal on your drive to work and you’ll be exposed to words such as undulate, appeasing, embers, carrion, divination, acquaint, resounded, coercion, inversion, stifled, deviant, sullen, oblivion, cunning, condescend, abound, enrapture, wary, reverence, endeared, discern, oblige, covet, demeanor, contusion, adagio, intrusion, and endeavor.

2.  HMS Pinafore, Gilbert and Sullivan. Okay, seriously, any Gilbert and Sullivan you can get yourself to enjoy is going to fill you with vocab words. This show alone has got saucy, frivolous, depraved, resigned, melodious, consolation, menial, pine, gallant, eloquence, pennant, sprightly, articled, tar, dictatorial, furl, scorn, domineering, tyrant, protrude, audacious, anguish, ignoble I didn’t even make it through half of the songs. And this might be the lightest on vocab of all the Gilbert and Sullivan choices.

3. Black on Both Sides, Mos Def. If you’re a rap fan, this is a fantastic album that you probably already have in your collection. If not, you might check it out if you want the chance to pick up words such as armament, sentiment, brandish, dispossessed, rivalry, saturated, infatuate, glisten, nemesis, scrutinize, staccato, vibrantly, apparition, odyssey, treacherous, testament, beneficent, manifest, reverence, temperament, firmaments, ubiquitous, ephemera, and flagrant, to name just a few.
Read more

Okay, the title shouldn’t describe them as activities that teachers hate, so much as activities that this teacher hates. I don’t hate them because they’re completely useless, but I hate them because they distract well-meaning and hard-working students. Studying for the GRE is time-consuming and hard enough without inefficient strategies.

There are certain study strategies that exasperated students have in common. When a student tells me that they’re following one of these strategies, the rest of the story is usually, and my score isn’t going up at all. Here are, in my opinion, the four big ones, and their better alternatives.

Binging on problems

This is a big one. Stories that start with, I did all the problems in the book or I bought an extra set of problems and did every single one usually end with but I’m not getting any better!

It’s not that doing all the problems in the book is a bad thing, but chances are if you’re doing that many problems, you aren’t giving them the time they deserve. Doing problems is a good way to assess what you know, but it’s actually not a great way to get better at doing problems. That comes when you review what you’ve done.

Wonder if you’re doing too many problems with not enough review? Go back and do 10 problems you did last week, timed. Do you remember how to tackle them? If so, you’re probably reviewing enough. If not, you might want to tackled fewer problems in more depth in order to see a better payout.
Read more