### GRE Problems: the Good, the Bad, and the Ugly

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I like to think of GRE problems as belonging to three categories: good, bad, and ugly. These categories are a little different for each test taker, but everyone can use them to make better decisions on the GRE. Read more

### How To: Knowledge versus Skills

For me, the material you need to study for the GRE can be divided into two groups. No, not verbal and math. Knowledge and skills. Differentiating these two groups is important because they are learned in very different ways.

**Learning Knowledge**

So far, I would bet that most of your study time, from elementary school through college, was devoted to learning information. The skill of remembering facts is something that most of us have practiced quite a bit in the school realm. And sure, some of us are better than others at doing so, but mostly we at least have an idea where to start.

The knowledge, or information and facts, tested on the GRE would include vocabulary words, properties of numbers, mathematical definitions, and mathematical formulas.

I’ve written in the past about lots of unique ways to learn vocabulary, but ultimately I think that the techniques for learning knowledge fit into four categories:

**(1) ****Drill. **This would include writing words and definitions, making and reviewing flashcards, listing out numbers that fit a certain property, and writing and re-writing formulae. All these methods have their place.

**(2) ****Explain. **It’s generally easier to remember something if you understand it. For that reason, trying to explain a fact is a good way to learn it. This category would include studying with a partner, defining a word using its roots, and proving a mathematical formula.

**(3) ****Link. **Tying new information to information you already know is a good way to remember it. This would include finding a vocabulary word in a TV show or song, linking a word to its antonym, using one math formula to remember another, or building more specific geometry rules from the rules you already know.

**(4) ****Use. **I find that the saying “use it or lose it” is pretty applicable to learning. This category would include using new vocabulary in conversation or emails, writing sentences with vocab words, and doing practice math exercises.

There’s probably not that much new here so far. But that’s the key: we’re only halfway done.

**That’s not enough!**

Many students feel frustrated with the GRE because they feel like they know and understand the underlying math or vocabulary, but still aren’t seeing their scores improve as much as they would like. If you’re in the boat, don’t panic!

If you feel like you understand the underlying material but aren’t seeing your score improve as quickly as you’d like, or even at all, it might be that you’ve only worked on the **knowledge** and haven’t yet worked on the **skills**. Or, you’ve worked on the skills, but in the wrong way.

It’s not that your time has been wasted – you **need** that underlying knowledge to succeed on the test. But on its own, it won’t be enough.

So, what are the skills we need, and how do we learn them?

**Learning Skills**

Skills are learned differently than knowledge. You didn’t make flashcards to learn to play the piano. You didn’t learn to ice skate by writing the names of ice skating moves over and over in a book.

If you want to know the capital of Maine, and you don’t know, there’s no way to figure it out on your own. You have to look it up, and once you look it up, at least for that moment, you know the answer. That’s knowledge, and it’s often learned in that way: don’t know, give up, look at the answer, know, repeat.

Skills don’t work like that. If you show up at a piano lesson, and the teacher asks you to play a song for the first time, you’ll probably try it and make a lot of mistakes. What then? Well, what you don’t do is ask the teacher to play it for you and then say, “Oh yeah, that sounds right – I got it now!” and then move on without ever looking at it again.

I hope that piano lesson scenario sounds crazy to you. And similarly, I hope you can see why doing a math problem, getting it wrong, reading the answer, understanding it, and moving on is equally crazy. Being able to solve a math problem requires some underlying knowledge, but ultimately, it’s a skill, like playing the piano or running a marathon.

Because of that, you have to practice it like a skill. The skills on the GRE would include things such as solving a multiple choice geometry problem, solving a quantitative comparison question, guessing on a quantitative comparison question, solving a sentence completion question, staying calm during a timed exam, and deciding when to move on from a question.

How do you practice skills? Generally, I would employ a 4-part process:

**(1) ****Try it timed. **Just like the piano student in the above example, you should give the problem a try from the beginning. This lets you practice your own set of testing skills: assessing the problem, timing, guessing, and moving on.

**(2) ****Re-work untimed.** What do you think that piano teacher would have the student do next? Most likely, go back and try to work on the parts of the song that were hard. Similarly, you should go back and try to work on the problem on your own. See if you can get unstuck and get yourself to the right answer.

At this stage, the piano teacher might also interject some tips or reminders. You can do the same for yourself by using resources such as your strategy guides, other problems you’ve done, or definitions you don’t remember if you need them.

**(3) ****Use the answers (sparingly). **If that piano student is really stuck, the teacher might show him or her what to do – but only until the student gets unstuck. You should do the same with your answers. If you need to, start reading the answer, but only until you come across something you did wrong and didn’t recognize. Then, stop, and go back to working on your own as far as you can. Repeat this process as needed.

**(4) ****Record a take-away. **When you’re playing the piano, you create muscle memory that lets you reuse what you’ve learned in other contexts later. Recording a take-away has a similar effect. This is the chance to look back at the problem and say, “Hmm, what could I have seen/known from the beginning that would have let me get this problem right the first time?” Then, write down a sentence that takes the form of, “When I see _________ in a problem, ____________________,” where the first blank tells you what trigger to look for, and the second blank tells you what to remember, what rule to apply, what to think about, or what you can expect to happen in the answer.

It’s not that most of us have never learned a skill – all of us have. Even if you haven’t played a sport or a musical instrument, you probably know how to drive, use a computer, and do all kinds of unique things at your job. It’s just that we don’t often apply those skill-learning skills to academic tasks – but for the GRE, they will make a big difference.

### Zoom In, Zoom Out

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?

- 140
- 145
- 150
- 190
- 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