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Welcome to part 3 of the article series on analyzing your GRE practice tests. As we discussed in the first and second parts of this series, we’re basing the discussion on the metrics that are given in Manhattan Prep tests, but you can extrapolate to other tests that give you similar performance data. If you haven’t already read those, do so before you continue with this third part. Read more

Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.

Welcome to part 2 of the process for analyzing your GRE practice tests. As we discussed in the first part of this series, we’re basing the discussion on the metrics that are given in Manhattan Prep tests, but you can extrapolate to other tests that give you similar performance data.

Last time, we discussed how to assess the data provided in the “question list”—the list that shows the questions you received and how you performed on each one. This week, we’re going to interpret the analysis given in the Assessment Reports. Read more

I’ve been on a story problem kick lately. People have a love / hate relationship with these. On the one hand, it’s a story! It should be easier than “pure” math! We should be able to figure it out!

On the other hand, we have to figure out what they’re talking about, and then we have to translate the words into math, and then we have to come up with an approach. That’s where story problems start to go off the rails.

You know what I mean, right? Those ones where you think it’ll be fine, and then you’re a minute or two in and you realize that everything you’ve written down so far doesn’t make sense, but you’re sure that you can set it up, so you try again, and you get an answer but it’s not in the answer choices, and now you’ve crossed the 3-minute mark…argh!

So let’s talk about how to make story problems REAL. They’re no longer going to be abstract math problems. You’re riding Train X as it approaches Train Y. You’re the store manager figuring out how many hours to give Sue so that she’ll still make the same amount of money now that her hourly wage has gone up.

Note: I’ve used GMAT problems in this article because the makers of the GRE don’t allow us to re-publish their problems. I’d rather work from actual problems written by standardized test-writers, just to show you how well this technique does work on real problems. I’ve chosen two problems that could just as easily be seen on the GRE.

Try this GMATPrep® problem:

* ” Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

“(A) 2

“(B) 3

“(C) 4

“(D) 6

“(E) 8”

Yuck. A work problem.

Except… here’s the cool thing. The vast majority of rate and work problems have awesome shortcuts. This is so true that, nowadays, if I look at a rate or work problem and the only solution idea I have is that old, annoying RTD (or RTW) chart… I’m probably going to skip the problem entirely. It’s not worth my time or mental energy.

This problem is no exception—in fact, this one is an amazing example of a complicated problem with a 20-second solution. Seriously—20 seconds!

You own a factory now (lucky you!). Your factory has 6 machines in it. At the beginning of the first day, you turn on all 6 machines and they start pumping out their widgets. After 12 continuous days of this, the machines have produced all of the widgets you need, so you turn them off again.

Let’s say that, on day 1, you turned them all on, but then you turned them off at the end of that day. What proportion of the job did your machines finish that day? They did 1/12 of the job.

Now, here’s a key turning point. Most people will then try to figure out how much work one machine does on one day. (Many people will make the mistake of thinking that one machine does 1/12 of the job in one day.) But don’t go in that direction in the first place! If you were really the factory owner, you wouldn’t start writing equations at this point. You’d figure out what you need by testing some scenarios. 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

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“Many a true word is said in jest.”—I don’t know, but I heard it from my mother.

Once upon a time in America, when I was a boy, my father, an engineer, said to me, “You can make numbers do anything you want them to do.”  This was the beginning of my cynicism.  But never mind that.  My father was fluent in four languages: English, German, French, and Algebra.  And his comment relied on the fact that most people can’t read Algebra.  Teaching GRE classes, I combat the fact that many people can’t read Algebra.  Because, like my father, the GRE exploits that weakness.  Thus, for many, preparing for the quantitative portion of the GRE is akin to studying a foreign language.  (Yes, I know that even many native speakers feel that preparing for the verbal portion of the GRE is also akin to studying a foreign language.  But that’s a different topic.)  In any case, you want to make your Algebra as fluent as your French. . .yes, for most of you, that was one of those jokes.

I know that some of you disagreed with the above and feel that the problem is an inability to understand math.  But that’s not true, at least on the level necessary to succeed on the GRE.  If you really didn’t have enough synapses, they wouldn’t let you out without a keeper—because you couldn’t tip, or comparison shop, or count your change.  It’s a literacy problem.  Think of our GRE math units.  Truthfully, the algebra unit is often a death march.  By the end, as country folk say, I often feel like I’m whipping dead horses.  On the other hand, the word problem unit concerning probability and combinations, putatively* a more advanced topic, usually goes really well.  Why?  Because folks can read the words and understand their meaning.  Conversely, folks just stare at the algebraic symbols as if they were hieroglyphics.  The problem is that putting a Rosetta Stone in the book bag would make it weigh too much. . .kidding.  But if you can’t read the hieroglyphics, the mummy will get you—just like in the movies.

It really is a literacy issue and should be approached in that fashion.  You still don’t believe me?  You want specific examples?  I got examples, a pro and a con.  On the affirmative side, I once worked one on one with a man who came to me because his math was in shreds.  Because he couldn’t read what the symbols were saying.  Partly because his mother had once said, “Your sister is the one that’s good at math.”  As far as the GRE is concerned, she was wrong, and so was your mother, if she said that.  Anyway, one day I gave him a high level word problem concerning average daily balances on a credit card.  He looked at it for about 30 seconds, and he didn’t write anything on his scrap paper.  Then he turned to me and said the answer was blah blah.  And he was right.  I looked at him and said, “How did you do that?  You’re not that good.”  (Yes, this is also an example of how mean I am to private students.)  But—and here’s the real punch line—he said, “It was about debt; I understood what the words meant.”  And there you go.

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When it comes to studying for the quant portion of the GRE, I’m a big advocate of mixing a variety of study styles. The GRE pulls questions from a big selection of question types and content areas, and pulling your study habits from a variety of strategies can help you keep up.

I encourage you to take a look at your study patterns and see if anything’s missing. Are you only practicing in short stints but never working for a full-exam-length of time? Are you only practicing mixed sets but never targeting particular question types? You might want to consider mixing it up!

Systematic vs. Cherry-picking

There is clearly merit to a systematic study approach. Working your way through your study materials in order ensures that you cover all the material you need to prepare for the test. It also ensures that you give adequate time to each area.

On the other hand, cherry-picking the areas you want to study lets you focus your attention on the areas that most need your attention. It also allows you to study effectively on a crunched schedule if you already have a comfortable, working knowledge of math basics.

These strategies can be effectively combined to maximize their benefits. Do you want to cover all the material? Yes. But what happens when you get to a topic you don’t understand? Don’t fixate and get stuck there; note it and move on! The math concepts on the exam are related to one another, so there’s a good chance that when you come back to a topic later, you’ll understand it differently than the first time around. You also may want to break away from your study system and pay some immediate attention to concepts that newly make sense to you, or that you thought you had mastered but then notice you’ve forgotten.

Depth vs. Breadth
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I remember in a high school chemistry class, my teacher said, There are a few magic numbers. One of them is pi. One of them is e. Anyone know another one? Jane? I had no idea what he was talking about. Eight? I guessed. Obviously I missed the point.

But today’s magic number is seven. While there are lots of different ways to classify numbers, there are seven categories of numbers that make all the difference when trying to move quickly and correctly through the Quantitative Comparison section of the GRE.

Seven Important Categories of Numbers

Picture a number line. In the middle, you’ve got zero. (Okay, I know the number line doesn’t have a middle. But you get the idea.) On either side of that, you have positive and negative proper fractions. (For the rest of this post, I’m just going to use fractions to refer to proper fractions, meaning fractions with an absolute value less than one.) Next, moving outward, you hit one and negative one. And then, you hit positive and negative integers other than one.

While there are other categories of numbers that matter (primes, perfect squares, odds, evens, etc.), these are the seven that come to my mind fastest when I’m trying to come up with two alternative results in a QC questions.  When we’re trying to find two different results, we always look to try numbers that are fundamentally different. And these categories churn out some fast differences that are important in matters that QC cares about testing.

When are these sets of numbers most helpful? I’m glad you asked.

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I’ve got another one for you from our 5 lb. Book of GRE Practice Problems, and this one’s serious. I took it from the Advanced Quant chapter. Try it out and then we’ll chat!

 Triplets Adam, Bruce, and Charlie enter a triathlon. There are nine competitors in the triathlon. If every competitor has an equal chance of winning, and three medals will be awarded, what is the probability that at least two of the triplets will win a medal?

(A) 3/14

(B) 19/84

(C) 11/42

(D) 15/28

(E) 3/4

© ManhattanPrep, 2013

Yuck. I’m not a fan of probability in general and this one is particularly annoying. Why? Because they ask for the probability that at least two will win. Most of the time, when a probability question uses at least or at most language, we can use the cool 1 “ x shortcut because there’s only one not-included case.

For example, if I tell you I’m going to flip a coin three times, I might ask you to calculate the probability that I’ll get at least one heads. There’s only one case where I wouldn’t: zero heads. So you can just calculate the probability of zero heads and subtract from 1.

But we can’t do that here, because it’s possible for just 1 twin to win a medal and it’s also possible for zero twins to win a medal. Sigh.

Okay, how are we going to tackle this? Probability is a measure of the number of desired outcomes divided by the total number of possibilities. Let’s figure out the total number of possibilities first.

Take a look at the question again. Is this one of those questions where the order matters? If you don’t win, you don’t win. If you do win, does the question make a distinction between coming in first, second, or third?

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We know that carrying around GRE study materials can be a hassle.  Some days you just can’t carry an extra 5 lbs in your backpack/messenger bag /satchel/kangaroo pouch/suitcase.  As such, students often turn to flash cards for convenient, on-the-go studying.

Up to this point our flash cards have only been a vocabulary building tool and over the past year, students have asked that we offer cards for the quant section of the exam.  It seems that students’ commutes were unbearable (or at least less enjoyable) when they didn’t afford a chance to study for the GRE quant section.  Well, fear not, commuters Math Flash Cards are now available! (If you will, please imagine that last sentence being accompanied by the Superman theme.  You know the one; it has the triumphant horn section.)

Our new math flash cards provide math drills for all skill levels and include easy-to-follow explanations to help you build fundamental math skills for the GRE.  You can use these cards as a teaching tool, or for rapid quant drills.  These 500 cards cover a wide variety of quant topics including algebra, geometry, word problems, number properties, and more.  If you are looking for bite-sized math practice, these cards are for you.

We’ve got another problem for you from our new book, the 5 lb Book of GRE Practice Problems. The book contains more than 1,100 pages of practice problems (and solutions), so you can drill on anything and everything that might be giving you trouble.

This regular problem solving question asks us to pick one correct answer (other variations might ask us to select more than one answer or to type in our own answer). Give yourself approximately 2 minutes to finish (or make a guess).
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