Originally Posted by
zorrillo
There are plenty of test takers out there who have a penchant for mathematics or who have dealt with numbers throughout their academic life. These are the lucky guys who can score high on the GRE quantitative with little or no effort. If you are one of these wiz kids, chances are you won’t need to read this article. But let’s face it; many of us are out of touch with high school mathematics, or simply aren’t the ‘math-types’. If you’re one such hard gainer, you’ll need to put in some extra effort to achieve your goal of scoring well. But obviously, your time and energy limits the amount of extra effort you can put in. So how do you go about maximizing the effectiveness of your preparation? Read on.
But this is not really math…
You may have already heard that the GRE quantitative section has changed in terms of structure and content. Just compare any paper-based quantitative test from Barron’s with that from the Power-Prep CD and you’ll realize they’re vastly different. While the prior deals with a lot of clumsy numbers, the latter involves very little numbers (the use of alphabet letters like a,b,c, etc. in place of numerical values) and instead stresses heavily on basic math concepts like number theory, statistics (SD, mean, mode, etc.), series problems, etc. The scratch paper is fast becoming redundant and you’ll be surprised to know that even the most pencil-happy test taker needs hardly 2 of the 6 pages they provide you with. Why did ETS introduce this change all of a sudden? It remains a mystery, but I speculate (and this is my personal view only) that the reason they brought about this change is because they realized that tying up test-takers in cumbersome calculations was not the best way to test their analytical ability. They needed to generalize the test a bit and stress more on understanding basic concepts. Ironically, although a majority of the people feel that the test has become more difficult, the percentile score of test takers has remained almost constant. A score of 800 is still 92 percentile. What it means is that the test has not become harder nor easier -the difficulty level is the same. The only switch is from the type of questions asked, and if you prepare with this new trend in mind, you’ll be inching closer to the high score that you’ve always dreamt of.
Give yourself time
I was shocked to learn recently that there are some people out there who take the test on a month’s preparation because they have ‘other commitments to attend to’. If getting a high score is important to you, you must give yourself a comfortable 2.5-3 months to prepare for the GRE. If not, then don’t harbor any hopes of scoring well and be content with an average score. However, don’t overdo it; 3 months are more than enough. Your mind is an old engine (considering you’re already over 20) that will come spluttering to a stop if you overwork it. Right. As far as math is concerned, make it a point to solve a few exercises on an almost daily basis, even if it’s just for an hour. Regular practice is important because it improves your speed of calculation, and time on the real test is an important factor. If you’re an average math ability person, speed is even more important to you since you’ll spend most of your time working out an approach to the problem rather than doing calculations. Do your math everyday, religiously.
Practice, Practice…but how?
If you’ve just begun your preparation, your first step should be to solve all the math exercises in the Barron’s guide. In this book, each math concept is given separately followed by a set of exercises based on that concept. This arrangement is very useful because it helps to gauge how well you can apply the concept you’ve just learnt and pinpoint your weak areas. If you’re a non-math test-taker, the Barron’s guide is an indispensable part of your preparation because it covers all the basic definitions related to number theory (prime numbers, whole numbers, etc.) and geometry (peculiar properties of certain figures). But remember that all the necessary concepts are not covered here.
Next, start going through the math review provided on the Power-Prep CD. If you haven’t registered for your test yet and don’t have the CD, download it from the ETS website. This review covers the concepts which are not given in Barron’s (statistics and probability, for example). Solve every exercise provided in this review and keep a personal notebook to note down those questions that you find difficult. After you’ve gone through the Barron’s guide and the ETS math review, you can safely assume you have with you all the concepts that are tested on the GRE.
If you want some Smart Alec ‘tricks’ and ‘shortcuts’ of attacking certain kinds of problems, which you feel could save you a lot of time, get Kaplan’s GRE book and turn to page 333. They provide some useful tips on tackling typical problems which may appear on the GRE. However, the limitation of this book is that, unlike Barron’s, it does not provide enough examples and exercises to help you learn to apply these ‘tricks’. You’re like a carpenter with all the files and saws but no wood to cut. But it doesn’t hurt to adopt these anyway; you never know when you might need them. Kaplan also suggests unique approaches to attack certain kinds of questions. For example, the “do same thing to both columns", “pick numbers” approaches. You may want to go through these to see if you find them useful. Of course, you may already be using some of these techniques (picking numbers, for example).
You should try and finish all this theory revision within a month’s time, while attempting practice exercises side-by-side. Now that you’re equipped with all the necessary weapons, it’s time to start target practice. Open to the practice tests given at the end of Barron’s and start attempting the quantitative sections under timed conditions. It’s all right if you’re finding it hard to finish all the questions in time (30 questions in 30 minutes) in the beginning; speed will come with practice. Just try and get the answers right. You may want to mark in red the questions you got wrong and get them corrected from the answer key provided. If you still don’t understand them, you can post them here at TestMagic. But remember that you won’t see many questions like these on the real test. That is something different altogether, and easier.
Which brings me to my next point. Jump to the exercises provided in the Power-Prep software to find out for yourself what the real test questions look like. Don’t fret if you find these difficult at first; you’ll get the hang of them really soon. You know you’ve got the hang of them when you find that you can answer certain questions orally, without having to write down anything. Obviously, these are the easier questions and you’ll encounter them only at the beginning or in the middle of a test. You may also encounter some totally new concepts here, like graphical representation of a normal distribution, for example. Take note of them and take a look at the explanations provided. You should keep the Power-Prep software close to your heart for the next few weeks until your test. This is what the questions on the real test are going to look like.
You can also attempt the tests provided in Kaplan’s and Princeton Review CD. Do these when you’re bored and tired, or if you’re forcing yourself to do some math. The reason I say this is because these third-rate questions are very effective in vexing you out pretty soon and making you feel sleepy. But I suspect the reason they have this effect on you is because they exercise your gray cells by making you perform fast calculations, which improve your speed of solving problems. Just like the local storekeeper who is fast with calculations since he deals with them on a daily basis. And if you have time on your hands, you should certainly not ignore this extra practice. Just remember that these are not the questions you will be asked on the GRE and the scores you get here are not indicative of your probable GRE scores. You can get a perfect 800 here and still end up with a 750 on the actual test if you involve yourself too much with non-official prep material.
Pay special attention to the following concepts, since they’re tested most often on the real GRE.
1.Statistics (mean, mode, SD, range, ND, graphical representation of ND)
2.Quadratic equations (roots, type of roots, number of roots, positive and negative roots, etc.)
3.Series (AP, GP, series definition, nth term of a series, etc.)
4.Number theories (divisors, remainders, GCD, LCM, prime factors, number line, etc.)
5.Probability (counting principle, basic probability, coin and die tossing, arrangements, etc.)
6.Speed and work problems (relation between speed, distance and time, rule of 3, rule of 5, etc.)
7.Some other concepts (ratios, inequalities, etc.)
Now here are some tips for getting that high score.
The Silly Mistake epidemic
This is the number one reason why even the best math brains end up scoring 750-790 instead of the perfect score. This phenomenon is so common, that only a very few are gifted with the eternal vigilance necessary to avoid being struck by it. I was so vexed with it myself that I thought I was doomed to make a small mistake somewhere. By making yourself aware of the common types of silly mistakes you can greatly reduce becoming susceptible to them. What you have to do is to constantly keep them at the back of your mind during the test, and while solving a problem, just run a mental check to see whether your approach falls prey to most common types. Since each individual may find different concepts problematic, the best remedy is to make a list of your own math vices, which can be drawn from the many practice exercises that you solve. After a while, you’ll start seeing a pattern where you make the same kind of silly mistakes again and again. Note them down carefully. For example, some of the common types of silly mistakes are as follows.
1.Not considering zero, fractions and negative numbers while solving inequalities or picking numbers. Remember that when ETS say a number is real, it can be positive, negative, fractional or zero. Don’t assume it’s always positive and don’t draw your own conclusions.
2.Taking leave of common sense. Sometimes we get so involved with the nitty-gritties of mathematics that we start functioning like automatons and stop thinking. Don’t fall prey to this trap. For example, what is the probability that a number amongst the first 1000 positive integers is divisible by 8? Don’t start counting the multiples of 8! The figure of 1000 is a red herring. Use a little common sense. The numbers will be 8,16,24,32…So, 1 in every 8 numbers is a multiple of 8, even if you consider the first million integers. So Probability is 1/8 (Question from Power-Prep.)
3.Not drawing figures. Drawing figures, especially in questions relating to geometry, speed, etc. makes the question ten times easier to understand. Drawing figures also makes the question more true to life. For example, if ETS tells you that Sally lives 10 miles due west of John and Anna lives 14 miles due north of John, you can bet your farm they want you to use the Pythagoras theorem. Don’t miss the obvious; draw a diagram.
4.Forgetting definitions. If you forget that 1 is not a prime number, you’re making life hard for yourself. Definition questions are the easiest to solve.
Take it easy, hombre!
Take my word for it. The 45 minutes provided to solve 28 questions are enough to solve every question twice. The reason being that you won’t get stuck up in complex calculations on the real test, since it involves very little clumsy mathematics. If you know the concept, you can solve the question within seconds and also be sure you’ve got it right. You must make full use of this to check your answer if you feel you’ve gone wrong somewhere. On my test, there were many instances where I arrived at an obviously wrong answer or felt that my approach was leading me nowhere. I jettisoned my line of thought and adopted a totally different approach and resolved the question. I don’t know how much time I spent in resolving questions, but the time limit was enough to resolve atleast the first 15 questions. Approach with a cool, calm and composed mind and re-check those answers that you feel are wrong. Don’t give up too easily on a question, especially if it’s within the first 15. You need to give in your best to get these right.
Guessing intelligently
If indeed you do get trapped somewhere, you must not waste too much time on a question that stubbornly refuses to crack open. After you’ve practiced solving a lot of questions, you’ll realize that correct answers have a peculiar knack of ‘looking correct’. What I mean is that when you arrive at good looking numbers like 100, you just ‘know’ that your answer is right. From my personal experience, here are some examples of patterns of correct answers. As a warning, remember that these are my personal observations only and are not always true.
1.In a quantitative comparison question the answers are quite often close to each other in value. For example, if you start expanding column A and arrive at an answer of 4, and if the value in column B is 5, your answer is probably right. Please note that this is not always true.
2.If you arrive at an improbable value, you’ve probably gone wrong somewhere. Although the questions on the test are purely theoretical, they are often true to life. So, if you’re comparing the ages of Jane, Jack and Mandy and if you calculate Jack’s age to be 100 years, you’ve probably gone wrong somewhere. This has more to do with common sense, actually.
3.If you get stuck in complex math or are left with 2 equations and 3 unknowns, abandon your line of thought and try a different approach. A dead end is a dead end and there’s no way out, except to try a different route.
4.If a question encountered sometime through the test looks strikingly simple, you’re probably being led into a trap. Run mental checks to see if you’re considering all the possible situations.
5.If you find you’re required to apply some basic concepts like Pythagoras theorem, binomial expansion, etc. then you’re probably on the right track. Application of concepts is exactly what most questions demand.
With practice, you’ll develop a knack for spotting right answers, and this will help you immensely while making intelligent guesses. Now you know why everybody makes such a hullabaloo about “practice makes perfect”.
The single most important requirement – The ‘open sky’ approach.
This is not really my brainchild and I read about it on some IIT (Indian Institute of Technology) website. They summed it up in one sentence straight: “To do well on the GRE you require a free and uncluttered mind”. This is so true. It was pathetic to see so many students on the test day, outside the test center, with open books, cramming something last minute. If you have to keep referring to your book (and unfortunately for them, on the test day) then you haven’t prepared well since you aren’t sure of yourself. Learn everything you can lay your hands on, but on the test day, your mind should be totally blank. Your mind should be like a Swiss Army Knife with all it’s blades in closed posisition, but ready to whip out any one when necessary. You never know what concept you may have to use on your test question, but you should feel confident that it’s there somewhere in your mind and that you can recall it when necessary. Sure, you’ll get your share of jitters on the test day, but those should not arise from a lack of confidence.
You can be a math wiz too..
High scores on the GRE quantitative are so common, that it’s no longer such a big deal. All the more reason why you should get it too. With a little effort and sincerity, it’s not all that difficult to achieve. With a high score, no one can dispute math is not your cup of tea. Good luck!