gre math bible ebook - · pdf fileiii about this book if you don’t have a pencil in your...

QuestionSolution.Com
www.QuestionSolution.com

Additional educational titles from Nova Press (available at novapress.net):
GRE Prep Course (624 pages, includes software)
GMAT Prep Course (624 pages, includes software)
GMAT Math Bible (528 pages)
Master The LSAT (560 pages, includes software, and 2 official LSAT exams)
The MCAT Physics Book (444 pages)
The MCAT Biology Book (416 pages)
The MCAT Chemistry Book (428 pages)
SAT Prep Course (640 pages, includes software)
SAT Math Bible (480 pages)
Law School Basics: A Preview of Law School and Legal Reasoning (224 pages)
Vocabulary 4000: The 4000 Words Essential for an Educated Vocabulary (160 pages)
Copyright 2008 by Nova PressAll rights reserved.
Duplication, distribution, or data base storage of any part of this work is prohibited without prior writtenapproval from the publisher.
ISBN 1889057495
GRE is a service mark of Educational Testing Service, which was not involved in the production of, anddoes not endorse, this book.
Nova Press11659 Mayfield Ave., Suite 1Los Angeles, CA 90049
Phone: 1-800-949-6175E-mail: [email protected]: www.novapress.net

iii
ABOUT THIS BOOK
If you dont have a pencil in your hand, get one now! Dont just read this bookwrite on it, study it,scrutinize it! In short, for the next four weeks, this book should be a part of your life. When you havefinished the book, it should be marked-up, dog-eared, tattered and torn.
Although the GRE is a difficult test, it is a very learnable test. This is not to say that the GRE isbeatable. There is no bag of tricks that will show you how to master it overnight. You probably havealready realized this. Some books, nevertheless, offer "inside stuff" or "tricks" which they claim will enableyou to beat the test. These include declaring that answer-choices B, C, or D are more likely to be correctthan choices A or E. This tactic, like most of its type, does not work. It is offered to give the student thefeeling that he or she is getting the scoop on the test.
The GRE cannot be beaten. But it can be masteredthrough hard work, analytical thought, and bytraining yourself to think like a test writer. Many of the exercises in this book are designed to prompt you tothink like a test writer. For example, you will find Duals. These are pairs of similar problems in whichonly one property is different. They illustrate the process of creating GRE questions.
The GRE math sections are not easynor is this book. To improve your GRE math score, you mustbe willing to work; if you study hard and master the techniques in this book, your score willimprovesignificantly.
This book will introduce you to numerous analytic techniques that will help you immensely, not onlyon the GRE but in graduate school as well. For this reason, studying for the GRE can be a rewarding andsatisfying experience.
To insure that you perform at your expected level on the actual GRE, you need to develop a level ofmathematical skill that is greater than what is tested on the GRE. Hence, about 10% of the math problemsin this book (labeled "Very Hard") are harder than actual GRE math problems.
Although the quick-fix method is not offered in this book, about 15% of the material is dedicated tostudying how the questions are constructed. Knowing how the problems are written and how the testwriters think will give you useful insight into the problems and make them less mysterious. Moreover,familiarity with the GREs structure will help reduce your anxiety. The more you know about this test, theless anxious you will be the day you take it.

CONTENTS
ORIENTATION 7
Part One: MATH 13Substitution 15Defined Functions 28Math Notes 33Number Theory 37Quantitative Comparisons 56Hard Quantitative Comparisons 71Geometry 78Coordinate Geometry 205Elimination Strategies 220Inequalities 230Fractions & Decimals 243Equations 259Averages 274Ratio & Proportion 285Exponents & Roots 304Factoring 316Algebraic Expressions 322Percents 330Graphs 347Word Problems 376Sequences & Series 397Counting 405Probability & Statistics 413Permutations & Combinations 426Functions 467Miscellaneous Problems 488
Part Two: SUMMARY OF MATH PROPERTIES 503
Part Three: DIAGNOSTIC/REVIEW TEST 513

ORIENTATION
Format of the Math SectionsThe math section consists of three types of questions: Quantitative Comparisons, Standard MultipleChoice, and Graphs. They are designed to test your ability to solve problems, not to test your mathematicalknowledge.
The math section is 45 minutes long and contains 28 questions. The questions can appear in anyorder.
FORMATAbout 14 Quantitative ComparisonsAbout 9 Standard Multiple ChoiceAbout 5 Graphs
Level of DifficultyGRE math is very similar to SAT math, though surprisingly slightly easier. The mathematical skills testedare very basic: only first year high school algebra and geometry (no proofs). However, this does not meanthat the math section is easy. The medium of basic mathematics is chosen so that everyone taking the testwill be on a fairly even playing field. This way, students who majored in math, engineering, or sciencedont have an undue advantage over students who majored in humanities. Although the questions requireonly basic mathematics and all have simple solutions, it can require considerable ingenuity to find thesimple solution. If you have taken a course in calculus or another advanced math topic, dont assume thatyou will find the math section easy. Other than increasing your mathematical maturity, little you learned incalculus will help on the GRE.
Quantitative comparisons are the most common math questions. This is good news since they aremostly intuitive and require little math. Further, they are the easiest math problems on which to improvesince certain techniquessuch as substitutionare very effective.
As mentioned above, every GRE math problem has a simple solution, but finding that simple solutionmay not be easy. The intent of the math section is to test how skilled you are at finding the simplesolutions. The premise is that if you spend a lot of time working out long solutions you will not finish asmuch of the test as students who spot the short, simple solutions. So, if you find yourself performing longcalculations or applying advanced mathematicsstop. Youre heading in the wrong direction.

8 GRE Math Bible
Experimental SectionThe GRE is a standardized test. Each time it is offered, the test has, as close as possible, the same level ofdifficulty as every previous test. Maintaining this consistency is very difficulthence the experimentalsection. The effectiveness of each question must be assessed before it can be used on the GRE. A problemthat one person finds easy another person may find hard, and vice versa. The experimental sectionmeasures the relative difficulty of potential questions; if responses to a question do not perform to strictspecifications, the question is rejected.
The experimental section can be a verbal section or a math section. You wont know which section isexperimental. You will know which type of section it is, though, since there will be an extra one of thattype.
Because the bugs have not been worked out of the experimental sectionor, to put it more directly,because you are being used as a guinea pig to work out the bugsthis portion of the test is often moredifficult and confusing than the other parts.
This brings up an ethical issue: How many students have run into the experimental section early in thetest and have been confused and discouraged by it? Crestfallen by having done poorly on, say, thefirstthough experimentalsection, they lose confidence and perform below their ability on the rest of thetest. Some testing companies are becoming more enlightened in this regard and are administeringexperimental sections as separate practice tests. Unfortunately, ETS has yet to see the light.
Knowing that the experimental section can be disproportionately difficult, if you do poorly on aparticular section you can take some solace in the hope that it may have been the experimental section. Inother words, do not allow one difficult section to discourage your performance on the rest of the test.
Research SectionYou may also see a research section. This section, if it appears, will be identified and will be last. Theresearch section will not be scored and will not affect your score on other parts of the test.
The CAT & the Old Paper-&-Pencil TestThe computer based GRE uses the same type of questions as the old paper-&-pencil test. The only differ-ence is the medium, that is the way the questions are presented.
There are advantages and disadvantages to the CAT. Probably the biggest advantages are that you cantake the CAT just about any time and you can take it in a small room with just a few other peopleinsteadof in a large auditorium with hundreds of other stressed people. One the other hand, you cannot return topreviously answered questions, it is easier to misread a computer screen than it is to misread printedmaterial, and it can be distracting looking back and forth from the computer screen to your scratch paper.
PacingAlthough time is limited on the GRE,

gre math bible ebook - · pdf fileiii about this book if you don’t have a pencil in your...

Documents