GRE : Math Prep Course

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If you don't have a pencil in your hand, get one now! Don't just read this book—write on it, study it, scrutinize it! In short, for the next four weeks, this book should be a part of your life. When you have finished 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 is "beatable." There is no bag of tricks that will show you how to master it overnight. You probably have already realized this. Some books, nevertheless, offer "inside stuff" or "tricks" which they claim will enable you to beat the test. These include declaring that answer-choices B, C, or D are more likely to be correct than choices A or E. This tactic, like most of its type, does not work. It is offered to give the student the feeling that he or she is getting the scoop on the test. The GRE cannot be "beaten." But it can be mastered—through hard work, analytical thought, and by training yourself to think like a test writer. Many of the exercises in this book are designed to prompt you to think like a test writer. For example, you will find "Duals." These are pairs of similar problems in which only one property is different. They illustrate the process of creating GRE questions. TheGRE math sections are not easy—nor is this book. To improve your GRE math score, you must be willing to work; if you study hard and master the techniques in this book, your score will improve—significantly. This book will introduce you to numerous analytic techniques that will help you immensely, not only on the GRE but in graduate school as well. For this reason, studying for the GRE can be a rewarding and satisfying experience. To insure that you perform at your expected level on the actual GRE, you need to develop a level of mathematical skill that is greater than what is tested on the GRE. Hence, about 10% of the math problems in 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 to studying how the questions are constructed. Knowing how the problems are written and how the test writers think will give you useful insight into the problems and make them less mysterious. Moreover, familiarity with the GRE's structure will help reduce your anxiety. The more you know about this test, the less anxious you will be the day you take it. FEATURES: Comprehensive Review: Twenty-three chapters provide comprehensive review of GRE math. Practice: Includes 166 examples and more than 623 exercises! Arranged from easy to medium to hard to very hard. Diagnostic Test: The diagnostic test measures your strengths and weaknesses and directs you to areas you need to study more. Dual Exercises: These are pairs of similar GRE problems in which only one property is different. They give you insight into how GRE problems are constructed. Performance: If your target is a 700+ score, this is the book! Table of Contents ORIENTATION 7 Part One: MATH 13 Substitution 15 Defined Functions 28 Math Notes 33 Number Theory 37 Quantitative Comparisons 56 Hard Quantitative Comparisons 71 Geometry 78 Coordinate Geometry 205 Elimination Strategies 220 Inequalities 230 Fractions & Decimals 243 Equations 259 Averages 274 Ratio & Proportion 285 Exponents & Roots 304 Factoring 316 Algebraic Expressions 322 Percents 330 Graphs 347 Word Problems 376 Sequences & Series 397 Counting 405 Probability & Statistics 413 Permutations & Combinations 426 Functions 467 Miscellaneous Problems 488 Part Two: SUMMARY OF MATH PROPERTIES 503 Part Three: DIAGNOSTIC/REVIEW TEST 513