新东方·GRE数学备考策略与模拟试题

To the Student vii

Guide to Using This Book ix

1 The GRE General Math Exam 1

Exam Structure 1

Question Types 2

Multiple-Choice Questions 2

Multiple-Answer Questions 3

Quantitative Comparison Questions 3

Numeric Entry Questions 4

Topics and Scoring 5

Calculator Use 6

Problems 8

Solutions 9

2 STRATEGIES AND PROBLEM SOLVING 13

Test-Taking Strategies 13

Problem Solving 14

General Strategies 16

Use a Diagram 16

Pay Attention to Units 20

Use Numbers Instead of Variables 21

Strategies for Multiple-Choice Questions 22

Test Answers Starting with C 22

Use Numbers Instead of Variables 22

Eliminate Choices, Then Guess 23

Strategies for Data Interpretation Questions 24

Estimate, Don’t Calculate 25

Try to Visualize Rather Than Calculate 25

Strategies for Quantitative Comparison

Questions 26

Do the Same Thing to Each Quantity 26

Compare, Don’t Calculate 27

Replace Variables with Numbers 27

Choose a Good Number for the Whole 28

Guess 29

Strategies for Numeric Entry Questions 30

Don’t Simplify Fractions 30

Strategies for Multiple-Answer Questions 31

Problems 31

Solutions 34

3 NUMBERS 39

Numbers 40

Operations 40

Basic Properties 40

Absolute Value 42

Order of Operations: PEMDAS 43

Problems 45

Basic Problems 45

GRE Problems 45

Integers 46

Consecutive Integers 48

Problems 48

Basic Problems 48

GRE Problems 50

Number Theory 52

Divisibility Rules 52

Odds and Evens 54

Prime Numbers 55

Greatest Common Factor and Lowest Common Multiple 57

Problems 58

Basic Problems 58

GRE Problems 59

Fractions 61

Equivalent Fractions 62

Mixed Fractions 64

Operations on Fractions 65

Simplifying Complex Fractions 68

Solving Fraction Problems with Diagrams 69

Problems 70

Basic Problems 70

GRE Problems 72

Decimals 74

Converting Between Fractions and Decimals 75

Comparing Decimal Numbers 76

Operations on Decimals 76

Multiplying or Dividing by Problems 77

Basic Problems 77

GRE Problems 78

Radicals and Exponents 79

Simplifying Radicals 80

Defining Powers 81

Rules for Working with Powers 82

Problems 83

Basic Problems 83

GRE Problems 84

Solutions 86

Numbers 86

Integers 87

Number Theory 90

Fractions 94

Decimals 98

Radicals and Exponents 100

4 ALGEBRA 103

Polynomials and Factoring 103

Problems 107

Basic Problems 107

GRE Problems 108

Solving Equations 110

Solving Systems of Linear Equations 113

Problems 115

Basic Problems 115

GRE Problems 117

Inequalities 119

Problems 122

Basic Problems 122

GRE Problems 123

Functions 125

Problems 127

Basic Problems 127

GRE Problems 128

Solutions 129

Polynomials and Factoring 129

Solving Equations 131

Inequalities 134

Functions 137

5 DATA ANALYSIS 139

Percentages 139

Problems 142

Averages 144

Problems 148

Charts and Graphs 150

Problems 153

Counting 157

Venn Diagrams 158

Partitions 159

Counting Commas 160

Problems 161

Basic Problems 161

GRE Problems 162

Probability 163

Problems 165

Solutions 168

Percentages 168

Averages 169

Charts and Graphs 171

Counting 173

Probability 175

6 GEOMETRY 179

Perimeter 180

Problems 183

Basic Problems 183

GRE Problems 184

Angles 186

Problems 189

Basic Problems 189

GRE Problems 190

Triangles 192

Triangle Inequality 194

Pythagorean Theorem 195

Problems 197

Basic Problems 197

GRE Problems 199

Polygons 201

Regular Polygons 202

Quadrilaterals 204

Problems 206

Basic Problems 206

GRE Problems 207

Area 209

Connecting Area and Perimeter 212

Problems 213

Basic Problems 213

GRE Problems 214

Surface Area and Volume 217

Surface Area 217

Volume 219

Problems 221

Basic Problems 221

GRE Problems 222

Solutions 224

Perimeter 224

Angles 227

Triangles 229

Polygons 231

Area 234

Surface Area and Volume 237

7 SAMPLE EXAMS AND SOLUTIONS 241

Sample Test 1 245

Sample Test 2 253

Answers and Complete Solutions to Sample Exams 259

Appendix: Suggested Facts to Memorize 271

Index 273