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
