The Quantitative Reasoning section of the GRE General Test evaluates mathematical knowledge, quantitative problem-solving, numerical reasoning, and data interpretation. According to the Educational Testing Service (ETS), the syllabus comprises four official mathematical content areas: Arithmetic, Algebra, Geometry, and Data Analysis.

1. Arithmetic

- 1.1. Number Systems

• Natural numbers

• Whole numbers

• Integers

• Rational and irrational numbers

• Real numbers

• Positive and negative numbers

• Odd and even numbers

• Prime and composite numbers

- 1.2. Basic Arithmetic Operations

• Addition, subtraction, multiplication, and division

• Order of operations (PEMDAS/BODMAS)

• Properties of arithmetic operations

• Mental calculations and estimation

- 1.3. Number Properties

• Factors and multiples

• Divisibility rules

• Prime factorization

• Greatest common factor (GCF)

• Least common multiple (LCM)

• Remainders

• Consecutive integers

- 1.4. Fractions

• Proper and improper fractions

• Mixed numbers

• Equivalent fractions

• Simplifying fractions

• Fraction operations

• Comparing fractions

- 1.5. Decimals

• Decimal operations

• Terminating decimals

• Repeating decimals

• Converting fractions and decimals

• Rounding and approximation

- 1.6. Percentages

• Percentage calculations

• Percentage increase and decrease

• Percentage change

• Successive percentage changes

• Discounts and markups

• Profit and loss

• Simple and compound interest

- 1.7. Ratios and Proportions

• Ratios

• Proportional relationships

• Direct and inverse variation

• Unit rates

• Scale factors

- 1.8. Exponents and Radicals

• Laws of exponents

• Positive, negative, and zero exponents

• Fractional exponents

• Square roots and cube roots

• Simplifying radical expressions

• Scientific notation

- 1.9. Absolute Values and Number Lines

• Absolute value expressions

• Distance on a number line

• Ordering real numbers

• Absolute value equations and inequalities

- 1.10. Numerical Sequences

• Arithmetic sequences

• Geometric sequences

• Number patterns

• Finding missing terms

2. Algebra

- 2.1. Algebraic Fundamentals

• Variables and constants

• Algebraic expressions

• Like and unlike terms

• Simplifying expressions

• Substitution and evaluation

- 2.2. Algebraic Operations

• Expanding expressions

• Factoring expressions

• Polynomial operations

• Algebraic fractions

• Simplifying rational expressions

- 2.3. Linear Equations

• One-variable linear equations

• Equations involving fractions

• Literal equations

• Translating word problems into equations

- 2.4. Linear Inequalities

• One-variable inequalities

• Compound inequalities

• Inequality graphs

• Interval notation

- 2.5. Simultaneous Equations

• Systems of linear equations

• Substitution method

• Elimination method

• Systems of inequalities

- 2.6. Quadratic Equations

• Quadratic expressions

• Factoring quadratics

• Completing the square

• Quadratic formula

• Discriminant

• Quadratic inequalities

- 2.7. Functions

• Function notation

• Domain and range

• Evaluating functions

• Linear functions

• Quadratic functions

• Function graphs

- 2.8. Coordinate Geometry

• Cartesian coordinate system

• Coordinate points

• Distance between points

• Midpoint formula

• Slope of a line

• Equations of straight lines

• Parallel and perpendicular lines

• x-intercepts and y-intercepts

• Graphs of equations and inequalities

- 2.9. Algebraic Word Problems

• Age problems

• Number problems

• Distance-rate-time problems

• Work-rate problems

• Mixture problems

• Cost and revenue problems

3. Geometry

- 3.1. Basic Geometry

• Points, lines, rays, and line segments

• Parallel and perpendicular lines

• Angles and angle relationships

• Complementary and supplementary angles

• Angles formed by transversals

- 3.2. Triangles

• Types of triangles

• Interior and exterior angles

• Triangle inequality

• Isosceles triangles

• Equilateral triangles

• Right triangles

• 30°–60°–90° triangles

• 45°–45°–90° triangles

• Pythagorean theorem

• Perimeter and area of triangles

- 3.3. Quadrilaterals

• Squares

• Rectangles

• Parallelograms

• Rhombuses

• Trapezoids

• Perimeter and area calculations

- 3.4. Polygons

• Regular and irregular polygons

• Interior angle sums

• Exterior angle sums

• Polygon perimeter and area

- 3.5. Circles

• Radius and diameter

• Circumference

• Area of circles

• Arcs and central angles

• Arc lengths

• Sector areas

• Chords and tangents

- 3.6. Congruence and Similarity

• Congruent figures

• Similar triangles

• Corresponding angles and sides

• Scale factors

• Area and volume scaling

- 3.7. Three-Dimensional Geometry

• Cubes

• Rectangular prisms

• Cylinders

• Surface area

• Volume

• Space diagonals

- 3.8. Geometric Measurement

• Length and distance

• Perimeter

• Area

• Surface area

• Volume

• Unit conversions

4. Data Analysis

- 4.1. Descriptive Statistics

• Mean

• Median

• Mode

• Range

• Weighted average

• Standard deviation

• Variance as a supporting concept

• Quartiles

• Interquartile range (IQR)

• Percentiles

- 4.2. Data Representation

• Tables

• Frequency tables

• Bar graphs

• Line graphs

• Pie charts

• Histograms

• Scatterplots

• Box-and-whisker plots

• Frequency distributions

- 4.3. Data Interpretation

• Reading graphs and tables

• Comparing data sets

• Identifying trends

• Calculating percentages from graphs

• Ratios from data

• Rates of change

• Interpreting scales and units

- 4.4. Probability

• Basic probability

• Sample spaces and events

• Complementary events

• Independent events

• Dependent events

• Mutually exclusive events

• Compound probability

• Conditional probability

- 4.5. Counting Methods

• Fundamental counting principle

• Factorials

• Permutations

• Combinations

• Arrangements and selections

• Venn diagrams

• Inclusion-exclusion principle

- 4.6. Probability Distributions

• Discrete random variables

• Probability distributions

• Expected value

• Normal distributions

• Symmetric distributions

- 4.7. Data Relationships

• Positive and negative associations

• Correlation versus causation

• Interpreting scatterplots

• Outliers

• Comparing statistical distributions

5. Applied Mathematics and Word Problems

These are cross-cutting practice categories rather than separate official ETS content areas.

- 5.1. Rate, Time, and Distance

• Speed calculations

• Average speed

• Relative speed

• Travel time

• Unit conversions

- 5.2. Work and Productivity

• Individual work rates

• Combined work

• Pipes and tanks problems

• Work completion time

- 5.3. Financial Mathematics

• Profit and loss

• Discounts

• Markups

• Tax calculations

• Interest calculations

• Price comparisons

- 5.4. Mixtures and Proportions

• Mixture ratios

• Concentrations

• Percentage composition

• Weighted averages

- 5.5. Mathematical Modeling

• Translating verbal statements into equations

• Identifying mathematical relationships

• Formulating constraints

• Selecting appropriate solution methods

6. GRE Quantitative Reasoning Question Types

ETS uses four official question types, and questions may also appear within Data Interpretation sets.

- 6.1. Quantitative Comparison

• Comparing Quantity A and Quantity B

• Determining greater or smaller values

• Identifying equal quantities

• Recognizing insufficient information

- 6.2. Multiple Choice — Single Answer

• Solving quantitative problems

• Selecting one correct answer

• Using answer elimination

• Testing answer choices

- 6.3. Multiple Choice — Multiple Answers

• Selecting all correct answers

• Testing mathematical conditions

• Evaluating multiple possibilities

- 6.4. Numeric Entry

• Integer answers

• Decimal answers

• Fraction answers

• Exact numerical calculations

- 6.5. Data Interpretation Sets

• Graph-based problems

• Table-based problems

• Statistical comparisons

• Multi-question data analysis

7. Quantitative Reasoning Skills and Test Strategies

- 7.1. Mathematical Reasoning

• Logical deduction

• Pattern recognition

• Mathematical estimation

• Recognizing equivalent expressions

- 7.2. Problem-Solving Techniques

• Backsolving

• Substituting convenient values

• Working backward

• Eliminating incorrect choices

• Recognizing shortcuts

- 7.3. Calculation Skills

• Mental arithmetic

• Fraction-decimal conversions

• Approximation

• Strategic calculator use

• Checking answers

- 7.4. Time Management

• Question prioritization

• Avoiding unnecessary calculations

• Recognizing difficult problems

• Accuracy under time pressure

• Reviewing calculations

GRE Quantitative Reasoning: Syllabus Summary

No., Main topic, Study emphasis

1. Arithmetic, Number properties and calculations

2. Algebra, Equations, inequalities, functions

3. Geometry, Shapes, angles, areas, volumes

4. Data Analysis, Statistics, probability, graphs

5. Applied Mathematics, Word problems and modeling

6. GRE Question Types, Comparison, multiple choice, numeric entry

7. Test Strategies, Reasoning, accuracy, speed

Important: The actual GRE Quantitative Reasoning syllabus is based on high-school-level mathematics, generally no higher than second-year algebra, along with introductory statistics. Trigonometry, calculus, advanced mathematics, and formal geometric proofs are not tested.

For official preparation, use the ETS GRE Math Review (PDF) and the ETS Quantitative Reasoning Overview.