# GRE Quantitative Reasoning Review Course

## Math Basics

### Lesson 1: Operations Basics

- Addition and Subtraction
- Associative Property
- Distributive Property
- Exponents and Roots
- Integers, Decimals, and Fractions
- Multiplication and Division
- Order of Operations

### Lesson 2: Factors and Multiples

- Greatest Common Factor
- Least Common Multiple
- Multiples
- Multiples and Least Common Multiples
- Prime Numbers, Factoring, and Prime Factorization

### Lesson 3: Unit Conversions

## Fractions

### Lesson 1: Fraction Basics

- Changing Mixed Numbers to Improper Fractions
- Converting Improper Fractions to Mixed Numbers
- Fractions of a Whole
- Improper Fractions and Mixed Numbers
- Ordering Fractions

### Lesson 2: Fraction Operations

- Adding and Subtracting Fractions
- Converting Improper Fractions to Mixed Numbers and Decimals
- Converting Mixed Numbers to Decimals and Improper Fractions
- Converting Percentages to Decimals and Fractions
- Multiplying and Dividing Fractions

## Decimals

### Lesson 1: Decimal Basics

### Lesson 2: Decimal Operations

- Adding and Subtracting Decimals
- Changing a Number from Standard Form to Scientific Notation
- Converting Decimals to Fractions and Percentages
- Converting Decimals to Improper Fractions and Mixed Numbers
- Dividing Decimals
- Multiplying Decimals
- Scientific Notation

## Solving Equations

### Lesson 1: Equation Basics

- Absolute Value
- Arithmetic Sequences
- Solving Equations Using All Four Basic Operations
- Solving Equations Using Addition and Subtraction
- Solving Equations Using Multiplication and Division
- Solving Equations with Absolute Value

### Lesson 2: Inequalities

- Equations and Inequalities
- Graphing Solutions to Linear Inequalities
- Linear Inequalities
- Solving Absolute Value Inequalities
- Solving Inequalities Using All Four Basic Operations

### Lesson 3: Linear System of Equations

- Comparison of Methods for Solving System of Equations
- Linear Equations Basics
- System of Linear Equations
- System of Equations Basics

### Lesson 4: Graphing of Linear Equations and Functions

- Changing Constants in Graphs of Functions: Linear Functions
- Changing Constants in Graphs of Functions: Quadratic Equations
- Graphing Absolute Value Equations
- Graphing Linear Equations
- Graphing the Inverse of a Function
- Graphs of Functions
- Solutions of a Quadratic Equation on a Graph
- Using a Graph

### Lesson 5: Word Problems

- Right Triangle Word Problems
- Word Problems and Addition
- Word Problems and Division
- Word Problems and Multiplication
- Word Problems and Subtraction

## Geometry

### Lesson 1: Angle Basics

### Lesson 2: Triangles

- Area and Perimeter of a Triangle
- Measurements for Similar Triangles
- Measurements for Similar Triangles – Continued
- Measurements for Similar Triangles – Continued II
- Proof that a Triangle is 180 Degrees
- Similar Triangles

### Lesson 3: Circles

- Area and Circumference of a Circle
- Finding Measurements for Parts of a Circle
- Unit Circles and Standard Position

### Lesson 4: Volume and Surface Area of 3D Shapes

- 3D Geometric Shapes
- Volume and Surface Area of a Cube
- Volume and Surface Area of a Pyramid
- Volume and Surface Area of a Rectangular Solid
- Volume and Surface Area of a Circular Cone
- Volume and Surface Area of a Circular Cylinder
- Volume and Surface Area of a Sphere

## Probability, Statistics, Percentages, Ratios, and Proportions

### Lesson 1: Probability

### Lesson 2: Percentages, Ratios, and Proportions

- Calculation of a Percentage
- Computation with Percentages
- Finding the Percentage Decrease
- Finding the Percentage Increase
- Percentages
- Proportions
- Proportions and Percents
- Proportions in the Real World
- Ratios and Percentages

## GRE Quantitative Reasoning Review

The GRE—also known by its full name, the Graduate Record Examination—is an important exam for anyone looking to continue their education by enrolling in a graduate school program. As such, the GRE is meant to assess whether the prospective applicant possesses the skills necessary to thrive in a graduate school environment. The current edition of the GRE splits into three sections: Quantitative Reasoning, Verbal Reasoning, and Analytical Writing. If you’re reading this page, you’re likely interested in developing study tools for the Quantitative Reasoning section of the GRE. First things first, it will help to go over exactly what Quantitative Reasoning is.

Quantitative Reasoning basically covers math-related subjects. More specifically, this portion of the test seeks to assess your skill with rudimentary mathematical functions. It is worth noting, however, that the mathematical operations you’ll find on the Quantitative Reasoning section of the GRE cover far more than basic arithmetic. You can also expect to see such subjects as data analysis, geometry, and algebra. You won’t have to worry about studying materials any higher than what you’d expect to see on the usual high school exam—such as Calculus. This means you can limit your studying to just the four aforementioned subjects.

Why are you still being tested on math this far into your academic career? The answer is simple. No matter which academic program you’ll join once you complete your admissions process, you’ll need to possess and be able to demonstrate some mathematical knowledge. This is a core subject which, while lacking a 100 percent certainty of showing up in your graduate-level curriculum, is still important to know regardless.

Whether you’re a math whiz or struggle with numbers, we at Mometrix Test Preparation strive to give you all the tools you’ll need to ace this important exam and leave a lasting impression on those in charge of your graduate program admissions. This is why we offer such a wide breadth of study tools to you on this page and the rest of our website. Through us, you’ll have access to a wealth of valuable materials, including this GRE Quantitative Reasoning study guide, as well as a GRE Quantitative Reasoning practice test and GRE Quantitative Reasoning flashcards.

## What Is Featured on the GRE Quantitative Reasoning Section?

The GRE Quantitative Reasoning test features a wider variety of question formats than any other part of the exam. Specifically, you will find questions asking you to give a free numeric answer; multiple choice questions where you can choose either more than one option or merely one option; and questions where you will have to analyze two different quantities. Additionally, questions are organized in either one of two ways: as a cluster of questions relating to a specific piece of data, or individually and within its own context. You will be given a total of 70 minutes to complete both halves of the exam—or approximately 35 minutes for both parts of it. Each half of the GRE Quantitative Reasoning section spans about 20 questions in length.

One good point about this portion of the exam—for those who aren’t as skilled with math or just appreciate the convenience—is the allowance of calculators throughout the section’s duration. This goes for both the digital version of the Quantitative Reasoning section as well as the paper version. However, you may only use a standard calculator. No advanced models are allowed, unless you specifically prove your case for needing the extra help. The purpose of the calculator is to help you through questions that would otherwise be too laborious to solve manually. While the calculator has been included on this exam for your convenience, you should not rely on it too much. It is still worthwhile for you to study and reacquaint yourself with mathematical principles and properties. The calculator is a tool, and it will be up to you to know how to use it properly. Sometimes mental math is more effective than the calculator, and be sure to pay close attention to your keystrokes as you use your calculator to compute equations.

To help you understand the test as thoroughly as possible, we will go over both the question formats and mathematical subjects you can expect to find on the Quantitative Reasoning exam in further detail.

## Question Formats

The questions on the Quantitative Reasoning portion will be written as one of the five following types. It is worth noting that you could potentially see more than one of these formats grouped together in one “set,” which corresponds with a piece of data presented to you for analytical purposes. Some questions on this section are framed in wholly theoretical contexts, while others are modeled after realistic situations. You should be prepared to see both question scenarios on the exam and know how to approach and respond to them both.

### Data Sets

Questions relying on data interpretation typically come together in one bundle, which will be tied to a given piece of data—whether it be a chart, line plot, or some other depiction of information. All of the corresponding questions will request you to evaluate the data supplied to you in one way or another. This variety of questions can fall under the ‘numeric entry’ or ‘multiple choice’ categories. When approaching these questions, be sure to devote enough attention to the data being provided to you. The test is self-contained, and you cannot use outside information to help solve these questions, regardless of how relevant they are to the material. However, don’t pore over the data for too long. Give it as much attention as possible to understand questions and solve them adequately. Each illustration you’ll come across for data interpretation questions are exact-size, enabling you to interpret them more easily.

### Quantitative Comparison

As implied by the title, questions under the Quantitative Comparison category want you to look at two quantities and judge them based on size. Prior to answering this question type, you will be presented with a data depiction about the two quantities you are meant to evaluate. This could be through an algebraic equation or an illustration paired with numerals. You will have to answer whether one of them outranks the other in size, whether enough information exists to make that judgment, or whether they are both the same size.

### Numeric Entry

Numeric entry-based questions will typically require more precision from your answers than any other question format featured on the Quantitative Reasoning section. In some cases, you will have to answer with a decimal, fraction, or integer. When answer questions of this type, be sure to read carefully and know exactly what the question wants you to do. Look at the blank where your answer will be written for tips on how to solve the equation, check over your work after you compute your answer, and be sure to follow any and all clues given by the question so you arrive at the best possible answer. There is the likely possibility you will have to perform some rounding to come to an answer for a few numeric entry questions. In this case, also pay careful attention to what type of rounding must be performed. You do not have to round if the question does not specify that you must.

### Multiple Choice

There are two variants of multiple choice questions found within the Quantitative Reasoning exam: those where you must choose multiple correct answers, and those where you must choose just one answer.

The multiple answer multiple choice questions will provide you with a selection of options to pick from, and it will be up to you to decide which options solve the question most accurately. There will not always be any indication of just how many answer choices are correct. Before you try to answer questions of this variety, be sure to note whether or not there is a specific amount of correct answers you must choose. While solving these questions, one of the best strategies to remember is to closely examine to what you are being asked to solve. This will help you to immediately decide which answer choices are incorrect by default and, as a result, help you to budget your time efficiently.

The single answer multiple choice questions also provide you with a selection of options, from which you must choose one as the most correct option. While this particular question format is one of the most commonly administered on a national and international basis, we have a few tips for you on how to solve this question format as effectively and easily as you can. Before you solve a question, glance at your answer choices to figure out the numerical range for your answer. Estimation and guessing are perfectly reasonable responses to some questions; however, if your answer resembles no other options for that particular question, you may want to look over your work and try to solve the problem again for a closer answer.

### Subjects

As stated before, the subjects included within the Quantitative Reasoning exam won’t exceed anything you’d find on the averagel high school exam. This excludes higher-level subjects such as Trigonometry. Below we will go over the subjects and what you will need to know about each of them.

### Data Analysis

Data analysis involves taking a grouping of information and using it to draw statistical conclusions. You typically would have encountered this subject either in your undergraduate years, or while you were still in high school. The questions under this particular knowledge category will involve different means of computing numerical information; basic elements of statistical calculations, such as the range, mean, mode, and median; probability estimations of assorted varieties; and deciphering different presentations of data such as plots and tables.

### Arithmetic

Arithmetic is one of the first mathematical principles you ever learned, starting with addition and subtraction when you began elementary school. The arithmetic you’ll encounter within the Quantitative Reasoning section, however, is a little more advanced than kindergarten addition and subtraction. You’ll also be expected to demonstrate your abilities with numeric arrangement, integers and their qualities, decimals, even and odd numbers, number line properties, estimation, and much more.

### Geometry

Geometry is a high school subject and comprised of the mathematical analysis of two- and three-dimensional shapes. For this subject, you’ll have to demonstrate knowledge of how to properly calculate the width of angles; the properties of lines and how they interact; the application of the Pythagorean theorem; the properties of various shapes, including triangles and circles; and the measurements necessary to evaluate three-dimensional shapes, including volume and area.

### Algebra

You likely first came into contact with Algebra in middle or high school. The algebra questions featured on the GRE Mathematical Reasoning exam are similar to what you’ve already experienced. Specifically, algebra-focused questions on this section of the exam will involve elements such as line slopes, exponents and their traits, inequalities, figuring out simple equations and finding the values of variables, plotting graphs, and various word problems which will involve the formulation of distinct and relevant equations.

While this overview of the GRE Quantitative Reasoning section isn’t 100 percent comprehensive, we hope it will serve as a good launching pad for you when it comes to figuring out a study plan for this section of the exam. On the rest of this page, you’ll find a more complex GRE Quantitative Reasoning study guide, which can help you prepare further. Elsewhere on our site, you’ll be able to find a GRE Quantitative Reasoning practice test and GRE Quantitative Reasoning flashcards to enhance your studying as you see fit. We at Mometrix Test Preparation are here to help you along the path to success. Good luck, and happy studying!

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Last updated: 04/26/2016

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