If you are in the middle of preparing for the GRE or even just beginning, you know that GRE quantitative reasoning is a significant part of the exam. Thus, it will be advantageous for you to have a GRE quant syllabus or “lay of the land” when it comes to GRE exam topics, so you can get a rough picture of the road ahead. In other words, by knowing the math topics tested, you can estimate how long it may take you to succeed in GRE math. This article will walk through the types of questions you can expect to see in the quant section of the GRE.

## Here are the topics we’ll cover:

Let’s start with a general overview of the GRE quant section.

## The GRE Quant Section

Excluding the experimental section, there are five sections on the GRE. They include one analytical writing section (with two essay prompts), two verbal reasoning sections, and two quant sections.

Each of the two GRE quant sections contains 20 questions and, of course, can span a variety of topics, which we will discuss shortly. There are also four major question types:

- Multiple Choice – Single Answer
- Multiple Choice – Multiple Answer
- Quantitative Comparison
- Numeric Entry

Another important feature of the GRE math section is that you can use an onscreen calculator. While this calculator is quite basic, it does help when you have to deal with tedious calculations. However, as we have mentioned in previous articles, you need to be strategic when using the GRE calculator.

KEY FACT:

There are four major question types on the GRE quant section.

Now, let’s discuss each problem type in more detail.

### Multiple Choice – Single Answer

The most common and recognizable question on the GRE is multiple choice – single answer, more commonly known as multiple-choice questions. These questions are pretty much your run-of-the-mill questions, testing problem-solving skills that you have seen hundreds of times in your high school or college math classes. You are given a problem to answer, five answer choices, and one of the five choices is the correct answer.

Note that on the exam, there will not be letter answer choices; instead, you will see round “radio buttons” in front of each answer choice. You will simply click on the radio button of the answer choice you want to select.

Let’s practice a basic multiple choice – single answer question now.

#### Multiple Choice – Single Answer Example

Hank has a total of 20 T-shirts, some blue and some red. If he has 4 more blue shirts than red shirts, how many blue shirts does he have?

##### Solution:

We can let the number of red shirts = r and the number of blue shirts = b. Now we can create the following equations:

Equation One: b + r = 20

Equation Two: b = r + 4

We can substitute r + 4 for b in equation one, and we have:

r + 4 + r = 20

2r = 16

r = 8

We see that the number of red shirts is 8, but we are asked the number of blue shirts. We substitute r = 8 into equation two:

b = r + 4

b = 8 + 4

b = 12

**Answer: E**

KEY FACT:

The most familiar question type on the GRE is the multiple choice – single answer question.

Next, let’s discuss multiple choice – multiple answer questions.

### Multiple Choice – Multiple Answer

Multiple choice – multiple answer questions are just what they sound like! Instead of selecting just one answer, you have the option of selecting multiple answers. Keep in mind that **there is no partial credit. **In other words, you must choose all the correct answers to get credit for a correctly answered question.

Also, if you are concerned that you may not know when you are presented with a multiple-answer question, the “radio buttons” next to each answer choice are square instead of round.

Let’s practice with an example.

#### Multiple Choice – Multiple Answer Example

If 12 < 4x – 8 < 20, then what are the possible values of x?

Select all that apply.

##### Solution:

We can simplify the given inequality:

12 < 4x – 8 < 20

First, we can add 8 to both sides of the inequality, so we have:

20 < 4x < 28

Next, we can divide both sides by 4:

5 < x < 7

Since x is greater than 5 but less than 7, we see that x can be 5.4, 6, and 6.3.

**Answer: C, D, and E**

KEY FACT:

multiple choice – multiple answer questions may have more than one correct answer.

Next, let’s discuss Quantitative Comparison questions.

### Quantitative Comparison

Quantitative Comparison questions (or QC questions) are a unique GRE question type. The essence of a QC question is that you are usually given some information in what we call the problem stem. You are then given two quantities, A and B. It’s your job to determine whether quantity A is greater than quantity B (or vice versa), whether the two quantities are equal, or whether we do not have enough information to determine a consistent relationship between the two quantities. In addition to using your math skills, you can lean on your logical reasoning skills when you’re solving these questions.

The answer choices that always appear in these questions are listed below:

- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given

**Since these answer choices do not change, you should memorize them! **That way, you can save a few seconds when answering these questions.

Let’s practice with an example.

#### Quantitative Comparison Example

2y – z = 2v – u

Quantity A:

2y + u

Quantity B:

2v + z

##### Solution:

We can manipulate the given information as follows:

2y – z = 2v – u

First, we add u to both sides:

2y – z + u = 2v

Next, we add z to both sides:

2y + u = 2v + z

Since 2y + u equals 2v + z, the two quantities are equal.

**Answer: C**

KEY FACT:

Unique to the GRE is the Quantitative Comparison (QC) question, for which you must compare two quantities and determine the relationship between them.

Next, let’s discuss Numeric Entry questions.

### Numeric Entry

The best way to describe a Numeric Entry question is that it’s pretty much the same thing as a multiple choice – single answer question, except there are no answer choices provided. You must input your answer into a box instead of selecting an answer choice.

A cool feature of the Numeric Entry question is that, when using the onscreen calculator, you can click “transfer display,” and whatever is on your calculator display will automatically transfer to the answer box.

Let’s practice an example below.

#### Numeric Entry Example

On four math tests, Tobias scored 90, 84, 92, and 90. What would he have to score on the fifth test to make his average 96 for all five tests?

##### Solution:

Let’s let x = the score on the fifth test. We can use the average formula to determine x:

(90 + 84 + 92 + 90 + x) / 5 = 88

90 + 84 + 92 + 90 + x = 440

356 + x = 440

x = 84

**Answer: 84**

KEY FACT:

The Numeric Entry question type on the GRE requires that you type an answer into the answer box. There are no answer choices from which to choose.

Now that we have reviewed the question types, let’s discuss the quant topics on the GRE.

## The Major GRE Quant Topics

There are roughly 21 major GRE math topics. The GRE math syllabus breakdown is below:

- Basic Arithmetic
- Linear Equations
- Quadratic Equations
- Exponents and Roots
- Number Properties
- Inequalities
- Absolute Value
- General Word Problems
- Rates
- Work
- Unit Conversions
- Ratios
- Percents
- Overlapping Sets
- Statistics
- Combinations and Permutations
- Probability
- Geometry
- Coordinate Geometry
- Functions and Sequences
- Data Interpretation

The above list is pretty much every major quant topic you might see on your GRE. Of course, because there are just 40 quant questions, you don’t know how many questions you will see on each topic. So, as we have discussed in many previous articles, you’ll want to take a structured and topical approach to your prep to ensure that you’ll master all the GRE quant test content.

KEY FACT:

There are roughly 21 major GRE math topics.

Next, let’s review the many important subtopics within each major math topic! We will start with basic arithmetic.

### Basic Arithmetic Subtopics

Basic arithmetic covers everything you need to know to deal with components of more advanced questions. Any good study plan will have you learn basic arithmetic before you learn more advanced topics. The topic covers the following:

- Adding and subtracting fractions
- Multiplying and dividing fractions
- Decimal rules
- Estimation shortcuts
- PEMDAS
- Basics of factorials

Let’s take a look at linear equations next.

### Linear Equations Subtopics

Linear equations are the bread and butter of algebra. I can’t stress enough how important algebra is for almost everything that will come your way on GRE quant. For example, you will notice that your algebra skills play a large role in solving word problems, ratios, or even geometry questions. So, make sure not to rush learning about linear equations.

Here is a list of some of the subtopics to expect from that topic:

- Solving equations with one variable
- Solving equations with multiple variables
- Substitution method of solving a system of linear equations
- Combination method of solving a system of linear equations
- Expressing one variable in terms of another variable

Next, let’s discuss quadratic equations.

### Quadratic Equations Subtopics

Quadratic equations are a step up difficulty-wise from linear equations, and they can pop up in other GRE quant topics, such as Combinations, Probability, and Geometry, among other topics. Some quadratic equations subtopics are as follows:

- FOILing
- Factoring a quadratic trinomial
- 3 common quadratic identities
- The Zero Product Property
- Eliminating fractions from equations

Our next topic is exponents and roots.

### Exponents and Roots Subtopics

Exponents and roots is an interesting topic because it’s tied to a select number of rules. The good news is that if you know those rules and processes, you really should not have any issues solving these types of questions. Below are some of the exponent and roots subtopics:

- Combining exponential expressions – multiplication and division
- Adding and subtracting exponents or roots
- Simplifying non-perfect roots
- Rationalizing fractions
- Fractional exponents

Let’s move on to number properties.

### Number Properties Subtopics

Number properties is a topic concerned with how numbers “behave.” This topic covers the properties that help to express the basic characteristics or features of real numbers. For example, we all know basic properties and types of integers, but there are some special situations that fall within the realm of number properties.

Here are the major subtopics of number properties:

- Integers
- Even/odd integers
- Positive/negative integers
- Prime numbers
- LCM and GCF
- Remainder theory
- Evenly spaced sets
- Divisibility
- Units digit patterns

Another important topic tested on the GRE is inequalities and absolute value.

### Inequalities and Absolute Value Subtopics

Inequalities and absolute value concepts build on many of the rules you learn for linear equations, with certain caveats. For example, you can add or subtract inequalities (just as you can equations), but you can’t divide or multiply an inequality by a variable whose sign is unknown (unlike in equations). Absolute value is quite similar. Short of a few rules, you will use many of the techniques you learn for linear equations to answer absolute value questions.

Some subtopics of inequalities and absolute value are below:

- Equations and inequalities
- Adding and subtracting inequalities
- Multiplying an inequality by a negative number
- Compound inequalities
- Absolute value equations
- Adding and subtracting absolute values
- When two absolute value expressions are equal to each other

Let’s move on to general word problems.

### General Word Problems Subtopics

General word problems are the “heart” of all word problems on the GRE. The basis of this topic is that we translate words into equations. While there are many possible word problem topics, the more common ones are below:

- Age problems
- Profit and loss
- Consecutive integers
- Price and salary problems
- Inequality word problems

Next, let’s discuss rates, work, and unit conversions.

### Rates, Work, and Unit Conversions Subtopics

Rates and work are similar topics, as they use two similar formulas: rate x time = distance and rate x time = work. Additionally, as these problems become more complicated, there may be an added layer of unit conversions that is folded into these questions.

Some of the subtopics of rates, work, and unit conversions are as follows:

- Rates and work problems with variables
- Average rate problems
- Converging and diverging rate questions
- Combined worker questions
- Opposing worker questions
- Catch-up rate questions
- Round trip rate questions
- Basic unit conversions
- Unit conversions with squared and cubed units

Let’s move on to percents and ratios.

### Percents and Ratios Subtopics

A ratio is a comparison between two or more quantities. Because ratios are often expressed as fractions, they are closely related to decimals and percents. Ratios and percents are topics taught in elementary and middle school, and so many GRE students may need a deep review of these topics. Here are the details of what you will need to cover:

- Two-part and three-part ratios
- The ratio multiplier
- Ratios and proportions
- Basic percents
- The five types of percent expressions
- Percent change

Now let’s discuss a small but important topic on the GRE: overlapping sets.

### Overlapping Sets Subtopics

In the simplest situation, an overlapping set occurs when we have two categories, and there is at least one element that is a member of both categories. This situation gives rise to the need for a sophisticated way of disentangling the numbers of elements in each category individually, or the number of elements in both sets, or in neither set. We use a variety of methods to solve overlapping sets questions. Here are the subtopics tested:

- The set-matrix
- Percents and fractions in the set-matrix
- The venn diagram for three overlapping sets

Our next topic is statistics and probability.

### Statistics and Probability Subtopics

In the two topics of statistics and probability, you will find many subtopics normally covered in an elementary statistics course. The good news is that the advanced subjects of confidence intervals and hypothesis testing, also covered in that intro course, are not in the GRE syllabus. Here are the subtopics that you will encounter:

- Average (arithmetic mean), median, and mode
- Evenly spaced sets
- Weighted average
- Range and standard deviation
- Basic probability facts
- The addition rule and mutually exclusive events
- The multiplication rule and independent events

A topic related to statistics and probability is combinations and permutations, which we’ll look at now.

### Combinations and Permutations Subtopics

Combinations and permutations both refer to methods of counting the number of ways that a certain task can be completed. Combinations are used when the order in which a task is completed does not matter. Permutations, in contrast, are used when the order of completion does matter. Here are the subtopics you’ll need to know:

- The combinations formula
- The fundamental counting principle
- Combinations with and without restrictions
- The permutation formula
- Distinguishable and indistinguishable items
- Circular permutations
- Creating codes

Let’s move on to Geometry.

### Geometry Subtopics

You have probably not encountered the study of geometry since high school. Therefore, a rigorous review of many geometry subtopics should be high on your priority list if you want to confidently answer geometry questions on the GRE. Here are the subtopics you’ll need to know:

- Lines, rays, and line segments
- Intersecting and parallel lines
- Angles
- Polygons
- Triangles
- The Pythagorean theorem
- Scalene, isosceles, and equilateral triangles
- Quadrilaterals and parallelograms
- Rectangles, squares, and trapezoids
- Circles
- Inscribed and circumscribed shapes
- Solid geometry (cubes, rectangular prisms, and right circular cylinders)
- Areas and volumes of geometric objects

Our next topic is coordinate geometry.

### Coordinate Geometry Subtopics

You may be unfamiliar with the term “coordinate geometry,” but it simply refers to an activity you did many times in high school math: graphing points and shapes in the coordinate plane (the xy- axis). This topic is well-represented on the quant section of the GRE, so having a solid background in this topic will serve you well. Here is a breakdown of coordinate geometry:

- The axes and the quadrants
- Slope and slope-intercept form of a line
- Parallel and perpendicular lines
- The distance formula
- The midpoint formula
- Circles in the coordinate plane
- Graphing inequalities

Another topic from algebra is functions and sequences.

### Functions and Sequences Subtopics

Functions are like math machines in which an input is manipulated to produce an output. The function notation f(x) may be a bit intimidating, but with a bit of practice, you should be able to demystify functions.

Sequences are simply number patterns. The GRE will not test you on the more convoluted sequences, but a solid understanding of basic sequences – arithmetic and geometric – will serve you well.

Here are the subtopics you’ll need to know:

- Domain and range
- Compound functions
- Graphs of functions
- Word problems with functions
- Arithmetic sequences
- Geometric sequences

Our final major quant category is Data Interpretation.

### Data Interpretation Subtopics

In each of the two quant sections of the GRE, you will be presented with a set of data and/or a graphic obtained from data. You will then be presented with two questions pertaining to the graph and the analysis/interpretation of the underlying data. Familiarity with charts and graphs will be necessary in order to answer these four questions. Here are the possible subtopics to study:

- Review of mean, median, mode, range, and standard deviation
- Frequency table
- Pie chart
- Bar graph and Pareto chart
- Venn diagram
- Contingency table
- Dotplot
- Stemplot
- Boxplot
- Column chart
- Scatterplot, linear regression, and correlation
- The Bell Curve

## In Summary

There are two quant sections on the GRE, each containing 20 questions. There are four question types that you will encounter in these two sections:

- Multiple Choice – Single Answer
- Multiple Choice – Multiple Answer
- Quantitative Comparison
- Numeric Entry.

There are roughly 21 major quant topics on the GRE. Each of these has about 5-8 subtopics, which we have listed and discussed in this article.

## What’s Next?

Knowing the GRE math subjects is a great start. Now it’s time to start reviewing and learning these topics. Now that you know which GRE quantitative reasoning topics are covered on the exam, you can get started with your prep by first estimating how long you’ll need to study for the GRE, so that you earn the score you need to get into your dream school!