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Last Updated on January 11, 2024
Whether you have been studying for months or are just getting started with your GRE math prep, I’m sure you know that Quant is a significant component of the GRE. While the Quant tested on the GRE may seem daunting at first because there is so much to learn, the good news is that it is very learnable. If you can study smart and work hard, you can succeed in GRE quant! This article will discuss some strategies for preparing for GRE quant, and then provide 10 GRE Quantitative Reasoning practice questions.
Here are the topics we’ll cover:
- What Are the GRE Quant Topics?
- The Best Way to Prepare for GRE Quant
- The GRE Quant Question Types
- GRE Quant Practice Questions
- Practice Question 1: Linear Equations – MC – Single-Answer
- Practice Question 2: Number Properties – MC – Multiple-Answer
- Practice Question 3: Exponents – MC – Single-Answer
- Practice Question 4: Inequalities – QC
- Practice Question 5: Functions – Numeric Entry
- Practice Question 6: Lines – MC – Multiple Answers
- Practice Question 7: Counting Principle – Numeric Entry
- Practice Question 8: Percents – QC
- Practice Question 9: Geometry – QC
- Practice Question 10: Word Problems – MC – Single-Answer
- In Summary
- What’s Next?
To get started, let’s review the basics of GRE quant.
The GRE has two Quantitative Reasoning sections. The first section contains 12 questions, and the second section contains 15 questions.
There are 24 major topics that will be tested in these 27 Quant questions when you take your GRE:
- Algebra
- Linear and Quadratic Equations
- Number Properties
- Roots
- Exponents
- Inequalities
- Absolute Value
- General Word Problems
- Rates
- Work Problems
- Unit Conversions
- Ratios
- Percents
- Statistics
- Overlapping Sets
- Combinations
- Permutations
- Probability
- Geometry
- Coordinate Geometry
- Sequences
- Functions
- Data Analysis Problems
- Data Interpretation Questions
If you do some quick math, you see that 40 divided by 24 is around 1.8. So, based on that calculation, you can expect to see 1.8 questions per Quant topic on the GRE or on official practice tests. Unfortunately, however, the question distribution is not quite that simple! Part of what makes the Quantitative Reasoning section of the GRE so challenging is that you do not know which topics and how many GRE math problems from each topic you’ll see on any given GRE.
For example, on one test, you may see four geometry questions and two exponents questions, and on another, you may see two geometry questions and five exponents questions. So, this begs the question, what is the best way to prepare for GRE quant? Let’s discuss that now.
TTP PRO TIP:
Do not expect to see the same number of questions from each topic on every GRE you take.
The Best Way to Prepare for GRE Quant
While we have discussed the best way to prepare for the GRE in other articles, we can review some of the finer points here.
Here are two facts that should help shape how we prepare:
- The number of questions we see on any Quant topic is unpredictable.
- There are 27 major Quant topics but just 40 Quant questions on the GRE.
Given these two facts, to ace GRE Quant, you must be prepared for anything that might come up on the test. That means you need to study in an organized and topical way rather than haphazardly and randomly. Topical learning means learning just one topic at a time, and then practicing just that topic until you have achieved mastery.
TTP PRO TIP:
Topical learning will help you systematically learn the vast number of GRE topics you must know to be successful on test day.
Let’s review a specific example from the Target Test Prep GRE prep course. We can look at the chapter on work problems.
An Example of Topical Studying
The TTP study guide is set up so that students focus on one major topic at a time, then answer practice questions on just that topic.
The TTP Work chapter contains the following topics related to work problems:
- Rate-Time-Work Formula
- Determine an Object’s Work Rate
- The Matrix Approach to Solving Work Problems
- The Major Types of Work Problems
- Single Worker Problems
- Single Worker Problems With Variables in the Answer Choices
- Combined Worker Problems
- Two Objects Work Together for the Same Amount of Time
- Two Objects Work Together, but One Object Stops Before Completion
- Two Objects Work Together, but One Object Has an Unknown Time
- Percent of a Job Done and a Fraction of a Job Done
- Opposing Worker Problems
- Adding Combined Rates
- Relative Rate Work Problems
- The Rate of One Worker Is Expressed as a Multiple of the Rate of Another Worker
- The Rate of One Worker Is Slower or Faster Than the Rate of Another Worker
- Change in Worker Problems
As you can see, there are many topics just in work problems! This is why our Quantitative Reasoning syllabus has students focus on just this problem type before moving to something new.
In fact, our chapters present two to three questions after each concept taught, to solidify that concept, and then provide 100+ GRE Math practice questions with solutions to complete after each chapter.
TTP PRO TIP:
To learn so much on each GRE Quant topic, you must engage in topical learning.
With that in mind, let’s briefly discuss the importance of engaging in topical GRE Quantitative Reasoning practice.
Topical Practice Ingrains What You Have Learned
So, you have successfully learned a Quant topic (such as work questions). You diligently immersed yourself in the content, taking notes and creating your own GRE math flashcards.
Now you need to practice what you have just learned. In an ideal scenario, you should practice a minimum of 50 questions on each topic. For example, in the TTP study plan for work questions, students complete 7 easy, medium, and hard tests totaling 105 questions. After completing so many questions, it’s easy to see where you are weak and thus where you need to improve.
TTP PRO TIP:
After engaging in topical learning, be sure to complete at least 50 questions on the topic you just learned.
The last thing to cover before jumping into some GRE Quantitative practice questions is the types of GRE math questions you can expect to see on your exam.
The GRE Quant Question Types
Whether you are taking the actual GRE or doing GRE Quant practice problems, expect to see four types of GRE questions.
- Multiple-Choice (MC) Single-Answer
- Multiple-Choice (MC) Multiple-Answer
- Quantitative Comparison (QC) Questions
- Numeric Entry Questions
Let’s quickly review each of these problem types and practice some questions.
Multiple-Choice Single-Answer
Multiple-choice single-answer is the most common question type on the GRE. These questions are traditional problem-solving questions. Each question has five answer choices with only one correct answer.
Multiple-Choice Multiple-Answer
Multiple-choice multiple-answer questions allow for multiple correct answers. There are often more than five answer choices. Some questions may have three answer choices, and others may have eight. You must select all correct answers to correctly answer these questions, as there is no partial credit!
Quantitative Comparison
Roughly 10 of the 27 Quant questions on the GRE are Quantitative Comparison (QC) questions.
Quantitative Comparison questions are the most “unique” GRE question type. In QC questions, you need to evaluate two quantities (A and B) to determine whether one is larger than the other, whether the quantities are equal, or whether you do not have enough information to determine a definitive answer.
Quantitative Comparison Answer Choices
We’ve already mentioned that QC questions are unique to the GRE. Thus, even the most seasoned math students will need to spend time learning the best strategies for correctly answering these questions.
But first, the basics: memorize the QC answer choices. Every QC question has the same 4 answer choices, so memorizing them will save time and make answering the questions easier and more automatic.
Here are the answer choices:
For more detailed information on solving QC questions, read these 10 tips for answering GRE Quantitative Reasoning questions.
Numeric Entry
Numeric Entry questions are similar to single-answer multiple-choice questions in terms of the types of questions asked. The difference is that you must type in your answer rather than select it from several options.
Now that we have done an overview of the GRE question types, let’s jump into some practice!
GRE Quant Practice Questions
In the sample questions provided, we will label the Quant topic tested, question type, and the main Quant topic tested.
Practice Question 1: Linear Equations – MC – Single-Answer
If 6n = 12x + 24 and 3m = 3x – 12, what is n in terms of m?
- m + 12
- 2m + 12
- m + 6
- 2m + 8
- 3m + 12
Solution:
We can simplify the first equation by dividing each term by 6, giving us:
n = 2x + 4 (equation 1)
Next, we can simplify the second equation by dividing each term by 3, giving us:
m = x – 4
m + 4 = x (equation 2)
We can substitute m + 4 from equation 2 for x in equation 1, giving us:
n = 2(m + 4) + 4
n = 2m + 8 + 4
n = 2m + 12
Answer: B
Practice Question 2: Number Properties – MC – Multiple-Answer
If n is a positive integer, what is the possible units digit of n^3? Select all that apply.
- 0
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
Solution:
To determine the possible units digits of n, let’s raise all digits from 0 to 9 to the 3rd power to determine the possible units digits. If the math gets too large, you can also use your calculator.
0^3 = 0
1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
7^3 = 343
8^3 = 512
9^3 = 729
Thus, 0, 1, 2, 3, 4, 5, 6, 7, and 9 are correct answers.
Answer: A, B, C, D, E, F, G, H, J
Practice Question 3: Exponents – MC – Single-Answer
If 3^10 + 3^13 = 28 * 27^4x, then x is equal to which of the following?
- 1/6
- 1/3
- 5/7
- 5/6
- 6/7
Solution:
First, we must factor out 3^10 on the left-hand side of the equation, giving us:
3^10(1 + 3^3) = 28 * 27^4x
3^10(1 + 27) = 28 * 27^4x
3^10(1 + 27) = 28 * 27^4x
3^10 * 28 = 28 * 27^4x
3^10 = 27^4x
Next, since 27 = 3^3, we have:
3^10 = (3^3)^4x
3^10 = 3^12x
10 = 12x
10/12 = 5/6 = x
Answer: D
Practice Question 4: Inequalities – QC
m + n = 27 and 3m – 2n < 8
Quantity A:
n
Quantity B:
14
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
Solution:
Since we need information about n, let’s get the inequality in terms of n by using substitution. First, we can isolate m, so we have:
m = 27 – n
Next, we can substitute 27 – n for m in the inequality, giving us:
3(27 – n) – 2n < 8
81 – 3n – 2n < 8
81 – 5n < 8
-5n < -73
n > 73/5
n > 14⅗
Since n is greater than 14⅗, we see that quantity A is always greater than quantity B.
Answer: A
Practice Question 5: Functions – Numeric Entry
If f(x) = 2x – 3 and f(f(n)) = 7, what is the value of n?
Solution:
Using the given function, we know that f(n) = 2n – 3. Working outward, we see that:
f(n) = 2n – 3
f(f(n)) = f(2n – 3)
f(2n – 3) = 2(2n – 3) – 3
Therefore, f(f(n)) = 2(2n – 3) – 3 = 4n – 6 – 3 = 4n – 9, and since f(f(n)) = 7, we have:
4n – 9 = 7
4n = 16
n = 4
Answer: 4
Practice Question 6: Lines – MC – Multiple Answers
If (u, v) is a point on the line with equation y = mx + b, which of the following must be true?
Indicate all such answers.
- b = mu – v
- 4v = 4mu + 4b
- b^2 = v^2 – 2vmu + m^2u^2
Solution:
A point is on a line if and only if the x- and y-coordinates at that point can be plugged into the equation of that line and the equation holds true. Thus, if (u, v) is a point on the line, then it must be true that v = mu + b, which we will call the basic equation. We’ll be looking for this equation as we rearrange the terms of each answer choice.
A. b = mu – v
v = mu + b (basic equation)
b = v – mu
Because this is not the same as answer choice A, this is not a correct answer choice.
B. 4v = 4mu + 4b
v = mu + b (basic equation)
4v = 4mu + 4b
This must be true.
C. b^2 = v^2 – 2vmu + m^2u^2
v = mu + b (basic equation)
b = v – mu
b^2 = (v – mu)^2
b^2 = (v – mu)(v – mu)
b^2 = v^2 – 2vmu + m^2u^2
This must be true.
Answer: B and C
Practice Question 7: Counting Principle – Numeric Entry
If Ardella’s Sandwich Shop serves 3 types of bread, 4 types of meat, and 5 types of cheese, how many different ways could a customer choose a sandwich, if a sandwich must contain 1 type of bread, 1 meat, and 1 cheese?
Solution:
There are 3 ways to choose the bread, 4 ways to choose the meat, and 5 ways to choose the cheese. We use the Fundamental Counting Principle to calculate that there are 3 x 4 x 5 = 60 different ways to choose a sandwich.
Answer: 60
Practice Question 8: Percents – QC
Quantity A:
14% of 9.778,443,000
Quantity B:
9.778,443,000% of 14
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
Solution:
Quantity A: 14% of 9.778,443,000 is 9.778,443,000 x 14/100 = (9.778,443,000 x 14) / 100
Quantity B: 9.778,443,000% of 14 is 9.778,443,000 / 100 x 14 = (9.778,443,000 x 14) / 100
We see that Quantity A is equal to Quantity B.
Alternate Solution:
Since we know that x% of y is always equal to y% of x, we know that 14% of 9.778,443,000 is equal to 9.778,443,000% of 14.
Answer: C
Practice Question 9: Geometry – QC
Quantity A:
a
Quantity B:
d + c
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
Solution:
The sum of the interior angles of a triangle equals 180 degrees. Thus, b + d + c = 180, and d + c = 180 – b. In addition, angle a and angle b form a straight line. Therefore, a + b = 180, and hence a = 180 – b.
Since both a and d + c are equal to 180 – b, they must be equal to each other, i.e., a = d + c. In fact, we have a theorem that states that the exterior angle of a triangle is equal to the sum of the two remote interior angles, so it must be true that a = d + c.
Thus, Quantity A is equal to Quantity B.
Answer: C
Practice Question 10: Word Problems – MC – Single-Answer
Abba is four times as old as Mabel. Ten years ago, Abba was nine times as old as Mabel. How old is Mabel today?
- 4
- 16
- 20
- 48
- 64
Solution:
First let’s define their present ages.
A = Abba’s age today and M = Mabel’s age today.
We are told that Abba is four times as old as Mabel, so we have:
A = 4M (equation 1)
This means that 10 years ago, Abba was (A – 10) and Mabel was (M – 10).
Since 10 years ago, Abba was nine times Mabel’s age at that time, we create a second equation:
A – 10 = 9(M – 10)
A – 10 = 9M – 90
A = 9M – 80 (equation 2)
Equation 1 tells us that A = 4M, so we can substitute that for A in equation 2:
4M = 9M -80
5M = 80
M = 16
Mabel’s present age is 16.
Answer: B
In Summary
GRE Quantitative Reasoning presents two sections containing a total of 27 questions. There are 24 major topics covered in these questions, and there is no way to predict exactly which topics will be tested. So, the best way to study the material tested on the GRE is topically, learning one topic at a time until you have mastered it.
There are 4 question types on the GRE:
- Multiple-Choice Single-Answer
- Multiple-Choice Multiple-Answer
- Quantitative Comparison
- Numeric Entry
The Quantitative Comparison (QC) question type is unique to the GRE, so it is important to practice QC questions, including memorizing the 4 standard answer choices.
In this article, we presented 10 GRE practice questions representing a variety of topics and question types. It is important to be familiar and comfortable with all the topics and the types of questions you may encounter when you take the GRE.
What’s Next?
If this article has been helpful in providing you with a variety of GRE Quant questions to practice, you might consider another one that provides a breakdown of the GRE math section and provides additional practice questions. Remember, the more you properly practice, the better prepared you’ll be on test day.
Good luck!
