No matter if you have been prepping for a while or are just beginning your GMAT Focus studying, you know that the Quantitative Reasoning section is a challenging component of the GMAT. While the math tested on the GMAT may seem overwhelming, the good news is that it is very learnable, especially with the GMAT model questions we’ll present you in this article. If you study smart and work hard, you can master GMAT Quant!
In this article, we will focus on GMAT Quant, concentrating on GMAT model questions that will anchor you to a variety of core topics that are commonly tested on the exam.
Here are the topics we’ll cover:
- What Are the GMAT Quant Topics?
- Optimal GMAT Quant Preparation
- Problem-Solving (PS) Quant Model Questions
- In Summary
- What’s Next?
To get started, let’s review the basics of GMAT Quant.
What Are the GMAT Quant Topics?
The GMAT has one Quantitative Reasoning section. In this section, you’ll have 45 minutes to answer 21 problem-solving (PS) questions. These PS questions are all multiple-choice with 5 answer choices.
There are 23 major topics that will be tested in the 21 Quant questions when you see on your GMAT. Notably missing from this list are Geometry and Data Analysis/Data Interpretation. Geometry is no longer tested on the GMAT, and Data Analysis/Data Interpretation is now tested in the Data Insights section of the GMAT.
- Arithmetic
- Algebra
- Linear Equations
- Quadratic Equations
- Number Properties and Theory
- Roots
- Exponents
- Inequalities
- Absolute Value
- General Word Problems
- Rates
- Work Problems
- Unit Conversions
- Ratios
- Percents
- Statistics
- Overlapping Sets
- Combinations
- Permutations
- Probability
- Coordinate Geometry
- Sequences
- Functions
Considerations
If you do some quick math, you see that with 23 topics and 21 questions, you can expect to see roughly one question for each Quant topic on the GMAT 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 GMAT so challenging is that you do not know which topics and how many GMAT math questions from each topic you’ll see on any given exam.
For example, on one test, you may see four function questions and two exponent questions, and on another, you may see one function question and four exponent questions. Similar variance in the number of questions you could see applies to the other topics as well.
TTP PRO TIP:
Do not expect to see the same number of questions from each topic on every GMAT test or practice test you take.
So, this begs the question, what is the best way to prepare for GMAT Quant? Let’s discuss that now.
Optimal GMAT Quant Preparation
While we have discussed several ways to prepare for the GMAT in other articles, we can review some of the key points here.
Here are two crucial facts that should guide us in how we prepare:
- The number of questions we see on any Quant topic is unpredictable.
- There are 23 major Quant topics but just 21 Quant questions on the GMAT.
With these two facts in mind, to nail GMAT Quant, you must be prepared for anything that might be presented. To accomplish that goal, your studying must be organized, and one great way to organize your studying is to employ topical learning. Simply put, topical learning means learning just one topic at a time and then practicing only that topic until you have achieved mastery. So, you can see how topical learning keeps your studying from being haphazard and random.
TTP PRO TIP:
Topical learning will keep you focused on learning the huge number of GMAT topics you must master to be successful on test day.
Let’s review a specific example of topical studying from the Target Test Prep GMAT Prep course. We can look at the chapter on Statistics.
An Example of Topical Studying
The TTP study plan is set up so that students focus on one major topic at a time and then answer practice questions on just that topic.
The TTP Statistics chapter contains the following topics:
- The Average
- Evenly-Spaced Sets
- Counting the Multiples of Integer A or B in a Set of Consecutive Integers
- Weighted Averages
- Median
- Mode
- Range
- Standard Deviation
- When the Standard Deviation of a Set is Zero
As you can see, there are many subtopics just about Statistics! And Statistics is just one of 19 chapters in the course. So, you can see how important it is to focus on just one topic at a time.
Our chapters present two or three questions after each concept taught to solidify that concept. At the end of each chapter, we then provide 100+ GMAT sample questions with solutions to build and reinforce mastery of the math topics in that chapter.
TTP PRO TIP:
To keep your GMAT Quant learning organized, focused, and on track, you must engage in topical learning.
Topical Practice Reinforces What You Have Learned
So, you have successfully learned a Quant topic (such as Statistics). You diligently immersed yourself in the content, reading the material, taking notes, and creating your own GMAT math flashcards. You’re at the end of the chapter. What to do next?
Now you need to practice what you have just learned. In an ideal situation, you will practice at least 50 questions on each topic. For example, in the TTP study plan for work questions, students complete 11 easy, medium, and hard tests totaling 165 questions. After completing so many questions, it’s easy to identify your strengths and your weaknesses.
TTP PRO TIP:
After engaging in topical learning, be sure to complete at least 50 questions on the topic you just learned.
Problem-Solving (PS) Quant Model Questions
All 21 Quant questions on the GMAT Quant section are problem-solving (PS) multiple-choice questions with 5 answer choices. However, there is an additional Quant question type that you will encounter in the Data Insights section of the GMAT: the Data Sufficiency (DS) question. Our article about GMAT Data Sufficiency (DS) questions will answer your questions and give you lots of practice with this question type that is unique to the GMAT Data Insights section.
Linear Equations
Linear equations are the heart and soul of algebra and calculus, so it’s no wonder that your ability to recognize, manipulate, and solve them is a critical skill. This model question asks you to manipulate, substitute, and solve for a variable.
KEY FACT:
Solving linear equations is one of the most important skills needed for GMAT Quant success.
Model Question 1: Linear Equations
If 6q = 12x + 24 and 3r = 3x – 12, what is q in terms of r?
- 2r + 12
- r + 12
- r + 6
- 2r + 8
- 3r + 12
Solution:
We simplify the first equation by dividing by 6, giving us:
q = 2x + 4 (eq.1)
Next, we divide the second equation by 3 and isolate x, giving us:
r = x – 4
x = r + 4 (eq. 2)
We can substitute r + 4 from eq. 2 for x in eq. 1, giving us:
q = 2(r + 4) + 4
q = 2r + 8 + 4
q = 2r + 12
Answer: A
Number Properties
The patterns of units digits of numbers raised to positive integer powers is a recurring type of problem asked on the GMAT. To master questions of this type, pay special attention to the Number Properties topic during your test preparation.
TTP PRO TIP:
Knowing the patterns of units digits raised to positive integer powers will hold you in good stead for solving GMAT questions about number properties.
Model Question 2: Number Properties
Which of the following is the units digit of 3^22?
- 1
- 3
- 5
- 7
- 9
Solution:
Let’s look at the pattern that is created by raising the base 3 to consecutive positive integer powers:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243 (We can ignore this result, as it indicates that the pattern starts repeating with 3^5.)
We see that the pattern of units digits is 3, 9, 7, 1.
Now, let’s note that the units digit of 3^4, 3^8, 3^12 and 3 raised to any power that is a multiple of 4 will yield a units digit of 1.
So, using that observation, we see that the units digit of 3^20 is 1. Now, if we follow the pattern of 3, 9, 7, 1, 3, 9, 7, 1, …, we see that 3^21 will have a units digit of 3, and 3^22 will have a units digit of 9.
Answer: E
Exponents
During your prep, It is critical that you memorize and practice the rules of exponents. The basic rules are the following:
(x^a)(x^b) = x^(a + b) Multiplication Rule
(x^a)^b = x^(ab) Power to a Power Rule
Our model question below uses the concept of equating exponents when we have the same base.
KEY FACT:
Two important rules of exponents are the multiplication rule and the power-to-a-power rule.
Model Question 3: Exponents
If 3^12 + 3^15 = 28 * 27^5x, then x is equal to which of the following?
- 1/4
- 3/4
- 4/5
- 5/6
- 2
Solution:
First, we factor out 3^12 from the two terms on the left-hand side of the equation, giving us:
3^12(1 + 3^3) = 28 * 27^5x
3^12(1 + 27) = 28 * 27^5x
3^12(28) = 28 * 27^5x
3^12 = 27^5x
Next, we must get the same base for the quantities on each side of the equation. Since 27 = 3^3, we have:
3^12 = (3^3)^5x
3^12 = 3^15x
We have the same base, so we can equate the exponents:
12 = 15x
12/15 = 4/5 = x
Answer: C
Inequalities
Inequalities and equations are solved in similar ways. However, there are a few differences to keep in mind when you’re solving inequalities:
- If you multiply or divide an inequality by a negative number, you must reverse the inequality sign.
- If you want to divide an inequality by a variable, you may not perform the division if you can’t determine the sign of the variable.
KEY FACT:
If you multiply or divide an inequality by a negative number, reverse the inequality sign.
Model Question 4: Inequalities
(-7x + 5) / 3 + 1 < 12
Which of the following could be the value of x?
- -10
- -4
- 6
- I only
- II only
- III only
- I and II only
- II and III only
Solution:
Let’s solve for x, remembering that if we multiply or divide by a negative number, we reverse the sign of the inequality.
We can start by subtracting 1 from both sides:
(-7x + 5) / 3 + 1 < 12
Next, let’s multiply both sides by 3:
(-7x + 5) / 3 < 11
We can now subtract 5 from both sides:
-7x + 5 < 33
Finally, let’s divide both sides by -7, remembering to flip the inequality sign:
-7x < 28
x > -4
Answer: C
Functions
A function is a rule that assigns each input exactly one output. We use function notation to show this relationship. For example, if we have a quadratic function f(x) = x^2 + 4x, then if we input 3 for x, we have f(3) = 3^2 + 4(3) = 21.
Another important function concept is the compound (or composite) function, in which the output of one function is the input of the same or another function. For example, if f(x) = 4x and g(x) = x^2 – 8, then the value of f(g(3)) is the notation of the compound function, where we first use 3 as the input of the g(x) function and then use the result to plug into the f(x) function, as follows:
g(3) = 3^2 – 8 = 9 – 8 = 1
Since g(3) = 1, we substitute 1 for x into the f(x) function:
f(g(3)) = f(1) = 4(1) = 4
Let’s now look at a similar example.
KEY FACT:
A function uses an input to create exactly one output.
Model Question 5: Functions
If f(x) = 4x + 3 and f(f(m)) = 13, what is the value of m?
- -2
- -1/2
- 1
- 1/2
- 8/9
Solution:
Using the given function, we know that f(m) = 4m + 3. Working from the inside out, we see that:
f(m) = 4m + 3
f(f(m)) = f(4m + 3)
f(4m + 3) = 4(4m + 3) + 3
f(4m + 3) = 16m + 12 + 3
f(4m + 3) = 16m + 15
Therefore, f(f(m)) = f(4m + 3) = 16m + 15, and since f(f(m)) = 13, we have:
16m + 5 = 13
16m = 8
m = 8/16 = 1/2
Answer: D
Coordinate Geometry
Even though Geometry is no longer tested on the GMAT, the topic of Coordinate Geometry is still on the list. Coordinate Geometry deals with graphing geometric figures in the coordinate plane. The most common coordinate geometry topic is the line, with slope-intercept form of y = mx + b, where m is the slope of the line and b is the y-intercept.
KEY FACT:
Even though Geometry is no longer tested on the GMAT, Coordinate Geometry is.
Model Question 6: Coordinate Geometry
If the equation of line Q in standard form is 12x + 3y = 11, what is the slope of line Q?
- -4
- -3
- 1
- 3
- 4
Solution:
Let’s rearrange the terms to change the equation from standard form to slope-intercept form, y = mx + b:
12x + 3y = 11
3y = -12x + 11
y = -4x + 11/3
We see that the slope of the line is -4.
Answer: A
The Fundamental Counting Principle
Combinatorics is a branch of mathematics that quantifies the number of ways to choose, list, or order items or tasks. Combinatorics includes the topics of combinations, permutations, and the fundamental counting principle.
The fundamental counting principle states that if there are n items of one type and m items of another type, then there are n x m ways to choose one of each item. This concept is extended to multiple types of items and is used in the following model question.
KEY FACT:
You’ll encounter questions on GMAT Quant that require the use of the fundamental counting principle.
Model Question 7: Counting Principle
If Marvella’s Sandwich Shop offers 4 types of bread, 3 types of cheese, and 5 types of meat, how many different sandwiches could be chosen, if a sandwich must contain 1 type of bread, 1 cheese, and 1 meat?
- 12
- 24
- 30
- 48
- 60
Solution:
There are 4 ways to choose the bread, 3 ways to choose the cheese, and 5 ways to choose the meat.
Using the fundamental counting principle, we see that there are 4 x 3 x 5 = 60 different ways to choose a sandwich.
Answer: E
Percents
A solid knowledge of percents and the types of word problems that involve percents is important for getting a high GMAT Quant score. Be sure to review the following types of percent calculations during your GMAT prep:
- Percent of
- Percent greater than
- Percent less than
- What percent
- Percent change
TTP PRO TIP:
Familiarize yourself with the various percent question types that are included in the GMAT Quant section.
Model Question 8: Percents
On Tuesday, Clarice answered 38 algebra homework problems, and on Wednesday she answered 28 algebra homework problems. What is the approximate percent change in the number of homework problems she answered from Tuesday to Wednesday?
- 10% decrease
- 26.3% decrease
- 26.3% increase
- 35.7% decrease
- 35.7% increase
Solution:
The “old” value is 38, and the “new” value is 28. We use the percent change formula:
(New – Old) / Old x 100%
(28 – 38) / 38 x 100%
-10/38 x 100%
-0.263 x 100%
-26.3%
A negative value for a percent change means that it is a percent decrease. Thus, the number of homework problems she answered from Tuesday to Wednesday decreased by about 26.3%
Answer: B
Probability
Two common probability questions involve (1) the probability of either of two events happening or (2) the probability that both events happen.
- “Either/or” probability formulas
- P(A or B) = P(A) + P(B) (If A and B are mutually exclusive events)
- P(A or B) = P(A) + P(B) – P(A and B)
- “And” probability formulas
- P(A and B) = P(A) x P(B) (If A and B are independent events)
- P(A and B) = P(A) x P(B|A)
It’s important to know the conditions under which each of these formulas is used.
TTP PRO TIP:
Know the probability rules and when to use each of them.
Model Question 9: Probability
In the algebra class, there are 6 boys and 11 girls. In the calculus class, there are 7 boys and 5 girls. If one student is selected at random, what is the probability that the student is either a girl or from the calculus class?
- 5/29
- 12/29
- 16/29
- 23/29
- 28/29
Solution:
Let’s summarize what we know. First, we know that the total number of students is 6 + 11 + 7 + 5 = 29. There are 11 + 5 = 16 girls, and there are 7 + 5 = 12 students in Calculus class.
The key word in the question is “or.” It indicates that one of the addition rules of probability will be used. Because the randomly chosen student can be both a girl and from Calculus class, we know that those two events are NOT mutually exclusive. Thus, we will use the second addition rule of probability.
P(Girl or Calculus) = P(Girl) + P(Calculus) – P(Girl and Calculus)
P(Girl or Calculus) = 16/29 + 12/29 – 5/29
P(Girl or Calculus) = 23/29
Note that we double-counted the 5 girls in Calculus class, so we subtract out those 5 girls once from our calculation. The addition rule we used does that for us.
Answer: D
Word Problems
The GMAT asks a variety of word problems, including traditional age, length, and money problems you may recall from algebra class. Additionally, you’ll encounter business questions such as price per item, profit/loss, and salary questions. They all require one common skill: the ability to translate words into equations. The model question presented here gives you practice at doing just that.
KEY FACT:
The GMAT Quant section can include word problems covering a variety of topics, such as age, length, money, price, profit/loss, and salary. Know how to solve questions of each type.
Model Question 10: Word Problems
June is three times as old as Agnes. Four years ago, June was five times as old as Agnes. What is the sum of their current ages?
- 32
- 36
- 40
- 48
- 64
Solution:
First, let’s define their present ages:
A = Agnes’s age today and J = June’s age today.
We are told that June is three times as old as Agnes, so we have:
J = 3A (equation 1)
This means that four years ago, Agnes was (A – 4) and June was (J – 4).
Since 4 years ago, June’s age was five times Agnes’ age, we create a second equation:
J – 4 = 5(A – 4)
J – 4 = 5A – 20
J = 5A – 16 (equation 2)
Equation 1 tells us that J = 3A, so we can substitute 3A for J in equation 2:
3A = 5A – 16
-2A = -16
A = 8
Thus, Agnes’ current age is 8, and June’s current age is (3)(8) = 24. The sum of their current ages is 8 + 24 = 32.
Answer: A
In Summary
The GMAT Focus Edition presents one Quantitative section with 21 questions, all of which are multiple-choice questions with 5 answer choices. There are 23 major topics covered in these questions, and you cannot predict exactly which topics will be tested. Therefore, the best way to study the material tested on the GMAT is topically. You learn and practice one topic at a time until you have mastered it.
In this article, we presented 10 GMAT question examples representing a variety of topics. It is important to be familiar and comfortable with all the topics you may encounter when you take the GMAT.
What’s Next?
If this article has been helpful in providing you with a variety of GMAT Quant questions to practice, you might consider another one that provides the top 10 tips for earning a great GMAT score.
Remember, the more you properly practice, the better prepared you’ll be on test day.
Good luck!
