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Author:  MathRevolution [ 13 Jan 2016, 10:21 ]
Post subject:  Overview of GMAT Math Question Types and Patterns on the GMAT

A complete breakdown of GMAT Math question types and its history

Updated on Aug 20th, 2020

What should you study more? Arithmetic? Geometry? Probability? All?
When preparing for the GMAT, test-takers often ask about which math concepts are covered on the GMAT and about the most common question types that appear in the actual test. Therefore, in this article, I will not only delve into past trends but also the current trend of the GMAT Math test. Also, I will discuss the types of questions that appear on the test every month. You can also find our observations regarding the hardest question types that appear on the test here: The Ultimate Q51 Guide

The scope of Math Tested on the GMAT

1. Topics that appear frequently on the GMAT - This is what you need to study and know:

• Integer: Questions in this section involve dividing an integer $$n$$ by 5 or 10, solving the units digit for an integer $$n$$, finding the remainder of an integer $$n$$ after dividing it by 3 or 9, and solving for factors and prime factors.
• Geometry: Questions in this section involve Pythagorean Theorem, special angles (1:1:$$\sqrt{2}$$, 1:$$\sqrt{3}$$:2), and solving for the area of different figures.
• Statistics: Questions in this section involve finding the average, standard deviation, median, and range.
• Speed Rate: Questions in this section involve solving average speed rate problems.
• Inequality: Questions in this section involve inequality questions that ignore squares and DS questions related to the inclusion relation.
• Equation: Questions in this section involve calculations using $$(a − b)(a + b) = a^2 − b^2.$$
• DS questions: Common Mistake Type questions that are determined and categorized by Math Revoluition

NOTE: Please refer to the table below for additional types of questions that appear on the test. However, remember that the types mentioned above are the most common types of questions.

 Quant Topics and Types of Questions Tested on the GMAT Today Topics Questions that frequently appear Questions that appear occasionally Questions that infrequently appear Integer Remainders Factors multiples Evens and odds Prime factors GCD and LCM Remainder questions after dividing the number by 4 or 8 Consecutive integers Estimated integers Modula questions Gaussian integers Perfect numbers Numbers, Fractions, Decimals Decimal digits Rounding numbers Mixed and compound fractions Number lines Terminating decimals Reciprocals Undefined functions Non-real numbers Ratios, Rates, Proportions, and Percentages Properties of ratios Properties of work rates Percent changes Average speed Round trips Matching ratios Inverse proportions Equations Basics of factoring Polynomial equations Algebraic expressions Discount problems Profit problems Duplicated square roots Mixture problems Data interpretation problems Indeterminate and impossible equations Exponents Properties of exponents Comparison of exponents Operations of numbers with exponents Inequalities Five fundamental concepts 3 properties Relationship between a question and the conditions (DS) 1 is standard Maximum and minimum ranges The effect of negative numbers Positive numbers Non-zero numbers Non-negative numbers Absolute Value 4 properties 7 frequent cases Distance between x and y on a number line Relationship between the nth root and absolute value Two types of absolute value inequalities Counting Methods Factorials Combinations Permutations with the same letters Permutations Circular permutations At least (counting methods) Permutations with restrictions on the order Probability Events and probability Relationship between numbers and ratios At least (probability) The rule of addition in probability Binomial Theorem Independent and exclusive events Statistics Means Medians Ranges Standard deviations Harmonic means Modes Sets with the same elements Normal distributions Modes Relationships among mean, median, range, and standard deviation Geometry Pythagorean Theorem Circles Lines Properties of triangle sides Special angle problems Areas of geometric diagrams Cubes Rectangular solids Circular cylinders Spheres Regular n-polygons (DS) Quadrilaterals Number of diagonals in n-polygons Diagonal Theory Heron’s Theory Area of parallelograms and trapezoids Coordinate Geometry Quadrants Line equations x- and y-intercepts Parabolas Symmetric axis Discriminant Equation of a circle Distance between points and a line Functions Functions with repeated intervals Additional graphs Reflections Binary operations Domains Codomains Ranges Equation of an ellipse Sets Venn Diagrams Intersections Unions Complements Addition rule 3 sets Subsets Start with the intersection Disjoint or mutually exclusive sets Difference between two sets Sequences Arithmetic and geometric sequences Counting consecutive integers Simple and compound interest rates Sum of arithmetic and geometric sequences Other sequences Counting consecutive multiples Adding the reciprocals of consecutive integers

Note: Max Lee, founder of Math Revolution has been analyzing these types of questions for decades.

2. Mathematical concepts that are partially covered

In the case of sequences, only fundamental concepts such as arithmetic and geometric sequences are included within the scope of the test. This means more complex concepts like difference sequences will not be tested.

There are also questions regarding probability and statistics, but these questions tend to be fairly simple. In other words, concepts like combinations with repetition, conditional probability, discriminating distributions, and average deviations will not be on the test. In the end, test-takers are not trying to go to a graduate program in mathematics!

3. Questions/Topics that Never Appear

The level of GMAT Math is generally what people learn in high school.
This means that the scope of GMAT Math does not include difficult concepts like trigonometrical functions, logarithms, differentiation, integration, or limits. Also, even though basic concepts such as calculating volume and areas of geometric figures and finding diagonal length appear in the test, more difficult concepts such as vectors or inner products do not appear.

During decades of experience in teaching GMAT Math, I have encountered only 2 matrix questions. Due to its infrequency, we can say matrixes are not included within the scope of GMAT Math. Additionally, questions regarding imaginary numbers - a complex number ($$\sqrt{-1} = i$$) - also are not included in GMAT Math.

NOTE: During my extensive experience teaching GMAT Math, I found some patterns on the GMAT test. It was that some questions, which were on the test in 2001, have reappeared recently. Even though I cannot give any assurance as to whether GMAC - the question bank of GMAT Math – reutilizes its questions, I believe that it occasionally uses some questions that appeared on previous exams along with new questions it creates every year.

History and Evolution of GMAT Math

In this part, I will analyze GMAT Math trends beginning from 2001, the year when I started teaching.

 Evolution of Topics Tested Since 2001 Topics 2001 - 2005 2006 - 2011 2011 - Today NOTE Arithmetic 40% 40% 30% Consistent Algebra 35% 30% 30% Consistent Geometry 10% 10% 15% The number of questions is increasing, and the questions are becoming more difficult. Word Problems 5% 5% 5% The number of work rate questions is increasing. Data Interpretation 5% 5% 10% The number of questions is increasing, and the questions have characteristics related to daily life. Common Mistake Types 3 and 4(A or B) 5% 5% 10% The number of questions is increasing, and the questions are becoming more difficult.

Note: This table is based on my decades of experience.

Conclusion

I want to emphasize that it would be especially helpful for those preparing for the GMAT Math to focus on mastering the integer and statistics sections. In fact, I have seen students who get every integer and statistics question right in prep tests (mock tests distributed freely by GMAC) and achieve late 40’s. Additionally, I want to advise test-takers to focus on studying questions that appear every month.

As explained earlier, integer questions are the most common type of questions (not only the number of questions but the number of different types of integer questions are numerous). Hence, spending more time learning these areas than on other concepts would be an effective and time-efficient way to tackle GMAT Math.

Also, the recent trend of GMAT Math is that questions contain characteristics of daily life. Thus, it would be helpful for test-takers to have a general understanding of the culture of the United States. Additionally, questions involving geometric figures are increasing in number. I want to advise test-takers to spend some time learning this concept.

As mentioned earlier, questions are becoming wordier. So, while studying the Official Guide, please spend some time observing the trend and styles of the questions. It is vital for test-takers to regularly exercise generating equations after reading difficult and wordy questions.

As many test-takers are already aware, solving 31 questions in just 62 minutes is very challenging. Therefore, it is important to have strategies for time management. Many people can solve simple questions in approximately 1 minute with no problems. However, those who solve questions using the conventional method of approach take approximately 5 minutes to solve just one difficult question. Thus, it is very helpful to learn various techniques and tips that can guide test-takers to solve difficult questions in approximately 2 minutes.

The average GMAT score is 38 (it is 33 for the United States alone). However, I firmly believe that if test-takers clearly understand about GMAT Math trends and the history of the test, they will not only be able to exceed the average score but will be able to score at least 45 or even get a score of 49 to 51. Thank you so much for reading this article, and I wish you the best of luck.

*** We are math experts, and if you find any grammatical issues – that is because we spend all of our time focusing on math, sorry grammar. Note that the information herein is based on the knowledge and experience of Max Lee, Founder of Math Revolution who has taught 30,000+ students and solved 100,000+ problems over the last few decades. He discovered and analyzed types of GMAT Math questions after continuous and numerous interviews with students who wrote the GMAT exam. Thus, please note that the information herein is based solely on the experience of Max Lee. Due to the nature of the test and lack of transparency regarding the algorithm used in preparing the questions, this guide is a best-effort attempt based on the best information available. If you have any questions or other information to share, please feel free to post it here for the benefit of the community.

 Author: chetan2u [ 16 Jan 2016, 22:52 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT nycgirl212 wrote:is it possible to get an explanation of the solutions for #1, 2, 3, 6, 9, 11, 12, 13?Example 1: On a certain transatlantic crossing, 40 percent all passengers held round-trip tickets. Additionally, they also took their laptops aboard the ships. If 20 percent of the passengers with round-trip tickets did not take their laptops aboard the ship, what percent of the ship’s passengers held round-trip tickets?A. 33.3% B. 45% C. 50% D. 65% E. 66.6%The Q no 1 is not correct..on one hand we are already given "40% all passengers held round-trip tickets." and then we are asked 'what percent of the ship’s passengers held round-trip tickets"...so what is intended to ask is not clear as the answer is already given as 40%..MathRevolution, you will require to look into the Q..

 Author: MathRevolution [ 17 Jan 2016, 22:13 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT This question is frequently on GMAT Math lately, which is 2 by 2 question.Attachment: GCDS overview of GMAT에 대한 댓글답변 (20160118).jpg [ 33.78 KiB | Viewed 187855 times ] On the above, suppose all the passengers 100p(if there is %, use 100 since it is per cent. p is an initial for passengers). Passengers who brought a round ticket and a laptop is 40% of the total passengers, which is 40p. However, what 20% means is that x=10 is derived from 40p:xp=80%:20%=4:1. That is, 40p+10p=50p, which means 50% of the passengers have round tickets. Therefore, the answer is C.

 Author: OC2910 [ 14 Jan 2016, 11:09 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT Please tell Books for exhaustive practice for the sections

 Author: ruhibhatia [ 15 Jan 2016, 04:26 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT MathRevolution , can you please explain the solution of the below question.When both positive integers a and b are divided by 7, both have a remainder of 4. What is the remainder when ab3 is divided by 7?A. 6 B. 5 C. 4 D. 3 E. 2Can we assume that a and b and single digit integers, since abc3 is a three-digit integer?

 Author: nycgirl212 [ 16 Jan 2016, 13:28 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT is it possible to get an explanation of the solutions for #1, 2, 3, 6, 9, 11, 12, 13?

 Author: MathRevolution [ 16 Jan 2016, 21:36 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT oishik2910! We currently have our own book for internal teaching purpose for our own members but we are planning to publish the 3 books through Amazon by the end of Feb. Or, if you are interested in free videos and free core theory, you may join the membership in our site.

 Author: MathRevolution [ 16 Jan 2016, 21:42 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT nycgirl212! As this section is for general GMAT strategies and questions, if you want to know how to solve these questions, you may post the questions in Math Forum then we can post reply.

 Author: chetan2u [ 16 Jan 2016, 22:43 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT ruhibhatia wrote:MathRevolution , can you please explain the solution of the below question.When both positive integers a and b are divided by 7, both have a remainder of 4. What is the remainder when ab3 is divided by 7?A. 6 B. 5 C. 4 D. 3 E. 2Can we assume that a and b and single digit integers, since abc3 is a three-digit integer?Hi ruhi,there are two things which ab3 can mean..a three digit number or a*b*3..1)if ab3 is three digit number, as you have said a and b should be a single digit..so a and b have to be 4, as the next number to leave a remainder of 4 would be 11, which is not a single digit number..so our number is 443.. and remainder when 443 is divided by 7 is 2..2)if ab3 actually meant a*b*3...remainder will be 4*4*3=48..48 when divided by 7 leaves a remainder 6..Hope it helps u

 Author: ruhibhatia [ 17 Jan 2016, 02:01 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT hi chetan2u, thanks a lot for the explanation. I also followed similar approach and got 6 as my answer, but the post above has mentioned option C (i.e. 4) as the right answer.

 Author: MathRevolution [ 06 Feb 2016, 21:38 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT If you are serious about hitting 49-51, you may find this post useful (Ultimate Guide Q51)the-ultimate-q51-guide-209801.html#p1641408

 Author: Geathser [ 19 Feb 2016, 21:33 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT The understandable explanation. It is really helps to me

 Author: MathRevolution [ 02 Mar 2016, 23:20 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT Questions related to geometry are continuously increasing. Let’s have a look at the example of the recent trend. (ex 4)Attachment: GEOMETRY.jpg [ 2.98 KiB | Viewed 184506 times ] If n regular pentagons are tangent each other in points of a circle as above figure, n=? A. 8 B. 9 C. 10 D. 11 E. 12Answer: CQuestions like the above are increasing. Therefore, students preparing for GMAT should focus on geometry more intensively.

 Author: MathRevolution [ 06 Mar 2016, 04:41 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT Furthermore, not only simple but also analysing questions are also frequently given. Let's have a look at the question below.(ex 5)There is Fi.A) If i is an even number, the inner figure is a horizontal rectangle. If i is an odd number, the inner figure is a vertical rectangle.B) If remainders are 2,1,0, dividing i with 3, each outer figure is circle, triangle, and rectangle.C) If i is an even number and an inbetween area of 2 figures is an odd number, it is an area of an inner figure.Which one is possible for the figure of F32?Attachment: FIGURE.jpg [ 8.17 KiB | Viewed 183792 times ] Answer: A

 Author: MathRevolution [ 11 Mar 2016, 06:16 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT Moreover, the mistake type 3 and 4 are substantially increasing. Let's have a look at a recent question.(ex 6) If a and b are positive integers, what is the greatest common factor of a and b?1) a=b+12) a=26Show SpoilerAnswer In this case, C is an answer though you should apply the mistake type 4(A) as it is an integer question, which is one of the key questions. For 1), GCD(a,b)=1. That is, it is always 1, which is unique and sufficient.Therefore, the answer is A.For these reasons, with increase of geometry and the mistake 3 and 4 questions, you should study in an organised and logical way.

 Author: MathRevolution [ 13 Mar 2016, 22:44 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT In addition, for highly advanced integer questions are on the similar level of the question below. (ex 6) If m is a positive integer, is √13m an integer?1) 117m is the square of an integer.2) m/117 is the square of an integer.Answer: DIn this case, the answer is D since there is 1 variable. If you actually encounter a question like this, you might be confused. The advanced level of integer questions like this are frequently given.

 Author: MathRevolution [ 20 Mar 2016, 18:11 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT Also, geometry questions are rising continuously. Let's take the recent question as an example.(ex 4)Attachment: yin yang.jpg [ 4.6 KiB | Viewed 182753 times ] There is a yin-yang symbol shown as above figure such that its radius is 2. What is the area of the region shaded?1) Both arc MNO and arc OCD are the same semi-circles. 2) The area of region shaded is half of the area of the circleAnswer: BIn this case, 1) and 2) are the same, which makes D the answer. Just like the question above, slightly difficult and deriving 1)=2) questions which make D the answer are frequently given as well. This type of geometry questions are steadily on an upward tendency.

 Author: SD007 [ 21 Mar 2016, 09:41 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT Hello Math Revolution Team,Could you please use spoilers to reveal the answers to your questions ?Many Thanks !Posted from my mobile device

 Author: MathRevolution [ 24 Mar 2016, 17:06 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT Plus, inequality questions disregarding square frequently appear as well. Let’s have a look at the question below.(ex 5) If xy2z3<0, is xyz>0? 1) y<02) x<0Answer: AIn this case, if you disregard square in the original condition, ‘If xz<0’ is derived and ‘is xyz>0’ becomes ‘is y<0?’, which makes A the answer.This type of question is frequently given.

 Author: MathRevolution [ 27 Mar 2016, 01:58 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT Also, the highly advanced hidden integer questions frequently appear on exams.(ex 6) Tom, who has 50 math questions, will get 5 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 2 points per question. Then, which of the following can be the score if he solves all the 50 questions? A. 192 B. 193 C. 194 D. 195 E. 196Answer: C

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