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.

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Overview of GMAT Math Question Types and Patterns on the GMAT

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MathRevolution

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Which of the following points is reflect to y=-x at (-2,1)?

A. (-1, 2)
B. (1,-2)
C. (2,1)
D. (2,-1)
E. (1,2)

==> You can figure out a point reflecting to y=-x by substituting –y to x-coordinate and –x to y-coordinate. Then, (-2,1) --> (-1, -(-2))=(-1,2) is derived.

Hence, the answer is A.
Answer: A

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There are a bunch of buildings and their building numbers are all even numbers. If the numbers are 312 between 590 inclusive, what is the number of buildings?
A. 139 B. 140 C. 141 D. 142 E. 143

==> The number of consecutive even numbers of odd numbers=(the last term+the first term) )/2 +1. That is, (590-312)/2 +1=139+1=140. That is, (590-312)/2 +1=139+1=140 and the answer is B.

Answer: B

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What is the remainder when $2^k$ is divided by 10?
1) k is a positive multiple of 10
2) k is a positive multiple of 4

==> Modify the original condition and the question. The remainder dividing $2^k$ by 10 is $~2^1=~2, ~2^2=~4, ~2^3=~8, ~2^4=~6$. Thus, when it comes to ones, 2-->4-->8-->6-->2… are repeated, which means they have a cycle of four.

Hence, the answer is 2) and B.
Answer: B

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If f(n)=n(n+1), which of following is equal to f(8)/f(2)?
A. f(3) B. f(4) C. f(5) D. f(6) E. f(7)

==>You get f(8)/f(2)=8*9/2*3=4*3=f(3), so the answer is A.
Answer: A

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In the x-y plane, there is line K, (x/a)+(y/b)=1. What is the y-intercept of line K?
1) a=b
2) b=5

==> If you modify the original condition and the question, the y-intercept is the value of y when x=0, so if you substitute x=0, from y/b=1, you get y=b, so you only need to know b. According to con 2), it is unique and sufficient.

Therefore, the answer is B.
Answer: B

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A certain set X contains the number 20. Is the range of the numbers greater than 12?
1) The maximum of the set is 50
2) The set contains the number 25

==> In the original condition, from range=Max-min, there are 3 variables (r,M,m) and 1 equation (r=M-n), and in order to match the number of variables to the number of equations, there must be 2 more equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. However, for con 1), if Max=20, set X already includes 20, so the range is at least 50-20=30>12, hence it is always yes and sufficient.

Therefore, the answer is A.
Answer: A

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When $8^x=16$, x=?

A. $\frac{2}{3}$
B. $\frac{3}{2}$
C. $\frac{3}{4}$
D. $\frac{4}{3}$
E. $\frac{4}{5}$

==>From $8^x=16$ to$2^3^x=2^4$, you get $3x=4, x=\frac{4}{3}$. Therefore, the answer is D.
Answer: D

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If m and n are positive integers, what is the value of m+n?
1) m/n=3/5
2) The greatest common divisor of m and n is 5

==>In the original condition, there are 2 variables (m, n) for the right triangle, and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), you get M=3*5=13 and n=5*5=25, so m+n=25+15=40, hence it is unique and sufficient.

Therefore, the answer is C.
Answer: C

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Updated on: 17 Feb 2017, 23:14

Originally posted by BillyZ on 13 Feb 2017, 20:59.
Last edited by BillyZ on 17 Feb 2017, 23:14, edited 1 time in total.

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MathRevolution

Below is the 5051 question.

Is $x<xy<y$?
1) $x<y$
2) $0<x<1<y$

==> In the original condition, there are 2 variables (x,y), so C is highly likely to be the answer. Through 1) & 2), 2) is true, and from 2) $x<1$, both sides of the equation can be multiplied by y, and you get $xy<y$. From $1<y$, you multiply both sides of the equation by $x$, you get $x<xy$, then you get $x<xy<y$, hence yes, and sufficient. B is the answer
Answer: B

Dear MathRevolution & Bunuel, If $x=0.5$ and $y=1.5$, statement 1 still valid. Why D is not the answer?

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MathRevolution

Could you please provide me information about which type of question comes under
1. DATA interpretation
2. Common Mistake Type (CMT)

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What is the range of 30 consecutive even numbers?

A. 54 B. 56 C. 58 D. 60 E. 62

==> The number of consecutive numbers become (last-first/2)+1=(range/2)+1. In other words, from (range/2)+1=30, you get range/2=29, range=2(29)=58.

The answer is C.
Answer: C

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Is -3<x<4?

1) -2<x<3
2) -4<x<4

==> In the original condition, there is 1 variable (x) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), it is always yes, hence it is sufficient. For con 2), x=0 yes, but x=-3.5 no, hence it is not sufficient.

Therefore, the answer is A.
Answer: A

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2x+3y=?

1) 2x+4y=3
2) 4x+6y=6

==> In the original condition, you get 2x+3y=(1/2)(4x+6y)=? From con 2), you get 4x+6y=6, hence it is unique and sufficient.

Therefore, the answer is B.
Answer: B

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10+8÷3×6-2=?

A. 24
B. 34
C. 22
D. 12
E. 11

==> When calculating the numbers, even if there are no brackets, multiplication and division come first.
You get 10+8÷3×6-2=10+(8/3)6-2=10+16-2=24.

The answer is A.
Answer: A

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If $x^2=2x+1, x^3$=？

A. 4x
B. 5x+2
C. 5x-1
D. 3x+2
E. 3x-2

==> $x^3=x(x^2)=x(2x+1)=2x^2+x=2(2x+1)+x=5x+2$
Answer: B

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If a, b, and c are integers, is abc an even?

1) a+b is an even
2) b+c is an even

==> In the original condition, there are 3 variables (a,b,c) and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), if (a,b,c)=(1,1,1), you get a+b+c=1+1+1=3=odd, so no, but if (a,b,c)=(2,2,2), you get a+b+c=2+2+2=6=even, so yes, hence it is not sufficient.

The answer is E.
Answer: E

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Which of the following is equal to
$3^m7^{m-1}$?

$A. 3(21^m)$
$B. 7(21^m)$
$C. 3(21^{m-1})$
$D. 7(21^{m-1})$
$E. 21^{m-1}$

==> From $3^m7^m^-^1=3(3^m^-^1)(7^m^-^1)=3(3*7)^m^-^1=3(21^m^-^1)$, the answer is C.

Answer: C

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Questions related to geometry are continuously increasing. Let’s have a look at the example of the recent trend.

(ex 4)

Attachment:

GEOMETRY.jpg

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. 12

Show Spoiler

Answer: C

Questions like the above are increasing. Therefore, students preparing for GMAT should focus on geometry more intensively.

Can someone please explain the solution of this question?

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n=?
1) twice n equals to n+1
2) n times n equals to n
==> In the original condition, there is 1 variable (n) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer.
For con 1), from 2n=n+1, you get n=1, hence sufficient.
For con 2), from $n^2=n$ and $n^2-n=0$, n(n-1)=0, you get n=0,1, hence it is not unique and not sufficient.

The answer is A.
Answer: A

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If x and y are integers greater than 1 and x>y, what are the values of x and y?
1) x+y=13
2) xy=22

==> In the original condition, there are 2 variables (x,y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), you get x=11 and y=2, hence it is unique and sufficient. The answer is c. However, this is an integer question, one of the key questions, so you apply CMT 4(A).
For con 1), from (x,y)=(11,2),(10,3), it is not unique and not sufficient.
For con 2), you only get (x,y)=(2,11), hence it is unique.

Therefore, the answer is B, not C.
Answer: B