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Graduate Management Admission Test (GMAT) Quantitative Reasoning Syllabus
The Quantitative Reasoning syllabus for Graduate Management Admission Test (GMAT) in full: 5 chapters, 21 topics and 48 sub-topics, every one listed below, plus 50 Quantitative Reasoning flashcards with answers.
Quantitative Reasoning syllabus: all 5 chapters
Expand any chapter to see its topics and sub-topics.
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Arithmetic Foundations
5 topics- Properties of Integers
- Factors, multiples and divisibility rules
- Prime numbers and prime factorisation
- Even, odd and consecutive integers
- Greatest common divisor and least common multiple
- Fractions, Decimals and Percentages
- Converting between fractions, decimals and percentages
- Percentage increase, decrease and successive change
- Profit, loss, discount and mark-up
- Ratios and Proportions
- Simplifying and combining ratios
- Direct and inverse proportion
- Partnership and mixture splits
- Exponents, Roots and Order of Operations
- Laws of exponents and negative/fractional powers
- Square roots and simplifying radicals
- BIDMAS/PEMDAS sequencing
- Number Properties and Remainders
- Remainder patterns and cyclicity of units digits
- Absolute value on the number line
- Properties of Integers
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Algebra
5 topics- Linear Equations and Inequalities
- Solving single-variable equations
- Simultaneous equations (substitution and elimination)
- Inequalities and sign-flip rules
- Quadratic Equations
- Factorising and the quadratic formula
- Roots, discriminant and sum/product relationships
- Algebraic Expressions
- Expanding and factorising polynomials
- Common identities and difference of squares
- Functions and Sequences
- Function notation and substitution
- Arithmetic and geometric sequences
- Word Problem Translation
- Converting English statements to equations
- Age, work-rate and digit problems
- Linear Equations and Inequalities
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Word Problems and Applied Maths
5 topics- Rate, Speed, Distance and Time
- Average speed and relative motion
- Round-trip and meeting-point problems
- Work and Rate
- Combined work rates
- Inverse relationship of rate and time
- Mixtures and Solutions
- Weighted concentration calculations
- Alligation technique
- Interest and Growth
- Simple interest
- Compound interest and growth factors
- Overlapping Sets
- Two-set Venn diagrams
- Three-set and matrix-based set problems
- Rate, Speed, Distance and Time
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Statistics and Counting
3 topics- Descriptive Statistics
- Mean, median and mode
- Range and standard deviation concepts
- Weighted averages
- Counting Methods
- Fundamental counting principle
- Permutations and arrangements
- Combinations and selections
- Probability
- Single and combined events
- Independent vs mutually exclusive events
- Complementary probability
- Descriptive Statistics
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Problem Solving Strategy
3 topics- Estimation and Approximation
- Rounding to eliminate answer choices
- Back-solving from Answer Choices
- Plugging in numbers and testing options
- Time Management per Question
- Pacing benchmarks and guess-and-move decisions
- Estimation and Approximation
Graduate Management Admission Test (GMAT) Quantitative Reasoning flashcards — 50 questions with answers
What defines a prime number, and what is the only even prime?
A prime number is an integer greater than $1$ with exactly two positive divisors: $1$ and itself. The only even prime is $2$.
State the divisibility rules for $3$ and for $9$.
An integer is divisible by $3$ if the sum of its digits is divisible by $3$; it is divisible by $9$ if the sum of its digits is divisible by $9$.
For consecutive integers, what is true about the product of any $n$ consecutive integers regarding divisibility?
The product of any $n$ consecutive integers is always divisible by $n!$. For example, the product of $3$ consecutive integers is divisible by $3! = 6$.
How do you find the total number of factors of an integer from its prime factorization?
If $N = p_1^{a_1} p_2^{a_2}\cdots p_k^{a_k}$, the number of positive divisors is $(a_1+1)(a_2+1)\cdots(a_k+1)$. E.g. $12 = 2^{2}\cdot 3^{1}$ has $(2+1)(1+1)=6$ factors.
What are the rules for the parity (odd/even) of products and sums of integers?
Even $\times$ anything $=$ even; odd $\times$ odd $=$ odd. For sums: odd $+$ odd $=$ even, even $+$ even $=$ even, odd $+$ even $=$ odd.
How do you convert a fraction $\frac{a}{b}$ to a percentage?
Multiply by $100$: $\frac{a}{b}\times 100\%$. For example, $\frac{3}{4}=0.75=75\%$.
What is the formula for percent change between an original value and a new value?
$$\text{Percent change} = \frac{\text{new} - \text{old}}{\text{old}}\times 100\%$$ A positive result is an increase, a negative result a decrease.
If a quantity increases by $20\%$ then decreases by $20\%$, what is the net change?
A net decrease of $4\%$. Multiplying factors: $1.20\times 0.80 = 0.96$, so the result is $96\%$ of the original.
How do you compare two fractions $\frac{a}{b}$ and $\frac{c}{d}$ without finding a common denominator?
Cross-multiply (for positive $b,d$): $\frac{a}{b} > \frac{c}{d}$ if $a\,d > b\,c$.
What does a ratio $a:b:c$ tell you about actual quantities, and how do you find them given a total?
It gives relative parts. Total parts $= a+b+c$; each quantity $=\frac{\text{its part}}{a+b+c}\times \text{total}$. The ratio fixes proportions, not absolute values.
What is the difference between a direct proportion and an inverse proportion?
Direct: $y = kx$ (as $x$ increases, $y$ increases); their ratio is constant. Inverse: $y = \frac{k}{x}$ (as $x$ increases, $y$ decreases); their product $xy = k$ is constant.
State the product, quotient, and power rules for exponents.
$$a^{m}\cdot a^{n}=a^{m+n},\quad \frac{a^{m}}{a^{n}}=a^{m-n},\quad (a^{m})^{n}=a^{mn}$$
What do a negative exponent and a zero exponent mean?
$a^{-n}=\frac{1}{a^{n}}$ and $a^{0}=1$ for any $a\neq 0$.
How is a fractional exponent interpreted as a root?
$$a^{m/n}=\sqrt[n]{a^{m}}=\left(\sqrt[n]{a}\right)^{m}$$ For example, $8^{2/3}=\left(\sqrt[3]{8}\right)^{2}=4$.
What is the order of operations (PEMDAS/BODMAS)?
Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
In division with remainder, how are dividend, divisor, quotient, and remainder related?
$$\text{dividend} = \text{divisor}\times\text{quotient} + \text{remainder}$$ where $0 \leq \text{remainder} < \text{divisor}$.
What is the relationship between the GCD and LCM of two positive integers $a$ and $b$?
$$\gcd(a,b)\times \operatorname{lcm}(a,b) = a\times b$$
How do you find the units digit of a large power, e.g. $7^{n}$?
Find the cycle of units digits. For $7$: $7,9,3,1$ repeating with period $4$. Take $n \bmod 4$ to locate the position (using the 4th value when the remainder is $0$).
What are the steps to solve a linear equation in one variable?
Collect variable terms on one side and constants on the other, combine like terms, then divide by the coefficient of the variable. Whatever you do to one side, do to the other.
What special rule applies when you multiply or divide an inequality by a negative number?
You must reverse the inequality sign. E.g. from $-2x < 6$ you get $x > -3$.
Show the other 30 Quantitative Reasoning flashcards
How do you solve a system of two linear equations by elimination?
Scale one or both equations so a variable's coefficients match, add or subtract to eliminate that variable, solve for the remaining variable, then back-substitute.
State the quadratic formula for $ax^{2}+bx+c=0$.
$$x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$$
What does the discriminant $b^{2}-4ac$ tell you about a quadratic's roots?
If $b^{2}-4ac>0$: two distinct real roots; if $=0$: one repeated real root; if $<0$: no real roots (two complex roots).
For roots of $ax^{2}+bx+c=0$, what are the sum and product of the roots?
Sum of roots $= -\dfrac{b}{a}$; product of roots $= \dfrac{c}{a}$ (Vieta's formulas).
List the three common special-product/factoring identities tested on the GMAT.
$$(a+b)^{2}=a^{2}+2ab+b^{2},\quad (a-b)^{2}=a^{2}-2ab+b^{2},\quad a^{2}-b^{2}=(a+b)(a-b)$$
How do you combine algebraic fractions such as $\frac{a}{b}+\frac{c}{d}$?
Use a common denominator: $$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$$
What is a function, and what do domain and range mean?
A function assigns each input exactly one output. The domain is the set of allowed inputs; the range is the set of resulting outputs.
Give the formulas for the $n$th term and the sum of an arithmetic sequence.
$n$th term: $a_n = a_1 + (n-1)d$. Sum: $$S_n = \frac{n}{2}\left(a_1 + a_n\right) = \frac{n}{2}\left[2a_1+(n-1)d\right]$$
Give the formulas for the $n$th term and the sum of a geometric sequence.
$n$th term: $a_n = a_1 r^{\,n-1}$. Sum of $n$ terms: $$S_n = a_1\frac{r^{n}-1}{r-1}\quad (r\neq 1)$$
When translating word problems, how are 'is', 'of', 'percent', and 'more than' rendered in math?
'is' $\to =$; 'of' $\to \times$; 'percent' $\to \div 100$; '$x$ more than $y$' $\to y + x$; '$x$ less than $y$' $\to y - x$.
State the fundamental rate equation relating distance, speed, and time.
$$\text{distance} = \text{speed}\times \text{time},\qquad \text{speed}=\frac{\text{distance}}{\text{time}},\qquad \text{time}=\frac{\text{distance}}{\text{speed}}$$
How do you compute average speed for a round trip with two different speeds over equal distances?
Use total distance over total time, not the simple average of speeds. For equal distances at speeds $v_1,v_2$: $$\bar v = \frac{2v_1 v_2}{v_1+v_2}$$ (the harmonic mean).
How do relative speeds combine when two objects move toward each other versus in the same direction?
Toward each other (or closing): add speeds, $v_1+v_2$. Same direction (overtaking): subtract speeds, $|v_1-v_2|$.
If one worker finishes a job in $a$ hours and another in $b$ hours, how long do they take together?
Add their rates: combined rate $=\frac{1}{a}+\frac{1}{b}$, so time together is $$T = \frac{ab}{a+b}$$
What is the basic work equation, and how do rates add?
$\text{Work} = \text{Rate}\times\text{Time}$. Rates of workers acting together add: $R_{\text{total}} = R_1 + R_2 + \cdots$. Each individual rate is $\frac{1 \text{ job}}{\text{time}}$.
For a mixture, how do you find the amount of a component given concentration?
Amount of component $=$ concentration $\times$ total amount. When mixing, the component amounts add: $$c_1 V_1 + c_2 V_2 = c_{\text{final}}(V_1+V_2)$$
What is the weighted average formula, and when is it used in mixture problems?
$$\bar x = \frac{w_1 x_1 + w_2 x_2 + \cdots}{w_1 + w_2 + \cdots}$$ Used when combining groups of different sizes or concentrations; the result lies between the extremes, closer to the larger weight.
State the simple interest formula.
$$I = P\,r\,t$$ where $P$ is principal, $r$ the rate per period (as a decimal), and $t$ the number of periods. The total amount is $A = P(1+rt)$.
State the compound interest formula.
$$A = P\left(1+\frac{r}{n}\right)^{nt}$$ where $r$ is the annual rate, $n$ the compoundings per year, and $t$ the number of years.
What is the formula for the union of two overlapping sets?
$$|A\cup B| = |A| + |B| - |A\cap B|$$
For two groups with a 'neither' category, how do you account for all members of a total set?
$$\text{Total} = |A| + |B| - |A\cap B| + \text{Neither}$$ Subtract the overlap once because it was counted in both $|A|$ and $|B|$.
Define mean, median, and mode.
Mean: sum of values divided by count. Median: the middle value when ordered (average of the two middle values if the count is even). Mode: the most frequently occurring value.
What is the range of a data set, and how does it differ from standard deviation?
Range $=$ maximum $-$ minimum, measuring total spread from extremes. Standard deviation measures how far values typically lie from the mean; larger standard deviation means more dispersion.
What is the fundamental counting principle?
If one choice can be made in $m$ ways and an independent second choice in $n$ ways, the two together can be made in $m\times n$ ways. Extend by multiplying across all independent stages.
Give the formulas for permutations and combinations of $n$ items taken $r$ at a time.
$$P(n,r)=\frac{n!}{(n-r)!},\qquad C(n,r)=\frac{n!}{r!\,(n-r)!}$$ Permutations count ordered selections; combinations count unordered selections.
What is the basic probability formula for equally likely outcomes?
$$P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$$ with $0 \leq P \leq 1$.
How do you find the probability of A or B, and of the complement of an event?
$P(A\cup B)=P(A)+P(B)-P(A\cap B)$. For independent events, $P(A\cap B)=P(A)\,P(B)$. Complement: $P(\text{not }A)=1-P(A)$.
What is a good estimation strategy when answer choices are spread far apart?
Round numbers to convenient values, compute the approximate result, and select the closest choice. Track whether rounding pushed the estimate up or down to avoid picking a near-miss trap answer.
What is back-solving (plugging in the answer choices), and which choice should you test first?
Substitute the numeric answer choices into the problem's conditions until one works. Start with the middle value (often choice C); if it is too large or too small, you can eliminate that direction's choices.
On the GMAT Quant section, roughly how much time should you budget per question, and what should you do when stuck?
The section gives about $2$ minutes per question on average. If a question runs well past that with no clear path, make an educated guess, mark it mentally, and move on—pacing protects your score more than any single hard question.
Graduate Management Admission Test (GMAT) Quantitative Reasoning FAQ
What is in the Graduate Management Admission Test (GMAT) Quantitative Reasoning syllabus?
Graduate Management Admission Test (GMAT) Quantitative Reasoning is split into 5 chapters: Arithmetic Foundations, Algebra, Word Problems and Applied Maths, Statistics and Counting and Problem Solving Strategy. Together they contain 21 topics and 48 sub-topics.
How many chapters are in Graduate Management Admission Test (GMAT) Quantitative Reasoning?
5 chapters, containing 21 topics and 48 sub-topics. The largest chapter is Arithmetic Foundations, with 5 topics.
Are there flashcards for Graduate Management Admission Test (GMAT) Quantitative Reasoning?
Yes — a 50-card Quantitative Reasoning deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.