Graduate Management Admission Test (GMAT) Quantitative Reasoning Syllabus

Quantitative Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Reasoning in Graduate Management Admission Test (GMAT), not a summary of it.

1. 1

   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
2. 2

   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
3. 3

   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
4. 4

   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
5. 5

   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

Quantitative Reasoning flashcards for Graduate Management Admission Test (GMAT)

25 of 50 cards from the Quantitative Reasoning deck — real questions with worked answers.

1. 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 $2$.

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 $9$.

3. 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 $3! = 6$.

4. 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.

5. 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.

6. How do you convert a fraction $\frac{a}{b}$ to a percentage?

   Multiply by $100$: $\frac{a}{b}\times 100\%$. For example, $\frac{3}{4}=0.75=75\%$.

7. 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.

8. 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.

9. 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 $a\,d > b\,c$.

10. 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.

11. 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.

12. State the product, quotient, and power rules for exponents.

    $$a^{m}\cdot a^{n}=a^{m+n},\quad \frac{a^{m}}{a^{n}}=a^{m-n},\quad (a^{m})^{n}=a^{mn}$$

13. What do a negative exponent and a zero exponent mean?

    $a^{-n}=\frac{1}{a^{n}}$ and $a^{0}=1$ for any $a\neq 0$.

14. How is a fractional exponent interpreted as a root?

    $$a^{m/n}=\sqrt[n]{a^{m}}=\left(\sqrt[n]{a}\right)^{m}$$ For example, $8^{2/3}=\left(\sqrt[3]{8}\right)^{2}=4$.

15. What is the order of operations (PEMDAS/BODMAS)?

    Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

16. In division with remainder, how are dividend, divisor, quotient, and remainder related?

    $$\text{dividend} = \text{divisor}\times\text{quotient} + \text{remainder}$$ where $0 \leq \text{remainder} < \text{divisor}$.

17. What is the relationship between the GCD and LCM of two positive integers $a$ and $b$?

    $$\gcd(a,b)\times \operatorname{lcm}(a,b) = a\times b$$

18. 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 $0$).

19. 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.

20. 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 $x > -3$.

21. 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.

22. State the quadratic formula for $ax^{2}+bx+c=0$.

    $$x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$$

23. 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).

24. 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).

25. List the three common special-product/factoring identities tested on the GMAT.

    $$(a+b)^{2}=a^{2}+2ab+b^{2},\quad (a-b)^{2}=a^{2}-2ab+b^{2},\quad a^{2}-b^{2}=(a+b)(a-b)$$

See more Quantitative Reasoning flashcards →

Planning Quantitative Reasoning for Graduate Management Admission Test (GMAT)

Quantitative Reasoning (Graduate Management Admission Test (GMAT)) FAQ