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 GMAT, not a summary of it.

1. 1

   Arithmetic

   4 topics

   • Operations with integers
   • Fractions and decimals
   • Percentages
   • Ratio and proportion
2. 2

   Algebra

   4 topics

   • Solving linear equations
   • Quadratic equations
   • Inequalities
   • Functions
3. 3

   Geometry

   4 topics

   • Properties of shapes
   • Area and perimeter
   • Volume and surface area
   • Coordinate geometry
4. 4

   Data Analysis

   3 topics

   • Descriptive statistics
   • Probability and combinatorics
   • Data interpretation

Quantitative Reasoning flashcards for GMAT

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

1. What is the order of operations (PEMDAS) for evaluating an arithmetic expression?

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

2. State the rules for the sign of a product or quotient of two integers.

   Same signs give a positive result ($+\times+=+$, $-\times-=+$); different signs give a negative result ($+\times-=-$, $-\times+=-$).

3. What is the difference between a prime number and a composite number?

   A prime has exactly two distinct positive divisors ($1$ and itself), e.g. $2,3,5,7$; a composite has more than two divisors, e.g. $4,6,8,9$. The number $1$ is neither.

4. State the divisibility rules for $3$ and for $9$.

   An integer is divisible by $3$ if the sum of its digits is divisible by $3$, and divisible by $9$ if the digit sum is divisible by $9$.

5. What are the greatest common divisor (GCD) and least common multiple (LCM), and how are they related to the product of two positive integers?

   GCD is the largest integer dividing both; LCM is the smallest positive integer both divide. They satisfy $\text{GCD}(a,b)\times\text{LCM}(a,b)=a\times b$.

6. How do you add two fractions with different denominators?

   Convert to a common denominator, then add numerators: $\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$.

7. How do you divide one fraction by another?

   Multiply by the reciprocal of the divisor: $\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}=\frac{ad}{bc}$.

8. How do you convert a fraction to a decimal, and what distinguishes a terminating decimal?

   Divide numerator by denominator. In lowest terms, the decimal terminates iff the denominator's only prime factors are $2$ and/or $5$; otherwise it repeats.

9. What is the formula for percentage change, and what distinguishes increase from decrease?

   $\text{percent change}=\frac{\text{new}-\text{old}}{\text{old}}\times100\%$. A positive result is an increase, a negative result is a decrease.

10. How do you find a percent of a number, and how do you increase a value by $p\%$?

    A percent of a number: multiply by the decimal form, e.g. $30\%$ of $x$ is $0.30x$. To increase by $p\%$, multiply by $\left(1+\frac{p}{100}\right)$; to decrease, multiply by $\left(1-\frac{p}{100}\right)$.

11. Why is a $20\%$ increase followed by a $20\%$ decrease not a return to the original value?

    The operations multiply: $1.20\times0.80=0.96$, so the net effect is a $4\%$ decrease, because each percent applies to a different base.

12. State the formulas for simple interest and compound interest.

    Simple: $A=P(1+rt)$. Compound: $A=P\left(1+\frac{r}{n}\right)^{nt}$, where $r$ is the annual rate, $n$ the compoundings per year, $t$ years.

13. What is the defining property of a proportion, and how do you solve one?

    A proportion states two ratios are equal, $\frac{a}{b}=\frac{c}{d}$. Solve by cross-multiplying: $ad=bc$.

14. How does direct proportion differ from inverse proportion?

    Direct: $y=kx$, so $\frac{y}{x}$ is constant and both rise together. Inverse: $y=\frac{k}{x}$, so $xy$ is constant and one rises as the other falls.

15. If a quantity is divided in the ratio $2:3:5$, what fraction does each part represent?

    The total has $2+3+5=10$ parts, so the parts are $\frac{2}{10}$, $\frac{3}{10}$, and $\frac{5}{10}$ of the whole.

16. What are the steps to solve a linear equation such as $3x+5=20$?

    Isolate the variable using inverse operations: subtract $5$ to get $3x=15$, then divide by $3$ to get $x=5$.

17. How many solutions can a system of two linear equations in two variables have, and what does each case mean geometrically?

    One solution (lines intersect), no solution (parallel lines), or infinitely many (identical lines).

18. State the two main algebraic methods for solving a system of linear equations.

    Substitution (solve one equation for a variable and substitute) and elimination (add or subtract scaled equations to cancel a variable).

19. What is the quadratic formula for $ax^{2}+bx+c=0$?

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

20. How does the discriminant $b^{2}-4ac$ determine the nature of a quadratic's roots?

    If $b^{2}-4ac>0$ there are two distinct real roots; if $=0$ one repeated real root; if $<0$ no real roots (two complex roots).

21. State Vieta's formulas relating the roots $r_1,r_2$ of $ax^{2}+bx+c=0$ to its coefficients.

    Sum of roots $r_1+r_2=-\frac{b}{a}$; product of roots $r_1 r_2=\frac{c}{a}$.

22. List the three common special-product/factoring identities.

    $(a+b)^{2}=a^{2}+2ab+b^{2}$; $(a-b)^{2}=a^{2}-2ab+b^{2}$; $a^{2}-b^{2}=(a+b)(a-b)$.

23. What happens to an inequality when you multiply or divide both sides by a negative number?

    The direction of the inequality sign must be reversed, e.g. $-2x<6$ becomes $x>-3$.

24. How do you solve the absolute-value inequality $|x|<a$ and $|x|>a$ for $a>0$?

    $|x|<a$ means $-a<x<a$ (a single interval); $|x|>a$ means $x<-a$ or $x>a$ (two rays).

25. What is a function, and what are its domain and range?

    A function assigns each input exactly one output. The domain is the set of allowed inputs; the range is the set of resulting outputs.

See more Quantitative Reasoning flashcards →

Planning Quantitative Reasoning for GMAT

Quantitative Reasoning (GMAT) FAQ