GRE (Graduate Record Examinations) 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 GRE (Graduate Record Examinations), not a summary of it.

1. 1

   Arithmetic

   6 topics

   • Properties of Integers
     • Factors, multiples, and divisibility
     • Prime numbers and prime factorization
     • Even, odd, and remainders
   • Fractions, Decimals, and Percent
     • Conversions among forms
     • Percent increase, decrease, and change
   • Ratios, Proportions, and Rates
     • Direct and inverse proportion
     • Work and speed-distance-time rates
   • Exponents and Roots
     • Laws of exponents
     • Square roots and radical simplification
   • Absolute Value and Number Line
     • Distance interpretation
     • Sequences and ordering
   • Estimation and Approximation
     • Rounding strategies for speed
2. 2

   Algebra

   6 topics

   • Algebraic Expressions and Operations
     • Simplifying and factoring
     • Polynomial multiplication
   • Linear Equations and Inequalities
     • Single-variable solutions
     • Systems of linear equations
   • Quadratic Equations
     • Factoring and the quadratic formula
     • Roots and discriminant
   • Functions and Relations
     • Function notation and evaluation
     • Domain and range
   • Coordinate Geometry
     • Slope and line equations
     • Graphs of lines, parabolas, and intercepts
   • Word Problem Translation
     • Setting up equations from text
3. 3

   Geometry

   5 topics

   • Lines and Angles
     • Parallel lines and transversals
     • Complementary and supplementary angles
   • Triangles
     • Angle sum and exterior angles
     • Pythagorean theorem and special triangles
     • Similarity and congruence
   • Quadrilaterals and Polygons
     • Area and perimeter formulas
     • Interior angle sums
   • Circles
     • Circumference and area
     • Arcs, sectors, and inscribed angles
   • Three-Dimensional Figures
     • Volume and surface area of prisms and cylinders
4. 4

   Data Analysis

   5 topics

   • Descriptive Statistics
     • Mean, median, mode, and range
     • Standard deviation and quartiles
   • Data Interpretation from Graphs
     • Tables, bar graphs, and line graphs
     • Pie charts and scatterplots
   • Counting Methods
     • Permutations and combinations
     • Fundamental counting principle
   • Probability
     • Single and compound events
     • Independent and mutually exclusive events
   • Distributions
     • Normal distribution and percentiles
5. 5

   Question Formats and Strategy

   5 topics

   • Quantitative Comparison Questions
     • Comparing Quantity A and Quantity B
     • Recognizing the four answer choices
   • Multiple-Choice (Single Answer)
     • Back-solving and plugging in numbers
   • Multiple-Answer Selection
     • Selecting all values that apply
   • Numeric Entry Questions
     • Entering integers, decimals, and fractions
   • On-Screen Calculator Use
     • When to use and avoid the calculator

Quantitative Reasoning flashcards for GRE (Graduate Record Examinations)

25 of 53 cards from the Quantitative Reasoning deck — real questions with worked answers.

1. What are the only even prime number and the smallest prime number?

   2 is both the only even prime number and the smallest prime number. 1 is not prime.

2. For integer division, what does it mean to say x is divisible by y, and how do you express it?

   x is divisible by y if x = y times some integer (the remainder is 0). Then y is a factor/divisor of x and x is a multiple of y.

3. What is the result of adding/multiplying integers by parity: even+even, even+odd, odd+odd, and even×any, odd×odd?

   even+even=even, even+odd=odd, odd+odd=even. even×anything=even; odd×odd=odd.

4. How do you find the GCD and LCM of two numbers using their prime factorizations?

   GCD = product of shared prime factors raised to the lowest power present in both. LCM = product of all prime factors raised to the highest power present in either. Also GCD×LCM = product of the two numbers.

5. How do you convert a percent to a decimal and a decimal to a percent?

   Percent to decimal: divide by 100 (move decimal 2 left), e.g. 45% = 0.45. Decimal to percent: multiply by 100 (move decimal 2 right), e.g. 0.45 = 45%.

6. What is the percent change formula, and how does it differ from percent of?

   Percent change = (new − old)/old × 100%. 'X percent of Y' = (X/100)×Y. Percent change is always relative to the original value.

7. How do you add or subtract fractions with different denominators?

   Find a common denominator (often the LCM), convert each fraction, then add/subtract the numerators and keep the common denominator. Simplify the result.

8. A quantity increases 20% then decreases 20%. What is the net percent change?

   A 4% net decrease. Multiply by 1.20 then 0.80 = 0.96, i.e. 96% of the original, a 4% loss. Successive percent changes are not additive.

9. In a ratio a:b, how do you find actual quantities given a total?

   Add the ratio parts (a+b) to get total parts, divide the actual total by total parts to get one part's value, then multiply by a and by b. Each actual value = (part/total parts)×total.

10. What is the distance-rate-time relationship and how is average speed computed?

    Distance = rate × time. Average speed = total distance ÷ total time (NOT the average of the speeds), unless the times spent at each speed are equal.

11. How do you set up and solve a proportion a/b = c/d?

    Cross-multiply: a×d = b×c, then solve for the unknown. Proportions assume the two ratios are equal.

12. State the product and quotient rules for exponents with the same base.

    Product: a^m × a^n = a^(m+n). Quotient: a^m ÷ a^n = a^(m−n).

13. What do a^0, a^(−n), and a^(1/n) equal?

    a^0 = 1 (for a≠0). a^(−n) = 1/a^n. a^(1/n) = the nth root of a.

14. State the power-of-a-power and power-of-a-product rules for exponents.

    (a^m)^n = a^(m×n). (ab)^n = a^n × b^n. And (a/b)^n = a^n/b^n.

15. What is √(ab) and √(a/b) in terms of separate roots, and is √(a+b) = √a + √b?

    √(ab) = √a × √b and √(a/b) = √a/√b (for nonnegative values). But √(a+b) ≠ √a + √b in general.

16. How is absolute value |x| defined, and what does it represent on the number line?

    |x| = x if x ≥ 0, and −x if x < 0. It represents the distance of x from 0 on the number line, so it is always nonnegative.

17. How do you solve the equation |x − a| = b for b > 0?

    Set up two cases: x − a = b or x − a = −b, giving x = a + b or x = a − b. These are the two points at distance b from a.

18. What does the inequality |x| < c (c > 0) translate to, and what does |x| > c translate to?

    |x| < c means −c < x < c (a single interval). |x| > c means x < −c or x > c (two separate intervals).

19. What is rounding and how do you round a number to a given place value?

    Look at the digit immediately to the right of the target place: if it is 5 or greater, round up; if less than 5, round down (keep the digit). Replace digits to the right with zeros (or drop after a decimal).

20. How can you estimate a product or quotient quickly for a sanity check?

    Round each number to one or two significant figures, compute with the rounded values, and track the magnitude (powers of 10). Use it to confirm the answer's order of magnitude is reasonable.

21. What is the distributive property and how is it used to expand a(b + c)?

    a(b + c) = ab + ac. It distributes multiplication over addition/subtraction and is the basis for expanding and factoring expressions.

22. What does it mean to combine like terms in an algebraic expression?

    Like terms have identical variable parts (same variables to the same powers). Combine them by adding/subtracting their coefficients, e.g. 3x + 5x = 8x; 3x and 3x² are not like terms.

23. Give the FOIL expansion of (a + b)(c + d).

    ac + ad + bc + bd (First, Outer, Inner, Last).

24. State the three common special-product/difference factoring identities.

    (a+b)² = a²+2ab+b²; (a−b)² = a²−2ab+b²; a²−b² = (a+b)(a−b).

25. How do you solve a linear equation in one variable such as 3x + 5 = 20?

    Isolate the variable using inverse operations: subtract 5 (3x = 15), then divide by 3 (x = 5). Keep the equation balanced by doing the same to both sides.

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