What math is on the GRE Quantitative Reasoning section?
GRE Quantitative Reasoning covers four content areas: Arithmetic (number properties, fractions, percentages, ratios), Algebra (equations, inequalities, functions), Geometry (lines, angles, triangles, circles, coordinate geometry), and Data Analysis (statistics, probability, data interpretation). The content does not exceed first-year undergraduate mathematics — no calculus, no trigonometry. Scores range from 130 to 170 in one-point increments.
GRE Quantitative Reasoning is frequently described as "just high school math" — which is technically accurate and practically misleading. The content ceiling is moderate; the difficulty ceiling is high. ETS designs Quant questions to require conceptual insight rather than computational brute force, and the most difficult questions are specifically engineered to punish test-takers who rely on standard calculation approaches. Understanding the architecture of the exam — question types, content distribution, difficulty mechanics — is the prerequisite for significant score improvement.
Section Structure
The GRE General Test includes two Quantitative Reasoning sections. Each contains 12 questions with a 21-minute time limit (the 2023 shorter format). An on-screen calculator is provided. Unlike the Verbal section, where vocabulary knowledge sets a hard floor, Quant performance is almost entirely driven by strategy and pattern recognition rather than knowledge accumulation.
| Question Type | Questions Per Section | Time Budget Per Question |
|---|---|---|
| Quantitative Comparison | 4-5 | 90-120 seconds |
| Multiple Choice (single answer) | 4-5 | 90-120 seconds |
| Multiple Choice (multiple answers) | 0-2 | 90-120 seconds |
| Numeric Entry | 0-2 | 120-150 seconds |
| Data Interpretation (clustered) | 2-4 | Varies by cluster |
Data Interpretation questions appear in sets sharing a common graphic or data source. Plan for 4-6 minutes on a full DI cluster.
Content Area Distribution
ETS publishes approximate content weights for each of the four domains:
| Content Area | Approximate % of Questions | Key Sub-Topics |
|---|---|---|
| Arithmetic | 20-25% | Integers, fractions, decimals, percent, ratio, prime numbers, absolute value |
| Algebra | 25-30% | Linear equations, quadratics, inequalities, word problems, functions, exponents |
| Geometry | 20-25% | Lines/angles, triangles, quadrilaterals, circles, 3D solids, coordinate geometry |
| Data Analysis | 25-30% | Mean/median/mode, standard deviation, probability, counting, data interpretation |
Data Analysis and Algebra together account for more than half of all Quant questions in most test instances. Test-takers who neglect probability, counting methods, and standard deviation leave a disproportionate number of points on the table.
Quantitative Comparison: The Most Strategic Question Type
QC questions present two quantities — Quantity A and Quantity B — and ask you to determine their relationship using one of four answer choices:
- (A) Quantity A is greater
- (B) Quantity B is greater
- (C) The two quantities are equal
- (D) The relationship cannot be determined from the information given
The QC format is unique because the answer choices never change. This creates a specific strategic opportunity: you are never asked to compute an exact value. You are asked to determine a relationship. This is a fundamentally different task than solving a math problem, and test-takers who treat QC as computation problems will consistently take longer than necessary and make more errors.
QC Strategy: Comparison Before Computation
The core principle: determine whether you can establish the relationship without finding exact values. Techniques:
Simplification: If both quantities share a common element, simplify by removing it. If QA = x + 7 and QB = x + 3, the answer is always A regardless of x (assuming x is defined). You do not need to know x.
Estimation: For questions involving square roots, percentages, or large numbers, estimation to one significant figure is often sufficient to determine the relationship.
Picking numbers: When variables are present with no restrictions, test specific values. Test a positive integer, a fraction between 0 and 1, a negative number, and zero. If different values produce different relationships, the answer is D.
Rearranging: Treat the comparison as an inequality. You can add or subtract the same value from both sides (preserving direction), but multiplying or dividing by a negative flips the inequality.
The Five Common QC Traps
Trap 1: Assuming variables are positive integers. GRE variables can be zero, negative, or fractional. A question that yields A > B for positive integers may yield B > A or A = B for other valid values. Always test edge cases.
Trap 2: Geometric figure assumptions. Diagrams are not drawn to scale unless stated. A triangle that looks isosceles may not be. Angle sizes in diagrams are not reliable.
Trap 3: Missing constraints on D. Test-takers overuse answer D. If you can definitively prove a relationship holds for all valid values of the variables, D is wrong even if the problem looks underdetermined.
Trap 4: Squared quantities. If both quantities are squared, both are non-negative. QA = x^2 and QB = 9 — many test-takers answer C (thinking x = 3), missing that x could be -3 or any value, and x^2 = 9 only when x = ±3, making the answer D.
Trap 5: Absolute value. QA = |x - 3| and QB = |x| - 3 are not equivalent. Failing to simplify absolute value expressions correctly is a consistent error.
"Quantitative Comparison questions are designed to test mathematical reasoning, not calculation speed. The student who recognizes that a problem can be solved by simplification rather than by computing both quantities has a significant time and accuracy advantage." — ETS, GRE Quantitative Reasoning: Mathematical Conventions, 2024
Word Problem Translation Framework
GRE word problems — whether in MC or QC format — require accurate translation of natural language into mathematical relationships. The most common translation errors:
| English Phrase | Mathematical Meaning | Common Error |
|---|---|---|
| "x is y percent of z" | x = (y/100) × z | Reversing y and z |
| "x is y percent more than z" | x = z(1 + y/100) | Using y/100 instead of 1 + y/100 |
| "x is y percent less than z" | x = z(1 - y/100) | Same error |
| "the ratio of x to y is 3:5" | x/y = 3/5 | Reversing ratio direction |
| "x is divided by y, the remainder is r" | x = ky + r for some integer k | Forgetting k exists |
| "the average of x, y, z is 10" | x + y + z = 30 | Computing mean rather than sum |
The sum-of-terms approach to averages is underused. Most average word problems become straightforward when you work with sums rather than averages throughout.
Data Interpretation Clusters
Data Interpretation questions appear in sets of two to four questions sharing a common data source: a table, bar chart, line graph, pie chart, or scatter plot. The source never presents exactly the data you need — you must derive, compute, or infer.
Strategies:
- Read the title and axis labels of the graphic before reading questions. Know what variables are being measured and their units.
- Questions often involve percent change, ratio, or estimation. Be comfortable computing these from raw data under time pressure.
- Estimation is valid. An answer that requires computing 3,847 / 12,391 exactly is testing whether you can estimate 31% quickly.
DI clusters are the highest time-cost questions on Quant. A cluster of four questions may take 6-8 minutes. If you fall behind, DI clusters are where that time deficit grows. Prioritize understanding the data source before reading the questions.
Essential Formula Reference
These formulas appear repeatedly across GRE Quant:
| Category | Formula | Common Application |
|---|---|---|
| Percent change | ((New - Old) / Old) x 100 | Business/economics word problems |
| Distance-rate-time | d = rt | Travel problems |
| Simple interest | I = Prt | Finance problems |
| Compound interest | A = P(1 + r/n)^(nt) | Finance problems |
| Combinations | C(n,r) = n! / (r!(n-r)!) | Counting problems |
| Permutations | P(n,r) = n! / (n-r)! | Ordering problems |
| Triangle area | (1/2) x base x height | Geometry |
| Circle area | pi x r^2 | Geometry |
| Circle circumference | 2 x pi x r | Geometry |
| Pythagorean theorem | a^2 + b^2 = c^2 | Right triangles |
| Special triangles | 30-60-90: sides 1, sqrt(3), 2; 45-45-90: sides 1, 1, sqrt(2) | Geometry |
| Standard deviation | Conceptual understanding of spread | Data Analysis |
| Sum of interior angles | (n-2) x 180 for n-sided polygon | Geometry |
Memorize these. None of them are provided in the GRE test interface.
Geometry: Key Concepts and Common Mistakes
Geometry accounts for roughly 20-25% of questions. The most consistently tested concepts:
Triangles: The sum of any two sides must exceed the third side (triangle inequality). ETS uses this to create QC traps. Know that the largest angle is opposite the largest side. The exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
Circles: Inscribed angle theorem — an inscribed angle is half the central angle subtending the same arc. This appears regularly in medium and hard questions. A tangent line to a circle is perpendicular to the radius at the point of tangency.
Coordinate geometry: Slope formula, midpoint formula, distance formula, and the relationship between parallel lines (equal slopes) and perpendicular lines (slopes that are negative reciprocals) are all tested.
3D geometry: Surface area and volume of rectangular prisms and cylinders appear regularly. The diagonal of a rectangular solid uses an extended Pythagorean theorem: d^2 = l^2 + w^2 + h^2.
"The most common geometry errors on the GRE involve making unwarranted assumptions about diagrams. Test-takers assume angles are right angles when they appear to be, or assume lengths are equal when segments look equal. The exam exploits this tendency explicitly." — Eli Meyer, GRE Quant instructor, Manhattan Prep faculty (public writing, 2023)
Data Analysis: Statistics and Probability
Data Analysis is often the lowest-scored area for liberal arts graduates taking the GRE for STEM programs and the lowest-scored for STEM students who underestimate its complexity. Key concepts:
Standard deviation: ETS never asks you to compute standard deviation from scratch. It tests conceptual understanding — which set of numbers has higher standard deviation, how adding/removing data points changes spread, and whether two distributions with the same mean can have different spreads.
Probability: GRE probability questions use basic probability (P(A) = favorable outcomes / total outcomes), conditional probability, and complementary probability (P(A) = 1 - P(not A)). The complementary approach is often faster than direct computation.
Counting: Combinations (when order does not matter) and permutations (when order matters) appear in 3-5 questions per test. The fundamental counting principle — if event A has m outcomes and event B has n outcomes, both together have m×n outcomes — handles most basic counting questions without combinatorics formulas.
| Probability Concept | Formula/Rule | Example Application |
|---|---|---|
| Basic probability | P = favorable/total | Drawing cards, rolling dice |
| Complementary | P(A) = 1 - P(not A) | "At least one" problems |
| Independent events | P(A and B) = P(A) x P(B) | Sequential independent events |
| Mutually exclusive | P(A or B) = P(A) + P(B) | Non-overlapping outcomes |
| Overlapping events | P(A or B) = P(A) + P(B) - P(A and B) | Venn diagram problems |
Score Percentiles and Difficulty Targeting
The Quant section is scored on the same 130-170 scale as Verbal. Quant scores are generally higher across the population because the content is accessible:
| Score | Percentile Rank |
|---|---|
| 170 | 96th |
| 167 | 88th |
| 163 | 74th |
| 160 | 61st |
| 155 | 39th |
| 150 | 20th |
| 145 | 8th |
The mean Quant score for all GRE test-takers is approximately 153-154 — notably higher than the Verbal mean. For engineering and computer science PhD programs, scores below 165 are considered weak. For social science and humanities PhD programs, 155+ is typically acceptable.
"For quantitative master's programs and STEM PhDs, we use Quantitative Reasoning as a primary screen. A score below the 85th percentile — roughly 163 — raises questions that the applicant must address with extraordinary strength elsewhere in their application." — Director of Graduate Admissions, Engineering School, major research university (survey response, ETS, 2023)
Number Properties: The Hidden Foundation of GRE Quant
Number properties questions appear throughout GRE Quant embedded in other question types — QC questions about whether an expression is always positive, multiple choice questions about prime factorization, word problems about divisibility. Test-takers who study arithmetic as "fractions and percentages" without covering number properties leave a consistent gap in their preparation.
Integer Properties Most Frequently Tested
Even and odd numbers: An even number has 2 as a factor. An odd number does not. Key rules that appear in QC and MC questions:
- Even + Even = Even
- Odd + Odd = Even
- Even + Odd = Odd
- Even x Even = Even
- Even x Odd = Even
- Odd x Odd = Odd
The non-obvious rule: Even x Any integer = Even. This means if either factor in a product is even, the product is always even — regardless of the other factor.
Prime numbers: A prime number has exactly two factors: 1 and itself. Note that 2 is the only even prime number. 1 is not prime (it has only one factor). The first 10 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Memorize these.
Divisibility rules: Divisibility by 2 (last digit is even), 3 (sum of digits divisible by 3), 4 (last two digits divisible by 4), 5 (last digit 0 or 5), 6 (divisible by both 2 and 3), 9 (sum of digits divisible by 9). These allow rapid divisibility testing without long division.
LCM and GCF: The Least Common Multiple is the smallest integer divisible by both numbers. The Greatest Common Factor is the largest integer that divides both numbers. For word problems involving scheduling, packaging, or grouping, LCM and GCF provide direct answers that test-takers who try to enumerate possibilities take much longer to find.
Exponent Rules
| Rule | Expression | Example |
|---|---|---|
| Product rule | x^a x x^b = x^(a+b) | x^3 x x^4 = x^7 |
| Quotient rule | x^a / x^b = x^(a-b) | x^5 / x^2 = x^3 |
| Power rule | (x^a)^b = x^(ab) | (x^3)^4 = x^12 |
| Zero exponent | x^0 = 1 (for x not zero) | 7^0 = 1 |
| Negative exponent | x^(-a) = 1/x^a | x^(-2) = 1/x^2 |
| Fractional exponent | x^(1/n) = nth root of x | x^(1/2) = sqrt(x) |
Negative exponents appear in hard QC questions where test-takers compare x^(-2) and x^(-3). The comparison depends on whether x is greater than 1, between 0 and 1, equal to 1, or negative — another edge-case QC trap.
Word Problem Categories and Their Solution Frameworks
GRE word problems appear in five recurring categories. Recognizing the category immediately directs the solution method:
Rate problems (speed, work, mixture): Set up a rate equation. For work problems involving two agents working together: 1/R1 + 1/R2 = 1/Total. For distance problems: D = R x T. For mixture problems: build a weighted average equation.
Percent problems: Translate the English precisely (see translation table above). Compound percent change is multiplicative: increasing by 20% then decreasing by 20% yields 0.80 x 1.20 = 0.96 of the original — a 4% decrease, not 0%.
Set problems (Venn diagrams): Use the inclusion-exclusion formula: |A or B| = |A| + |B| - |A and B|. For three-set problems: |A or B or C| = |A| + |B| + |C| - |A and B| - |A and C| - |B and C| + |A and B and C|.
Sequence problems: Arithmetic sequences (constant difference) and geometric sequences (constant ratio) appear in 2-3 Quant questions per test. Arithmetic sum formula: Sum = n/2 x (first + last). Geometric sum formula: Sum = a x (1 - r^n)/(1 - r).
Function problems: GRE function problems typically involve substituting values into defined functions (sometimes non-standard functions using symbols like # or @). Read the definition carefully and substitute mechanically.
| Problem Category | Key Formula/Framework | Common Error |
|---|---|---|
| Rate/work | 1/R1 + 1/R2 = 1/T | Inverting rates incorrectly |
| Compound percent | Multiplicative, not additive | Adding percentages instead of multiplying |
| Venn/sets | Inclusion-exclusion formula | Double-counting overlap |
| Arithmetic sequence | Sum = n/2 x (first + last) | Using wrong value for n |
| Function problems | Substitute mechanically | Misreading the function definition |
Avoiding the Calculator Dependence Trap
The on-screen calculator provided is a simple four-function calculator with a square root button. It is slower to use than mental arithmetic for most GRE calculations. Test-takers who rely on it for every calculation lose significant time.
Practice mental arithmetic for:
- Percentages of round numbers (20% of 350 = 70)
- Squaring two-digit numbers (17^2 = 289)
- Estimating square roots (sqrt(50) is between 7 and 7.5, closer to 7.1)
- Fraction arithmetic (3/4 + 1/6 = 9/12 + 2/12 = 11/12)
Reserve the calculator for:
- Multi-step decimal computations
- Large number multiplication when exact answers are required
- Standard deviation conceptual verification when working a practice problem
References
ETS. GRE General Test Quantitative Reasoning: Preparing for the Quantitative Reasoning Measure. 2024. https://www.ets.org/gre/test-takers/general-test/prepare/content/quantitative-reasoning.html
ETS. GRE General Test Mathematical Conventions. 2024. https://www.ets.org/pdfs/gre/gre-math-conventions.pdf
ETS. Interpretive Data for the GRE General Test, July 2021 - June 2024. 2024. https://www.ets.org/pdfs/gre/gre-guide-table-1a-151a.pdf
ETS. Test and Score Data Summary for the GRE General Test, 2022-2023. ETS, 2023.
Manhattan Prep. GRE Quantitative Strategy Guide (6th ed.). 2023. Kaplan Publishing.
Magoosh. GRE Math Formulas and Concepts to Know. 2023. https://magoosh.com/gre/gre-math-formula-ebook/
Princeton Review. Cracking the GRE Premium Edition (2024 edition). The Princeton Review, 2023.
Nova Press. GRE Math Prep Course. Jeff Kolby, 2023. Nova Press.
Kaplan. GRE Prep Plus 2024. Kaplan Test Prep, 2023.
ETS. GRE General Test: Guide to the Quantitative Reasoning Content Areas. 2023. https://www.ets.org/gre/test-takers/general-test/prepare.html