GRE Math Questions: Your Complete Guide to Conquering Quantitative Reasoning

Understanding the question formats is half the battle. Each type requires a slightly different strategic approach, and familiarity can shave precious minutes off your test time.

1. Quantitative Comparison Questions

These are uniquely GRE and often trip up first-time test-takers. You’ll see two quantities—Quantity A and Quantity B—and must determine their relationship. The answer choices never change:

• (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 secret to mastering these? Don’t calculate when you can compare. Many quantitative comparison questions can be solved by simplifying, estimating, or substituting values rather than grinding through arithmetic. When you see variables without restrictions, remember to test different number types: positive integers, negative numbers, fractions, and zero.

2. Multiple-Choice Questions (Single Answer)

These resemble the standardized test questions you’ve seen throughout your academic career. You’ll solve a problem and select one correct answer from five choices. The twist? GRE answer choices are carefully designed to include “trap answers”—options that result from common calculation errors.

For these questions, working backward from the answer choices can sometimes be faster than solving directly. If you’re stuck, plug answer choices into the problem to see which one works.

3. Multiple-Choice Questions (Select One or More Answers)

These are the questions that make test-takers nervous. You must select all correct answers—partial credit doesn’t exist. The question will either specify how many answers to choose or ask you to select “all that apply.”

Approach these systematically: evaluate each answer choice independently rather than trying to find a pattern. Just because (A) and (B) are correct doesn’t mean (C) will be.

4. Numeric Entry Questions

Here’s where you can’t rely on multiple-choice strategies. You’ll type your answer directly into a box (or two boxes for fractions). There’s no guessing assistance, and precision matters—though equivalent forms are accepted.

Double-check your arithmetic on these. A silly calculation error means zero points, and you won’t have answer choices to help you recognize when something’s off.

Every GRE math question draws from one of four fundamental content areas. The reassuring reality? None of this extends beyond what you likely covered in the sophomore year of high school.

Arithmetic

Don’t let the elementary-sounding name fool you. GRE arithmetic goes beyond basic operations to include:

• Properties of integers (divisibility, prime numbers, factorization)
• Operations with fractions, decimals, and percentages
• Ratios and proportions
• Powers and roots
• Sequences and patterns
• Absolute value and number line concepts

The catch? These concepts appear in word problems that require careful translation from English into mathematics. A question about “increasing a price by 20%” seems simple until time pressure kicks in.

Algebra

The GRE tests algebra at roughly the level of a second-year high school course. You’ll work with:

• Simplifying algebraic expressions
• Solving linear and quadratic equations
• Systems of equations
• Linear inequalities
• Functions and their graphs
• Coordinate geometry basics

Students pursuing quantitative degrees like data science or statistics will find these skills particularly relevant to their future coursework.

Geometry

Expect questions covering:

• Properties of triangles (including special right triangles: 45-45-90 and 30-60-90)
• Circles (area, circumference, arcs, sectors)
• Quadrilaterals and other polygons
• Parallel and perpendicular lines
• Three-dimensional figures (surface area and volume)
• The Pythagorean theorem

You won’t need to memorize complex proofs, but you should know essential formulas cold. The test provides no formula sheet.

Data Analysis

This category has grown in importance over recent test versions. You’ll encounter:

• Interpreting tables, graphs, and charts
• Descriptive statistics (mean, median, mode, range, standard deviation)
• Probability concepts
• Basic counting principles
• Percent change and weighted averages

Data interpretation questions often appear in sets where multiple questions reference the same graph or table. Read the data presentation carefully before diving into questions—noting units, scales, and any footnotes that might contain crucial information.

Let’s walk through representative questions from each category, focusing on the thinking process rather than just the solutions.

Sample 1: Quantitative Comparison – Algebra

Given: x > 0

Quantity A: (x + 1)²
Quantity B: x² + 1

Strategic approach: Rather than expanding immediately, substitute a simple value. Try x = 1:

• Quantity A: (1+1)² = 4
• Quantity B: 1 + 1 = 2

Quantity A is greater. But wait—you need to verify this holds for all positive x values. Try x = 0.5:

• Quantity A: (1.5)² = 2.25
• Quantity B: 0.25 + 1 = 1.25

Still, A is greater. Algebraically, (x+1)² = x² + 2x + 1, which exceeds x² + 1 by 2x whenever x > 0.

Answer: (A)

Sample 2: Multiple Choice – Arithmetic/Percentages

A store increased prices by 25%. Later, it offered a 20% discount on the new prices. What is the final price as a percentage of the original?

(A) 95%
(B) 100%
(C) 102%
(D) 105%
(E) 120%

Strategic approach: Use 100 as your starting value. After a 25% increase: 100 × 1.25 = 125. After a 20% discount: 125 × 0.80 = 100.

Answer: (B)

The trap here? Assuming a 25% increase and a 20% decrease would net to a 5% increase. Percentages don’t work that way when applied sequentially.

Sample 3: Numeric Entry – Ratios

In a mixture, the ratio of water to concentrate is 5:3. If 16 liters of water are used, how many liters of concentrate are needed?

Strategic approach: Set up a proportion: 5/3 = 16/x. Cross-multiply: 5x = 48. Therefore, x = 9.6

Answer: 9.6 liters

Sample 4: Data Interpretation

A bar graph shows Company X’s quarterly revenue (in millions): Q1 = $45, Q2 = $52, Q3 = $48, Q4 = $55. What was the percent increase from Q1 to Q4?

Strategic approach: Percent change = (New – Old)/Old × 100 = (55-45)/45 × 100 = 10/45 × 100 ≈ 22.2%

Answer: Approximately 22%

Sample 5: Geometry – Triangles

In triangle ABC, angle A = 50° and angle B = 60°. What is angle C?

Strategic approach: Triangles’ angles sum to 180°. So: 50 + 60 + C = 180, meaning C = 70°.

Answer: 70°

Sample 6: Quantitative Comparison – Statistics

A list contains 100 numbers with an average (arithmetic mean) of 50.

Quantity A: The median of the list
Quantity B: 50

Strategic approach: Consider different distributions. If all numbers equal 50, the median is 50 (quantities equal). But if the list is {1, 1, 1…1 (99 ones), 4951}, the mean is still 50, but the median is 1.

Answer: (D) – The relationship cannot be determined

Sample 7: Multiple Choice (Multiple Answers) – Number Properties

Which of the following could be the units digit of 7^n for some positive integer n? Select all that apply.

(A) 1
(B) 3
(C) 7
(D) 9
(E) 5

Strategic approach: Calculate the pattern of units digits: 7¹=7, 7²=49 (units digit 9), 7³=343 (units digit 3), 7⁴=2401 (units digit 1), 7⁵=16807 (units digit 7). The pattern repeats: 7, 9, 3, 1.

Answer: (A), (B), (C), (D)

Sample 8: Word Problem – Rates

Machine A produces widgets at a rate of 100 per hour. Machine B produces widgets at 80 per hour. Working together, how many hours would it take them to produce 900 widgets?

Strategic approach: Combined rate = 100 + 80 = 180 widgets per hour. Time = 900/180 = 5 hours.

Answer: 5 hours

Sample 9: Algebra – Functions

If f(x) = 2x² – 3x + 1, what is f(3)?

Strategic approach: Substitute x = 3: f(3) = 2(9) – 3(3) + 1 = 18 – 9 + 1 = 10

Answer: 10

Sample 10: Probability

A bag contains 4 red marbles and 6 blue marbles. If two marbles are drawn without replacement, what is the probability that both are red?

Strategic approach: First draw: 4/10. Second draw: 3/9 (one red marble removed). Combined: (4/10) × (3/9) = 12/90 = 2/15.

Answer: 2/15

Effective GRE preparation requires more than just reviewing content—it demands strategic practice that mimics test conditions.

Use the On-Screen Calculator Wisely

Yes, the GRE provides a basic calculator, but relying on it too heavily will slow you down. The calculator handles only basic operations—no scientific functions. Most questions are designed to be solved faster without it. Reserve calculator use for:

• Multi-digit multiplication or division
• Square roots of non-perfect squares
• Long decimal calculations

Practice mental math for simple operations. The seconds saved add up across 27 questions.

Master Time Management

With roughly 1.5 to 2 minutes per question, every second counts. Develop a pacing strategy:

• First pass: Answer questions you know quickly (aim for under 90 seconds each)
• Mark and move: Flag challenging questions rather than getting stuck
• Second pass: Return to flagged questions with remaining time

The section-adaptive format means your first section matters most. Don’t tank it by spending five minutes on a single question.

Know Your Formulas

Unlike some standardized tests, the GRE provides no formula sheet. Memorize these essentials:

• Area and perimeter formulas for common shapes
• The Pythagorean theorem and special right triangle ratios
• Distance, rate, and time relationships
• Simple and compound interest formulas
• Probability formulas
• Statistical measures (mean, median, standard deviation)

Practice with Official Materials

ETS publishes free GRE practice tests through its POWERPREP program. These remain the gold standard because they use actual retired test questions. Supplement with:

• ETS Official GRE Quantitative Reasoning Practice Questions
• The Official Guide to the GRE General Test
• ETS’s free GRE Math Review PDF

Awareness of common pitfalls can prevent costly errors on test day.

Misreading Question Stems

The GRE loves subtle wording. “Not equal to” versus “equal to,” “at least” versus “more than,” and “could be true” versus “must be true” change answers entirely. Read every question twice before solving.

Ignoring Units and Scale

Data interpretation questions especially prey on this. A graph showing “Revenue in Millions” means an axis reading of 50 represents $50,000,000—not $50. Check units before calculating.

Assuming Variables Are Positive Integers

Unless stated otherwise, variables can be negative, zero, fractions, or decimals. This matters enormously in quantitative comparison questions. Test multiple number types before concluding.

Overcomplicating Solutions

The GRE rewards elegant problem-solving. If your approach requires extensive calculation, you’re probably missing a simpler path. Look for shortcuts, estimation opportunities, and strategic number picking.

Rushing Through Data Interpretation Sets

When multiple questions reference the same graph or table, invest extra time in understanding the data before answering any questions. The upfront investment pays dividends across the set.

Score requirements vary dramatically by program type and selectivity. Here’s a realistic breakdown:

By Percentile

Score	Approximate Percentile
170	96th
165	89th
160	76th
155	59th
150	40th

By Program Type

STEM programs (engineering, computer science, data science): Aim for 165+ (89th percentile or higher). Competition is fierce, and many international applicants score exceptionally well on quantitative sections.

Business programs accepting GRE: Target 158-165, depending on program selectivity. Top MBA programs see average scores in the mid-160s.

Social sciences and humanities: Scores above 155 typically suffice, though quantitative-heavy programs like economics typically expect higher scores.

Programs waiving GRE requirements: If your target schools offer no-GRE admissions, you might bypass this entirely—though strong scores still strengthen applications.

A systematic approach outperforms scattered practice every time.

Month 1: Foundation Building

• Take a diagnostic practice test to identify weaknesses
• Review fundamental concepts in your weak areas
• Begin building a formula reference sheet
• Practice 10-15 questions daily, untimed

Month 2: Strategic Practice

• Increase to 20-30 questions daily
• Introduce timing constraints
• Focus on question types causing the most difficulty
• Take one full practice test weekly

Month 3: Test Simulation

• Complete full practice tests under exact test conditions
• Analyze every error in detail
• Refine pacing strategies
• Reduce new content review; focus on maintaining skills

One Week Before: Final Preparation

• Light review only—no cramming
• Ensure logistics (test center location, ID requirements) are confirmed
• Get adequate sleep and manage stress
• Trust your preparation