GRE Arithmetic: Guide, Formulas, Tips, & Practice Questions

Mastering GRE Arithmetic is essential to scoring well on the GRE Quant section. Whether you’re rusty with math or just need a refresher, this guide covers everything: key formulas, problem types, strategic tips, and expert-level GRE arithmetic practice questions with explanations.

Let’s dive into what the Educational Testing Service (ETS) expects you to know and how to solve problems efficiently on test day.

Read: How Long Is Each GRE Section? Timing Tips for Every Part of the Test

What Is GRE Arithmetic?

GRE Arithmetic forms the core of the Quantitative Reasoning section, testing not just your grasp of basic math, but your ability to apply it under pressure. It’s where fundamental concepts meet tricky formats, especially in Quantitative Comparison, Numeric Entry, and Multiple Choice questions.

At its core, arithmetic includes topics such as:

• Properties of integers - factors, multiples, prime numbers, even/odd, divisibility
• Fractions, decimals, and percents - conversions, operations, and percent change
• Ratios and proportions - solving for unknowns and scaling relationships
• Averages and weighted means - including how to reverse-engineer missing values
• Exponents and roots - especially square roots and exponent laws
• Absolute value - interpreting distance on the number line
• Ordering and estimation - using number sense to eliminate answer choices quickly

These aren’t just textbook topics, but they show up in real GRE word problems, comparison tasks, and trick questions that require you to reason logically, not just compute.

Expert Insight: Arithmetic is disproportionately tested in high-frequency problem types. Mastering it helps you move faster on test day and save precious time for harder algebra and geometry questions.

Read: How Long Is the GRE? Test Length, Section Breakdown, and Timing Tips

Must-Know GRE Arithmetic Formulas

Here are essential formulas to know cold:

Pro Tip: These are shortcuts for comparing values, estimating answers, and eliminating wrong answer choices quickly.

GRE Arithmetic Question Types (With Examples & Strategies)

You’ll encounter arithmetic in every GRE math format. The trick isn’t just solving—it’s solving efficiently under pressure. Here’s how GRE arithmetic shows up, plus what to watch for.

1. Quantitative Comparison Questions

These ask you to compare two values: Quantity A and Quantity B, and decide which is greater, or if they’re equal.

Example:

Quantity A: 1/2 + ¾

Quantity B: 5/4

Correct Answer: The two quantities are equal.

Strategy Tip: You don’t always have to calculate fully. Look for ways to simplify, estimate, or plug in test numbers if variables are involved.

2. Multiple Choice Questions

These are single-answer or multiple-answer questions that cover arithmetic concepts like:

• Fractions and decimals
• Averages and percents
• Ratios and proportions
• Word problems

Strategy Tip: Read carefully. If a question says “Select ALL that apply,” your approach needs to be more cautious and thorough.

3. Numeric Entry Questions

These require you to type in a number. No answer choices provided.

Common topics:

• Averages
• Percent change
• Proportions
• Basic equations

Strategy Tip: Always double-check your calculation. A single-digit mistake means zero points. Partial credit isn’t a thing.

4. Mixed Arithmetic Questions

These combine arithmetic with other areas like algebra or geometry. ETS uses these to test your ability to connect concepts and recognize patterns under pressure.

Example:

If x = 2 and y = 3, what is the value of: x² + 2xy + y²?

Step-by-step:

• x² = 4
• 2xy = 2 × 2 × 3 = 12
• y² = 9
• Total = 4 + 12 + 9 = 25

Correct Answer: 25

Key Insight: This is a disguised identity: (x + y)² = x² + 2xy + y². Knowing patterns like this saves time.

How to Approach GRE Arithmetic on Test Day

Arithmetic might seem straightforward—but on the GRE, it’s often wrapped in dense word problems, abstract comparisons, or layered logic. Whether it’s a GRE numeric entry question with no answer choices or a tricky GRE multiple choice question, the challenge is in the setup—not just the math.

Here’s how to stay sharp under pressure:

Expert Strategy: Step-by-Step Process That Works

Step #1: Clarify the question type. Are you solving for a value, a difference, or a relationship? Watch for key phrases like “how many different ways,” “which of the following,” or “must be true.”

Step #2: Estimate when possible. Especially for GRE numeric entry questions, estimation can help you quickly check whether your answer is in the right ballpark before committing.

Step #3: Don’t assume, but verify. In GRE multiple choice questions, small differences in wording (e.g., “could be true” vs. “must be true”) change the entire solving path. Read every word.

Step #4: Plug in numbers strategically. When variables like x and y are involved, choose simple numbers (2, 3, 5, 10) to make calculations easier and reveal patterns.

Step #5: Use scratch paper aggressively. Most test-day errors aren’t conceptual—they’re careless. Track your steps, label your variables, and double-check calculations.

Common Mistakes That Kill Scores

Pro Tip: ETS designs GRE multiple-choice questions with trap answers based on predictable mistakes. Use estimation and logic to eliminate those first, then calculate only if needed.

GRE Arithmetic Practice Questions (With Expert Answers & Explanations)

The questions below are designed to mirror official GRE math practice—not just in content, but in difficulty, logic, and structure. Whether you're focused on word problems, ratios, averages, quantitative comparison, or numeric entry, these GRE math practice questions will help you sharpen both accuracy and efficiency. These sample questions include a clear explanation to reinforce the core skill being tested and to show how top scorers approach these problems under time pressure.

If you're building out your GRE math practice routine, start with these representative problems, then identify which types slow you down, where you make setup mistakes, and how to adjust your solving strategy.

Question 1: Word Problem — Proportion & Rate

Question: A car travels 180 miles in 3 hours. At the same rate, how far will it travel in 5 hours?

Answer Choices:

A) 250 miles

B) 280 miles

C) 300 miles

D) 320 miles

Correct Answer: C) 300 miles

Explanation:

Use the rate formula:

Distance = Rate × Time

Rate = 180 ÷ 3 = 60 miles per hour

Then: 60 × 5 = 300 miles

What it tests: Proportions and unit rates are frequently tested in GRE multiple-choice questions and arithmetic word problems.

Question 2: Average + Consecutive Integers

Question: The average of five consecutive integers is 18. What is the sum of the first and last integers?

Correct Answer: 36

Explanation:

Let the five integers be:

x − 2, x − 1, x, x + 1, x + 2

The average = x → x = 18

First and last: (18 − 2) + (18 + 2) = 16 + 20 = 36

What it tests: Averages, symmetry of consecutive numbers, often used in GRE numeric entry questions to test reasoning and pattern recognition.

Question 3: Quantitative Comparison — Fractions

Question: Compare the two quantities:

• Quantity A: 2/3 + 1/6
• Quantity B: 1

Correct Answer: Quantity B is greater

Explanation:

2/3 + 1/6 = (4/6) + (1/6) = ⅚

Since 5/6 < 1, Quantity B is greater.

What it tests: Estimation, fraction operations, and quick reasoning, typical of quantitative comparison questions designed to test more than just calculation speed.

Question 4: Numeric Entry — Solving an Equation

Question: If 5x = 75, what is the value of x?

Correct Answer: 15

Explanation:

Divide both sides by 5:

x = 75 ÷ 5 = 15

What this tests: Simple equation-solving, core to GRE numeric entry questions, especially when embedded in longer word problems.

Tips to Practice GRE Arithmetic Effectively

Drill by Concept, Not Just Volume

More questions won’t help if they’re random. Target one arithmetic topic at a time, like percent change, ratios, or averages, and keep drilling it until your accuracy and speed improve. Build muscle memory before you mix concepts.

Train Under Test Pressure

Your goal isn’t just to get the question right, it’s to do it in under two minutes, with zero second-guessing. Use a timer. Simulate full quant sections. Know what it feels like to push through fatigue, not just solve problems at your own pace.

Analyze Your Mistakes Ruthlessly

Every wrong answer is a goldmine. Was your setup off? Did you misread a key phrase? Miss a negative sign? Keep a log of your most common errors—pattern spotting is how elite scorers make big jumps. Careless mistakes aren’t random; they’re predictable.

Study the Explanation, Not Just the Answer

If you get a question right but can’t explain why it works—or how else you could’ve solved it, you’re not done. Slow down. Break the problem apart. Could you have estimated instead of calculating? Could you eliminate answers without solving? Efficiency wins on test day.

Read: GRE Study Plan & Schedule: 1, 3, & 6-Month Templates (From a Pro Tutor)

Use Practice Questions That Actually Resemble the GRE

Don’t waste time on poorly written drills. Stick with question banks that mirror ETS logic and difficulty. The best free GRE practice questions come from the Educational Testing Service, Magoosh, and Leland. If a question feels harder or trickier than the real test, it probably is, and it’s not helping you.

GRE Arithmetic Word Problem Types to Know

Word problems are where arithmetic gets real—and where many test-takers lose time and points. These questions aren't just about calculation. They're about recognizing structure, setting up equations quickly, and solving under pressure.

Here are the core GRE arithmetic word problem types you need to know, plus what each one is really testing.

Distance / Rate / Time

Tests your ability to work with formulas like distance = rate × time and apply them in layered or back-to-back scenarios. Often includes unit conversions or average speed traps.

High-scorer tip: Always double-check whether rates are constant or changing across segments.

Mixtures and Ratios

These tests involve proportional reasoning in real-life formats: solutions, recipes, or investment blends. You'll often need to convert ratios into parts or set up proportional equations.

Common trap: Assuming ratios = totals. They rarely do. Break down into components before solving.

Averages and Weighted Averages

Goes beyond “add and divide.” The GRE frequently disguises these in group combinations or missing-value setups. Weighted averages appear when two groups with different sizes or values are merged.

What they test: Can you build or reverse-engineer the average formula based on what's missing?

Work Problems

These involve tasks completed at different rates—people, machines, or both. You'll often need to combine work rates or account for changing contributions over time.

GRE twist: They’ll give you one person’s rate, another’s time, and ask about both together. Get comfortable setting up equations like 1/x + 1/y = 1/z.

Set and Group Logic Problems

This is where arithmetic meets logic. Problems involve overlapping groups (e.g., students in multiple classes) and require you to calculate totals, differences, or intersections.

Essential skill: Use Venn diagrams or formulas like: Total = Group A + Group B − Both + Neither

Summary Cheat Sheet

Final Thoughts

Arithmetic is more than just basic math; it’s the foundation of your GRE quant strategy. From estimating on quantitative comparison questions to setting up proportions in complex word problems, the fundamentals show up everywhere. Mastering arithmetic means faster solving, fewer careless mistakes, and more confidence on test day.

If you’re hitting a plateau or struggling with consistency, don’t waste time guessing what to fix. Book a session with a GRE Quant coach who can break down your performance by question type, sharpen your strategy, and help you close the gap between your practice scores and your target score.

Want personalized drills, timed practice by concept, or a high-yield review plan? Your coach can help you build it and stick to it. Also, check out our GRE exam prep bootcamp and free events and group classes to unlock your full GRE potential!

See: The 10 Best GRE Tutors

Read these next:

• GRE Score Percentiles
• GRE Math Practice: Questions & Expert Tips
• GRE Score Range Explained (By Graduate Program Type)
• What Is a Good GRE Score? Percentiles, Targets, and What Schools Want
• How Late Can You Take the GMAT/GRE for MBA Applications?

FAQs

How much arithmetic is on the GRE?

• About 25–35% of GRE math questions rely on arithmetic topics like ratios, percentages, and number properties.

What’s the hardest part of GRE arithmetic?

• Often, it’s not the math, it’s translating tricky word problems or comparing two quantities under pressure.

Where can I find GRE arithmetic practice questions?

• Try the official ETS Math Review, or platforms like Magoosh and Leland for expert-reviewed questions.

Do I need to memorize formulas?

• Yes. Especially for average, percent change, and proportion problems.

What’s the best way to study?

• Mix practice questions, timed quizzes, and tutoring. Review every answer explanation carefully to improve.