GRE Arithmetic is not advanced mathematics. Every topic in this section was covered in school. What makes GRE Arithmetic challenging is the way questions are framed: familiar concepts in unfamiliar arrangements, designed to reward test takers who understand the underlying principles rather than those who have memorised formulas.
That distinction matters for preparation. Drilling formulas alone does not produce GRE Arithmetic competence. Understanding why the formulas work, and practising their application under time pressure, does.
Arithmetic is one of the four major topic areas in GRE Quant. For a complete picture of the section, the GRE Quant overview covers all four areas and how they are distributed across the section.
Want to know exactly where your GRE Quant score is leaking?
Take a free GRE diagnostic test. It gives you a section-wise score breakdown and identifies your weak areas within Quant before you invest more time in preparation.
GRE Arithmetic: What You Will Be Tested On
The word “arithmetic” comes from the Greek arithmos, meaning number. On the GRE, it refers not just to number theory but to a cluster of topics that together form roughly half of all Quant questions. Here is the breakdown:
Number Theory
Integers, fractions, exponents, remainders
Ratios
Interpreting, bridging, word problems
Percentages
Change, successive change, applications
Applications
Profit/Loss, Time/Distance, Time/Work
Percentages and their applications together account for around 40% of Arithmetic questions. Number Theory is foundational. Weaknesses there cascade into other topic areas. Both deserve the most preparation time.
1. Number Theory
Number Theory is the study of different types of numbers and their properties. On the GRE, it tests how numbers behave under operations like addition, subtraction, multiplication, division, and exponentiation. It is the foundation on which the rest of Arithmetic is built.
Number Theory on GRE Quant breaks into three categories:
a. Properties of Integers
This is the broadest category within Number Theory. Questions can draw on any of the following concepts:
Key concepts: Properties of Integers
- Types of numbers: Natural, Whole, Prime, Composite
- Division Algorithm and Divisibility Rules
- Factors and Multiples, with emphasis on HCF and LCM
- Remainder concepts (including the Chinese Remainder approach)
- Factorial notation and its properties
Medium
Number Theory: Remainders
If a number has a remainder of 4 upon division by 5 and a remainder of 2 upon division by 3, what remainder must it have upon division by 15?
A number with remainder 4 when divided by 5 takes the form 5k + 4. Listing values: 4, 9, 14, 19, 24…
A number with remainder 2 when divided by 3 takes the form 3p + 2. Listing values: 2, 5, 8, 11, 14, 17…
The first value common to both sequences is 14. When 14 is divided by 15, the remainder is 14 (since the dividend is less than the divisor, the remainder equals the dividend itself).
Answer: (E) 14
b. Properties of Fractions
This section tests fractions and decimals (real numbers). Questions consume time if you are not comfortable with the underlying mechanics. Common question types include comparing fractions, converting decimals to fractions, and identifying whether a fraction produces a terminating or recurring decimal.
Comparing fractions: Cross-multiplication method
vs
Cross-multiply: 17 × 25 = 425 vs 21 × 21 = 441
Rule: The fraction on the side of the larger product is the larger fraction.
Easy
Number Theory: Fraction Comparison
Which is greater: 17/21 or 21/25?
Enter the larger fraction as your answer.
Cross-multiply: 17 × 25 = 425. 21 × 21 = 441.
Since 441 > 425, the fraction on the right side of the comparison (21/25) is larger.
Answer: 21/25 is greater
c. Exponents and Roots
Exponent questions test the laws of indices, cyclicity of units digits, and maximum power of an integer in a factorial. Units digit cyclicity is particularly common in GRE questions and has a pattern-based solution that makes it much faster than direct calculation.
Units digit cyclicity: key patterns
- Powers of 2: cycle of 4 (2, 4, 8, 6, 2, 4, 8, 6…)
- Powers of 3: cycle of 4 (3, 9, 7, 1, 3, 9, 7, 1…)
- Powers of 9: cycle of 2 (9, 1, 9, 1…) where odd power gives 9, even power gives 1
- Powers of 4: cycle of 2 (4, 6, 4, 6…) where odd power gives 4, even power gives 6
- Any factorial n! where n ≥ 2 is always even
Medium
Number Theory: Units Digit Cyclicity
Find the units digit of 9^(8235!)
Numeric Entry: ___
Powers of 9 follow a cycle of 2: odd power gives units digit 9, even power gives units digit 1.
Any factorial n! where n ≥ 2 is an even number. Since 8235 > 2, the value 8235! is even.
Therefore 9^(8235!) = 9^(even number), which gives a units digit of 1.
Answer: 1
2. Ratios
See how you actually perform on GRE question types.
A free sample test with real GRE-style questions. Get your score and a study plan.
Ratios appear both as direct questions and as the underlying framework for several application topics, particularly Time and Distance and Time and Work. The basic concepts are simple. The GRE tests your ability to apply them within word problems that require careful translation of language into equations.
Key ratio operations tested on GRE
- Interpreting a ratio (2:3 means for every 2 of A there are 3 of B)
- Bridging ratios (combining two separate ratios through a common term)
- Performing operations on ratios without converting to decimals
- Word problems: age problems, digit problems, quantity distributions
Easy
Ratios: Direct Application
In a class of 35 students, boys and girls are in the ratio of 2:3. How many girls are there?
Numeric Entry: ___
Let the number of boys = 2x and the number of girls = 3x.
2x + 3x = 35 → 5x = 35 → x = 7
Number of girls = 3x = 3 × 7 = 21.
Answer: 21
Medium
Ratios: Age Word Problem
Six years ago, the ratio of ages of Bob and Joe was 2:5. Four years from now, the ratio of their ages will be 4:5. Find the sum of their present ages.
Numeric Entry: ___
Let Bob’s age six years ago = 2x, Joe’s age six years ago = 5x.
Four years from now: Bob’s age = 2x + 10, Joe’s age = 5x + 10.
Given ratio four years from now = 4:5:
(2x + 10) / (5x + 10) = 4/5
Cross-multiplying: 5(2x + 10) = 4(5x + 10) → 10x + 50 = 20x + 40 → 10 = 10x → x = 1
Bob’s present age = 2(1) + 6 = 8. Joe’s present age = 5(1) + 6 = 11. Sum = 19.
Answer: 19
3. Percentages
Percentages account for roughly 40% of Arithmetic questions when you include their applications. Direct percentage questions test calculation and change concepts. Application questions (Profit and Loss, Simple and Compound Interest) are extensions of the same principles. If your percentage foundation is solid, those application topics follow naturally.
Key percentage concepts tested on GRE
- Basic percentage calculations (part as a percentage of whole)
- Percentage change: (New Value – Old Value) / Old Value × 100
- Successive percentage change: applying two or more % changes sequentially
- Profit and Loss as applications of percentage change
- Simple and Compound Interest
Percentage Change = [(Final Value – Initial Value) / Initial Value] × 100
Easy
Percentages: Direct Calculation
The price of a ticket increased from $80 to $84. What is the percentage increase?
Numeric Entry: ___
Percentage Change = [(84 – 80) / 80] × 100
= [4 / 80] × 100
= 5%
Answer: 5%
4. Application-Based Topics
Application topics draw on Number Theory, Ratios, and Percentages simultaneously. Questions in these areas are typically word-problem format and require you to translate a situation into equations. They contribute 3 to 4 questions to the Quant section.
a. Profit, Loss, and Interest
These are percentage applications. If your percentage calculation is solid, these reduce to applying the same percentage change formula to a business context. The key distinctions: profit percentage is always calculated on Cost Price; discount percentage is always calculated on Marked Price.
Key reference: Profit, Loss, and Discount relationships
- Selling Price = Cost Price + Profit (or − Loss)
- Profit % = (Profit / Cost Price) × 100
- Discount = Marked Price − Selling Price
- Discount % = (Discount / Marked Price) × 100
Hard
Applications: Profit, Loss, Discount
A shopkeeper bought a pound of almonds at $4. He made a profit of 33.33% after giving a discount of 33.33%. Find the marked price of the pound of almonds.
CP = $4. Profit = 33.33% of CP = (1/3) × 4 = 4/3.
SP = CP + Profit = 4 + 4/3 = 16/3.
Let MP = x. Discount = 33.33% of MP = x/3.
Since Discount = MP − SP: x/3 = x − 16/3
Multiply through by 3: x = 3x − 16 → 2x = 16 → x = 8.
Answer: (D) $8
b. Word Problems Based on Number Theory
These questions test your ability to translate statements about HCF, LCM, or divisibility into algebraic equations. The key property to remember: for any two numbers, Product = HCF × LCM.
Hard
Applications: HCF and LCM
The sum of the LCM and HCF of two numbers is 760, and the LCM is 18 times their HCF. If one number is 360, what is the other number?
Let HCF = H, LCM = L. Given: L + H = 760 and L = 18H.
Substituting: 18H + H = 760 → 19H = 760 → H = 40.
Therefore L = 18 × 40 = 720.
Using: Product of two numbers = HCF × LCM:
360 × y = 40 × 720 = 28,800 → y = 28,800 / 360 = 80.
Answer: (D) 80
c. Time, Distance, and Work
These two topics appear most frequently in the application section, contributing 3 to 4 questions combined. They integrate number theory, ratios, and percentages into multi-step problems. The underlying relationships are simple but the GRE embeds them in scenarios that require careful reading.
Key reference: Time, Distance, and Work formulas
- Speed = Distance / Time (and therefore Time = Distance / Speed)
- If two people travel the same distance, their times are inversely proportional to their speeds
- Work done = Rate × Time (where Rate = 1 / Time to complete alone)
- Combined rate for two workers = Sum of individual rates
Medium
Applications: Time and Distance (Quantitative Comparison)
Stan drives at 60 mph from Town A to Town B, a distance of 150 miles. Ollie drives at 50 mph from Town C to Town B, a distance of 120 miles.
Time = Distance / Speed.
Stan’s time = 150 / 60 = 2.5 hours.
Ollie’s time = 120 / 50 = 2.4 hours.
Quantity A (2.5) > Quantity B (2.4).
Answer: (A) Quantity A is greater
Scoring below 160 in GRE Quant?
The guide on how to improve your GRE scores covers the most effective strategies for closing specific gaps in each section. For structured coaching, our GRE program includes dedicated Quant sessions built around your diagnostic results.
Frequently Asked Questions: GRE Quant Arithmetic
Arithmetic constitutes approximately 50% of the GRE Quant section, making it the single largest topic area. Within Arithmetic, percentages and their applications (Profit/Loss, Interest) account for the largest share, followed by Number Theory. Ratios appear both as direct questions and as the foundation for Time/Distance and Time/Work problems.
Engineering graduates often underestimate GRE Arithmetic because the topics appear familiar. The challenge is not the mathematical complexity but the way questions are framed: they test reasoning and pattern recognition under time pressure, not formula application. Engineers who have not recently practised school-level arithmetic in word problem format frequently lose time on questions they know conceptually. Targeted practice with GRE-style questions is necessary regardless of your mathematical background.
Percentages should be your first priority because they directly impact 40% of Arithmetic questions and their applications (Profit/Loss, Interest). Number Theory is second because weaknesses there affect multiple other topic areas. Ratios and their applications (Time/Distance, Time/Work) come third. Within Number Theory, remainder concepts and HCF/LCM problems are the most commonly tested sub-topics.
Yes. An on-screen calculator is available throughout the GRE Quant section. However, over-reliance on it slows you down. Most Arithmetic questions are designed so that the calculation is simple once you have the right approach. If a calculation feels complex enough to require the calculator, check whether you have missed a simpler path to the answer.
What to Do Next
Arithmetic is the right place to begin GRE Quant preparation because it is foundational and high-volume. Fix a weakness here and it pays off across multiple question types. A weakness here that goes unaddressed compounds into errors in Algebra, Data Analysis, and Geometry problems that use the same underlying concepts.
Work through the practice questions above with the solution hidden. Note where you got stuck, not just where you got it wrong. The sticking points reveal whether the issue is conceptual, a calculation habit, or unfamiliarity with the question format. Each of those has a different fix.
For context on how Arithmetic difficulty scales across GRE Quant, the guide on GRE math: easy vs difficult questions breaks down what separates medium from hard questions in each topic area.
Want expert guidance on GRE Quant?
Our GRE coaching includes section-specific Quant sessions covering all four topic areas with worked examples, practice sets, and mentor feedback on your approach.
