GRE Arithmetic: Practice Problems, Question Types, Syllabus, and Books

The GRE Quantitative Reasoning section tests your basic math skills, and within that section lies GRE arithmetic. It’s one of four key areas within GRE Quant, alongside algebra, geometry, and data analysis. GRE arithmetic focuses on core mathematical concepts like integer properties, divisibility rules, factorization, roots, percentages, exponents, ratios, and rates. Your GRE quant score can range from 130 to 170, so brushing up on arithmetic can significantly impact your overall performance.

So, let’s break down the GRE arithmetic section in detail. We’ll cover everything from the specific topics tested to the number of questions you can expect and the time allotted for each section. We’ll also provide practice questions to help you get comfortable with the question format and difficulty level. Finally, we’ll share some effective tips and tricks to approach GRE arithmetic problems strategically and efficiently.

Importance of the GRE Arithmetic

The GRE arithmetic section plays a critical role in your overall Quantitative Reasoning score. While the name might imply a basic review of addition and subtraction, GRE arithmetic digs deeper into fundamental mathematical concepts. It includes a wide range of topics such as properties of numbers, operations like exponents and roots, fractions, decimals, percentages, ratios, and even sequences. Mastering these areas forms the foundation for solving the more advanced math problems you’ll encounter on the GRE exam.

Strong performance in GRE arithmetic translates to a higher Quantitative Reasoning score, which can significantly boost your application’s competitiveness for graduate programs. Furthermore, a solid grasp of these arithmetic concepts is valuable beyond the GRE itself. These skills prove your ability to think critically, analyse data efficiently, and solve problems logically.

GRE Arithmetic Syllabus

The GRE Quantitative Reasoning section assesses your foundational understanding of arithmetic concepts. This includes revisiting familiar topics from middle school math, like the properties of integers (positives, negatives, evens, odds, primes, and divisibility), operations with exponents and roots, and working with the number line, including decimals. You’ll also be expected to demonstrate fluency in concepts like percentages, ratios, rates, and estimation.

While the problems themselves won’t be computationally intensive, these arithmetic skills serve as the building blocks for solving more complex problems that blend arithmetic with algebra and data analysis. The GRE quant section also emphasises your ability to apply these arithmetic concepts to solve word problems. Here, you’ll need to translate written descriptions into mathematical models using the appropriate arithmetic operations and reasoning.

Read also: GRE Exam Syllabus 2024

GRE Arithmetic Question Types

The GRE quant section tests your understanding of arithmetic concepts through four distinct question formats. You might be asked to compare the values of two quantities, choose a single answer from multiple choices, select one or more possible answers, or directly enter a numeric answer. Here’s a detailed breakdown of each:

1. Quantitative comparisons (QCs)

• Presented with two quantities denoted by A and B.

• You need to assess the relationship between A and B and choose one of the following options:

1. A is greater than B.

2. B is greater than A.

3. A equals B.

• Cannot be determined based on the information provided.

• These questions often involve manipulating algebraic expressions, estimating values, or leveraging properties of numbers (e.g., even/odd, divisibility).

• Focus on identifying key information and applying relevant arithmetic concepts to compare the quantities.

2. Multiple-choice: select one (single answer)

• This is the most common GRE format.

• You’ll see a question with a single correct answer from a set of multiple-choice options.

• Questions might involve solving word problems related to percentages, ratios, rates, averages, or working with basic algebraic expressions.

• Hone your problem-solving skills and practise applying arithmetic formulas to reach the correct answer.

3. Multiple-choice: select one or more (multiple answers)

• Similar to the single-answer format, you may need to select one or more options that are correct.

• This format often tests your understanding of multiple concepts or requires applying a single concept to various scenarios presented in the answer choices.

• Carefully analyse each answer choice and ensure it aligns with the question requirements before selecting it.

4. Numeric entry

• You’ll be asked to enter a numeric answer directly into a designated box.

• This format emphasises accurate calculations and avoids the potential pitfalls of choosing an incorrect answer choice.

• Be mindful of rounding or truncation rules if the answer involves decimals.

Read also: 15 Hardest GRE Math Questions with Answers

GRE Arithmetic Practice Problems

Question 1: The average (arithmetic mean) of three consecutive integers is 12. What is the value of the largest integer?

1. 10

2. 11

3. 12 

4. 13

5. 14

Explanation: Let x be the middle integer. The three consecutive integers are then x-1, x, and x+1. We know the average is 12, so we can set up the equation:

(x-1 + x + x+1) / 3 = 12

Combining like terms:

3x / 3 = 12

Simplifying:

x = 12

Since x is the middle integer, the largest integer is x+1, which is 12+1 = 13.

Answer: (d)

Question 2: If y = 2x + 5, what is the value of 3y - 2x?

Explanation: We are given the equation y = 2x + 5. We want to find the value of 3y - 2x. We can substitute the equation for y directly into the second expression.

3(2x + 5) - 2x

Expanding the parentheses:

6x + 15 - 2x

Combining like terms:

4x + 15

Since we are not solving for x and are only interested in the final value, we can simplify further. Notice that 15 can be expressed as 4 + 11. So we have:

4x + (4 + 11)

This can be rearranged as:

(4x + 4) + 11

The first term, 4x + 4, doesn’t affect the final answer because it will be a multiple of 4 and will not contribute to the unit digit. Therefore, the final answer will depend only on the value of 11.

Answer: (e)

Question 3: If 12 is 60% of a number, what is the number?

1. 18

2. 20

3. 22

4. 24

5. 26

Explanation: We can set up a proportion to find the unknown number. Let x be the number we're looking for.

12 / x = 60%

Remember, percent means “out of one hundred,” so 60% is equivalent to 60/100, which can be further simplified to 3/5.

Substituting:

12 / x = 3/5

Cross-multiplying:

5 * 12 = 3x

 Simplifying:

60 = 3x

x = 20

Answer: (b)

Question 4: A train travels 240 miles at a constant speed. If the trip takes 4 hours, what is the average speed of the train in miles per hour?

1. 30

2. 40

3. 50

4. 60

5. 70

Explanation: Average speed is defined as the total distance travelled divided by the total time taken. We are given the distance (240 miles) and the time (4 hours).

Average speed = Distance / Time

Speed = 240 miles / 4 hours

Speed = 60 miles/hour

Answer: (d)

Question 5: If set A contains 20 odd numbers and set B contains 30 even numbers, what is the total number of integers in sets A and B combined?

1. 25

2. 35

3. 40

4. 50

5. 60

Explanation: We simply need to add the number of elements in each set.

Total = Number in Set A + Number in Set B

Total = 20 + 30

Total = 50

Answer: (d)

Question 6: If 2 = 6, what is the value of 2x - 5?

1. 31

2. 41

3. 51

4. 61

5. 71

Explanation: We know the square root of x is 6. Squaring both sides of the equation will get rid of the radical.

x = 6^2

x = 36

Now we can substitute this value of x into the expression 2x - 5.

2 * 36 - 5

72 - 5

Answer: (c)

Question 7: A rectangular garden has a length that is 3 metres longer than twice its width. If the perimeter of the garden is 30 metres, what is the width of the garden?

1. 2

2. 3

3. 4

4. 5

5. 6

Explanation: Let w be the width of the garden. The length is then 2w + 3 metres.

The perimeter is the total length of all sides of the shape added together. In a rectangle, there are 2 lengths and 2 widths. We can set up an equation to represent the perimeter:

2 * width + 2 * (length) = perimeter

2w + 2(2w + 3) = 30

Expanding the parentheses:

2w + 4w + 6 = 30

Combining like terms:

6w + 6 = 30

Subtracting 6 from both sides:

6w = 24

Dividing both sides by 6:

w = 4 metres

Answer: (c)

Question 8: If set P contains only prime numbers less than 20, what is the sum of the numbers in set P?

1. 37

2. 41

3. 43

4. 77

5. 53

Explanation: Prime numbers are whole numbers greater than 1 that have exactly two factors: 1 and itself. The prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19.

To find the sum, we simply add all these numbers together.

2 + 3 + 5 + 7 + 11 + 13 + 17 + 19

Answer: (d)

Question 9: A recipe calls for 3 cups of flour and 2 cups of sugar. If Gabriela wants to make a double batch, how many total cups of flour and sugar will she need?

1. 6

2. 8

3. 10

4. 12

5. 14

Explanation: This is a straightforward problem testing basic arithmetic. Since Gabriela wants to make a double batch, she simply needs to double the amount of each ingredient.

Total cups = (2 batches) * (3 cups flour/batch) + (2 batches) * (2 cups sugar/batch)

= 6 cups flour + 4 cups sugar

= 10 cups total

Answer: (c)

Question 10: If the ratio of the price of apples to the price of oranges is 3:2, and apples cost $6 each, what is the price of oranges?

1. $2

2. $3

3. $5

4. $4

5. $6

Explanation: Ratios can be expressed as fractions. Here, the ratio 3:2 is equivalent to 3/2. We know apples cost $6, which represents the first value in the ratio (3). We need to find the price of oranges, which represents the second value (2) in the ratio.

Since the ratio represents a constant proportion between the prices, we can set up a proportion:

$6 (price of apples) / price of oranges = 3/2

Cross-multiplying:

2 * $6 = Price of oranges * 3

Simplifying:

$12 = Price of oranges * 3

Price of oranges = $4

Answer: (d)

Read also: GRE Data Interpretation Practice Questions with Solutions

GRE Arithmetic Preparation Books

GRE arithmetic preparation books are a valuable resource for anyone aiming to improve their score on the quantitative reasoning section of the GRE. These books provide a comprehensive review of the arithmetic topics tested on the GRE, along with practice questions and answer explanations to help you solidify your understanding. Here’s a closer look at some popular GRE arithmetic prep books:

1. McGraw-Hill Education’s Conquering GRE Maths

This book offers a thorough preparation for the arithmetic section with three full-length practice tests. It includes hundreds of practice questions covering all the tested areas, including number properties, basic arithmetic operations, algebra, geometry, and word problems.

Additionally, the book delves into various question types on the GRE, such as quantitative comparison, numeric entry, multiple-choice, and data analysis, providing specific strategies for solving each one effectively.

2. Maths Workout for the GRE by Princeton Review

The Princeton Review’s GRE Maths Workout provides a solid foundation in essential arithmetic concepts. It includes over 275 practice questions with detailed explanations that walk you through the thought process behind each solution. This book is particularly helpful for those who need to brush up on their arithmetic fundamentals. It also includes a handy glossary of terms for easy reference.

3. GRE Math Strategies by Manhattan Prep

For those seeking a deeper knowledge of GRE arithmetic, Manhattan Prep’s GRE Math Strategies offers in-depth coverage of the relevant topics. It goes beyond just presenting GRE practice questions; it provides comprehensive courses that break down each concept clearly. The book also includes targeted drill sets to hone your skills and extensive answer explanations that help you identify areas for improvement.

Read also: 10 Best GRE Prep Books for 2024

Tips and Tricks to Ace the GRE Arithmetic

By mastering these tips and practising consistently, you’ll be well on your way to acing the GRE arithmetic section.

1. Master the fundamentals

Don’t underestimate the power of a strong foundation in basic math. Brush up on concepts like percentages, ratios, exponents, and algebra. A solid grasp of these areas will help you solve many GRE arithmetic problems efficiently. Additionally, focus on number properties like divisibility rules, primes, and odd/even characteristics. Understanding these can help you quickly eliminate answer choices and solve problems with clever manoeuvring.

2. Develop strategic approaches

There’s more to the GRE than just calculation. Learn to estimate answers to eliminate wildly off-base options. When working with variables, substitute them with friendly numbers (like 2 or 5) to simplify calculations and visualise relationships. And if you get stuck, don’t be afraid to use the answer choices themselves! Plug them back into the equation and see which one yields a true statement. This “backsolving” technique can be extremely helpful.

3. Time management

The GRE quant section is a race against the clock. Practice solving problems under timed conditions to build speed and accuracy. Remember that it’s okay to skip a question that’s giving you trouble. Move on and come back to it later if you have extra time. This approach prevents you from getting bogged down and wasting precious minutes.

4. Seek out helpful resources

Take advantage of the GRE practice tests offered by many Yocket and other prep companies. These tests will help you identify your strengths and weaknesses in arithmetic, allowing you to focus your studying. Additionally, explore techniques like the “Something” method, which can be found in online video tutorials. This method solves complicated equations by assigning variables and working backwards to find the solution.

5. Consistent practice is key

Remember that there’s no substitute for consistent practice. By diligently working on GRE arithmetic problems, you’ll solidify your understanding of the fundamentals and become comfortable employing the strategies mentioned above. The more you practice, the more confident and prepared you’ll be to ace the GRE arithmetic section.

Read also: How to Prepare for the GRE Quantitative Reasoning Section?

From the Desk of Yocket

While seemingly basic, GRE arithmetic can be a surprisingly tricky area of the GRE. It covers a broader range of topics than simple addition and subtraction. It digs into the foundations of math, including the properties of integers, fractions, decimals, and even basic algebra concepts like exponents and roots. This well-rounded approach ensures you have a strong grasp of numerical operations.

The emphasis on arithmetic is a good thing. It tests your foundational understanding of numbers, which is crucial for success in other areas of the GRE quant section, like algebra and data analysis. By solidifying your arithmetic concepts, you’ll gain a strong base for solving more complex problems. To further enhance your preparation, consider using Yocket prep premium.