GRE Arithmetic Word Problems Practice Questions with Answers

Approximately 25% to 35% of the quantitative reasoning section on the GRE consists of word problems that test arithmetic logic. GRE arithmetic word problems translate everyday scenarios into mathematical expressions involving integers, fractions, percentages, and ratios. Success on these questions requires more than just memorizing formulas; it demands the ability to dissect a paragraph and identify the underlying operations. By refining your approach to these problems through targeted GRE Prep, you can significantly improve your speed and accuracy on test day.

Concept Explanation

GRE arithmetic word problems are mathematical challenges presented in a narrative format that require translating text into numerical equations involving basic operations, percentages, or ratios. These problems often test your grasp of number theory and practical calculations. The core strategy involves three steps: identifying the unknown variables, setting up an equation based on the relationships described, and solving for the target value. Common themes include rate-time-distance, work-rate, mixtures, and interest calculations.

To excel, you must recognize specific "trigger words" that correlate to mathematical symbols. For example, the word "is" typically represents an equals sign $=$, while "of" often indicates multiplication $\times$. When dealing with percentages, remember that "percent" literally means "per one hundred," so $15\%$ becomes $\frac{15}{100}$. Using tools like an AI Question Generator can help you practice these translations across various difficulty levels.

Solved Examples

Review these examples to understand how to break down complex text into manageable steps.

1. Example 1 (Percentages): A jacket is originally priced at $120. It is first discounted by 20%, and then an additional 10% discount is applied to the sale price. What is the final price of the jacket?

   1. Calculate the first discount: $20\% \text{ of } \$120 = 0.20 \times 120 = \$24$.

   2. Subtract from the original: $\$120 - \$24 = \$96$.

   3. Calculate the second discount on the new price: $10\% \text{ of } \$96 = 0.10 \times 96 = \$9.60$.

   4. Subtract for the final price: $\$96 - \$9.60 = \$86.40$.

2. Example 2 (Ratios): The ratio of apples to oranges in a basket is 3:5. If there are 40 oranges, how many apples are there?

   1. Set up a proportion: $\frac{3}{5} = \frac{x}{40}$.

   2. Cross-multiply to solve for $x$: $5x = 3 \times 40$.

   3. Simplify: $5x = 120$.

   4. Divide: $x = 24$. There are 24 apples.

3. Example 3 (Average/Mean): The average of five numbers is 18. If one of the numbers is removed, the average of the remaining four numbers is 20. What was the value of the removed number?

   1. Find the total sum of the original five: $5 \times 18 = 90$.

   2. Find the total sum of the remaining four: $4 \times 20 = 80$.

   3. Subtract the new sum from the original sum: $90 - 80 = 10$. The removed number is 10.

Practice Questions

Test your skills with these GRE arithmetic word problems ranging from basic to advanced.

1. A car travels at a constant speed of 60 miles per hour. How many minutes will it take for the car to travel 45 miles?

2. In a group of 120 students, 60% are female. If 25% of the female students are majoring in biology, how many female biology majors are there?

3. If a printer can produce 15 pages per minute, how many hours will it take to print 2,700 pages?

4. The price of a gallon of gas increased from $3.20 to $4.00. What was the percentage increase in the price?

5. A mixture contains water and alcohol in a ratio of 7:3. If there are 21 liters of water, what is the total volume of the mixture in liters?

6. If $x$ is an integer and 3x + 7 > 22, what is the smallest possible value for $x$?

7. A bank account earns 5% simple annual interest. If the initial deposit was $2,000, what is the total amount in the account after 3 years?

8. A worker is paid $15 per hour for the first 40 hours worked in a week and $22.50 per hour for any overtime. If the worker earned $735 in one week, how many hours did they work in total?

9. Three people—Alice, Bob, and Charlie—share a prize. Alice receives $\frac{1}{3}$ of the prize, Bob receives $\frac{2}{5}$, and Charlie receives the remaining $400. What was the total prize amount?

10. If the sum of three consecutive odd integers is 57, what is the largest of these integers?

Answers & Explanations

1. 45 minutes: Time = Distance / Speed. $\frac{45}{60} = 0.75$ hours. Since there are 60 minutes in an hour, $0.75 \times 60 = 45$.

2. 18 students: Number of females = $0.60 \times 120 = 72$. Biology majors = $0.25 \times 72 = 18$.

3. 3 hours: Total minutes = $2,700 / 15 = 180$. Total hours = $180 / 60 = 3$.

4. 25%: Percentage increase = $\frac{ \text{New} - \text{Old}}{ \text{Old}} \times 100$. $\frac{4.00 - 3.20}{3.20} = \frac{0.80}{3.20} = 0.25 = 25\%$.

5. 30 liters: Ratio 7:3 means $7x = 21$, so $x = 3$. Alcohol = $3(3) = 9$. Total = $21 + 9 = 30$.

6. 6: 3x > 15, so x > 5. The smallest integer greater than 5 is 6.

7. $2,300: Interest = $\text{Principal} \times \text{Rate} \times \text{Time}$. $2000 \times 0.05 \times 3 = 300$. Total = $2000 + 300 = 2300$.

8. 46 hours: Base pay = $40 \times 15 = 600$. Overtime pay = $735 - 600 = 135$. Overtime hours = $135 / 22.50 = 6$. Total = $40 + 6 = 46$.

9. $1,500: Alice and Bob share $\frac{1}{3} + \frac{2}{5} = \frac{5+6}{15} = \frac{11}{15}$. Charlie's share is $1 - \frac{11}{15} = \frac{4}{15}$. If $\frac{4}{15}x = 400$, then $x = 1500$.

10. 21: Let the integers be $n, n+2, n+4$. $3n + 6 = 57 \Rightarrow 3n = 51 \Rightarrow n = 17$. The largest is $17 + 4 = 21$.

1. A shirt costs $40 after a 20% discount. What was the original price?

• A$48
• B$50
• C$52
• D$60

Frequently Asked Questions

What are the most common arithmetic topics on the GRE?

The GRE focuses heavily on percentages, ratios, fractions, and basic number properties like divisibility and prime numbers. You will also frequently encounter problems involving averages, rates, and simple probability in word problem formats.

How can I improve my speed in solving word problems?

Speed improves by practicing the translation of English phrases into mathematical operations and using the AI Exam Simulator to get used to the test's timing. Learning to estimate answers can also help you quickly eliminate incorrect multiple-choice options.

Do I need to memorize complex formulas for GRE arithmetic?

Most arithmetic word problems can be solved using basic logic and fundamental formulas like $\text{Distance} = \text{Rate} \times \text{Time}$. Focus on understanding the relationships between numbers rather than rote memorization of niche formulas.

Can I use a calculator on the GRE arithmetic section?

Yes, an on-screen calculator is provided during the quantitative reasoning section of the GRE. However, it is often faster to solve arithmetic word problems using mental math or scratch paper for simple calculations.

What is the "back-solving" strategy?

Back-solving involves plugging the provided multiple-choice answers back into the word problem to see which one works. This is particularly effective for complex algebraic word problems where setting up an equation might be time-consuming.