Easy GRE Arithmetic Practice Questions Practice Questions

Concept Explanation

Arithmetic on the GRE Graduate Record Examination focuses on the fundamental properties of numbers, operations, and basic number theory. These Easy GRE Arithmetic Practice Questions are designed to reinforce your grasp of integers, fractions, decimals, percentages, and the order of operations. Success in this section requires not just knowing how to calculate, but understanding concepts like divisibility, prime factorization, and the properties of even and odd numbers. By mastering these basics, you build the foundation necessary for more complex GRE Prep topics such as algebra and data analysis. You can also use an AI Question Generator to create personalized drills that target your specific weak points in these core areas.

Solved Examples

1. Order of Operations: Evaluate the expression $15 - 3 \times (4 + 2) \div 2$.
   1. First, perform the operation inside the parentheses: $4 + 2 = 6$.
   2. Substitute back: $15 - 3 \times 6 \div 2$.
   3. Perform multiplication and division from left to right: $3 \times 6 = 18$, then $18 \div 2 = 9$.
   4. Finally, subtract: $15 - 9 = 6$.
   5. The final answer is 6.
2. Percentage Calculation: If a shirt originally costs $40 and is on sale for 25% off, what is the sale price?
   1. Calculate the discount amount: $0.25 \times 40 = 10$.
   2. Subtract the discount from the original price: $40 - 10 = 30$.
   3. The sale price is $30.
3. Prime Factorization: What is the greatest prime factor of 84?
   1. Factor the number: $84 = 2 \times 42$.
   2. Continue factoring: $42 = 2 \times 21$.
   3. Factor 21: $21 = 3 \times 7$.
   4. The prime factors are 2, 3, and 7.
   5. The greatest prime factor is 7.

Practice Questions

1. What is the value of $\frac{3}{4} + \frac{1}{2} - \frac{1}{8}$?

2. If $x$ is an even integer and $y$ is an odd integer, is $(x + y)^2$ even or odd?

3. A car travels 180 miles on 6 gallons of gasoline. How many miles can it travel on 11 gallons at the same rate?

4. Which of the following is the largest: $0.5$, $\frac{2}{3}$, $0.6$, or $\frac{5}{8}$?

5. Find the sum of all prime numbers between 10 and 20.

6. If 15% of a number is 45, what is the number?

7. Evaluate $|-5| - |7 - 12|$.

8. A group of 5 friends spends $125 on dinner. If they want to leave a 20% tip on the total bill, what is the total amount they will pay?

9. What is the remainder when 127 is divided by 6?

10. Convert $\frac{7}{20}$ to a percentage.

Answers & Explanations

1. Answer: $\frac{9}{8}$ (or 1.125). To add fractions, find a common denominator (8). $\frac{6}{8} + \frac{4}{8} - \frac{1}{8} = \frac{9}{8}$.
2. Answer: Odd. The sum of an even and an odd integer is always odd. An odd number squared (odd \u00d7 odd) is always odd.
3. Answer: 330 miles. Find the unit rate: $180 \div 6 = 30$ miles per gallon. Multiply by 11 gallons: $30 \times 11 = 330$.
4. Answer: $\frac{2}{3}$. Convert to decimals: $0.5$, $0.666...$, $0.6$, and $0.625$. The largest is $\frac{2}{3}$.
5. Answer: 60. The prime numbers between 10 and 20 are 11, 13, 17, and 19. $11 + 13 + 17 + 19 = 60$.
6. Answer: 300. Set up the equation $0.15x = 45$. Divide both sides by 0.15: $x = 45 \div 0.15 = 300$.
7. Answer: 0. $|-5| = 5$. $|7 - 12| = |-5| = 5$. So, $5 - 5 = 0$.
8. Answer: $150. Calculate the tip: $0.20 \times 125 = 25$. Total: $125 + 25 = 150$.
9. Answer: 1. $127 \div 6 = 21$ with a remainder of 1 since $6 \times 21 = 126$.
10. Answer: 35%. To convert a fraction to a percentage, multiply by 100: $\frac{7}{20} \times 100 = 7 \times 5 = 35$.

1. Which of the following is an irrational number?

• A\( \sqrt{4} \)
• B\( 0.333... \)
• C\( \pi \)
• D\( \frac{22}{7} \)

Frequently Asked Questions

What arithmetic topics are most common on the GRE?

Common topics include properties of integers, percent change, ratios, and basic operations with fractions and decimals. You should also be comfortable with exponents and square roots, as these appear frequently in quantitative comparisons.

Are calculators allowed for GRE arithmetic questions?

Yes, an on-screen calculator is provided during the computer-delivered GRE for basic arithmetic operations. However, it is often faster to perform simple mental math or use GRE practice questions with explanations to learn estimation shortcuts.

How do I handle negative numbers in absolute value problems?

The absolute value of a number is its distance from zero on a number line, which is always non-negative. For example, $|-5|$ and $|5|$ both equal 5, so you simply remove the negative sign if one exists inside the bars.

What is the difference between a prime number and a composite number?

A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. A composite number has more than two factors; for example, 4 is composite because its factors are 1, 2, and 4.

How does the GRE test ratios?

Ratios are usually tested through word problems requiring you to find unknown quantities or scale values up and down. Understanding how to set up proportions is a key skill for these GRE practice questions with answers.