Easy GRE Arithmetic Practice Test Practice Questions

Arithmetic represents approximately 25 percent of the Quantitative Reasoning section on the GRE, focusing on fundamental number properties and basic operations. Whether you are tackling integers, fractions, or percentages, building a solid foundation through an Easy GRE Arithmetic Practice Test Practice Questions set ensures you don't lose points on simple calculations. This section of the exam tests your ability to apply basic mathematical concepts rather than your ability to perform complex, high-level calculus.

Success on the GRE requires more than just knowing how to add and subtract; it requires a deep familiarity with how the Educational Testing Service (ETS) structures these problems. By utilizing an adaptive GRE practice test, you can identify whether your weaknesses lie in number properties or ratio-based word problems. This guide provides a structured approach to mastering these basics through clear explanations and realistic practice scenarios.

Concept Explanation

Arithmetic on the GRE involves the study of integers, fractions, decimals, percentages, and the properties of numbers such as primality and divisibility. At its core, this subject area requires you to manipulate real numbers using the four basic operations—addition, subtraction, multiplication, and division—while adhering to the order of operations (PEMDAS). Key concepts include understanding the difference between rational and irrational numbers, identifying factors and multiples, and calculating ratios and proportions. For students looking for a comprehensive overview of the exam structure, visiting the GRE Prep hub is an excellent starting point. Additionally, tools like the AI MasterPlan can help organize your study schedule to cover these arithmetic foundations efficiently before moving on to algebra or geometry.

Solved Examples

1. Integer Properties: If $n$ is an even integer and $m$ is an odd integer, which of the following must be odd: $n + m$, $nm$, or $n^2$?
   1. Step 1: Test with small numbers. Let $n = 2$ (even) and $m = 3$ (odd).
   2. Step 2: Calculate $n + m = 2 + 3 = 5$. 5 is odd.
   3. Step 3: Calculate $nm = 2 \times 3 = 6$. 6 is even.
   4. Step 4: Calculate $n^2 = 2^2 = 4$. 4 is even.
   5. Conclusion: Only $n + m$ must be odd.
2. Percentage Change: The price of a shirt was originally $40. If the price increases by 20% and then decreases by 10%, what is the final price?
   1. Step 1: Calculate the increase. $20\% \text{ of } 40 = 0.20 \times 40 = 8$. New price = $40 + 8 = 48$.
   2. Step 2: Calculate the decrease from the new price. $10\% \text{ of } 48 = 0.10 \times 48 = 4.8$.
   3. Step 3: Subtract the decrease. $48 - 4.8 = 43.2$.
   4. Final Answer: The price is $43.20.
3. Ratios: In a bag of marbles, the ratio of red marbles to blue marbles is 3:5. If there are 40 blue marbles, how many red marbles are there?
   1. Step 1: Set up a proportion: $\frac{3}{5} = \frac{x}{40}$.
   2. Step 2: Cross-multiply to solve for $x$: $5x = 3 \times 40$.
   3. Step 3: Simplify: $5x = 120$.
   4. Step 4: Divide by 5: $x = 24$.
   5. Final Answer: There are 24 red marbles.

Practice Questions

1. What is the greatest common factor (GCF) of 24 and 60?

2. A recipe calls for $\frac{3}{4}$ cup of sugar. If you want to make $\frac{1}{2}$ of the recipe, how much sugar do you need?

3. Solve for the value: $$15 - (3 + 2)^2 \div 5$$

4. Which of the following is a prime number: 9, 15, 21, or 23?

5. If a car travels at a constant speed of 65 miles per hour, how many miles will it travel in 3 hours and 30 minutes?

6. Convert 0.85 into a fraction in its simplest form.

7. A jacket is on sale for 30% off the original price of $120. What is the sale price?

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

9. If $x$ is the smallest prime number and $y$ is the smallest composite number, what is $x + y$?

10. A set of numbers consists of {4, 8, 12, 16, 20}. What is the average (arithmetic mean) of this set?

Answers & Explanations

1. Answer: 12. List the factors of 24 (1, 2, 3, 4, 6, 8, 12, 24) and 60 (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60). The largest number appearing in both lists is 12.
2. Answer: $\frac{3}{8}$. To find half of the recipe, multiply the sugar amount by $\frac{1}{2}$: $\frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}$.
3. Answer: 10. Follow PEMDAS: Parentheses first $(3+2=5)$, then Exponents $(5^2=25)$, then Division $(25 \div 5 = 5)$, then Subtraction $(15 - 5 = 10)$.
4. Answer: 23. A prime number has exactly two factors: 1 and itself. 9 is divisible by 3; 15 by 3 and 5; 21 by 3 and 7. 23 has no other factors.
5. Answer: 227.5 miles. Convert 3 hours 30 minutes to 3.5 hours. Distance = Speed $\times$ Time: $65 \times 3.5 = 227.5$.
6. Answer: $\frac{17}{20}$. Write 0.85 as $\frac{85}{100}$. Divide both the numerator and denominator by their greatest common divisor, 5: $\frac{85 \div 5}{100 \div 5} = \frac{17}{20}$.
7. Answer: $84. Calculate the discount: $0.30 \times 120 = 36$. Subtract from original: $120 - 36 = 84$.
8. Answer: 1. $127 \div 6 = 21$ with a remainder. $21 \times 6 = 126$. $127 - 126 = 1$.
9. Answer: 6. The smallest prime number is 2. The smallest composite number is 4. $2 + 4 = 6$. (Note: 1 is neither prime nor composite).
10. Answer: 12. Sum the numbers: $4 + 8 + 12 + 16 + 20 = 60$. Divide by the count of numbers: $60 \div 5 = 12$.

1. Which of the following is the correct decimal equivalent of the fraction 7/8?

• A0.78
• B0.825
• C0.875
• D0.75

Frequently Asked Questions

What arithmetic topics are most common on the GRE?

The GRE frequently tests number properties (even/odd, divisibility), percent change, ratios, and basic operations with fractions and decimals. You should also be comfortable with exponents and square roots in their simplest forms.

Do I get a calculator for the GRE arithmetic section?

Yes, an on-screen calculator is provided during the Quantitative Reasoning section, but it is basic and only handles simple operations. Relying too heavily on it can slow you down, so mental math for simple arithmetic is highly recommended.

Is 1 considered a prime number on the GRE?

No, by mathematical definition, 1 is not a prime number because a prime number must have exactly two distinct factors. Similarly, 1 is not considered a composite number; it is unique.

How is "average" defined on the GRE?

On the GRE, the term "average" refers specifically to the arithmetic mean. You calculate it by finding the sum of all terms in a set and dividing that sum by the total number of terms.

What is the difference between a factor and a multiple?

A factor is a number that divides evenly into another number (e.g., 3 is a factor of 6). A multiple is the product of a number and an integer (e.g., 12 is a multiple of 6).