GRE Quant Exam Questions Practice Questions with Answers

Forty questions comprise the quantitative reasoning measure of the GRE, testing your proficiency in arithmetic, algebra, geometry, and data analysis. These GRE Quant Exam Questions assess not just mathematical knowledge, but also your ability to reason quantitatively and solve problems using mathematical models. To succeed on this section of the GRE Prep journey, you must move beyond basic calculation and focus on the logic behind the numbers. Many students find that using an AI Exam Simulator significantly improves their timing and accuracy by mimicking the adaptive nature of the actual test.

Concept Explanation

GRE Quant Exam Questions are standardized problems designed to measure a candidate's ability to interpret and analyze quantitative information through four primary content areas. These areas include Arithmetic (properties of integers, fractions, and percent), Algebra (equations, inequalities, and functions), Geometry (properties of shapes and coordinate geometry), and Data Analysis (statistics, probability, and data interpretation). The exam utilizes three main question formats: Multiple-choice (Single Answer), Multiple-choice (One or More Answers), and Quantitative Comparison. In Quantitative Comparison, you must determine the relationship between two quantities using four standard options. Because the test is section-level adaptive, the difficulty of your second math section depends entirely on your performance in the first. For those looking to organize their study schedule efficiently, a personalized study plan can help balance these diverse topics over several weeks.

Solved Examples

Reviewing these worked examples will help you understand the logic required for common GRE math problems.

1. Algebra: Linear Equations
   If $3x + 7 = 22$, what is the value of $x^2 - 5$?
   1. Isolate the variable: Subtract 7 from both sides: $3x = 15$.
   2. Solve for $x$: Divide by 3: $x = 5$.
   3. Substitute the value into the final expression: $5^2 - 5 = 25 - 5 = 20$.
   4. The final answer is 20.
2. Geometry: Circles and Squares
   A square is inscribed in a circle with a radius of 4. What is the area of the square?
   1. Identify the relationship: The diameter of the circle is the diagonal of the inscribed square.
   2. Calculate the diameter: $d = 2 \times r = 8$.
   3. Use the area formula for a square using its diagonal: $\text{Area} = \frac{d^2}{2}$.
   4. Calculate: $\frac{8^2}{2} = \frac{64}{2} = 32$.
   5. The area of the square is 32.
3. Data Analysis: Probability
   A bag contains 4 red marbles, 6 blue marbles, and 10 green marbles. If two marbles are drawn at random without replacement, what is the probability that both are blue?
   1. Calculate total marbles: $4 + 6 + 10 = 20$.
   2. Probability of the first blue marble: $\frac{6}{20} = \frac{3}{10}$.
   3. Probability of the second blue marble (given one blue is gone): $\frac{5}{19}$.
   4. Multiply the probabilities: $\frac{3}{10} \times \frac{5}{19} = \frac{15}{190}$.
   5. Simplify the fraction: $\frac{3}{38}$.

Practice Questions

Test your skills with these GRE Quant Exam Questions ranging from basic arithmetic to complex data sets.

1. If $n$ is an integer and $n^2$ is odd, which of the following must be true? (A) $n$ is even (B) $n$ is odd (C) $n+1$ is odd (D) $n/2$ is an integer.
2. Quantity A: The average (arithmetic mean) of 15, 17, 22, and 26. Quantity B: 20. Compare the two quantities.
3. A laptop's price was reduced by 20% to $800. What was the original price?

4. A rectangular garden has a perimeter of 40 meters. If the length is 12 meters, what is the area in square meters?
5. Simplify the expression: $\frac{3^5 \times 3^2}{3^4}$.
6. Quantity A: $|x + 2|$. Quantity B: $|x| + 2$. Compare the quantities given $x < 0$.
7. In a group of 50 people, 30 like coffee, 25 like tea, and 10 like both. How many people like neither?
8. Find the value of $x$ if $2^{(x-3)} = 32$.
9. If the ratio of boys to girls in a class is 3:5 and there are 40 students total, how many girls are in the class?
10. What is the slope of the line passing through points (2, 5) and (4, 11)?

Answers & Explanations

1. Answer: (B). If the square of an integer is odd, the integer itself must be odd. For example, $3^2 = 9$ (odd), while $4^2 = 16$ (even).
2. Answer: Quantity A is greater. Sum = $15 + 17 + 22 + 26 = 80$. Mean = $80 / 4 = 20$. Wait, 80 divided by 4 is exactly 20. Re-check: $15+17=32$, $22+26=48$, $32+48=80$. The quantities are equal.
3. Answer: $1,000. Let $P$ be the price. $0.80P = 800$. Dividing 800 by 0.8 gives 1,000.
4. Answer: 96. Perimeter $2L + 2W = 40$. If $L=12$, then $24 + 2W = 40$, so $2W = 16$ and $W = 8$. Area = $12 \times 8 = 96$.
5. Answer: 27. Using exponent rules: $3^{(5+2-4)} = 3^3 = 27$.
6. Answer: Quantity B is greater. If $x = -1$, Quantity A is $|-1+2| = 1$, while Quantity B is $|-1|+2 = 3$. For any negative number, the addition happens after the absolute value in B, making it larger.
7. Answer: 5. Total = (Coffee) + (Tea) - (Both) + (Neither). $50 = 30 + 25 - 10 + N$. $50 = 45 + N$, so $N = 5$.
8. Answer: 8. Since $32 = 2^5$, we have $x - 3 = 5$, which means $x = 8$.
9. Answer: 25. Total parts = $3 + 5 = 8$. Each part = $40 / 8 = 5$. Girls = $5 \times 5 = 25$.
10. Answer: 3. Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{11 - 5}{4 - 2} = \frac{6}{2} = 3$.

1. If a circle has an area of \( 16\pi \), what is its circumference?

• A4\pi
• B8\pi
• C16\pi
• D32\pi

Frequently Asked Questions

What math topics are covered in the GRE Quant section?

The GRE focuses on high school-level mathematics including arithmetic, algebra, geometry, and data analysis. It specifically avoids higher-level math like trigonometry or calculus.

Can I use a calculator on the GRE Quant exam?

Yes, a basic on-screen calculator is provided during the computer-delivered test for simple arithmetic operations. It includes a square root function and follows the standard order of operations.

How is the GRE Quant section scored?

The section is scored on a scale of 130 to 170 in one-point increments. Your raw score is based on the number of correct answers and then converted to a scaled score through a process called equating.

How much time do I have for each GRE Quant section?

In the current shorter GRE format, you typically have 21 minutes for the first section and 26 minutes for the second section. This requires a pace of approximately 1.5 to 2 minutes per question.

What is a Quantitative Comparison question?

These questions ask you to compare two quantities (A and B) and determine if A is greater, B is greater, they are equal, or if the relationship cannot be determined. They often require logical estimation rather than full calculation.