GRE Quant Practice Test Practice Questions with Answers

Sixty-eight percent of test-takers score between 145 and 158 on the Quantitative Reasoning section, making every point a critical differentiator for graduate admissions. Success on this exam requires more than just knowing basic arithmetic; it demands a strategic approach to problem-solving under strict time constraints. A high-quality GRE Quant Practice Test offers the most effective way to identify knowledge gaps in arithmetic, algebra, geometry, and data analysis. By simulating the exact environment of the GRE General Test, you can build the mental stamina needed for the actual exam day. This guide provides a comprehensive set of practice questions designed to mirror the difficulty and format of the official test.

Concept Explanation

The GRE Quantitative Reasoning section measures your ability to interpret and analyze quantitative information, solve problems using mathematical models, and apply basic concepts of arithmetic, algebra, geometry, and data analysis. The section typically consists of two 18-minute or 23-minute sub-sections (depending on the version of the test) featuring Quantitative Comparison, Multiple-choice (Select One), Multiple-choice (Select One or More), and Numeric Entry questions. Unlike higher-level mathematics, the GRE focuses on high school-level concepts but presents them in complex, logical ways. To excel, students must be proficient in number theory, coordinate geometry, and statistical measures like standard deviation. Utilizing a structured GRE Prep plan ensures that you cover all four major content areas systematically rather than focusing only on your strengths.

Solved Examples

Review these solved examples to understand the logic required for different GRE question formats.

1. Quantitative Comparison: Compare Quantity A and Quantity B.
   Condition: $x > 0$
   Quantity A: $x^2 + 1$
   Quantity B: $(x + 1)^2$
   Solution:
   1. Expand Quantity B: $(x + 1)^2 = x^2 + 2x + 1$.
   2. Subtract $x^2 + 1$ from both quantities.
   3. Quantity A becomes $0$; Quantity B becomes $2x$.
   4. Since the condition states $x > 0$, then $2x$ must be greater than $0$.
   5. Therefore, Quantity B is greater.
2. Algebraic Word Problem: A car travels at a constant speed of 60 miles per hour. How many minutes does it take the car to travel 45 miles?
   Solution:
   1. Use the formula $\text{Time} = \frac{ \text{Distance}}{ \text{Speed}}$.
   2. Calculate hours: $\frac{45}{60} = 0.75$ hours.
   3. Convert hours to minutes: $0.75 \times 60 = 45$ minutes.
   4. The answer is 45.
3. Geometry: A circle is inscribed in a square with a side length of 10. What is the area of the circle?
   Solution:
   1. If a circle is inscribed in a square, its diameter is equal to the side length of the square.
   2. Diameter $d = 10$, so radius $r = 5$.
   3. Area of a circle formula: $A = \pi r^2$.
   4. Substitute the radius: $A = \pi (5)^2 = 25\pi$.
   5. The final area is $25\pi$.

Practice Questions

Test your skills with these GRE Quant Practice Test questions. Use a scratchpad and a basic on-screen calculator as you would during the exam.

1. If $3x + 7 = 22$, what is the value of $(x - 2)^2$?
2. Quantity A: The number of distinct prime factors of 30.
   Quantity B: The number of distinct prime factors of 60.
3. A bag contains 4 red marbles, 6 blue marbles, and 10 yellow marbles. If one marble is picked at random, what is the probability that it is NOT red?

4. The average (arithmetic mean) of five numbers is 20. If a sixth number, 44, is added to the set, what is the new average?
5. Solve for $y$: $$\frac{2}{3}y - 4 = 10$$
6. In a group of 50 students, 28 study Spanish, 22 study French, and 8 study both. How many students study neither language?
7. A rectangular garden has a perimeter of 60 feet. If the length is twice the width, what is the area of the garden in square feet?
8. Quantity A: $\sqrt{64} + \sqrt{36}$
   Quantity B: $\sqrt{64 + 36}$
9. If $a$ and $b$ are integers such that $a^2 = 49$ and $b^3 = 27$, what is the minimum possible value of $a - b$?
10. A store increases the price of an item by 20%, then applies a 20% discount to the new price. What is the final price as a percentage of the original price?

Answers & Explanations

1. 9: Solve $3x + 7 = 22 \rightarrow 3x = 15 \rightarrow x = 5$. Substitute into the expression: $(5 - 2)^2 = 3^2 = 9$.
2. The two quantities are equal: Prime factors of 30 are 2, 3, and 5 (count = 3). Prime factors of 60 are 2, 3, and 5 (count = 3). Note that while 60 has more factors, it does not have more distinct prime factors.
3. 0.8 or 4/5: Total marbles = $4 + 6 + 10 = 20$. Marbles that are not red = $6 + 10 = 16$. Probability = $\frac{16}{20} = 0.8$.
4. 24: Sum of first five numbers = $5 \times 20 = 100$. New sum = $100 + 44 = 144$. New average = $\frac{144}{6} = 24$.
5. 21: Add 4 to both sides: $\frac{2}{3}y = 14$. Multiply by $\frac{3}{2}$: $y = 14 \times \frac{3}{2} = 21$.
6. 8: Use the formula $n(A \cup B) = n(A) + n(B) - n(A \cap B)$. Total studying languages = $28 + 22 - 8 = 42$. Neither = $50 - 42 = 8$.
7. 200: Let width be $w$, then length is $2w$. Perimeter $2(w + 2w) = 60 \rightarrow 6w = 60 \rightarrow w = 10$. Length = 20. Area = $10 \times 20 = 200$.
8. Quantity A is greater: Quantity A = $8 + 6 = 14$. Quantity B = $\sqrt{100} = 10$. 14 is greater than 10.
9. -10: $a$ can be 7 or -7. $b$ must be 3. To minimize $a - b$, use the smallest $a$: $-7 - 3 = -10$.
10. 96%: Let the original price be 100. Increase by 20%: $100 \times 1.2 = 120$. Decrease by 20%: $120 \times 0.8 = 96$.

For more advanced practice, you can explore complex reasoning problems or use our AI Question Generator to create custom sets based on your weak areas. Regular retrieval practice is scientifically proven to improve long-term retention of mathematical formulas and logic shortcuts.

1. If a set of numbers consists of {2, 4, 6, 8, 10}, what is the standard deviation compared to the set {12, 14, 16, 18, 20}?

• AThe first set has a higher standard deviation
• BThe second set has a higher standard deviation
• CThe standard deviations are equal
• DThe standard deviation cannot be determined

Frequently Asked Questions

What math subjects are covered in the GRE Quant section?

The exam covers four main areas: Arithmetic (properties of integers, percent, ratio), Algebra (equations, inequalities, functions), Geometry (parallel lines, circles, polygons, coordinate geometry), and Data Analysis (statistics, probability, and data interpretation). It does not include trigonometry or calculus.

Can I use a calculator on the GRE Quantitative Reasoning section?

Yes, a basic on-screen calculator is provided during the computer-based test. It includes the four basic operations, square roots, and a decimal function, but you should use it sparingly to save time on simple mental math.

How is the GRE Quant section scored?

Quant scores range from 130 to 170 in one-point increments. The score is based on the number of correct answers (raw score) and then adjusted through a process called equating to account for variations in difficulty between different test versions.

What is a good GRE Quant score for engineering programs?

Top-tier engineering and STEM programs often look for scores in the 163-170 range. However, requirements vary significantly by university, so you should check the average scores of admitted students for your specific target programs.

How long should I study for the GRE Quant section?

Most students find success by studying for 2 to 4 months, dedicating 5-10 hours per week. This allows enough time to refresh mathematical concepts, practice pacing strategies, and take multiple full-length practice tests to track progress.