GRE Quantitative Reasoning Practice test – Download PDF

The GRE’s Quantitative Reasoning section aims to evaluate a student’s mathematical abilities and their capacity for quantitative reasoning. In order to perform exceptionally well in this section, it is crucial to practise as much as you can by utilizing a variety of GRE practice tests.

Below, you will get the official GRE Quantitative Reasoning Practice Questions with detailed explanations. Also, get practice test papers pdf below. Download the pdf for offline use.

These tests encompass a wide range of questions that encompass all the topics one can expect to encounter on the actual exam, such as arithmetic, algebra, geometry, and data analysis.

By practicing with these tests, individuals can become familiar with the test format, question types, and develop effective time management skills. Additionally, it is advantageous to thoroughly review detailed explanations for each question in order to grasp the underlying concepts and strategies for solving them efficiently.

 GRE Practice Questions for Quantitative Reasoning

Below, we have provided a list of Practice Questions for Quantitative Reasoning in pdf format. Always, remember a person who never stop trying leads to success and it is possible only through practice. So, practise as much as you can for your success in the upcoming GRE exam.

Questions with answers from GRE Quantitative reasoning section

Question: A rectangular garden measuring 30 meters by 40 meters is to be surrounded by a walkway of uniform width. If the area of the walkway is to be one-fourth the area of the garden, what must be the width of the walkway?

Answer: Let the width of the walkway be ( w ) meters. The area of the garden is ( 30 \times 40 = 1200 ) square meters. The area of the walkway is ( \frac{1}{4} \times 1200 = 300 ) square meters. The dimensions of the garden plus walkway are ( (30 + 2w) ) by ( (40 + 2w) ). The area of the garden plus walkway is ( (30 + 2w)(40 + 2w) ). The area of just the walkway is the total area minus the area of the garden, which gives us the equation ( (30 + 2w)(40 + 2w) – 1200 = 300 ). Solving for ( w ), we find that ( w = 5 ) meters.

Question: A company sells two products, P and Q. The profit from selling one unit of P is $20 and from Q is $30. Last month, the company sold a total of 200 units and made a profit of $4500. How many units of each product were sold?

Answer: Let ( x ) be the number of units of P sold and ( y ) be the number of units of Q sold. We have two equations: ( x + y = 200 ) (total units sold) and ( 20x + 30y = 4500 ) (total profit). Solving this system of equations, we get ( x = 150 ) and ( y = 50 ).

Question: If the probability that an event will occur is ( \frac{2}{3} ), what is the probability that the event will not occur twice in two independent trials?

Answer: The probability that the event will not occur in one trial is ( 1 – \frac{2}{3} = \frac{1}{3} ). Since the trials are independent, the probability that the event will not occur in both trials is ( \left(\frac{1}{3}\right)^2 = \frac{1}{9} ).

Question: A train travels from Station A to Station B at a speed of 60 km/h and returns at a speed of 90 km/h. What is the average speed for the round trip?

Answer: The average speed for a round trip is given by the formula Average Speed=Speed1​+Speed2​2×Speed1​×Speed2​​ . Plugging in the values, we get Average Speed=60+902×60×90​=15010800​=72 km/h .

Question: If the price of an item is increased by 25% and then decreased by 20%, what is the net percentage change in the price?

Answer: Let the original price be $100. After a 25% increase, the new price is $125. A 20% decrease on $125 is $25, so the final price is $125 – $25 = $100. The net percentage change is 0%.

Question: A rectangle’s length is twice its width. If the perimeter of the rectangle is 60 cm, what are its dimensions?

Answer: Let the width be ( w ) cm. Then the length is ( 2w ) cm. The perimeter is ( 2(w + 2w) = 60 ). Solving for ( w ), we get ( w = 10 ) cm and the length is ( 20 ) cm.

Question: A company has two types of machines, type A and type B. Type A machines can produce 100 units per hour, while type B machines produce 80 units per hour. If the company operates 5 type A machines and 3 type B machines, how many units are produced in 4 hours?

Answer: In 4 hours, type A machines produce ( 5 \times 100 \times 4 = 2000 ) units, and type B machines produce ( 3 \times 80 \times 4 = 960 ) units. The total production is ( 2000 + 960 = 2960 ) units.

Question: A school has 1200 students. If 40% are boys, how many girls are there in the school?

Answer: If 40% are boys, then 60% are girls. The number of girls is ( 0.60 \times 1200 = 720 ).

Question: A ladder leans against a wall forming a 60-degree angle with the ground. If the top of the ladder is 15 feet from the ground, how long is the ladder?

Answer: Using the sine function, ( \sin(60^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} ). The length of the ladder (hypotenuse) is ( \frac{15}{\sin(60^\circ)} \approx 17.32 ) feet.

Question: A car travels the first third of a certain distance with a speed of 30 km/h, the next third with a speed of 50 km/h, and the last third with a speed of 20 km/h. What is the average speed for the entire trip?

Answer: Let the total distance be ( 3d ). The time for each third is ( \frac{d}{30} ), ( \frac{d}{50} ), and ( \frac{d}{20} ) hours, respectively. The total time is ( \frac{d}{30} + \frac{d}{50} + \frac{d}{20} ) hours. The average speed is ( \frac{3d}{\frac{d}{30} + \frac{d}{50} + \frac{d}{20}} \approx 28.57 ) km/h.

Question: In a class of 50 students, 18 play football, 17 play basketball, and 15 play both. How many students do not play either sport?

Answer: Using the principle of inclusion-exclusion, the number of students playing at least one sport is ( 18 + 17 – 15 = 20 ). Therefore, ( 50 – 20 = 30 ) students do not play either sport.

Question: A fruit seller buys oranges at $4 per dozen and sells them at $1 for 3 oranges. How many oranges must he sell to make a profit of $20?

Answer: The cost price per orange is ( \frac{4}{12} = \frac{1}{3} ) dollars. The selling price per orange is $1 for 3, or ( \frac{1}{3} ) dollars. The profit per orange is ( \frac{1}{3} – \frac{1}{3} = 0 ), so he cannot make a profit by selling oranges at this price.

Question: A tank is filled by Pipe A in 2 hours and by Pipe B in 3 hours. When both pipes are opened, how long will it take to fill the tank?

Answer: Pipe A’s rate is ( \frac{1}{2} ) tank/hour, and Pipe B’s rate is ( \frac{1}{3} ) tank/hour. Together, they fill ( \frac{1}{2} + \frac{1}{3} = \frac{5}{6} ) tank/hour. The tank will be filled in ( \frac{1}{\frac{5}{6}} = 1.2 ) hours, or 1 hour and 12 minutes.

Short types questions with answers

1. What is 7% of 350?
   • Answer: 24.5
2. If ( x = 3 ) and ( y = -2 ), what is ( x^2 + y^2 )?
   • Answer: 13
3. What is the median of the set {3, 7, 9, 5, 21}?
   • Answer: 7
4. Solve for ( y ): ( 2y – 4 = 10 )
   • Answer: 7
5. If ( 5x + 3 = 2x + 15 ), what is ( x )?
   • Answer: 4
6. What is the area of a triangle with base 8 cm and height 7 cm?
   • Answer: 28 cm²
7. If ( 4^x = 64 ), what is ( x )?
   • Answer: 3
8. What is the slope of the line ( y = 3x + 4 )?
   • Answer: 3
9. If the sum of a number and its reciprocal is ( \frac{10}{3} ), what is the number?
   • Answer: 3 or ( \frac{1}{3} )
10. What is the probability of rolling a sum of 8 on two six-sided dice?
    • Answer: ( \frac{5}{36} )
11. If ( 3x – 2y = 12 ) and ( x + y = 7 ), what is ( y )?
    • Answer: 2
12. What is the volume of a cylinder with radius 3 cm and height 5 cm?
    • Answer: 45π cm³
13. If ( \frac{x}{3} = 5 ), what is ( x )?
    • Answer: 15
14. What is the sum of the angles in a pentagon?
    • Answer: 540°
15. If ( x ) is directly proportional to ( y ), and ( x = 10 ) when ( y = 2 ), what is ( x ) when ( y = 3 )?
    • Answer: 15
16. What is the greatest common divisor of 36 and 54?
    • Answer: 18
17. If ( 5x – 2 = 3x + 6 ), what is ( x )?
    • Answer: 4
18. What is the range of the set {2, 4, 6, 8, 10}?
    • Answer: 8
19. If ( x ) is inversely proportional to ( y ), and ( x = 8 ) when ( y = 2 ), what is ( y ) when ( x = 4 )?
    • Answer: 4
20. What is the standard deviation of the set {2, 4, 4, 4, 5, 5, 7, 9}?
    • Answer: Approximately 2.138
21. If ( x + y = 10 ) and ( x – y = 4 ), what are ( x ) and ( y )?
    • Answer: ( x = 7 ), ( y = 3 )
22. What is the interest earned on $200 invested at 5% annual interest for one year?
    • Answer: $10
23. If ( 2x + 3y = 12 ) and ( x – y = 1 ), what is ( x )?
    • Answer: 3
24. What is the exterior angle of a regular hexagon?
    • Answer: 60°
25. If ( x ) is 30% of ( y ), what percent of ( x ) is ( y )?
    • Answer: 333.33%
26. What is the sum of the interior angles of a nonagon?
    • Answer: 1260°
27. If ( 3x + 4y = 12 ) and ( x – 2y = 3 ), what is ( y )?
    • Answer: 1
28. What is the factorial of 5 (5!)?
    • Answer: 120
29. If ( x ) is 20% more than ( y ), what percent of ( y ) is ( x )?
    • Answer: 120%
30. What is the sum of the first 5 prime numbers?
    • Answer: 28

Quantitative Reasoning topic-wise questions with answers

1. Arithmetic:
   • Q 1: If (x + 2y = 10) and (2x – y = 4), what is the value of (x)?
     • Answer: (x = 3)
   • Q 2: What is the sum of the first 10 positive integers?
     • Answer: (55)
   • Question 3: If (a + b = 7) and (a – b = 3), what is the value of (a^2 – b^2)?
     • Answer: (16)
2. Algebra:
   • Q 4: Solve for (x): (3x + 2 = 8)
     • Answer: (x = 2)
   • Q 5: If (2x + 3y = 12) and (3x – 2y = 6), what is the value of (x + y)?
     • Answer: (4)
   • Q 6: What is the value of (\frac{1}{x} + \frac{1}{y}) if (x = 3) and (y = 4)?
     • Answer: (\frac{7}{12})
3. Geometry:
   • Q 7: What is the area of a rectangle with length (6) units and width (4) units?
     • Answer: (24) square units
   • Q 8: If the circumference of a circle is (18\pi), what is its radius?
     • Answer: (3) units
   • Q 9: What is the volume of a cube with side length (5) units?
     • Answer: (125) cubic units
4. Data Interpretation:
   • Q 10: Given the following data, what is the average of the numbers: (2, 4, 6, 8, 10)?
     • Answer: (6)
   • Q 11: If the mean of a set of numbers is (20) and there are (5) numbers, what is their sum?
     • Answer: (100)
   • Q 12: In a survey, (60%) of people prefer tea over coffee. If (300) people were surveyed, how many prefer tea?
     • Answer: (180)
5. Quantitative Comparison:
   • Q 13: Compare (x) and (y): (x = 5) and (y = 3)
     • Answer: (x > y)
   • Q 14: Compare (\frac{1}{x}) and (\frac{1}{y}): (x = 2) and (y = 4)
     • Answer: (\frac{1}{x} < \frac{1}{y})
   • Q 15: Compare (2x) and (x^2): (x = 3)
     • Answer: (x^2 > 2x)

GRE Practice Questions for Quantitative Reasoning

How do I improve my GRE Quantitative Reasoning score?

Enhancing your GRE Quantitative Reasoning score requires a methodical approach to studying and practicing. Here are some guidelines to help you improve your results:

• Master the Basics: Ensure you have a strong understanding of fundamental math concepts to better analyze and solve problems in the quantitative section.
• Identify Question Types: Familiarize yourself with the various question formats you will encounter, such as quantitative comparison, problem-solving, and data interpretation.
• Consistent Practice: Dedicate time to practicing a wide range of problems to recognize patterns and grasp the test’s format.
• Address Weaknesses: Pinpoint your areas of weakness and concentrate on improving them until they become strengths.
• Time Management: Develop effective time management skills by practicing under timed conditions to enhance your speed and accuracy.
• Utilize Reliable Resources: Make use of reputable GRE preparation materials like books, online courses, and practice tests from trusted sources.
• Learn Test Strategies: Develop strategies to answer questions more efficiently, including elimination techniques and educated guessing when needed.
• Practice in Test-like Conditions: Take full-length practice tests under conditions that replicate the actual exam to build endurance and reduce test anxiety.
• Analyze Errors: Review your mistakes after practice sessions to understand why you erred and how to avoid similar mistakes in the future.
• Seek Feedback: If possible, seek feedback on your performance from a tutor or study group to gain valuable insights you may have overlooked.

How to utilize GRE Quantitative Reasoning Practice Test

• Begin by taking a practice test to identify your strengths and weaknesses.
• Refresh your knowledge of basic math concepts like algebra, geometry, and data analysis.
• Take a close look at the questions you answered incorrectly to understand your errors.
• Concentrate your study on the topics where you need the most improvement.
• Consistent practice is essential for mastering the Quantitative Reasoning section.
• Simulate real exam conditions by timing your practice sessions.
• Study with materials that offer detailed explanations for each answer.
• Develop techniques for efficient problem-solving and time management.
• Periodically take full-length tests to build endurance and boost your confidence.
• Continuously review your performance and repeat practice tests to track your progress.

FAQs

1. What topics are covered in the GRE Quantitative Reasoning section?
   • The section includes arithmetic, algebra, geometry, and data analysis.
2. How many questions are in the GRE Quantitative Reasoning section?
   • There are 20 questions per section, with two sections of total 40 questions.
3. What types of questions are on the GRE Quantitative Reasoning test?
   • Questions include quantitative comparison, multiple-choice, and numeric entry.
4. How long do I have to complete each Quantitative Reasoning section?
   • Each section is timed at 35 minutes, giving you a total of 1 hour and 10 minutes.
5. Is there a passing score for the GRE Quantitative Reasoning test?
   • The GRE does not have a passing score; it’s scored on a scale of 130-170.
6. Can I use a calculator on the GRE Quantitative Reasoning section?
   • Yes, a basic on-screen calculator is provided for use during the test.
7. How should I prepare for the GRE Quantitative Reasoning test?
   • Regular practice with sample questions, reviewing math concepts, and taking timed practice tests are effective preparation strategies.

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