Free GRE Quantitative Reasoning Practice Set

Free GRE Quantitative Reasoning Practice Test 2024 is vital for your preparation across verbal, quantitative, and analytical writing sections. Regularly completing online Free GRE Quantitative Reasoning Practice Tests enhances your understanding of various question types and improves performance evaluation. The official ETS website offers a range of GRE practice materials, and online courses can further aid in efficient exam preparation.

GeeksforGeeks provides Free GRE Quantitative Reasoning Practice Tests and other GRE Quantitative Reasoning Practice Tests, expertly crafted to help you excel. Whether you're starting or fine-tuning skills, our GRE Free Writing Practice Tests are essential for acing the exam.

Que 1. If 3x+2=11, what is the value of x?

Explanation: Subtract 2 from both sides to get 3x=9. Then divide both sides by 3 to get x=3.

Answer: x=3x

Que 2. The average (arithmetic mean) of 5, 10, 15, and 20 is:

Explanation: Add the numbers: 5+10+15+20=50. Divide by the number of values (4): 50÷4=12.5

Answer: 12.5

Ques 3. If a car travels 150 miles in 2.5 hours, what is the average speed in miles per hour?

Explanation: Divide the total distance by the total time: 150÷2.5=60

Answer: 60 miles per hour

Ques 4. Solve for y: 2y−7=3y+4.

Explanation: Subtract 2y from both sides to get −7=y+4. Then subtract 4 from both sides to get y=−11.

Answer: y=−11.

Ques 6. If f(x) = x^2 - 3x + 2, find f(2).

Explanation: Substitute 2 for ( x ): f(2) = 2^2 - 3(2) + 2 = 4 - 6 + 2 = 0.

Answer: 0

Ques 7. Expand the expression (x + 3)(x - 2).

Explanation: Use the distributive property: x^2 - 2x + 3x - 6 = x^2 + x - 6.

Answer: ( x^2 + x - 6 )

Ques 8. If ( x^2 = 16 ), what are the possible values of ( x )?

Explanation: Take the square root of both sides: ( x = \pm 4).

Answer: ( x = 4 ) or ( x = -4 )

Ques 9. What is the area of a triangle with a base of 8 cm and a height of 5 cm?

Explanation: Use the formula for the area of a triangle: ( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 5 = 20

Answer: 20 cm²

Ques 10. What is the circumference of a circle with a radius of 7 cm?

Explanation: Use the formula for the circumference: ( 2\pi r = 2 \times 3.14 \times 7 = 43.96)

Answer:43.96 cm

Ques 11. Find the length of the hypotenuse of a right triangle with legs of length 6 cm and 8 cm.

Explanation: Use the Pythagorean theorem: ( \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10).

Answer: 10 cm

Ques 12. What is the volume of a cylinder with a radius of 3 cm and a height of 5 cm? (Use ( \pi \approx 3.14 )

Explanation: Use the formula for the volume of a cylinder: ( \pi r^2 h = 3.14 \times 3^2 \times 5 = 3.14 \times 9 \times 5 = 141.3.

Answer: 141.3 cm³

Ques 13. The mean of five numbers is 8. If four of the numbers are 7, 9, 12, and 5, what is the fifth number?

Explanation: Let the fifth number be ( x ). Then \frac{7 + 9 + 12 + 5 + x}{5} = 8 . Simplify to get ( \frac{33 + x}{5} = 8 ). Multiply both sides by 5 to get ( 33 + x = 40 ). Subtract 33 to get ( x = 7 ).

Answer: 7

Ques 14. A survey of 200 people found that 120 like coffee, 150 like tea, and 80 like both. How many people do not like either coffee or tea?

Explanation: Use the principle of inclusion and exclusion: ( 120 + 150 - 80 = 190 ). Thus, ( 200 - 190 = 10 ).

Answer: 10

Ques 15. A dataset contains the numbers 5, 7, 9, 11, and 13. What is the median?

Explanation: The median is the middle number in a sorted list. The sorted list is already given: 5, 7, 9, 11, 13. The middle number is 9.

Answer: 9

Ques 16. A jar contains 4 red, 5 blue, and 6 green marbles. If one marble is picked at random, what is the probability it is blue?

Explanation: The total number of marbles is ( 4 + 5 + 6 = 15 ). The probability of picking a blue marble is ( \frac{5}{15} = \frac{1}{3}).

Answer: ( \frac{1}{3})

Ques 17. Simplify the expression: ( 3(x - 2) + 4 ).

Explanation: Distribute the 3: \( 3x - 6 + 4 = 3x - 2 \).

Answer: ( 3x - 2 )

Ques 18. If ( x ) is directly proportional to ( y ) and ( x = 10 ) when ( y = 2 ), what is ( x ) when ( y = 8 )?

Explanation: If \( x \) is directly proportional to ( y ), ( x = ky ). Using ( x = 10 ) and ( y = 2 ), ( k = 5 ). Therefore, when ( y = 8 ), ( x = 5 \times 8 = 40).

Answer: 40

Ques 19. If ( 2x + 3 = 9 ), what is the value of ( x )?

Explanation: Subtract 3 from both sides to get ( 2x = 6 ). Then divide both sides by 2 to get ( x = 3).

Answer: ( x = 3 )

Ques 20. A right triangle has one leg of 5 cm and a hypotenuse of 13 cm. What is the length of the other leg?

Explanation: Use the Pythagorean theorem: Let the other leg be ( x ). Then ( 5^2 + x^2 = 13^2 ). Simplify to get ( 25 + x^2 = 169 ). Subtract 25 to get ( x^2 = 144 ). Take the square root to get ( x = 12 ).

Answer: 12 cm

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