GRE Quantitative FREE Practice Test- Quantitative Reasoning Test-3

GRE Quantitative FREE Practice Test 2024 is vital for your preparation across verbal, quantitative, and analytical writing sections. Regularly completing online GRE Quantitative FREE Practice Test 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 GRE FREE Practice Test Questions and other GRE Free Writing 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.

Arithmetic

1. Question: If ( \frac{2}{3}x - 5 = \frac{1}{3}x + 7 ), what is the value of ( x )?

Explanation: Subtract ( \frac{1}{3}x ) from both sides to get ( \frac{1}{3}x - 5 = 7 ). Add 5 to both sides to get ( \frac{1}{3}x = 12 ). Multiply both sides by 3 to get ( x = 36 ).

Answer: ( x = 36 )

2. Question: The average (arithmetic mean) of five numbers is 14. If four of the numbers are 10, 12, 18, and 20, what is the fifth number?

Answer: 10

Explanation: Let the fifth number be ( x ). The sum of the numbers is ( 5 \times 14 = 70 ). The sum of the given four numbers is ( 10 + 12 + 18 + 20 = 60 ). Therefore, ( x = 70 - 60 = 10 ).

3. Question: If a car travels at an average speed of 55 miles per hour for the first 2 hours and 65 miles per hour for the next 3 hours, what is the total distance traveled?

Answer: 305 miles

Explanation: Calculate the distance for each segment and then sum them: ( 55 \times 2 = 110 ) and ( 65 \times 3 = 195 ). Total distance = ( 110 + 195 = 305 ) miles.

4. Question: Simplify the expression ( \frac{5}{x} + \frac{3}{2x} ).

Explanation: Find a common denominator (2x): ( \frac{5 \times 2}{2x} + \frac{3}{2x} = \frac{10 + 3}{2x} = \frac{13}{2x} ).

Answer: ( \frac{13}{2x} )

Algebra

5. Question: Solve for ( y ): ( 4y - 3(2y + 1) = 5 ).

Answer: ( y = -4 )

Explanation: Distribute the -3: ( 4y - 6y - 3 = 5 ). Combine like terms: ( -2y - 3 = 5 ). Add 3 to both sides: ( -2y = 8 ). Divide by -2: ( y = -4 ).

6. Question: If ( f(x) = 2x^2 - 3x + 1 ), find ( f(-1) ).

Answer: 6

Explanation: Substitute -1 for ( x ): ( f(-1) = 2(-1)^2 - 3(-1) + 1 = 2 + 3 + 1 = 6 ).

7. Question: Expand the expression ( (2x - 3)(x + 4) ).

Answer: ( 2x^2 + 5x - 12 )

Explanation: Use the distributive property: ( 2x^2 + 8x - 3x - 12 = 2x^2 + 5x - 12 ).

8. Question: If ( x^2 - 5x + 6 = 0 ), what are the possible values of ( x )?

Answer: ( x = 2 ) or ( x = 3 )

Explanation: Factor the quadratic equation: ( (x - 2)(x - 3) = 0 ). Therefore, ( x = 2 ) or ( x = 3 ).

Geometry

9. Question: What is the area of a trapezoid with bases of lengths 6 cm and 10 cm, and a height of 5 cm?

Answer: 40 cm²

Explanation: Use the formula for the area of a trapezoid: ( \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height} = \frac{1}{2} \times (6 + 10) \times 5 = \frac{1}{2} \times 16 \times 5 = 40 ).

10. Question: What is the volume of a cone with a radius of 3 cm and a height of 4 cm? (Use ( \pi \approx 3.14 ))

Answer: 37.68 cm³

Explanation: Use the formula for the volume of a cone: ( \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 3.14 \times 3^2 \times 4 = \frac{1}{3} \times 3.14 \times 9 \times 4 = \frac{1}{3} \times 3.14 \times 36 = 37.68 ).

11. Question: Find the length of the diagonal of a rectangle with length 8 cm and width 6 cm.

Answer: 10 cm

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

12. Question: What is the surface area of a sphere with a radius of 5 cm? (Use ( \pi \approx 3.14 ))

Answer: 314 cm²

Explanation: Use the formula for the surface area of a sphere: ( 4\pi r^2 = 4 \times 3.14 \times 5^2 = 4 \times 3.14 \times 25 = 314 ).

Data Analysis

13. Question: A dataset contains the numbers 5, 7, 9, 11, 13, and 15. What is the standard deviation?

Answer: 3.74

Explanation: Calculate the mean: ( \frac{5 + 7 + 9 + 11 + 13 + 15}{6} = 10 ). Calculate the squared differences from the mean, sum them, and divide by the number of values minus one:

[ \sqrt{\frac{(5-10)^2 + (7-10)^2 + (9-10)^2 + (11-10)^2 + (13-10)^2 + (15-10)^2}{5}} = \sqrt{\frac{25 + 9 + 1 + 1 + 9 + 25}{5}} = \sqrt{14} = 3.74 ]

14. Question: A survey of 300 people found that 180 like coffee, 120 like tea, and 90 like both. How many people like only coffee?

Answer: 90

Explanation: Use the principle of inclusion and exclusion: ( 180 - 90 = 90 ).

15. Question: A pie chart shows the distribution of expenses for a household: 25% for housing, 15% for food, 20% for transportation, and the rest for other expenses. What percentage is spent on other expenses?

Explanation: Calculate the total percentage for housing, food, and transportation: ( 25 + 15 + 20 = 60 ). Therefore, the percentage spent on other expenses is ( 100 - 60 = 40 ).

Answer: 40%

16. Question: A company's revenue increased from $200,000 in 2019 to $250,000 in 2020. What is the percentage increase?

Explanation: Use the percentage increase formula: ( \frac{250,000 - 200,000}{200,000} \times 100 = \frac{50,000}{200,000} \times 100 = 25\% ).

Answer: 25%

Mixed

17. Question: Simplify the expression: ( \frac{3x - 4}{x} + \frac{2x + 5}{x} ).

Explanation: Combine the fractions: ( \frac{3x - 4 + 2x + 5}{x} = \frac{5x + 1}{x} = 5 + \frac{1}{x} ).

Answer: ( 5 + \frac{1}{x})

18. Question: If ( x ) is inversely proportional to ( y ) and ( x = 10 ) when ( y = 2 ), what is ( x ) when ( y = 8 \)?

Explanation: If ( x ) is inversely proportional to ( y ), ( x = \frac{k}{y} ). Using ( x = 10 ) and ( y = 2 ), ( k = 20 ). Therefore, when ( y = 8 ), ( x = \frac{20}{8} = 2.5 ).

Answer: 2.5

19. Question: If ( 4x + 7 = 3x + 12 ), what is the value of ( x )?

Explanation: Subtract 3x from both sides to get ( x + 7 = 12 ). Then subtract 7 from both sides to get ( x = 5 ).

Answer: ( x = 5 )

20. Question: A right triangle has one leg of 8 cm and a hypotenuse of 17 cm. What is the length of the other leg?

Explanation: Use the Pythagorean theorem: Let the other leg be ( y ). Then ( 8^2 + y^2 = 17^2 ). Simplify to get ( 64 + y^2 = 289 ). Subtract 64 to get ( y^2 = 225 ). Take the square root to get ( y = 15 ).

Answer: 15 cm