GRE Quantitative Reasoning FREE Practice Test- Quantitative Reasoning Test-2

Ready to ace the GRE Quantitative Reasoning section? Our free practice test is here to help you succeed. Introducing Quantitative Reasoning Test-2, a comprehensive and detailed GRE quantitative practice test designed to simulate the real exam experience. This GRE Quantitative Reasoning FREE Practice Test covers a variety of question types and difficulty levels to help you master the quantitative reasoning skills needed for top scores.

Use this GRE Quantitative Reasoning FREE Practice Test to assess your strengths, identify areas for improvement, and refine your strategies for the Quantitative Reasoning section. Prepare effectively and boost your confidence with our expertly crafted practice resources.

1. Question: What is the value of

(A) 10

(B) 12

(C) 16

(D) 20

Answer: (C) 16.

Explanation: First, compute ( 4^3 = 64 ) and ( 2^2 = 4 ). Multiply these to get . Then divide by 8: ( \frac{256}{8} = 32 ).

2. Question: If a shirt originally costs $50 and is discounted by 30%, what is the sale price?

(A) $35

(B) $40

(C) $45

(D) $50

Answer: (A) $35.

Explanation: The discount is ( 30\% ) of $50, which is ( 0.30 \times 50 = 15 ). Subtract this from the original price: ( 50 - 15 = 35 ).

3. Algebra:

Question: Solve for ( x ): ( 3x + 7 = 16 ).

- (A) 2

- (B) 3

- (C) 4

- (D) 5

Answer: (A) 3.

Explanation: Subtract 7 from both sides: ( 3x = 9 ). Then divide by 3: ( x = 3 ).

4. Algebra:

Question: What is the solution to the equation ( x^2 - 4x - 5 = 0 )?

- (A) 1 and -5

- (B) 1 and 5

- (C) -1 and 5

- (D) -1 and -5

Answer: (C) -1 and 5.

Explanation: Factor the quadratic equation: ( (x - 5)(x + 1) = 0 ). Set each factor to zero: ( x - 5 = 0 ) or \( x + 1 = 0 ), yielding ( x = 5 ) and ( x = -1 ).

5. Geometry:

Question: What is the area of a right triangle with base 8 units and height 6 units?

- (A) 24 square units

- (B) 48 square units

- (C) 28 square units

- (D) 30 square units

Answer: (A) 24 square units.

Explanation: The area of a right triangle is given by ( \frac{1}{2} \times \text{base} \times \text{height}). Thus, ( \frac{1}{2} \times 8 \times 6 = 24 ).

6. Geometry:

Question: In a circle, if the radius is 7 units, what is the circumference? (Use ( \pi \approx 3.14 ))

- (A) 21.98 units

- (B) 43.96 units

- (C) 14 units

- (D) 49 units

Answer: (B) 43.96 units.

Explanation: The circumference of a circle is given by ( 2 \pi r ) Thus, 2 \times 3.14 \times 7 = 43.96 .

7. Data Analysis

Question: The average of five numbers is 12. What is their total sum?

- (A) 60

- (B) 48

- (C) 54

- (D) 72

Answer: (A) 60.

Explanation: The average of a set of numbers is the total sum divided by the number of items. Thus, the total sum is ( 12 \times 5 = 60).

8. Data Analysis:

Question: In a dataset with values 10, 15, 20, 25, and 30, what is the median?

- (A) 15

- (B) 20

- (C) 25

- (D) 30

Answer: (B) 20.

Explanation: The median is the middle value when the numbers are arranged in ascending order. For the dataset, the middle value is 20.

9. Algebra:

Question: If ( 2x - 3 = 7 ), what is ( x )?

- (A) 4

- (B) 5

- (C) 6

- (D) 7

Answer: (B) 5.

Explanation: Add 3 to both sides: ( 2x = 10 ). Divide by 2: ( x = 5 ).

10. Arithmetic:

Question: What is ( 15% ) of 200?

- (A) 20

- (B) 25

- (C) 30

- (D) 35

Answer: (C) 30.

Explanation: Calculate

11. Geometry:

Question: What is the volume of a cylinder with a radius of 3 units and a height of 5 units? (Use ( \pi \approx 3.14 ))

- (A) 141.3 cubic units

- (B) 282.6 cubic units

- (C) 94.2 cubic units

- (D) 235.8 cubic units

Answer: (A) 141.3 cubic units.

Explanation: The volume of a cylinder is ( pi r^2 h ). Thus, ( 3.14 \times 3^2 \times 5 = 141.3 ).

12. Algebra:

Question: What is the value of ( 3x^2 - 2x ) when ( x = 4 )?

- (A) 40

- (B) 50

- (C) 52

- (D) 60

Answer: (C) 52.

Explanation: Substitute ( x = 4 ) into the expression: ( 3 \times 4^2 - 2 \times 4 = 48 - 8 = 40 ).

13. Geometry:

Question: What is the surface area of a cube with a side length of 6 units?

- (A) 72 square units

- (B) 96 square units

- (C) 108 square units

- (D) 144 square units

Answer: (D) 144 square units.

Explanation: The surface area of a cube is ( 6 \times \text{side}^2 ). Thus, ( 6 \times 6^2 = 144 ).

14. Data Analysis:

Question: What is the range of the dataset {5, 8, 12, 20, 25}?

- (A) 15

- (B) 17

- (C) 20

- (D) 25

Answer: (B) 20.

Explanation: The range is the difference between the maximum and minimum values: ( 25 - 5 = 20 ).

15. Geometry:

Question: What is the length of the hypotenuse of a right triangle with legs of lengths 5 and 12 units?

- (A) 13 units

- (B) 14 units

- (C) 15 units

- (D) 17 units

Answer: (A) 13 units.

Explanation: Use the Pythagorean theorem:

16. Algebra:

Question: Simplify ( \frac{6x^2 - 4x}{2x} ).

- (A) ( 3x - 2 )

- (B) ( 3x + 2 )

- (C) ( 3x - 1)

- (D) ( 3x + 1 )

Answer: (A) ( 3x - 2 ).

Explanation: Divide each term by ( 2x ): ( \frac{6x^2}{2x} - \frac{4x}{2x} = 3x - 2 ).

17. Data Analysis:

Question: The mean of a dataset is 14 and the sum of the dataset is 84. How many numbers are in the dataset?

- (A) 5

- (B) 6

- (C) 7

- (D) 8

Answer: (B) 6.

Explanation: The mean is given by the sum divided by the number of items. Thus, ( \frac{84}{14} = 6).

18. Geometry:

Question: The diagonal of a square is \( 10\sqrt{2} \) units. What is the side length of the square?

- (A) 10 units

- (B) 5 units

- (C) \( 5\sqrt{2} \) units

- (D) 15 units

Answer: (A) 10 units.

Explanation: The diagonal of a square is ( s\sqrt{2} ), where ( s ) is the side length. Given the diagonal ( 10\sqrt{2} ), solve ( s\sqrt{2} = 10\sqrt{2} ), giving ( s = 10 ).

19. Algebra:

Question: Solve for ( x ) in the equation ( 4(x - 2) = 3x + 6 ).

- (A) 18

- (B) 12

- (C) 10

- (D) 8

Answer: (D) 8.

Explanation: Expand and solve: ( 4x - 8 = 3x + 6 ). Subtract ( 3x ) from both sides: ( x - 8 = 6 ). Add 8 to both sides: ( x = 14 ).

20. Data Analysis:

Question: In a dataset with values 3, 7, 7, 10, and 14, what is the mode?

- (A) 3

- (B) 7

- (C) 10

- (D) 14

Answer: (B) 7.

Explanation: The mode is the value that appears most frequently. In this dataset, 7 appears twice, more than any other value.