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.

1. Question: What is the value of \frac{4^3 \times 2^2}{8}

(A) 10

(B) 12

(C) 32

(D) 20

Answer: (C) 32.

Explanation: First, compute ( 4^3 = 64 ) and ( 2^2 = 4 ). Multiply these to get 256.. 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. Question: Solve for ( x ): ( 3x + 7 = 16 ).

(A) 2

(B) 3

(C) 4

(D) 5

Answer: (B) 3.

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

4. 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. 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. 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. 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. 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. 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. Question: Calculate ( 15% ) of 200?

(A) 20

(B) 25

(C) 30

(D) 35

Answer: (C) 30.

Explanation: 15% × 200 = 0.15 × 200 = 30.

11. 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 r² h ). Thus, ( 3.14 \times 3^2 \times 5 = 141.3 ).

12. Question: What is the value of ( 3x² - 2x ) when ( x = 4 )?

(A) 40

(B) 50

(C) 52

(D) 60

Answer: (A) 40.

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

13. 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) 216 square units

Answer: (D) 216 square units.

Explanation: The surface area of a cube is ( 6 \times \text{side}^2 ). Thus, ( 6 \times 6^2 = 216 ).

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

(A) 15

(B) 17

(C) 20

(D) 25

Answer: (C) 20.

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

15. 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: 5² + 12² = 13².

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

(A) 18

(B) 12

(C) 10

(D) 14

Answer: (D) 14.

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

20. 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.