Free GRE Quantitative Reasoning Practice Test: GRE Math Sectional Test-7

Free GRE Quantitative Reasoning Practice Test: GRE Math Sectional Test-7 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.

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Arithmetic

Question 1:

If ( x ) is a positive integer and ( 3x - 7 < 2x + 5 ), what is the greatest possible value of ( x )?

- A) 6

- B) 8

- C) 10

- D) 12

- E) 14

Answer: B) 8.

Explanation: Simplify the inequality: ( 3x - 7 < 2x + 5 ). Solving for ( x ), we get ( x < 12 ). The greatest integer value less than 12 is 8.

Question 2:

A bakery makes 120 cookies, which are divided equally among 4 boxes. Each box is sold for $15. What is the price per cookie?

- A) $0.25

- B) $0.50

- C) $1.00

- D) $1.25

- E) $1.50

Answer: B) $0.50.

Explanation: Each box contains cookies. Price per cookie =

Question 3:

A number is decreased by 40% and the result is 72. What was the original number?

- A) 100

- B) 120

- C) 150

- D) 160

- E) 180

Answer: D) 160.

Explanation: Let the original number be ( x ). Then, ( x - 0.4x = 72 ), which simplifies to ( 0.6x = 72 ). Solving gives ( x = 120 ).

Question 4:

If the average (arithmetic mean) of five consecutive integers is 25, what is the largest of these integers?

- A) 25

- B) 26

- C) 27

- D) 28

- E) 29

Answer: C) 27.

Explanation: Let the integers be ( x-2, x-1, x, x+1, x+2 ). Their average is ( x = 25 ). The largest number is ( 27 ).

Question 5:

A certain job pays $24 per hour for the first 40 hours worked in a week and 1.5 times that rate for any additional hours. If an employee earns $1,260 in one week, how many total hours did they work?

- A) 45

- B) 47

- C) 48

- D) 50

- E) 52

Answer: C) 48.

Explanation: Additional hourly rate = . Let ( x ) be the additional hours worked: ( 40 times 24 + 36x = 1,260 ). Solving gives ( x = 8 ). Total hours = ( 40 + 8 = 48 ).

Algebra

6. Question

Solve for ( x ):

- A) 3

- B) 6

- C) 9

- D) 12

- E) 15

Answer: C) 9.

Explanation: Simplify the left side: , we find ( x = 9 ).

Question 7:

If , what are the values of ( x )?

- A)

- B)

- C)

- D)

- E)

Answer: A)

E;xplanation: Simplify to . Therefore,

Question 8:

Solve for ( y ) in terms of ( x ) if ( 4x - 5y = 20 ).

- A)

- B)

- C)

- D)

- E)

Answer: B)

Explanation: Rearranging gives ( 5y = 20 - 4x ). Thus,

Question 9:

If ( x + 1 = 3(x - 2) ), what is the value of ( x )?

- A) 1

- B) 2

- C) 3

- D) 4

- E) 5

Answer: D) 4.

Explanation: Simplify: ( x + 1 = 3x - 6 ). Solving ( 7 = 2x ) gives ( x = 4 ).

Question 10:

For what value of ( k ) will the system of equations ( 2x + 3y = 12 ) and ( 4x + ky = 24 ) have no solution?

- A) 3

- B) 6

- C) 9

- D) 12

- E) 15

Answer: B) 6.

Explanation: The equations are parallel if the slopes are the same: , so ( k = 6 ).

Geometry

Question 11:

A rectangle has a width of 6 units and a perimeter of 32 units. What is the length of the rectangle?

- A) 8

- B) 10

- C) 12

- D) 14

- E) 16

Answer: B) 10.

Explanation: Perimeter formula: . Solving ( 2(l + 6) = 32 ) gives ( l = 10 ).

Question 12:

In a circle with a radius of 10, what is the area of a sector with a central angle of 72 degrees?

- A)

- B)

- C)

- D)

- E)

Answer: B)

Explanation: Sector area =

Question 13:

A right triangle has legs of lengths 8 and 15. What is the length of the hypotenuse?

- A) 16

- B) 17

- C) 18

- D) 19

- E) 20

Answer: B) 17.

Explanation: Using Pythagorean theorem:

Question 14:

What is the volume of a cube with a surface area of 54 square units?

- A) 18

- B) 27

- C) 36

- D) 45

- E) 64

Answer: B) 27.

Explanation: Surface area = . Solving ( s = 3 ). Volume = .

Question 15:

In a parallelogram, if one angle measures 70 degrees, what is the measure of an adjacent angle?

- A) 70

- B) 90

- C) 100

- D) 110

- E) 120

Answer: D) 110.

Explanation: Adjacent angles in a parallelogram are supplementary: ( 180 - 70 = 110 ).

Data Analysis

Question 16:

The weights of 5 dogs are 10, 12, 15, 15, and 20 pounds. What is the median weight?

- A) 12

- B) 13

- C) 15

- D) 16

- E) 17

Answer: C) 15.

Explanation: The median is the middle value of the ordered list: 10, 12, 15, 15, 20.

Question 17:

If 60% of a class of 50 students passed a test, how many students did not pass?

- A) 10

- B) 15

- C) 20

- D) 25

- E) 30

Answer: B) 20.

Explanation: Passed = . Not passed = ( 50 - 30 = 20 ).

Question 18:

A survey showed that 40% of respondents prefer coffee, 35% prefer tea, and the rest prefer neither. If 200 people responded, how many prefer neither?

- A) 50

- B) 60

- C) 70

- D) 80

- E) 90

Answer: C) 50.

Explanation: Neither = ( 100% - (40% + 35%) = 25% ). Therefore, .

Question 19:

A store sells apples in bags of 6. If a customer buys 4 bags, what is the standard deviation of the number of apples bought?

- A) 0

- B) 2

- C) 3

- D) 4

- E) 5

Answer: A) 0.

Explanation: Since all bags have the same number of apples (6), there's no variation, so the standard deviation is 0.

Question 20:

If the probability of rain on any given day is 0.3, what is the probability that it will rain exactly 2 out of the next 3 days?

- A) 0.189

- B) 0.216

- C) 0.243

- D) 0.267

- E) 0.300

Answer: B) 0.216.

Explanation: Use the binomial probability formula:

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