# Full-Length GRE Math Practice Test

Taking a Full-length GRE Math practice test is the best way to help you get familiar with the test format and feel more confident. Not only will this help you measure your exam readiness and solidify the concepts you’ve learned, but it is the best way to simulate test day.

To help you get the best out of this complete and realistic GRE Math practice test and prepare your mind and body for the actual test, we recommend that you treat this practice test as a real test. Prepare scratch papers, a pencil, a timer, and a calculator, and take the test in one sitting and follow the time limits to the minute.

Take the following full-length GRE Math practice test to simulate the test day experience. After you’ve finished, score your tests using the answer keys.**Good luck!**

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**Time to refine your Math skills with a practice test**

Take a REAL GRE Mathematics test to simulate the test day experience. After you’ve finished, score your test using the answer key.

**Before You Start**

- You’ll need a pencil, a calculator, and a timer to take the test.
- It’s okay to guess. You won’t lose any points if you’re wrong. So be sure to answer every question.
- After you’ve finished the test, review the answer key to see where you went wrong.
**Calculators are permitted for GRE****Math Test.**- Use the answer sheet provided to record your answers.
- The GRE Mathematics test contains a formula sheet, which displays formulas relating to geometric measurement and certain algebra concepts. Formulas are provided to test-takers so that they may focus on application, rather than the memorization, of formulas.
- For each multiple-choice question, there are five possible answers. Choose which one is best.

**Good Luck!**

**Best GRE Math*** *Prep Resource for 2022

*Prep Resource for 2022*

## GRE Math Practice Test

**Section 120 questions**

**Total time for this section:**35 Minutes

You can use a basic calculator in this section.

1-

**Quantity A **

**Quantity A****Quantity B**

**Quantity B**

The least prime factor of 77

The least prime factor of 136

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

2- 4 percent of \(x\) is equal to 6 percent of \(y\), where \(x\) and \(y\) are positive numbers.

**Quantity A **

**Quantity A****Quantity B**

**Quantity B**

\(x\)

\(y\)

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

3- \(x\) is an integer greater than zero.

**Quantity A **

**Quantity A****Quantity B**

**Quantity B**

\((\frac{1}{x})^2\)

\((\frac{1}{x})^3\)

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

4- \(a\) is real number.

\(a>0\)

**Quantity A **

**Quantity A****Quantity B**

**Quantity B**

\(|a|\)

\(|-a|\)

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

5- The average weight of 22 girls in a class is 62 kg and the average weight of 38 boys in the same class is 74 kg. What is the average weight of all the 60 students in that class?

A. 62.5

B. 64.2

C. 66.8

D. 69.6

E. 71.5

6- The volume of a sphere with a diameter of length 6 is how many times the volume of a sphere with a diameter of length \(\sqrt{6}\)?

(Volume of a sphere \(= \frac{4}{3} πr^3\))

A. \(\sqrt{6}\)

B. \(6\)

C. \(6\sqrt{6}\)

D. \(12\)

E. \(12\sqrt{6}\)

7- What is the solution of the following system of equations?

\(\begin{cases}\frac{x}{4}-\frac{y}{2}=2\\y+2x=1\end{cases}\)

A. \(x=-2, y=1\)

B. \(x=-2,y=-3\)

C. \(x=2,y=-3\)

D. \(x=2,y=3\)

E. \(x=2,y=1\)

8- If \(y=3^6\) then what is the value of \(y^{\frac{\sqrt{y}}{9}}\)?

A. \(3^2\)

B. \(3^6\)

C. \(3^9\)

D. \(3^{12}\)

E. \(3^{18}\)

9- Emma and Sophia have a family business. The profit of their business will be divided between Emma and Sophia in the ratio 5 to 7 respectively.

**Quantity A **

**Quantity A****Quantity B**

**Quantity B**

The money Emma receives when the profit is $768.

The money Sophia receives when the profit is $540.

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

10- In the \(xy\)-plane, the point \((6, -2)\) and \((-4, 3)\) are on line A. Which of the following equations of lines is parallel to line A?

A. \(y=-x\)

B. \(y=-\frac{1}{2} x\)

C. \(y=\frac{2}{3} x\)

D. \(y=\frac{3}{2} x\)

E. \(y=2x\)

11- If \((x-3)^4=256\) which of the following could be the value of \((x-5)(x-4)\)?

A. \(-6\)

B. \(-4\)

C. \(4\)

D. \(6\)

E. \(8\)

12- The average of \(x\) , \(y\) and 4 is 6 and \(x-y=-2\)

What is the value of \(x×y\)?

A. 18

B. 24

C. 36

D. 48

E. 54

13- The surface area of a cylinder is \(216π \space cm^2\). If its height is \(12 \space cm\), what is the radius of the cylinder?

A. 6 cm

B. 9 cm

C. 15 cm

D. 18 cm

E. 21 cm

14- If \(40 \%\) of A is \(80 \%\) of B, then B is what percent of A?

A. \(5 \%\)

B. \(50 \%\)

C. \(100 \%\)

D. \(150 \%\)

E. \(300 \%\)

A library has 280 books that include Mathematics, Physics, Chemistry, English, and History.

Use the following graph to answer questions 15 to 17.

15- What is the product of the number of Chemistry and number of History books?

A. 932

B. 1,568

C. 2,352

D. 3,160

E. 4,850

16- What are the values of angle \(α\) and \(β\)?

A. \(54^\circ, 72^\circ\)

B. \(75^\circ, 64^\circ\)

C. \(54^\circ, 45^\circ\)

D. \(108^\circ, 72^\circ\)

E. \(110^\circ, 54^\circ\)

17- The librarians decided to move some of the books in the Chemistry section to the Mathematics section. How many books are in the Mathematics section if now \(α=\frac{2}{5} γ\)?

A. 20

B. 24

C. 32

D. 36

E. 44

18- If \((x-3)^2+2>4x+3\), then x can equal to which of the following?

A. 0

B. 1

C. 2

D. 3

E. 4

19- In how many ways can 8 cards be placed in 5 positions if any cards can be placed in any position?

A. 40

B. 45

C. 50

D. 56

E. 64

20- Let \(r\) and \(p\) be constants. If \(x^2+9x+r\) factors into \((x + 3)(x + p)\), the values of \(r\) and \(p\) respectively are?

A. 9, 3

B. 9, 6

C. 18, 3

D. 18, 6

E. The answer cannot be found from the information given.

**Section 220 questions**

**Total time for this section:**35 Minutes

You can use a basic calculator in this section.

21- \(n\) is a natural number and \(\frac{1}{5^n} <\frac{1}{625}\)

**Quantity A **

**Quantity A****Quantity B**

**Quantity B**

\(4\)

\(n\)

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

22- The average of 5, 7, and \(x\) is 7.

**Quantity A **

**Quantity A****Quantity B**

**Quantity B**

\(x\)

average of \(x-3,x,2x\)

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

23-

\(\frac{4}{5}<x<\frac{6}{7}\)

**Quantity A **

**Quantity A****Quantity B**

**Quantity B**

\(x\)

\(\frac{5}{6}\)

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

24-

**Quantity A **

**Quantity A****Quantity B**

**Quantity B**

\((-3)^3\)

\((3)^3\)

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

25- If \(160 \%\) of a number is 128, then what is \(60 \%\) of that number?

A. 36

B. 42

C. 48

D. 56

E. 64

26-

**Quantity A **

**Quantity A****Quantity B**

**Quantity B**

\(6-4×8+[2+30×6]÷2\)

\([3+5×(-8)]+2-[6×4]÷8\)

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

27- If \(|a|<1\), then which of the following is true? (\(b>0\))?

I. \(–b<ba <b\)

II. \(-a<a^2<a\) if \(a<0\)

III. \(-8<3a-5<-2\)

A. I only

B. II only

C. I and III only

D. III only

E. I, II, and III

28- The ratio of boys and girls in a class is 7:9. If there are 64 students in the class, how many more boys should be enrolled to make the ratio 1 : 1?

A. 6

B. 8

C. 9

D. 10

E. 12

29-

**Quantity A **

**Quantity A****Quantity B**

**Quantity B**

\(\frac{x^7}{7}\)

\((\frac{x}{7})^7\)

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

30- A-line l is parallel to the \(x\)-axis and passes through the point \((3,-2)\). What is the slope of the line (\(m\)) and its \(y\)-intercept?

A. \(m=∞, y-intercept =3\)

B. \(m=∞, y-intercept =-2\)

C. \(m=0, y-intercept =3\)

D. \(m=0, y-intercept =-2\)

E. \(m=3, y-intercept =-2\)

31- The length of a rectangle is \(\frac{7}{4}\) times its width. If the width is 12, what is the perimeter of this rectangle?

A. 33

B. 44

C. 52

D. 66

E. 75

32- The marked price of a computer is D dollar. Its price decreased by \(30\%\) in January and later increased by \(20 \%\) in February. What is the final price of the computer in D dollars?

A. 0.60 D

B. 0.68 D

C. 0.79 D

D. 0.84 D

E. 1.04 D

33- In the following figure, what is the perimeter of ∆ ABC if the area of ∆ ADC is 42?

A. 28

B. 32

C. 36

D. 48

E. The answer cannot be determined from the information given

34- Removing which of the following numbers will change the average of the numbers to 5?

1, 3, 5, 7, 9, 11

A. 3

B. 5

C. 7

D. 9

E. 11

__Questions 35 to 37 are based on the following data__

35- Between which two of the months shown was there a twenty-five percent increase in the number of Shoes sold?

A. January and February

B. February and March

C. March and April

D. April and May

E. May and June

36- During the six-month period shown, what is the median number of pants and mean number of shirts per month?

A. 86.5, 149.16

B. 88.5, 158.32

C. 88, 159.55

D. 87.66, 161.2

E. 86.23, 159.75

37- How many pants need to be added in February until the ratio of a number of shirts to a number of pants in February equals two-thirds of this ratio in January?

A. 24

B. 38

C. 46

D. 55

E. 61

38- In the following figure, ABCD is a rectangle. If \(a=\sqrt{5}\), and \(b=2a\), find the area of the shaded region. (the shaded region is a trapezoid)

A. \(\sqrt{5}\)

B. \(2\)

C. \(4\)

D. \(2\sqrt{5}\)

E. \(4\sqrt{5}\)

39- In the following figure, ABCD is a rectangle, and E and F are points on AD and DC, respectively, and DE = 5 and DF = 3. The area of ∆BED is 20, and the area of ∆BDF is 24. What is the perimeter of the rectangle?

A. 24

B. 28

C. 36

D. 42

E. 48

40- What is the product of all possible values of \(x\) in the following equation?

\(|2x+6-3x-7|=5\)

A. \(-24\)

B. \(-12\)

C. \(8\)

D. \(12\)

E. \(24\)

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