Full-Length GRE Math Practice Test

\(a>0\) For education statistics and research, visit the National Center for Education Statistics.

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 2
20 questions
Total time for this section: 35 Minutes
You can use a basic calculator in this section.

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

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.

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-

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

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-

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-

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-

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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