Free GRE Quantitative Practice

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Quantitative Reasoning.
25 Questions.
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Section Directions
For each question, indicate the best answer, using the directions given.
Notes: All numbers used are real numbers.
All figures are assumed to lie in a plane unless otherwise indicated.
Geometric figures, such as lines, circles, triangles, and quadrilaterals, are not necessarily drawn to scale. That is, you should not assume that quantities such as lengths and angle measures are as they appear in a figure. You should assume, however, that lines shown as straight are actually straight, points on a line are in the order shown, and more generally, all geometric objects are in the relative positions shown. For questions with geometric figures, you should base your answers on geometric reasoning, not on estimating or comparing quantities from how they are drawn in the geometric figure.
Coordinate systems, such as x y planes and number lines, are drawn to scale; therefore, you can read, estimate, or compare quantities in such figures from how they are drawn in the coordinate system.
Graphical data presentations, such as bar graphs, circle graphs, and line graphs, are drawn to scale; therefore, you can read, estimate, or compare data values from how they are drawn in the graphical data presentation.
For each of Questions 1 through 9, compare Quantity A and Quantity B, using the additional information given, if any. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaning throughout the question.
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.
Example 1:
Quantity A: 2 times 6
Quantity B: 2 + 6
Solution: Quantity A is equal to 12 and Quantity B is equal to 8, so the correct answer for Example 1 is answer choice A, Quantity A is greater.
Example 2:
Refer to the figure.

Figure for Example 2
Begin skippable figure description.
The figure shows triangle PQR, where P is the leftmost vertex of the horizontal base PR and vertex Q is above PR. Point S lies on horizontal base PR and appears to be the midpoint of PR. Line segment QS is drawn from vertex Q to point S. The lengths of PS and SR appear to be equal.
End skippable figure description.
Quantity A: PS
Quantity B: SR
Solution: The correct answer for Example 2 is answer choice D. The relationship between PS and SR cannot be determined from the information given since equal measures cannot be assumed, even though PS and SR appear to be equal in the figure.
Question 1.
Refer to the figure.

Figure for Question 1

Begin skippable figure description.
The figure shows two right triangles. One of the triangles has a leg of length 4 and a leg of length x, and a hypotenuse of length 8. The other triangle has two legs, each of which is of length 4, and a hypotenuse of length y.
End skippable figure description.
Quantity A: x
Quantity B: 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.
From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Question 2.
It is given that

open parenthesis, x minus 2y, close parenthesis, times open parenthesis, x + 2y, close parenthesis, = 4

Quantity A: x squared, minus, 4 times the quantity y squared
Quantity B: 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.
From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Question 3.
A certain recipe requires three halves cups of sugar and makes 2 dozen cookies.
(1 dozen = 12)
Quantity A: The amount of sugar required for the same recipe to make 30 cookies
Quantity B: 2 cups
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.
From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Question 4.
A power station is located on the boundary of a square region that measures 10 miles on each side. Three substations are located inside the square region.
Quantity A: The sum of the distances from the power station to each of the substations
Quantity B: 30 miles
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.
From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Question 5.
It is given that
6 is less than x, which is less than 7,
and
y = 8
Quantity A: the fraction x over y
Quantity B: 0.85
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.
From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Question 6.
Refer to the figure.

Figure for Question 6
Begin skippable figure description.
The figure accompanying this question consists of a circle and triangle B O A, where O is the center of the circle and A and B are points that lie on the circle. In the triangle, the measure of angle B O A is 60 degrees.
End skippable figure description.
It is given that O is the center of the circle and the perimeter of triangle B O A is 6.
Quantity A: The circumference of the circle
Quantity B: 12
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.
From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Question 7.
Quantity A: The standard deviation of a set of 5 different integers, each of which is between 0 and 10
Quantity B: The standard deviation of a set of 5 different integers, each of which is between 10 and 20
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.
From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.

Question 8.
It is given that x is greater than 1.
Quantity A: x times, the fourth power of, open parenthesis, x squared, close parenthesis
Quantity B: open parenthesis, x cubed, close parenthesis, to the third power
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.
From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Question 9.
It is given that x is not equal to 0.
Quantity A: the absolute value of x + the absolute value of negative 2
Quantity B: the absolute value of the quantity x minus 2
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.
From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Questions 10 through 25 have several different answer formats, including both selecting answers from a list of answer choices and numeric entry. With each question, answer format instructions will be given.
Numeric Entry Questions
These questions require a number to be entered by marking entries in a grid according to the following instructions
Your answer may be an integer, a decimal, or a fraction, and it may be negative.
Equivalent forms of the correct answer, such as 2.5 and 2.50, are all correct. Although fractions do not need to be reduced to lowest terms, they may need to be reduced to fit in the grid.
Enter the exact answer unless the question asks you to round your answer.
If a question asks for a fraction, the grid will have a built-in division slash. Otherwise, the grid will have a decimal point.

The instructions for marking the entries will depend on whether a regular print or a large print test is being used to record your answers. If your answers are being entered into a regular print edition of the test, the following instructions apply:
Start your answer in any column, space permitting. Fill in no more than one entry in any column of the grid. Columns not needed should be left blank.
Write your answer in the boxes at the top of the grid and fill in the corresponding circles. You will receive credit only if your grid entries are clearly marked, regardless of the number written in the boxes at the top.

If your answers are being entered into a large print edition of the test, instead of filling in circles on the grid in steps 5 and 6, you will be asked to circle those entries.
Question 10.
This question has five answer choices, labeled A through E. Select the best one of the answer choices given.
The system of equations
7x + 3y = 12, and
3x + 7y = 6
is given.
If x and y satisfy the system of equations given, what is the value of x minus y?
A. two thirds
B. three halves
C. 1
D. 4
E. 6
Select and indicate the best one of the answer choices given.
Question 11.
This question has five answer choices, labeled A through E. Select all the answer choices that apply.
In triangle ABC, the measure of angle A is 25° and the measure of angle B is greater than 90°. Which of the following could be the measure of angle C?
Indicate all such measures.
A. 12°
B. 15°
C. 45°
D. 50°
E. 70°
Select and indicate all the answer choices that apply. The correct answer to a question of this type could consist of as few as one, or as many as all five of the answer choices.
Question 12.
This question has five answer choices, labeled A through E. Select the best one of the answer choices given.
What is the least integer n such that the fraction with numerator 1, and denominator 2 to the power n is less than 0.001 ?
A. 10
B. 11
C. 500
D. 501
E. There is no such least integer.
Select and indicate the best one of the answer choices given.
Question 13.
This question has five answer choices, labeled A through E. Select the best one of the answer choices given.
In the sunshine, an upright pole 12 feet tall is casting a shadow 8 feet long. At the same time, a nearby upright pole is casting a shadow 10 feet long. If the lengths of the shadows are proportional to the heights of the poles, what is the height, in feet, of the taller pole?
A. 10
B. 12
C. 14
D. 15
E. 18
Select and indicate the best one of the answer choices given.
Question 14.
This question has five answer choices, labeled A through E. Select the best one of the answer choices given.
If k is the smallest prime number greater than 21 and b is the largest prime number less than 16, then kb =
A. 299
B. 323
C. 330
D. 345
E. 351
Select and indicate the best one of the answer choices given.
Question 15.
This question does not have any answer choices; it is a numeric entry question.
To answer this question, enter a number in the answer space provided. The number entered cannot be a fraction.
The total amount of Judy’s water bill for the last quarter of the year was $40.50. The bill consisted of a fixed charge of $13.50 plus a charge of $0.0075 per gallon for the water used in the quarter. For how many gallons of water was Judy charged for the quarter?
To answer this question, enter a number in the answer space provided. The number can include a decimal point, and can be positive, negative, or 0. The number entered cannot be a fraction.
Question 16.
This question has five answer choices, labeled A through E. Select the best one of the answer choices given.
List R: 28, 23, 30, 25, 27
List S: 22, 19, 15, 17, 20
The median of the numbers in list R is how much greater than the median of the numbers in list S?
A. 8
B. 10
C. 12
D. 13
E. 15
Select and indicate the best one of the answer choices given.
Questions 17 through 20 are based on the following data.
Refer to the figure.

Data for Questions 17 through 20
Begin skippable data description.
The data is given in a bar graph. The title of the graph is Corporate Support for the Arts by Sector in 1988 and 1991. Under the title are two statements: “Total for 1988: $630 million” and “Total for 1991: $520 million”.
There are six sectors listed along the horizontal axis of the graph. Horizontal gridlines are drawn at 0%, 10%, 20%, 30%, and 40%.
For each of the six sectors the bars in the graph are as follows.
1. Financial Insurance, Real Estate sector. Bar for 1988, 5%. Bar for 1991, 26%.
2. Services sector. Bar for 1988, 17%. Bar for 1991, 22%.
3. Manufacturing sector. Bar for 1988, 31%. Bar for 1991, 20%.
4. Retail sector. Bar for 1988, 19%. Bar for 1991, 8%.
5. Wholesale sector. Bar for 1988, 8%. Bar for 1991, 6%.
6. Other sector. Bar for 1988, 20%. Bar for 1991, 18%.
End skippable data description.
Question 17.
This question does not have any answer choices; it is a numeric entry question.
To answer this question, enter a number in the answer space provided. The number entered cannot be a fraction.
The two corporate sectors that increased their support for the arts from 1988 to 1991 made a total contribution in 1991 of approximately how many million dollars?
Give your answer to the nearest 10 million dollars.
To answer this question, enter a number in the answer space provided. The number can include a decimal point, and can be positive, negative, or 0. The number entered cannot be a fraction.
Question 18.
This question has five answer choices, labeled A through E. Select the best one of the answer choices given.
How many of the six corporate sectors listed each contributed more than $60 million to the arts in both 1988 and 1991 ?
A. One
B. Two
C. Three
D. Four
E. Five
Select and indicate the best one of the answer choices given.
Question 19.
This question has five answer choices, labeled A through E. Select the best one of the answer choices given.
From 1988 to 1991, which corporate sector decreased its support for the arts by the greatest dollar amount?
A Services
B. Manufacturing
C. Retail
D. Wholesale
E. Other
Select and indicate the best one of the answer choices given.