Questions and Solutions for GRE Practice Test Second Edition. (Quantitative Reasoning Section 6 Part 1)

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These are explanations and step by step solutions for the second edition of the ETS Practice Book for the Paper-Based GRE Revised General Test (Quantitative Reasoning Section 6).

GRE Practice Test Second Edition - Complete Paper (pdf)

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 by sight or by measurement.

Coordinate systems, such as xy-planes and number lines, are drawn to scale; therefore, you can read, estimate, or compare quantities in such figures by sight or by measurement.

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 by sight or by measurement.

For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices and fill in the corresponding circle to the right of 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.

A symbol that appears more than once in a question has the same meaning throughout the question.

GRE Practice Test Second Edition. (Quantitative Reasoning Section 6 solution for question 1)

The length of each side of equilateral triangle T is 6 times the length of each side of equilateral triangle X.

Quantity A

1. The ratio of the length of one side of T to the length of another side of T

Quantity B

The ratio of the length of one side of X to the length of another side of X

GRE Practice Test Second Edition. (Quantitative Reasoning Section 6 solution for question 2)

Of 30 theater tickets sold, 20 tickets were sold at prices between $10 and $30 each and 10 tickets were sold at prices between $40 and $60 each.

Quantity A

2. The average (arithmetic mean) of the prices of the 30 tickets

Quantity B

$50

GRE Practice Test Second Edition. (Quantitative Reasoning Section 6 solution for question 3)

x > 1

Quantity A

3. x/(x + 1)

Quantity B

-x/(1 - x)

GRE Practice Test Second Edition. (Quantitative Reasoning Section 6 solution for question 4)

In the xy-plane, the point (1, 2) is on line j, and the point (2, 1) is on line k. Each of the lines has a positive slope.

Quantity A

4. The slope of line j

Quantity B

The slope of line k

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Related Topics:

More GRE Resources

These are explanations and step by step solutions for the second edition of the ETS Practice Book for the Paper-Based GRE Revised General Test (Quantitative Reasoning Section 6).

GRE Practice Test Second Edition - Complete Paper (pdf)

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 by sight or by measurement.

Coordinate systems, such as xy-planes and number lines, are drawn to scale; therefore, you can read, estimate, or compare quantities in such figures by sight or by measurement.

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 by sight or by measurement.

For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices and fill in the corresponding circle to the right of 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.

A symbol that appears more than once in a question has the same meaning throughout the question.

GRE Practice Test Second Edition. (Quantitative Reasoning Section 6 solution for question 1)

The length of each side of equilateral triangle T is 6 times the length of each side of equilateral triangle X.

Quantity A

1. The ratio of the length of one side of T to the length of another side of T

Quantity B

The ratio of the length of one side of X to the length of another side of X

GRE Practice Test Second Edition. (Quantitative Reasoning Section 6 solution for question 2)

Of 30 theater tickets sold, 20 tickets were sold at prices between $10 and $30 each and 10 tickets were sold at prices between $40 and $60 each.

Quantity A

2. The average (arithmetic mean) of the prices of the 30 tickets

Quantity B

$50

x > 1

Quantity A

3. x/(x + 1)

Quantity B

-x/(1 - x)

GRE Practice Test Second Edition. (Quantitative Reasoning Section 6 solution for question 4)

In the xy-plane, the point (1, 2) is on line j, and the point (2, 1) is on line k. Each of the lines has a positive slope.

Quantity A

4. The slope of line j

Quantity B

The slope of line k

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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