## GRE Quantitative Reasoning Test 01

**Question 1 of 15**

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices:

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

**10x = 10,000,000,000**

**Quantity A: x**

**Quantity B: 12**

- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given

**Question 2 of 15**

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices:

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

**Line A is represented by the following equation:**

**10y + 20x = 50**

**Quantity A: The y-intercept of Line A**

**Quantity B: The slope of Line A**

- The relationship cannot be determined from the information given
- Quantity A is greater
- The two quantities are equal
- Quantity B is greater

**Question 3 of 15**

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices:

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

**Figure is not drawn to scale**

**Quantity A: y/x**

** Quantity B: 3**

- Quantity A is greater
- The two quantities are equal
- Quantity B is greater
- The relationship cannot be determined from the information given

**Question 4 of 15**

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices:

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

**The following table displays the income Jane’s business earned and the percentage of that income she paid in taxes for the first half of the year.**

**Month Income earned ($) Percentage paid in taxes (%)**

January 10,000 10

February 50,000 30

March 20,000 20

April 10,000 10

May 30,000 20

June 90,000 40

**Quantity A: The average of the income tax Jane paid**

**Quantity B: 22% of Jane’s average income**

- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given

**Question 5 of 15**

**If q is the smallest composite number greater than 2 and p is the smallest prime number less than 10, what is p/q?**

- 1
- 0.5
- 2
- 4

**Question 6 of 15**

(**1/25 ^{n}) >1**

**For which value of n is the above statement true?**

- n = 1
- n = √2
- n = 1/2
- n = -1/2

**Question 7 of 15**

**Figure NOT drawn to scale**

**Lines l and m are parallel. O is the center of the circle. The measure of angle d is 45°. The length of line RS is √2/2. Line RS forms a right angle with line m.**

**What is the measure of angle a?**

- 30°
- 60°
- 90°
- 45°

**Question 8 of 15**

**Figure NOT drawn to scale**

**Lines l and m are parallel. O is the center of the circle. The measure of angle d is 45°. The length of line RS is √2/2. Line RS forms a right angle with line m.**

**What is the length of line PR?**

- √(2)/2
- √2
- 2√2
- 1

**Question 9 of 15**

**Figure NOT drawn to scale**

**Lines l and m are parallel. O is the center of the circle. The measure of angle d is 45°. The length of line RS is √2/2. Line RS forms a right angle with line m.**

**What is the diameter of circle O?**

- 1√2
- 1
- 2√2
- √2/2

**Question 10 of 15**

Directions: If the question specifies how many answer choices to select, select exactly that number of choices. If the question does not specify how many answer choices to select, select all that apply.

â€¢ The correct answer may be just one of the choices or may be as many as all of the choices

â€¢ No credit is given unless you select all of the correct choices and no others

**Figure NOT drawn to scale**

Circle A represents students who major in liberal arts at a certain university. Circle B represents students who major in the life sciences at that university, and circle C represents engineering majors at the same university.

**What does A⋃B represent?**

- Only liberal arts students
- Only life science students
- Only the subset of liberal arts and life science double-majors
- All liberal arts and life science students

**Question 11 of 15**

Directions: If the question specifies how many answer choices to select, select exactly that number of choices. If the question does not specify how many answer choices to select, select all that apply.

â€¢ The correct answer may be just one of the choices or may be as many as all of the choices

â€¢ No credit is given unless you select all of the correct choices and no others

**Figure NOT drawn to scale**

**Circle A represents students who major in liberal arts at a certain university. Circle B represents students who major in the life sciences at that university, and circle C represents engineering majors at the same university.**

**What does A∩B represent?**

- Only liberal arts students
- Only life science students
- All liberal arts and life science students
- The subset of liberal arts and life science double-majors

**Question 12 of 15**

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices:

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

**A☼ B = (AB)2 +(A + B)2**

**Quantity A Quantity B**

**2☼5 150**

- The two quantities are equal
- The relationship cannot be determined from the information given
- Quantity B is greater
- Quantity A is greater

**Question 13 of 15**

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices:

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

**The electrical engineering department at a certain graduate school in the United States (US) has a total of 36 students. The department has twice as many male students as female students and three times as many international students as students who are US citizens.**

**Quantity A: The number of students who are US citizens**

**Quantity B: The number of female students**

- Quantity A is greater
- The two quantities are equal
- Quantity B is greater
- The relationship cannot be determined from the information given

**Question 14 of 15**

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices:

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

**R is the center of the circle below:**

**Figure NOT drawn to scale**

**Quantity A: Half the circumference**

**Quantity B: The area of triangle QRS**

- Quantity A is greater
- Quantity B is greater
- The relationship cannot be determined from the information given
- The two quantities are equal

**Question 15 of 15**

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices:

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

**The graph below shows the gross domestic product (GDP) in trillions of US dollars for four countries between 2000 and 2008.**

**Quantity A : The combined GDP of Japan, China, and Canada in 2008**

**Quantity B : The GDP of the US in 2008**

- Quantity B is greater
- The relationship cannot be determined from the information given
- The two quantities are equal
- Quantity A is greater

## Solution for GRE Quantitative Reasoning Test 01

**Question 1: B**

*To determine the value of x, write 10,000,000,000 in scientific notation. Because the number has 10 zeros, it can be written as 1010. Therefore, 1010 = 10,000,000,000 and x = 10. Since 12 is greater than 10, quantity B is greater.*

**Question 2: B**

*Write the equation for Line A in slope-intercept form: y = mx + b where m is the slope and b is the y-intercept.
10y + 20x = 50
10y = -20x + 50
y = -2x + 5
Therefore, the slope of Line A is -2 and the y-intercept of Line A is 5. Hence quantity A is greater.*

**Question 3: B**

*The ratio of the sides of both triangles is 3:4:5. Therefore, x = 4 and y = 12. Since y/x = 3, both quantities are equal.
*

**Question 4: A**

*Calculate the income tax Jane paid each month by multiplying the percentage paid in taxes by the monthly income earned.
Month Income earned ($) Percentage paid in taxes (%)
January 10,000 10
February 50,000 30
March 20,000 20
April 10,000 10
May 30,000 20
June 90,000 40*

Jane’s average income tax is (1,000 + 15,000 + 4,000 + 1,000 + 6,000 + 36,000)/6 = $10,500 .

*Jane’s average income is (10,000 + 50,000 + 20,000 + 10,000 + 30,000 + 90,000)/6 = $35,000, and 22% of $35,000 = $7,700. Therefore, quantity A is greater.*

**Question 5: B**

*A prime number is a positive integer that is divisible by exactly two numbers: 1 and itself. A composite number is a positive integer that is divisible by more than just 1 and itself. The number 1 is neither prime nor composite. The smallest composite number greater than 2 is 4, and the smallest prime number less than 10 is 2. Therefore, p = 2,q = 4, and p/q = 1/2 = 0.5*

**Question 6: D**

*This problem can be solved by the process of elimination. If n is 1, then 1/25 is less than 1. Similarly, if n = √2 or if n = 1/2, then 1/(25 ^{√2}) and 1/(25^{1/2}) are both less than 1. However, if n= -1/2, then 1/(25^{-1/2}) = (25^{1/2}) = √25 = 5, which is greater than 1.*

**Question 7: D**

*Angles a and d are alternate interior angles of parallel lines and are therefore congruent. Since angle d measures 45°, angle a measures 45° as well.*

**Question 8: A**

*Since RS forms a right angle with line m and angle d measures 45°, angle c measures 45° as well. The measure of angle a is also 45°, making triangle PRS a 45°-45°-90° triangle. Hence, both sides of the triangle are equal. Line RS measures √(2)/2 units long. Therefore, line PR is also √(2)/2 units long.*

**Question 9: B**

*Triangle PRS is a 45°-45°-90° triangle with sides equal to ^{√2}/_{2}. Therefore, the hypotenuse of triangle PRS is 1. The hypotenuse of triangle PRS is also the diameter of circle O. Hence, the diameter of circle O is 1.*

**Question 10: D**

*A⋃B is the union of A and B. The union of two sets is all elements that are in either A or B or both. Therefore, A⋃B is the set of all liberal arts and life science students.*

**Question 11: D**

*A∩B is the intersection of A and B. The intersection of two sets is the set of all elements that are in both A and B. Therefore, A∩B represents the subset of liberal arts and life science double-majors. According to the diagram, this intersection also represents students who have part-time jobs, but this is not included among the answer choices*

**Question 12: C**

*First calculate 2☼5.
2☼ 5 = [(2)(5)] ^{2} + (2 + 5)^{2}
2☼ 5 = 10^{2} + 7^{2}
2☼ 5 = 100 + 49
2☼ 5 = 149*

*Since 149 is less than 150, quantity B is greater.*

**Question 13: C**

*Let x represent the number of female students and let y represent the number of students who are US citizens. Because the department has 36 students and twice as many male as female students,
x + 2x = 36
3x = 36
x = 12.*

Hence, the department has 12 female students. Because the department has three times as many international students as US citizens,

y + 3y = 36

4y = 36

y = 9.

*The department has 9 students who are US citizens. Hence, quantity B is greater.*

**Question 14: A**

*The circumference of a circle is C = 2πr, where r is the radius of the circle. Since R is the center of the circle, the radius of the circle is r = 2, and the circumference is C = (2)( π)(2) = 4π. Hence, half the circumference is 2π. The area of a triangle is 0.5bh, where b and h are the base and height of the triangle, respectively. Segment SR represents the base of the triangle and segment QR represents the height. Both the base and height are radii of the circle. So, b = h = 2. Therefore, the area of the triangle, A = (0.5)(2)(2) = 2. Since 2π is greater than 2, quantity A is greater.*

**Question 15: A**

*One can roughly estimate the 2008 GDP of Canada, Japan, and China to be $2, $5, and $5 trillion, which totals $12 trillion. The 2008 GDP of the US is greater than $14 trillion. Therefore, quantity B is greater.*