The Quantitative section covers four types of math: arithmetic, algebra, geometry, and data analysis. Arithmetic The types of arithmetic concepts you should prepare for in the Quantitative section include the following: ■ arithmetic operations—addition, subtraction, multiplication, division, and powers of real numbers ■ operations with radical expressions ■ the real numbers line and its applications ■ estimation, percent, and absolute value ■ properties of integers (divisibility, factoring, prime numbers, and odd and even integers) Algebra The types of algebra concepts you should prepare for in the Quantitative section include the following: ■ rules of exponents ■ factoring and simplifying of algebraic expressions ■ concepts of relations and functions ■ equations and inequalities ■ solving linear and quadratic equations and inequalities ■ reading word problems and writing equations from assigned variables ■ applying basic algebra skills to solve problems Geometry The types of geometry concepts you should prepare for in the Quantitative section include the following: ■ properties associated with parallel lines, circles, triangles, rectangles, and other polygons ■ calculating area, volume, and perimeter ■ the Pythagorean theorem and angle measure There will be no questions regarding geometric proofs. Data Analysis The type of data analysis concepts you should prepare for in the Quantitative section include the following: ■ general statistical operations such as mean, mode, median, range, standard deviation, and percentages ■ interpretation of data given in graphs and tables ■ simple probability ■ synthesizing information about and selecting appropriate data for answering questions – THE GRE QUANTITATIVE SECTION– 145  The Two Types of Quantitative Section Questions As stated earlier, the quantitative questions on the GRE will be either quantitative comparison or problem- solving questions. Quantitative comparison questions measure your ability to compare the relative sizes of two quantities or to determine if there is not enough information given to make a decision. Problem-solv- ing questions measure your ability to solve a problem using general mathematical knowledge. This knowl- edge is applied to reading and understanding the question, as well as to making the needed calculations. Quantitative Comparison Questions Each of the quantitative comparison questions contains two quantities, one in column A and one in column B. Based on the information given, you are to decide between the following answer choices: a. The quantity in column A is greater. b. The quantity in column B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given. Problem-Solving Questions These questions are essentially standard, multiple-choice questions. Every problem-solving question has one correct answer and four incorrect ones. Although the answer choices in this book are labeled a, b, c, d, and e, keep in mind that on the computer test, they will appear as blank ovals in front of each answer choice. Spe- cific tips and strategies for each question type are given directly before the practice problems later in the book. This will help keep them fresh in your mind during the test.  About the Pretest The following pretest will help you determine the skills you have already mastered and what skills you need to improve. After you check your answers, read through the skills sections and concentrate on the topics that gave you trouble on the pretest. The skills section is followed by 80 practice problems that mirror those found on the GRE. Make sure to look over the explanations, as well as the answers, when you check to see how you did. When you complete the practice problems, you will have a better idea of how to focus on your studying for the GRE. – THE GRE QUANTITATIVE SECTION– 146  Pretest Directions: In each of the questions 1–10, compare the two quantities given. Select the appropriate choice for each one according to the following: a. The quantity in Column A is greater. b. The quantity in Column B is greater. c. The two quantities are equal. d. There is not enough information given to determine the relationship of the two quantities. Column A Column B 1. z + w = 13 z + 3 = 8 zw 2. Ida spent $75 on a skateboard and an additional $27 to buy new wheels for it. She then sold the skateboard for $120. the money Ida received in excess of the total amount she spent $20 3. xy 4. –2(–2)(–5) (0)(3)(9) x° z° y° l 1 l 2 l 1 ʈ l 2 – THE GRE QUANTITATIVE SECTION– 147 1. abcde 2. abcde 3. abcde 4. abcde 5. abcde 6. abcde 7. abcde 8. abcde 9. abcde 10. abcde 11. abcde 12. abcde 13. abcde 14. abcde 15. abcde 16. abcde 17. abcde 18. abcde 19. abcde 20. abcde ANSWER SHEET Column A Column B 5. 11 10 + x 6. ᎏ 1 2 ᎏ + ᎏ 3 5 ᎏ ᎏ 1 2 + + 3 5 ᎏ 7. the area of shaded region PQS 36 8. R, S, and T are three consecutive odd integers and R Ͻ S Ͻ T. R + S + 1 S + T – 1 9. the area of the shaded 9 rectangular region 10. x 2 y Ͼ 0 xy 2 Ͻ 0 xy 2 R V S T U 4 3 Q R S P V T The length of the sides in squares PQRV and VRST is 6. – THE GRE QUANTITATIVE SECTION– 148 Directions: For each question, select the best answer choice given. 11. ͙(42 – 6 ෆ )(25 + ෆ 11) ෆ a. 6 b. 18 c. 36 d. 120 e. 1,296 12. What is the remainder when 6 3 is divided by 8? a. 5 b. 3 c. 2 d. 1 e. 0 13. In the figure above, BP = CP.Ifx = 120˚, then y = a. 30°. b. 60°. c. 75°. d. 90°. e. 120°. 14. If y = 3x and z = 2y, then in terms of x, x + y + z = a. 10x. b. 9x. c. 8x. d. 6x. e. 5x. A BC D P x° y° – THE GRE QUANTITATIVE SECTION– 149 15. The rectangular rug shown in the figure above has a floral border 1 foot wide on all sides. What is the area, in square feet, of the portion of the rug that excludes the border? a. 28 b. 40 c. 45 d. 48 e. 54 16. If ᎏ d 7n – – 3n d ᎏ = 1, which of the following must be true about the relationship between d and n? a. n is 4 more than d b. d is 4 more than n c. n is ᎏ 7 3 ᎏ of d d. d is 5 times n e. d is 2 times n 17. How many positive whole numbers less than 81 are NOT equal to squares of whole numbers? a. 9 b. 70 c. 71 d. 72 e. 73 9 ft. 6 ft. – THE GRE QUANTITATIVE SECTION– 150 . – 1 9. the area of the shaded 9 rectangular region 10. x 2 y Ͼ 0 xy 2 Ͻ 0 xy 2 R V S T U 4 3 Q R S P V T The length of the sides in squares PQRV and VRST is 6. – THE GRE QUANTITATIVE SECTION 148 Directions:. $20 3. xy 4. 2( 2) (–5) (0)(3)(9) x° z° y° l 1 l 2 l 1 ʈ l 2 – THE GRE QUANTITATIVE SECTION 147 1. abcde 2. abcde 3. abcde 4. abcde 5. abcde 6. abcde 7. abcde 8. abcde 9. abcde 10. abcde 11. abcde 12. . select the best answer choice given. 11. ͙( 42 – 6 ෆ ) (25 + ෆ 11) ෆ a. 6 b. 18 c. 36 d. 120 e. 1 ,29 6 12. What is the remainder when 6 3 is divided by 8? a. 5 b. 3 c. 2 d. 1 e. 0 13. In the figure