C H A P T E R T The GRE Quantitative Section his chapter will help you prepare for the Quantitative section of the GRE The Quantitative section of the GRE contains 28 total questions: ■ ■ 14 quantitative comparison questions 14 problem-solving questions You will have 45 minutes to complete these questions This section of the GRE assesses general high school mathematical knowledge More information regarding the type and content of the questions is reviewed in this chapter It is important to remember that a computer-adaptive test (CAT) is tailored to your performance level The test will begin with a question of medium difficulty Each question that follows is based on how you responded to earlier questions If you answer a question correctly, the next question will be more difficult If you answer a question incorrectly, the next question will be easier The test is designed to analyze every answer you give as you take the test to determine the next question that will be presented This is done to ascertain a precise measure of your quantitative abilities, using fewer test questions than traditional paper tests would use 143 Team-LRN – THE GRE QUANTITATIVE SECTION –  Introduction to the Quantitative Section The Quantitative section measures your general understanding of basic high school mathematical concepts You will not need to know any advanced mathematics This test is a simple measure of your availability to reason clearly in a quantitative setting Therefore, you will not be allowed to use a calculator on this exam Many of the questions are posed as word problems relating to real-life situations The quantitative information is given in the text of the questions, in tables and graphs, or in coordinate systems It is important to know that all the questions are based on real numbers In terms of measurement, units of measure are used from both the English and metric systems Although conversion will be given between English and metric systems when needed, simple conversions will not be given (Examples of simple conversions are minutes to hours or centimeters to millimeters.) Most of the geometric figures on the exam are not drawn to scale For this reason, not attempt to estimate answers by sight These answers should be calculated by using geometric reasoning In addition, on a CAT, some geometric figures may appear a bit jagged on the computer screen Ignore these minor irregularities in lines and curves They will not affect your answers There are eight symbols listed below with their meanings It is important to become familiar with them before proceeding further < >     ⊥ xy x is greater than y xy x is less than or equal to y xy x is greater than or equal to y xy x is not equal to y xy x is parallel to y x⊥y x is perpendicular to y B A C angle A is a right angle 144 Team-LRN – THE GRE QUANTITATIVE SECTION – 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 145 Team-LRN – THE GRE QUANTITATIVE SECTION –  The Two Types of Quantitative Section Questions As stated earlier, the quantitative questions on the GRE will be either quantitative comparison or problemsolving 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-solving questions measure your ability to solve a problem using general mathematical knowledge This knowledge 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 b c d The quantity in column A is greater The quantity in column B is greater The two quantities are equal 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 Specific 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 146 Team-LRN – THE GRE QUANTITATIVE SECTION – ANSWER SHEET  a a a a a a a b b b b b b b c c c c c c c d d d d d d d e e e e e e e 10 11 12 13 14 a a a a a a a b b b b b b b c c c c c c c d d d d d d d 15 16 17 18 19 20 e e e e e e e a a a a a a b b b b b b c c c c c c d d d d d d e e e e e e 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 b c d The quantity in Column A is greater The quantity in Column B is greater The two quantities are equal There is not enough information given to determine the relationship of the two quantities Column A Column B z + w = 13 z+3=8 z w 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 x° l1 z° l2 y° l1  l2 x y –2(–2)(–5) (0)(3)(9) 147 Team-LRN – THE GRE QUANTITATIVE SECTION – Column A Column B 11 10 + x  1+3  2+5 + 5 Q R S P V T The length of the sides in squares PQRV and VRST is the area of shaded region PQS 36 R, S, and T are three consecutive odd integers and R  S  T R+S+1 S+T–1 S T U R V the area of the shaded rectangular region x2y  xy2  10 x y 148 Team-LRN – THE GRE QUANTITATIVE SECTION – Directions: For each question, select the best answer choice given 11 (42 – 6 )(25 + 11) a b 18 c 36 d 120 e 1,296 12 What is the remainder when 63 is divided by 8? a b c d e 13 B C A x° y° P In the figure above, BP = CP If x = 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 149 Team-LRN D – THE GRE QUANTITATIVE SECTION – 15 ft ft The rectangular rug shown in the figure above has a floral border 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 d – 3n  16 If  7n – d = 1, which of the following must be true about the relationship between d and n? a n is more than d b d is more than n c n is 3 of d d d is times n e d is times n 17 How many positive whole numbers less than 81 are NOT equal to squares of whole numbers? a b 70 c 71 d 72 e 73 150 Team-LRN – THE GRE QUANTITATIVE SECTION – 6x –5 18 Of the following, which could be the graph of – 5x  –3 ? a b c d e Use the following chart to answer questions 19 and 20 Below HS Graduation 16% College Grad 20% Post-Graduate Education 4% High School Grads 60% 19 If the chart is drawn accurately, how many degrees should there be in the central angle of the sector indicating the number of college graduates? a 20 b 40 c 60 d 72 e more than 72 20 If the total number of students in the study was 250,000, what is the number of students who graduated from college? a 6,000 b 10,000 c 50,000 d 60,000 e more than 60,000 151 Team-LRN – THE GRE QUANTITATIVE SECTION –  Answers b Since z + = 8, z must be Since z + w = + w = 13, w must be b Ida spent $102 on her skateboard ($75 + $27) Therefore, in selling the skateboard for $120, she got $18 in excess of what she spent c In the figure, y = z because they are vertical angles Also, since l1  l2, z = x because they are corresponding angles Therefore, y = x b (–2)(–2)(–5) is less than zero because multiplying an odd number of negative numbers results in a negative value Since (0)(3)(9) = 0, column B is greater d The value of 10 + x is unknown because the value of x is not given, nor can it be found Therefore, it is impossible to know if the sum of this expression is greater than or equal to 11 4 1+3    a By looking at the first value, you know that 2 + 5  Since  + = and is  1, you know that column A is greater c In the figure, the two squares have a common side, RV, so that PQST is a 12 by rectangle Its area is therefore 72 You are asked to compare the area of region PQS with 36 Since diagonal PS splits region PQST in half, the area of region PQS is 2 of 72, or 36 b It is given that R, S, and T are consecutive odd integers, with R  S  T This means that S is two more than R, and T is two more than S You can rewrite each of the expressions to be compared as follows: R + S + = R + (R + 2) + = 2R + S + T – = (R + 2) + (R + 4) – = 2R + Since  3, then 2R +  2R + You might also notice that both expressions to be compared contain S: S + (R + 1) and S + (T – 1) Therefore, the difference in the two expressions depends on the difference in value of R + and T – Since T is four more than R, T –  R + a You must determine the area of the shaded rectangular region It is given that VR = 2, but the length of VT is not given However, UV = and TU = 3, and VTU is a right triangle, so by the Pythagorean theorem, VT = Thus, the area of RVTS (the shaded region) is 2, or 10, which is greater than 10 b It is given that x2y  and xy2  0, so neither x nor y can be If neither x nor y can be 0, then both x2 and y2 are positive By the first equation, y must also be positive; by the second equation, x must be negative That is, x   y 11 c (42 – 6 )(25 + 11) = (36)(3 6)  = 36  36  = 6 = 36 152 Team-LRN ...– THE GRE QUANTITATIVE SECTION –  Introduction to the Quantitative Section The Quantitative section measures your general understanding of basic high school mathematical concepts... point Then, to determine the placement of the decimal point in the answer, count the numbers located to the right of the decimal point in the decimals being multiplied The total numbers to the. .. numerator The denominator remains the same in the improper fraction 158 Team-LRN – THE GRE QUANTITATIVE SECTION – For example, convert 53 to an improper fraction First, multiply the denominator by the