The math concepts tested on the GMAT® Quantitative section basically consist of arithmetic, algebra, and geometry. Questions of each type will be mixed throughout the session, and many of the questions will require you to use more than just one concept in order to solve it. The majority of the questions will need to be solved using arithmetic. This area of mathematics includes the basic operations of numbers (addition, subtraction, multiplication, and division), properties and types of numbers, number theory, and counting problems. Algebra will also be included in a good portion of the section. Topics include using polynomials, com- bining like terms, using laws of exponents, solving linear and quadratic equations, solving inequalities, and simplifying rational expressions. Geometric concepts will appear in many of the questions and may be integrated with other concepts. These concepts require the knowledge and application of polygons, plane figures, right triangles, and formulas for determining the area, perimeter, volume, and surface area of an object. Each of these concepts will be dis- cussed in detail in Chapter 22. A portion of the questions will appear in a word-problem format with graphs, logic problems, and other discrete math areas scattered throughout the section. Remember that a few of the questions are experimental and will not be counted in your final score; however, you will not be able to tell which questions are experimental. CHAPTER About the Quantitative Section 19 317 The Quantitative section tests your overall understanding of basic math concepts. The math presented in this section will be comparable to what you encountered in middle school and high school, and the ques- tion level may seem similar to that on the SAT ® exam or ACT Assessment ® . Even though the questions are presented in different formats, reviewing some fundamental topics will be very helpful. This section tests your ability to use critical thinking and reasoning skills to solve quantitative problems.You will want to review how to solve equations, how to simplify radicals, and how to calculate the volume of a cube. However, the major- ity of the questions will also ask you to take the problem one step further to assess how well you apply and reason through the material. The two types of questions in the Quantitative section are problem solving and data sufficiency. You have already seen both types of questions in the pretest. Each type will be explained in more detail in the next section.  About the Types of Questions The two types of questions — problem solving and data sufficiency — each contains five answer choices. Both types of questions will be scattered throughout the section. Problem solving questions test your basic knowl- edge of math concepts — what you should have learned in middle school and high school. Most of these ques- tions will ask you to take this existing knowledge and apply it to various situations. You will need to use reasoning skills to analyze the questions and determine the correct solutions. The majority of the questions will contain a multistep procedure. When answering problem-solving questions, try to eliminate improba- ble answers first to increase your chances of selecting the correct solution. A Sample Problem Solving Question Directions: Solve the problem and choose the letter indicating the best answer choice. The numbers used in this section are real numbers. The figures used are drawn to scale and lie in a plane unless otherwise noted. Given integers as the lengths of the sides of a triangle, what is the maximum perimeter of a triangle where two of the sides measure 10 and 14? a. 27 b. 28 c. 48 d. 47 e. 52 Answer: d. Use the triangle inequality, which states that the sum of the two smaller sides of a triangle must be greater than the measure of the third side. By adding the two known sides of 10 + 14 = 24, this gives a maximum value of 23 for the third side because the side must be an integer. Since the perimeter of a polygon is the sum of its sides, the maximum perimeter must be 10 + 14 + 23 = 47. – ABOUT THE QUANTITATIVE SECTION – 318 The other type of question in this section is data sufficiency. Data sufficiency questions give an initial question or statement followed by two statements labeled (1) and (2). Given the initial information, you must determine whether the statements offer enough data to solve the problem. The five possible answer choices are as follows: a. Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself. b. Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself. c. The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2). d. The problem can be solved using EITHER statement (1) only or statement (2) only. e. The problem CANNOT be solved using statement (1) and statement (2) TOGETHER. This type of question measures the test taker’s ability to examine and interpret a quantitative problem and distinguish between pertinent and irrelevant information. To solve this particular type of problem, the test taker will have to be able to determine at what point there is enough data to solve a problem. Since these questions are seldom used outside of the GMAT exam, it is important to familiarize yourself with the for- mat and strategies used with this type of question as much as possible before taking the exam. Strategies can be used when answering data sufficiency questions. For example, start off by trying to solve the question solely by using statement (1). If statement (1) contains enough information to do so, then your only choice is between a (statement [1] only) or d (each statement alone contains enough information). If statement (1) is not enough information to answer the question, your choices boil down to b (statement [2] only), c (the statements need to be used together), or e (the problem cannot be solved using the infor- mation from both statements, and more information is needed). A Sample Data Sufficiency Question Directions: The following problem contains a question followed by two statements. Select your answer using the data in statement (1) and statement (2) and determine whether they provide enough information to answer the initial question. If you are asked for the value of a quantity, the information is sufficient when it is possible to determine only one value for the quantity. a. Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself. b. Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself. c. The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2). d. The problem can be solved using EITHER statement (1) only or statement (2) only. e. The problem CANNOT be solved using statement (1) and statement (2) TOGETHER. The numbers used are real numbers. If a figure accompanies a question, the figure will be drawn to scale according to the original question or information, but it will not necessarily be consistent with the infor- mation given in statements (1) and (2). – ABOUT THE QUANTITATIVE SECTION – 319 If x is a nonzero integer, is x positive? (1) x 2 is positive. (2) x 3 is positive. Answer: b. Substitute possible numbers for x.Ifx ϭ 2, then (2) 2 ϭ 4. If x ϭϪ2, then (Ϫ2) 2 ϭ 4, so state- ment (1) is not sufficient. Substituting into statement (2), if x ϭϪ2, then (Ϫ2) 3 ϭ (Ϫ2)(Ϫ2)(Ϫ2) ϭϪ8; the value is negative. If x ϭ 2, then 2 3 ϭ 2 ϫ 2 ϫ 2 ϭ 8; the value is positive. Therefore, from statement (2), x is positive. – ABOUT THE QUANTITATIVE SECTION – 320 . CHAPTER About the Quantitative Section 19 317 The Quantitative section tests your overall understanding of basic math concepts. The math presented in this section. perimeter must be 10 + 14 + 23 = 47. – ABOUT THE QUANTITATIVE SECTION – 318 The other type of question in this section is data sufficiency. Data sufficiency