Algebraic concepts on the GMAT are those normally covered in a first-year high school algebra course. The Quantitative Section does NOT cover the following skills and math areas: • Complex calculations involving large and/or unwieldy numbers • Advanced algebra concepts • Formal geometry proofs • Trigonometry • Calculus • Statistics (except for simple probability, arithmetic mean, and median) The following assumptions apply to all Quantitative questions: • All numbers used are real numbers. • All figures lie on a plane unless otherwise indicated. • All lines shown as straight are straight. Lines that appear “jagged” can be assumed to be straight (lines can look somewhat jagged on the computer screen). Problem Solving (22–23 questions) Problem Solving questions require you to work to a solution (a numerical value or other expression) and then find that solution among the five answer choices. Any of the Quantitative areas listed is fair game for a Problem Solving question. TEST DIRECTIONS The directions that follow are essentially what you’ll see during the pre-test tutorial and just prior to your first Problem Solving questions (you can access these directions at any time by clicking on the HELP button). Directions: Solve this problem and indicate the best of the answer choices given. Numbers: All numbers used are real numbers. Figures: A figure accompanying a Problem Solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie on a plane unless otherwise indicated. To review these directions for subsequent questions of this type, click on HELP. WHAT PROBLEM SOLVING QUESTIONS LOOK LIKE Let’s look at two Problem Solving questions that are similar to what you might see on the GMAT. (Answer choices are lettered A–E here. Remember, though, that on the actual GMAT, you’ll select among choices by clicking on one of five blank ovals, not letters.) This first problem is easy to understand, and no formulas or tricky math are needed to solve it. Among GMAT test takers, about 80 percent would answer this question correctly. NOTE Additional assumptions about figures (diagrams and graphics) are different for Problem Solving questions than for Data Sufficiency questions. Chapter 2: GMAT Questions: A First Look 33 www.petersons.com Village A’s population, which is currently 6,800, is decreasing at a rate of 120 each year. Village B’s population, which is currently 4,200, is increasing at a rate of 80 each year. At these rates, in how many years will the population of the two villages be equal? (A) 9 (B) 11 (C) 13 (D) 14 (E) 16 The correct answer is (C). One way to solve this problem is to subtract 120 from A’s population while adding 80 to B’s population—again and again until the two are equal—keeping track of the number of times you perform these simultaneous operations. (You’ll find that number to be 13.) But there’s a faster way to solve the problem that also helps you avoid computation errors. The difference between the two populations is currently 2600 (6800 2 4200). Each year that gap closes by 200 (120 1 80). So you can simply divide 2600 by 200 to determine the number of years for the gap to close completely. That’s easy math: 2600 4 200 5 13. Now here’s a more difficult Problem Solving question. To handle it, you need to understand rules involving exponents and their effect on the size and sign (positive or negative) of fractional numbers. Among GMAT test takers, only about 50 percent would respond correctly to this question. If 227 5 S 2 1 3 D k , what is the value of k ? (A) 29 (B) 23 (C) 2 1 3 (D) 1 3 (E) 3 34 PART I: GMAT Basics www.petersons.com The correct answer is (B). This question is asking you to determine the power that 2 1 3 must be raised to in order to obtain 227. First, look at the numbers in the question. Note that 227 5 (23) 3 . That’s a good clue that the answer to the question must involve the number 23. If the number we were raising to the power of k were 23, then the value of k would be 3. But the number we’re raising to the power is k is 2 1 3 , which is the reciprocal of 23. (By definition, the product of a number and its reciprocal is 1.) So you need to apply the rule that a negative exponent reciprocates its base. In other words, raising a base number to a negative power is the same as raising the base number’s reciprocal to the power’s absolute value. Therefore: S 2 1 3 D 23 5~23! 3 As you can see, that value of k is 23. KEY FACTS ABOUT GMAT PROBLEM SOLVING Important features of the Problem Solving format to keep in mind (some of these points are review): • Numerical answer choices are listed in order—from smallest in value to greatest in value. Notice in our first sample question that the numerical values in the answer choices got larger as you read down from A to E. That’s the way it is with every Problem Solving question whose answer choices are all numbers. There is one exception to this pattern. If a question asks you which answer choice is greatest (or smallest) in value, the answer choices will not necessarily be listed in ascending order of value—for obvious reasons. • Some Problem Solving questions will include figures (geometry figures, graphs, and charts). Most of the 5–8 geometry questions will be accompanied by some type of figure. Also, each Data Interpretation question will be accompanied by a chart or graph. • Figures are drawn accurately unless the problem indicates otherwise. Accompanying figures are intended to provide information useful in solving the problems. They’re intended to help you, not to mislead or trick you by their visual appearance. If a figure is not drawn to scale, you’ll see this warning near the figure: “Note: Figure not drawn to scale.” Data Sufficiency (14–15 questions) The Data Sufficiency format is unique to the GMAT; you won’t find it on any other standardized test. Each Data Sufficiency consists of a question followed by two statements—labeled (1) and (2). Your task is to analyze each of the two statements to determine whether it provides sufficient data to answer the question and, if neither suffices alone, whether both statements together suffice. NOTE Remember that on the actual GMAT screen, you’ll select your choice by clicking on one of five blank ovals instead of choosing among lettered answer choices. ALERT! In Data Sufficiency questions, figures are not necessarily drawn to scale. Chapter 2: GMAT Questions: A First Look 35 www.petersons.com Data Sufficiency problems cover the same mix of arithmetic, algebra, and geometry as Problem Solving questions. (Any of the Quantitative areas listed on page 32 is fair game for a Data Sufficiency question.) TEST DIRECTIONS The following directions are essentially what you’ll see during the pre-test tutorial and just prior to your first Data Sufficiency question. (You can access these directions at any time by clicking on the HELP button.) Notice that some of the directions are new. In other words, they don’t apply to Problem Solving questions. Directions: This Data Sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether: (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked; (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked; (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient; (D) EACH statement ALONE is sufficient to answer the question asked; (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed. Numbers: All numbers used are real numbers. Figures: A figure accompanying a Data Sufficiency problem will conform to the information given in the question, but will not necessarily conform to the additional information in statements (1) and (2). Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight. You may assume that positions of points, angles, regions, etc., exist in the order shown and that angle measures are greater than zero. All figures lie in a plane unless otherwise indicated. NOTE: In Data Sufficiency problems that ask you for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity. To review these directions for subsequent questions of this type, click on HELP. WHAT DATA SUFFICIENCY QUESTIONS LOOK LIKE As already noted, each Data Sufficiency consists of a question followed by two statements labeled (1) and (2). Let’s look at two examples, similar to what you’ll encounter on the GMAT. 36 PART I: GMAT Basics www.petersons.com (Answer choices are lettered A–E here. Remember, though, that on the actual GMAT, you’ll select among choices by clicking on one of five blank ovals, not letters.) This first question is a bit easier than average. Of all GMAT test takers, about 85 percent would respond correctly to it. How many quarts of oil will a car burn during a 3600-mile trip? (1) The car burns half a quart of oil every 1000 miles. (2) At a price of $1.50 per quart, the car uses $2.70 worth of oil during the trip. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient. (D) EACH statement ALONE is sufficient to answer the question asked. (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed. The correct answer is (D). To answer the question, you need to know the rate (the number of miles per quart) at which the car burns oil. Statement (1) provides the information you need. A half quart of oil is burned per 1000 miles; therefore, the car will burn 3.6 that amount over 3600 miles. Although you don’t need to do the math, the answer to the question is (3.6)(0.5) 5 1.8. You’ve narrowed the answer choices to (A) and (D). But can you see that statement (2) alone also provides the information you need to determine the rate? The amount of oil used 5 $2.70 4 $1.50. Again, although you don’t need to do the math, the quotient (and the answer to the question) is 1.8. Since either statement alone suffices to answer the question, the correct answer choice is (D). Chapter 2: GMAT Questions: A First Look 37 www.petersons.com This next Data Sufficiency question is a bit more difficult than average. Only about 55 percent of all GMAT test takers would respond correctly to it. What is the absolute value of the sum of two numbers? (1) The product of the two numbers is 6. (2) One number is 5 less than the other number. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not suffi- cient to answer the question asked. (B) Statement (2) ALONE is sufficient, but statement (1) alone is not suffi- cient to answer the question asked. (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient. (D) EACH statement ALONE is sufficient to answer the question asked. (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed. The correct answer is (C). Calling one number x and the other number y, statement (1) alone tells us only that xy 5 6, but gives no information about their sum. This narrows the answer choice options to (B), (C), and (E). Statement (2) alone tells us that the relationship between the two numbers can be written as y 5 x 2 5, but gives no information about their sum. The correct answer choice must be either (C) or (E). By considering statements (1) and (2) together, you can substitute x 2 5fory in the equation xy 5 6: x~x 2 5!56 x 2 2 5x 5 6 x 2 2 5x 2 6 5 0 You can factor the quadratic expression into two binomial factors, then find the roots of the equation—that is, the possible values of x: x 2 6 5 0orx 1 1 5 0 x 5 6or21 Hence, either x 5 6 and y 5 1, with sum 7, or x 521 and y 526, with sum 27. In either case, the absolute value of their sum is the same: 7. Since both statements together provide one and only one answer to the question, the correct answer choice is (C). You can also analyze this problem less formally. Based on statement (1) alone, try to think of some possibilities for the values of the two numbers that satisfy statement (1). Just using integers, the following four pairs should occur to you: 1 and 6, 2 and 3, 21 and 26, or 22 and 23. Since there’s more than one possibility, you can rule out answer choices (A) and (D). Statement (2) alone presents an infinite number of possibilities, doesn’t it? So you can also rule out choice (B). Together, statements (1) and (2) seem to rule out all integer pairs except 38 PART I: GMAT Basics www.petersons.com (1,6)and(21, 26). In either case, the absolute value of their sum is 7. But what about non-integers? Answering this question is where a bit of intuition or trial-and-error is required. You may try a few non-integer number pairs to satisfy yourself that none works. KEY FACTS ABOUT GMAT DATA SUFFICIENCY Keep in mind the following important features of the Data Sufficiency format (some of these points are review): • The answer choices are the exactly same for all Data Sufficiency questions. This is one feature that makes Data Sufficiency questions unique among other types of GMAT questions. • Data Sufficiency questions can vary widely in difficulty level. Assuming you’re familiar with their unique format, these questions are neither inherently easier nor more difficult than Problem Solving questions. The level of difficulty and complexity can vary widely (depending on the correctness of your responses to earlier questions). • A Data Sufficiency question that asks for a specific numerical value is answerable only if one and only one value results. Some, but not all, Data Sufficiency questions will ask for a particular numerical value. For example: What is the area of the circle? What is the value of x? What is the area of triangle ABC? How much did Sam pay for his book? • The two statements (1 and 2) will not conflict with each other. Perhaps you’re wondering which response you should choose—(D) or (E)—if you can answer the question with either statement alone, but get two conflicting answers. Don’t worry; this won’t happen. If you can answer the question using either statement alone, the answer will be the same in both cases. In other words, statements (1) and (2) will never conflict with one another. Why? The test makers design Data Sufficiency questions to avoid the “D vs. E” conundrum. • Figures are not necessarily drawn to scale, unless noted otherwise. Any figure accompanying a Data Sufficiency question will conform to the information in the question itself but will not necessarily conform to either statement (1) or (2). So although the figures are not designed to mislead you, they are not necessarily drawn to scale. • Calculating is not what Data Sufficiency is primarily about. Expect to do far less number crunching and equation solving for Data Sufficiency questions than for Problem Solving questions. What’s being tested here is your ability to recognize and understand principles, not to work step-by-step toward a solution. (That’s what Problem Solving is about.) TIP In Data Sufficiency questions, just as in Problem Solving questions, rely on the information in the question and statements, not on a figure’s appearance. Chapter 2: GMAT Questions: A First Look 39 www.petersons.com THE VERBAL SECTION (41 QUESTIONS, 75 MINUTES) The Verbal Section contains questions in three distinct formats: Critical Reasoning (14–15 questions) Sentence Correction (14–15 questions) Reading Comprehension (12–13 questions) Regardless of the format, each and every question in the Verbal Section offers five answer choices. Otherwise, each of the three formats is quite distinct. In the pages ahead, you can examine each one up close. Critical Reasoning (14–15 questions) Critical Reasoning questions are designed to measure your ability to understand, criticize, and draw reasonable conclusions from arguments. GMAT Critical Reasoning questions cover various aspects of reasoning and evaluating arguments. Here are the three basic aspects on which most of the exam’s 14–15 Critical Reasoning questions are based: • Identifying assumptions underlying an argument • Understanding the effect of additional evidence on an argument • Drawing strong inferences from stated premises Some GMAT Critical Reasoning questions will involve specific forms of reasoning or argument evaluation. Look for any of the following forms on your exam: • Recognizing a hypothesis that provides a good explanation for a set of observations • Recognizing an effective strategy, based on a set of premises and a stated objective • Making valid deductions from stated premises or recognizing an additional premise needed to validate a stated conclusion • Recognizing similarities in reasoning between different arguments TEST DIRECTIONS There are no special instructions for GMAT Critical Reasoning questions. The following simple directions are essentially what you’ll see during the pre-test tutorial and just prior to your first Critical Reasoning question (you can access these directions at any time by clicking on the HELP button): Directions: For this question, select the best of the answer choices given. WHAT CRITICAL REASONING QUESTIONS LOOK LIKE Each Critical Reasoning question consists of a paragraph-length passage, followed by a question about the passage and five answer choices. Let’s look at two Critical Reasoning 40 PART I: GMAT Basics www.petersons.com questions that are similar to what you might see on the GMAT. (Answer choices are lettered A–E here. Remember, though, that on the actual GMAT you’ll select among choices by clicking on one of five blank ovals, not letters.) This first question is a bit easier than average; among GMAT test takers, about 80 percent would answer it correctly. Ten years ago, Brand 1 was the most popular beer among consumers. Today, however, consumers buy twice as much Brand 2 beer as Brand 1, even though Brand 2 is nearly twice as expensive as Brand 1. Which of the following, if true, would best explain the apparent discrepancy described above? (A) Consumers of beer as a group consider a beer’s taste more important than its price. (B) Brand 2 beer has decreased in price over the last ten years. (C) Over the last ten years, wine has become a more popular beverage among consumers than beer. (D) Brand 2 beer is more readily available to consumers today than Brand 1 beer. (E) The minimum age at which a person can legally drink beer is lower today than ten years ago. The correct answer is (D). The best answer choice must explain why Brand 2 beer is more popular than Brand 1 beer despite its higher price. Only choice (D) provides an adequate explanation. If Brand 1 beer is not available, while Brand 2 is, then obviously a consumer will purchase Brand 2 and not Brand 1. Choice (A) might explain the discrepancy if consumers prefer the taste of Brand 2 beer over that of Brand 1 beer; however, we don’t know whether this is the case. Choice (B) might explain an increase in sales of Brand 2 beer; however, it fails to explain why Brand 2 is more popular today than Brand 1. Choice (C) might explain declining beer consumption generally; however, the popularity of wine is irrelevant to the popularity of one brand of beer compared to another brand of beer. Choice (E) might explain an increase in beer sales generally, but it does not explain why consumers buy more Brand 2 beer than Brand 1 beer. Chapter 2: GMAT Questions: A First Look 41 www.petersons.com This next Critical Reasoning question is a bit more difficult than average. Only about 50 percent of all GMAT test takers would respond correctly to it. Company Spokesperson: Charges that our corporation has discriminated against women in its hiring and promotion practices are demonstrably untrue. In fact, statistics show that greater than 60 percent of our corporation’s employees are women. The answer to which of the following questions would be most relevant in evaluating the argument above? (A) What is the average tenure, or length of employment, among the company’s women employees? (B) What percentage of the company’s employees in higher-level management positions are women? (C) What percentage of employees in competing companies are women? (D) How has the percentage of women employees at the company changed over time? (E) Is the chief executive officer of the company a man or a woman? The correct answer is (B). What makes this question difficult is that some of the incorrect answer choices are somewhat relevant to the argument, but their relevance is neither as clear nor as direct as choice (B). Let’s start with the correct answer. Although a large percentage of the company’s employees are women, it is entirely possible that these women generally occupy low-level positions while male employees generally hold higher-level jobs. One possible explanation for such a discrepancy would be that, when deciding whom to promote, the company discriminates against women. Hence, the answer to the question in choice (B) is highly relevant to evaluating the spokesperson’s denial that the company engages in this type of discrimination. The issue raised in choice (A) would be relevant to whether the company’s employee-termination practices are discriminatory, especially if the average tenure for women turned out to be significantly briefer than for men. However, the issue of tenure is not directly relevant to the company’s hiring or promotion practices. Nor is the issue raised in choice (C) directly relevant to the argument. For example, assume that the percentage of the company’s employees that are women is typical among firms in its industry. So what? Perhaps all of the firms discriminate against women or perhaps none does. As for choice (D), the company’s practices in the past are not directly relevant to its current practices. Choice (E) focuses on only one high-level employee, hardly a sufficient statistical sampling to prove a pattern of discrimination. Also, even with a female CEO, a company could very well engage in hiring and promotion practices that are unfair to women. 42 PART I: GMAT Basics www.petersons.com . to what you’ll encounter on the GMAT. 36 PART I: GMAT Basics www.petersons.com (Answer choices are lettered A–E here. Remember, though, that on the actual GMAT, you’ll select among choices. 5 6: x~x 2 5! 56 x 2 2 5x 5 6 x 2 2 5x 2 6 5 0 You can factor the quadratic expression into two binomial factors, then find the roots of the equation—that is, the possible values of x: x 2 6 5. currently 260 0 (68 00 2 4200). Each year that gap closes by 200 (120 1 80). So you can simply divide 260 0 by 200 to determine the number of years for the gap to close completely. That’s easy math: 260 0