Master gmat 2010 part 22 potx

• Whether one angle is larger (greater in degree measure) than another • Whether two lines are parallel or perpendicular • Whether two triangles are the same shape or size • Whether one segment of a pie chart is larger than another segment • Rely instead on the numbers and the textual information provided in the question and in the two statements. 11. In the figure above, is l 1 parallel to l 2 ? (1) q 1 y 5 s 1 w (2) p 1 x 5 180 The correct answer is (B). If you were to rely on the appearance of the figure, you’d see that the two lines look parallel. But remember: When it comes to GMAT Data Sufficiency, never measure with your eye! Rely instead on the numbers and other information in the problem. Here’s how to analyze this problem. Vertical angles (formed by intersecting lines) are always congruent. Thus, q 5 s and y 5 w. Accordingly, q 1 y must equal s 1 w in any event, and statement (1) alone does not suffice to answer the question. Given statement (2) alone, since p and x are supplementary, p must equal w (because w 1 x 5 180). Thus, corresponding angles are congruent and the two lines are parallel. KEYS TO SUCCESSFUL GMAT DATA SUFFICIENCY Here are some basic tips for solving Data Sufficiency problems. Apply these keys to the Practice Tests in Part VI, and then review them again just before exam day. Memorize the Answer Choices Don’t just learn the directions—memorize the answer choices. (Remember: they are always the same.) This way you’ll save time because you won’t need to refer to them for every question. Be Sure to Consider Each Statement Alone After analyzing statement (1), you’ll be surprised how difficult it can be to purge the information in statement (1) from your mind and start with a clean slate in considering statement (2). Be alert at all times to this potential problem. Chapter 8: Data Sufficiency and Analysis 193 www.petersons.com Don’t Do More Work Than Necessary Keep in mind that the Data Sufficiency format does not require you to answer the question. So once you’ve convinced yourself that a statement (1 or 2) suffices to answer the question, stop right there! You’d only be wasting your precious time by figuring out the answer itself. QUESTION 1 Once you recognized that each statement provides the missing piece to compute Judith’s ring cost, you know the correct answer is (D). There’s no need to do the math. Don’t Perform Endless Calculations You shouldn’t have to do involved calculations to get to the answer in a Data Sufficiency question. A few simple calculations may be required. But if you’re doing a lot of number crunching, you’ve probably missed the mathematical principle the question is asking about. QUESTION 2 Had we not used an organized approach to the problem, we would have had no choice but to start plugging in digit after digit (0 through 9). The more number crunching, the greater the chance for error. Look for a Quicker, More Intuitive Route to the Correct Answer The GMAT is testing, among other skills, your ability to find ingenious, unconventional, and intuitive solutions to conventional problems. Always look for a shortcut to performing calculations. You’ll save time, and you’ll avoid common computational errors. QUESTION 2 As you tackle more questions like question 2, you’ll learn to recognize when an answer depends on which values are used, and you won’t have to bother plugging in “test” numbers. Never Rely Solely on a Diagram or Figure Although a figure will conform to the information in the question, it won’t necessarily conform to either statement (1) or (2). So don’t use a Data Sufficiency figure to estimate or measure values, shapes, lengths, or other sizes. For example, don’t rely on a figure’s appearance to determine whether: • One line segment is longer than another • One angle is larger (greater in degree measure) than another • Two lines are parallel or perpendicular • Two triangles are the same shape or size • One segment of a pie chart is larger than another segment Rely instead on the numbers and textual information provided in the question and statements. 194 PART IV: GMAT Quantitative Section www.petersons.com QUESTION 4 In the figure, it appears that AB is equal in length to AC. If you had relied on the figure, your response to the question would have been wrong! Consider All the Possibilities for Unknowns When analyzing a Data Sufficiency question involving unknowns (variables such as x and y), unless the question explicitly restricts their value, consider positive and negative values, as well as fractions and the numbers zero (0) and 1. If the answer to the question depends on what kind of value you plug in, then the correct answer must be (E). QUESTION 3 We needed to consider negative as well as positive numbers; otherwise, we would have gotten the answer wrong. Look for Two Statements That Say Essentially the Same Thing Check to see if the two statements provide essentially the same information—just in a slightly different form. If they’re the same, you know the correct answer choice must be either (D) or (E). QUESTION 1 Notice that the two statements provided the same information—just in different forms. Check Each Statement for Numbers Needed to Answer the Question Use this approach for any Data Sufficiency problem involving formulas and calculations and when the question asks for a number. In a problem involving rate of motion (speed), for instance, if the question asks for a speed but does not provide the time (or does not provide the distance), rule out a statement that doesn’t supply the missing piece of the formula. QUESTION 3 In analyzing this question, we recognized early that neither statement alone supplied the numbers we needed. Don’t Try to Do All the Work in Your Head As with Problem Solving questions, don’t try to do too much work in your head. Avoid careless errors by using your pencil and scratch paper for all but the simplest mathematical steps. (Remember: Scratch paper and pencils will be provided at the testing center.) QUESTION 3 How far would you get with Question 3 without doing some pencil work—at a minimum, scratching out the two statements in different forms? Not very far! Chapter 8: Data Sufficiency and Analysis 195 www.petersons.com If Short on Time, Make a Reasoned Guess by Eliminating Answer Choices Keep in mind that if statement (1) alone is insufficient to answer the question, you can eliminate choices (A) and (D). On the other hand once you’ve determined that one of the statements alone is sufficient, you can eliminate choices (C) and (E). At this point, your odds of guessing correctly are 1 in 3, which is a lot better than 1 in 5 for a completely random guess. So if you’re having trouble analyzing one statement but are confident that the other statement is sufficient alone, make a guess and move on to the next question. QUESTIONS 1–4 In any of the four example questions, we could have stopped part way through our analysis and taken a reasoned guess. Remember: If you can get as far as ruling out one answer choice, you can rule out two. At that point, your odds look pretty good. THE 5-STEP PLAN FOR DATA ANALYSIS PROBLEMS Now that we’ve reviewed the basic strategies for solving Data Sufficiency problems, let’s try to tackle another special type of GMAT Quantitative problem, which the test makers call Data Analysis. This type of question is designed to gauge your ability to read and analyze data presented in graphical form and to calculate figures such as percentages, ratios, fractions, and averages based on the numbers you glean from the data. They can appear in either of the two basic formats: Problem Solving and Data Sufficiency. Expect to find two to four Data Analysis questions (typically in sets of two questions) interspersed with other questions in the GMAT Quantitative section. Each question in a set pertains to the same graphical data and each involves either one or two distinct graphical displays. Four types appear most frequently: Pie charts Tables Bar graphs Line graphs Here’s a 5-step approach that will help you to handle any set of Data Analysis questions: Look at the “big picture” first Read the entire question very carefully and look for a shortcut Perform the steps required to get the answer Check all answer choices for your own answer Check your calculations carefully We’ll apply this approach to two sample Data Analysis questions later in this chapter. 196 PART IV: GMAT Quantitative Section www.petersons.com Step One: Look at the “Big Picture” First Before plunging into the question(s), read all the information above and below the figure(s). Look particularly for: • Totals (dollar figures or other numbers) • Whether the numbers are in thousands or millions • How two or more figures are labeled • Whether graphical data are expressed in numbers or percentages Step Two: Read the Entire Question Very Carefully and Look for a Shortcut As you read, divide the question into parts, each of which involves a distinct step in getting to the answer. Pay particular attention to whether the question asks for: • An approximation • A percentage or a raw number • A comparison • An increase or a decrease In breaking the question down into tasks, look for a shortcut to save yourself work. Step Three: Perform the Steps Required to Get the Answer As you work, round numbers up or down (but not too far). Step Four: Check All Answer Choices for Your Own Answer If the question asks for a number, find the choice closest to your answer. Look for other answer choices that are “too close for comfort.” If you see any, or if your solution is nowhere near any of the choices, go to Step 5. Step Five: Check Your Calculations Carefully Make sure that the value and form (number, percentage, total, etc.) of your solution conforms to what the question asks. Check your rounding technique. Did you round off in the wrong direction? Did you round off too far? Chapter 8: Data Sufficiency and Analysis 197 www.petersons.com Sample Questions Both of these questions are based on the same two pie charts. INCOME AND EXPENSES–DIVISIONS A, B, C, AND D OF XYZ COMPANY (YEAR X) INCOME (Total Income = $1,560,000) EXPENSES (Total Expenses = $495,000) 12. During year X, by approximately what amount did Division C’s income exceed Division B’s expenses? (A) $125,000 (B) $127,000 (C) $140,000 (D) $180,000 (E) $312,000 13. With respect to the division whose percent of total income exceeded its percent of total expenses by the greatest amount among the four divisions, by approximately what amount did the division’s income exceed its own expenses? (A) $69,000 (B) $90,000 (C) $150,000 (D) $185,000 (E) $240,000 Before learning and applying the 5 steps, note the following key features of Data Analysis question sets: • The questions tend to be long and wordy. Get used to it; that’s the way the test makers design them. You’ll probably find that you have more trouble interpreting the questions than the figures. • Bar graphs and line charts are drawn to scale. Pie charts are not necessarily drawn to scale (you’ll see a note letting you know that it’s not). Visual scale is irrelevant when it comes to analyzing tables. • Important assumptions will be provided. Any additional information that you might need to know to interpret the figures will be indicated above and below the figures. (Be sure to read this information.) 198 PART IV: GMAT Quantitative Section www.petersons.com • Nearly all questions ask for an approximation. You’ll see some form of the word approximate in nearly all Data Analysis questions. This is because the test makers are trying to gauge your ability to interpret graphical date, not your ability to crunch numbers to the “nth” decimal place. • Many of the numbers used are almost round. This feature relates to the previous one. The GMAT rewards test takers who recognize that rounding off numbers (to an appropriate extent) will suffice to get to the right answer. So they pack Data Analysis figures with numbers that are close to “easy” ones. (The numbers in our pie chart set serve as good examples. For example, $1,560,000 is close to $1,500,000 million and $495,000 is close to $500,000.) • Figures are not drawn to deceive you or to test your eyesight. In bar graphs and line charts, you won’t be asked to split hairs to determine values. These figures are designed with a comfortable margin for error in visual acuity. Just don’t round up or down too far. Apply the 5-Step Plan Now let’s apply the steps you just learned to the above sample questions. Step 1: Size up the two charts and read the information above and below them. Notice that we’re only dealing with one company during one year here. Notice also that dollar totals are provided but that the pie segments are expressed only as percentages. That’s a clue that your main task in this set will be to calculate dollar amounts for various pie segments. Now read the first question. QUESTION 12 Question 12 is a moderately difficult question. Approximately 50% of test takers respond correctly to questions like it. Here’s the question again: 12. During year X, by approximately what amount did Division C’s income exceed Division B’s expenses? (A) $125,000 (B) $127,000 (C) $140,000 (D) $180,000 (E) $312,000 You already performed step 1, so move ahead to step 2. Step 2: This question involves three tasks: (1) calculate Division C’s income, (2) calculate Division B’s expenses, and (3) compute their difference. There’s no shortcut to these three tasks, so go on to step 3. Step 3: Division B’s expenses accounted for 26% of XYZ’s total expenses, given as $495,000. Rounding off these figures to 25% and $500,000, Division B’s expenses totaled approximately $125,000. Income from Division C sales was 20% of total XYZ income, given as $1,560,000. Rounding this total down to $1,500,000, income from Division C sales was approximately $300,000. Income from Division C sales exceeded Division B’s expenses by approximately $175,000. Chapter 8: Data Sufficiency and Analysis 199 www.petersons.com Step 4: The correct answer is (D). If you have extra time, go to step 5. Step 5: Make sure you started with the right numbers. Did you compare C’s income with B’s expenses (and not some other combination)? If you’re satisfied that the numbers you used were the right ones and that your calculations are okay, move on to the next question. QUESTION 13 Question 13 is a difficult question. Approximately 30% of test takers respond correctly to questions like it. Here’s the question again: 13. With respect to the division whose percent of total income exceeded its percent of total expenses by the greatest amount among the four divisions, by approximately what amount did the division’s income exceed its own expenses? (A) $69,000 (B) $90,000 (C) $150,000 (D) $185,000 (E) $240,000 Step 1: This is a complex question. First, you need to compare profitability among the four divisions. You can rule out Division B, since its percent of total expenses exceeded its percent of total income. That leaves Divisions A, C, and D. Step 2: For Divisions A, C, and D, compare percent of income and percent of expenses: Division A: 38% of total income and 35% of total expenses (3% difference) Division C: 20% of total income and 14% of total expenses (6% difference) Division D: 30% of total income and 25% of total expenses (5% difference) For Division C, (20%) ($1,560,000) 2 (14%) ($495,000) 5 $242,700. Step 3: Answer choice (E), $240,000, is the only one close to our approximation, so the correct answer is (E). Step 4: If you have time, rethink Step 3. Make sure you’re convinced that the difference in Division C’s percentages was greater than either A’s or D’s. Also ask yourself if $240,000 is in the right ballpark. If you’re confident in your analysis, move on to the next question. KEYS TO SUCCESSFUL GMAT DATA ANALYSIS Here are some basic tips you should follow for any type of Data Analysis question. Apply these keys to the Practice Tests in Part VI, then review them again just before exam day. Scroll Vertically to See the Entire Display Some vertical scrolling may be necessary to view the entire display, especially the information above and below the chart, graph, or table. Don’t forget to scroll up and down as you analyze each question. 200 PART IV: GMAT Quantitative Section www.petersons.com Don’t Confuse Percentages with Raw Numbers Most data analysis questions involve raw data as well as proportion—in terms of either percent, fraction, or ratio (usually percent). Always ask yourself: “Is the solution to this problem a raw number or a proportional number?” You can be sure that the testing service will “bait” you with appealing incorrect answer choices! Go to the Appropriate Chart (or Part of a Chart) for Your Numbers This point of advice may seem obvious; nevertheless, reading the wrong data is probably the leading cause of incorrect responses to data analysis questions! To ensure that you don’t commit this careless error, point your finger to the proper line, column, or bar on the screen; put your finger right on it, and don’t move it until you’re sure you’ve got the correct data. To Save Time, Round Off Numbers—But Don’t Distort Values Most Data Analysis questions ask for approximate values. So to save time, it’s okay to round off numbers; rounding off to the nearest appropriate unit or half-unit usually suffices to get to the correct answer. But don’t get too rough in your approximations. Also be sure to round off numerators and denominators of fractions in the same direction (either both up or both down), unless you’re confident that a rougher approximation will suffice. Otherwise, you’ll distort the value of the number. Handle Lengthy, Confusing Questions One Part at a Time Data Analysis questions can be wordy and confusing. Don’t panic. Keep in mind that lengthy questions almost always call for two discrete tasks. For the first task, read only the first part of the question. When you’re done, go back to the question and read the next part. Don’t Split Hairs Reading Line Charts and Bar Graphs These are the two types of figures that are drawn to scale. If a certain point on a chart appears to be about 40% of the way from one hash mark to the next, don’t hesitate to round up to the halfway point. (The number 5 is usually easier to work with than 4 or 6.) Formulate a Clear Idea About the Overall Size of the Number Called For The test makers pack Data Analysis questions with “sucker bait” answer choices for test takers who make common computational errors. The best way to keep yourself from falling into their trap is to ask yourself what sort of ballpark number you’re looking for in a correct answer. You might ask yourself: • Is it a double-digit number? • Is it a percentage that is obviously greater than 50 percent? • Is it a raw number in the thousands? By keeping the big picture in mind, you’ll catch the fact that you made an error in calculation. Chapter 8: Data Sufficiency and Analysis 201 www.petersons.com SUMMING IT UP • To successfully solve Data Sufficiency questions, size up the question first; size up the two statements and look for a shortcut to the correct answer; consider statement (1) alone; consider statement (2) alone; and consider both statements together if neither one alone is enough to answer the question. • Data Sufficiency questions focus on mathematical concepts rather than working toward a quantitative solution (as Problem Solving questions do)—so it’s important to size up the problem before trying to work the actual numbers or equations. • Watch for “red herring” statements that are irrelevant to the problem at hand. You’re looking for a statement that is sufficient to answer the question correctly. • Never assume that graphical figures are accurate. • For success in more advanced Data Analysis problems, handle parts one at a time before tackling the question as a whole. 202 PART IV: GMAT Quantitative Section www.petersons.com . For success in more advanced Data Analysis problems, handle parts one at a time before tackling the question as a whole. 202 PART IV: GMAT Quantitative Section www.petersons.com . instead on the numbers and textual information provided in the question and statements. 194 PART IV: GMAT Quantitative Section www.petersons.com QUESTION 4 In the figure, it appears that AB. carefully We’ll apply this approach to two sample Data Analysis questions later in this chapter. 196 PART IV: GMAT Quantitative Section www.petersons.com Step One: Look at the “Big Picture” First Before