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It's time to rock it on the GMAT. Check out these tips and tricks for answering tough questions.

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Cheat Sheet / Updated 04-05-2022

When you take the GMAT, make sure you take the required items with you to the test. Use these guidelines to help you get through the math, critical reasoning, sentence correction, and reading comprehensions questions — as well as for writing your analytical essay and conquering integrated reasoning questions.

View Cheat SheetArticle / Updated 04-06-2021

Each of the four Integrated Reasoning question types on the GMAT tests your analytical ability in a slightly different way, so your approach depends on the question format. Table analysis questions present you with a table that contains several columns of data, similar to the one shown. As you can see, a little bit of explanatory material precedes the table, but don’t waste too much time reading those words. Usually, everything you need to answer the question appears in the data table. The Sort By feature at the top of the table allows you to organize the information by column heading, an element that comes in handy when you analyze the three statements that follow the table. When you click on Sort By, a drop-down menu of all column headings appears. Clicking on the column heading in the menu causes the table to rearrange its data by that category. So, if you were to click on Cuisine Type in the drop-down menu in the preceding figure, the table would rearrange the order of the rows alphabetically so that all the American restaurants would be listed first, followed by the Asian, Italian, Latin, Mexican, Steakhouse, and Seafood restaurants, respectively. Using the information in the table, you decide whether the proper response to each statement is True or False, Inferable or Not Inferable, Yes or No, or some other similar either/or answer choice dictated by the specifications of the question. Then you indicate your choice by clicking on the circle next to the appropriate answer. These questions require you to manipulate data and make observations and calculations. Some of the most common calculations are statistical ones, such as percentages, averages, medians, and ratios, so table analysis questions can be some of the easiest questions to answer in the IR section. Here’s how to make sure you get them right: Jump to the question immediately. Most of the information you need appears in the table, so you rarely need to read the introductory paragraph that comes before the table. Glance at the column headings to get an idea of the type of information the table provides, and then move promptly to the question. Read the question carefully. You’re most likely to get tripped up on these questions simply because you haven’t read them carefully enough to figure out exactly what data they ask you to evaluate. Isolate the relevant column heading. Often, the key to answering a table analysis question is ordering the data properly. Quickly figure out which column provides you with the best way to arrange the data and sort by that column. For example, if you were asked for the neighborhood on the list with the most participating restaurants, you’d sort by neighborhood. Make accurate computations. Determine exactly what calculations the question requires and perform them accurately, either in your head or on the calculator. Based on the figure, for example, you could easily figure the restaurant with the greatest average daily number of meals sold by sorting by that column and glancing at the highest number. However, calculating which participating restaurant in the downtown neighborhood brought in the greatest average daily gross revenue may require the calculator to multiply each restaurant’s price per meal by its average daily number of meals sold. Make use of your noteboard. Keep track of more complex calculations on your noteboard. As you calculate each downtown restaurant’s average daily gross revenue, for example, record the results on your noteboard. Then you can easily compare the four values without having to memorize them. Table analysis questions may not require that you use all the data provided. For example, you didn’t need to evaluate Cuisine Type for any of the question parts in the example question. Don’t worry if you don’t use the data in some columns at all. Part of the task in answering table analysis questions is knowing what data is important and what’s irrelevant.

View ArticleArticle / Updated 04-01-2021

The coordinate plane doesn’t have wings, but it does have points that spread out infinitely. You may not have encountered the coordinate plane in a while (it isn’t something most people deal with in everyday life), so take just a minute to refresh your memory about a few relevant terms that may pop up on the GMAT. Although you won’t be asked to define the terms related to the coordinate plane, knowing what they mean is absolutely essential to answering GMAT math questions. Line dancing: Understanding coordinate geometry Before you get too engrossed in the study of coordinate geometry, ground yourself with an understanding of these essential terms: Coordinate plane: The coordinate plane is a perfectly flat surface where points can be identified by their positions, using ordered pairs of numbers. These pairs of numbers represent the points’ distances from an origin on perpendicular axes. The coordinate of any particular point is the set of numbers that identifies the location of the point, such as (3, 4) or (x, y). x-axis: The x-axis is the horizontal axis (number line) on a coordinate plane. The values start at the origin, which has a value of 0. Numbers increase in value to the right of the origin and decrease in value to the left. The x value of a point’s coordinate is listed first in its ordered pair. y-axis: The y-axis is the vertical axis (number line) on a coordinate plane. Its values start at the origin, which has a value of 0. Numbers increase in value going up from the origin and decrease in value going down. The y value of a point’s coordinate is listed second in its ordered pair. Origin: The origin is the point (0, 0) on the coordinate plane. It’s where the x- and y-axes intersect. Ordered pair: Also known as a coordinate pair, this duo is the set of two values that expresses the distance a point lies from the origin. The horizontal (x) coordinate is always listed first, and the vertical (y) coordinate is listed second. x-intercept: The value of x where a line, curve, or some other function crosses the x- The value of y is 0 at the x-intercept. The x-intercept is often the solution or root of an equation. y-intercept: The value of y where a line, curve, or some other function crosses the y- The value of x is 0 at the y-intercept. Slope: Slope measures how steep a line is and is commonly referred to as the rise over the run. What’s the point? Finding the coordinates You can identify any point on the coordinate plane by its coordinates, which designate the point’s location along the x- and y-axes. For example, the ordered pair (2, 3) has a coordinate point located two units to the right of the origin along the horizontal (x) number line and three units up on the vertical (y) number line. In the figure, point A is at (2, 3). The x-coordinate appears first, and the y-coordinate shows up second. Pretty simple so far, huh? On all fours: Identifying quadrants The intersection of the x- and y-axes forms four quadrants on the coordinate plane, which just so happen to be named Quadrants I, II, III, and IV. Here’s what you can assume about points based on the quadrants they’re in: All points in Quadrant I have a positive x value and a positive y. All points in Quadrant II have a negative x value and a positive y. All points in Quadrant III have a negative x value and a negative y. All points in Quadrant IV have a positive x value and a negative y. All points along the x-axis have a y value of 0. All points along the y-axis have an x value of 0. Quadrant I starts to the right of the y-axis and above the x-axis. It’s the upper-right portion of the coordinate plane. As shown in Figure 18-1, the other quadrants move counterclockwise around the origin. The figure also shows the location of coordinate points A, B, C, and D: Point A is in Quadrant I and has coordinates (2, 3). Point B is in Quadrant II and has coordinates (–1, 4). Point C is in Quadrant III and has coordinates (–5, –2). Point D is in Quadrant IV and has coordinates (7, –6). The GMAT won’t ask you to pick your favorite quadrant, but you may be asked to identify which quadrant a particular point belongs in.

View ArticleArticle / Updated 04-01-2021

The only Integrated Reasoning question type on the GMAT with more than one question that pertains to a set of data is the multi-source reasoning question. For this question type, the GMAT presents different kinds of information in a series of two or three tabs. Each tab conveys a relevant aspect of a set of circumstances. The topics of the scenarios vary greatly. You may have information concerning a certain scientific phenomenon, such as black holes or plant photosynthesis, or you may be asked to apply data that relates to business situations, such as hiring decisions or event planning. At least one of the tabs in the set contains several paragraphs of written information on a subject. Others may contain additional paragraphs or data contained in tables, charts, or graphs. You use the resources in all tabs to answer several questions, most of which have several parts. For example, this figure shows you the first tab for a sample multi-source reasoning scenario regarding guest reservations for a hotel’s wedding block. The email in this tab sets up the situation and provides you with the guidelines for the reservation. The following figure shows what you find when you click on the second tab: language from the contract between the Pearson family and the resort. When you click on the final tab, you may see a table with relevant data, such as the one in the following figure, which shows the wedding guest list and their reservation status. The multi-source reasoning questions appear in one of two formats: three-part table (similar to table analysis questions) or standard five-answer multiple-choice. Keep in mind that you have to answer all three parts of the first format to get credit for the one question. The multiple-choice format may be one of the easiest questions to answer in the IR section. You can use the process of elimination to narrow the answers, and you have to choose only one correct answer to get full credit for the question. The trickiest aspect of answering multi-source reasoning questions is sifting through the plethora of information to discover what’s relevant. Depending on the scenario, you may have to juggle information in tables, diagrams, articles, and so on to come up with correct answers. Here are some pointers to help you with the task: Summarize each tab. As you read through the information in each tab for the first time, record pertinent points to help you remember which tab holds what type of data. That way you don’t have to continually flip back and forth between screens as you answer questions. For example, summarize the contract details in the figure on your noteboard with quick notations such as 9/7, 8, & 9 = $135/night; < 3 nights = $150/night; before/after 9/7 or 9/9 = $175/night. Make connections. After you’ve seen the information in each tab, synthesize facts and figures from one tab with correlative data from another. Keep track of your findings on your noteboard. For example, you should notice as you read the information in the figures that you can correlate the data in the table in the final tab with the room-charge specifications in the second tab to figure out how much each guest will pay for resort rooms. Rely on what the test gives you. Some of the topics in multi-source reasoning scenarios may be familiar to you. Although familiarity may make the information more accessible to you, it may also influence you to answer questions based on what you know instead of what the exam tells you. For example, you shouldn’t answer any questions about the Pearson wedding sample scenario based on what you know about hotel booking from your own experience as a front-desk manager.

View ArticleArticle / Updated 04-01-2021

True to its name, the integrated reasoning section of the GMAT combines the critical reasoning skills tested in the verbal reasoning section with some of the math skills you use to solve quantitative reasoning questions. Therefore, if you’re well prepared for the GMAT’s math and verbal sections, you should do well in the IR section, too. Skills tested The most common math computations in the IR section involve these areas: Basic statistics, such as average, median, mode, and range Percentages Rate and distance Functions Geometry formulas You’ll need to apply these essentials of critical reasoning: Basic elements of logical arguments—premises, conclusions, and assumptions How to strengthen and weaken an argument Argument types—cause and effect, analogy, and statistical Integrated reasoning question format The IR section presents you with 12 questions, one question at a time, and you have 30 minutes to answer them. Almost every question has multiple parts. To get credit for answering a question correctly, you have to answer all of its parts correctly. You don’t receive partial credit for getting one part of the question correct. Unlike the verbal and quantitative reasoning sections, the IR section isn’t computer adaptive. So, the order in which you receive questions is preordained and not based on your performance. Your IR score is based on your answers to four types of questions. On average, you can expect to come across about three of each question type on the GMAT, but the actual number of questions of each type and the order in which they appear may vary. So, count on seeing at least a couple of each of these four question types crop up on your test: Table analysis: This three-part IR question offers you a spreadsheet of values that you can order in different ways by clicking the heading of each column. You use the data to make judgments about three pieces of information; each of your judgments has to be correct to get credit for the question. Two-part analysis: Based on a short, written explanation of a phenomenon, situation, or mathematical problem, you come up with the proper assertions or mathematical expressions that meet the two interrelated criteria presented in the question. Graphics interpretation: A graph or chart gives you all the data you need to complete the two missing pieces of information in one or two statements. You choose from a pull-down menu of several answer options to record your answers. Multi-source reasoning: These properly named questions present you with several sources of information, such as short passages, graphs and charts, and business documents, from which you draw logical conclusions to answer questions in either of two formats: standard five-answer multiple-choice questions and three-part questions that ask you to evaluate statements. To assist you with the mathematical computations you may need to make for some of the IR questions, the GMAT software provides you with a simple calculator. Whenever you need it, you click the box labeled Calculator and something that looks like the following figure appears. You select its functions by using your mouse. Don’t get too attached to it, though; the calculator is available only for IR questions, so you won’t be able to use it in the quantitative reasoning section. Because using a computer calculator can be awkward, you’ll likely answer most IR questions more quickly by using estimation or working out calculations by hand on your noteboard. Save the calculator for only the most complex or precise computations. How the IR section is scored Like the score you receive for the analytical writing section, your integrated reasoning score has no influence on your overall GMAT score, which consists of the combination of only your quantitative reasoning and verbal reasoning scores. Based on your performance in the IR section, your raw score is converted to a scaled score that ranges in whole numbers from 1 to 8 and is recorded separately from all the other scores. MBA programs decide how they use your IR score and may choose to disregard it altogether. So, your IR score is unlikely to make much of an impression unless it’s unusually low, in the 1-to-3 score range, or really high, such as the rare 7 or 8. A midrange score of 4, 5, or 6 likely won’t significantly hurt or help your chances of admission. How to make the most of your time on the IR section If you’ve already calculated that answering 12 questions in 30 minutes gives you 2.5 minutes to answer each question, you may be celebrating the fact that that gives you even more time per question than you have for the quantitative and verbal reasoning sections. Don’t get too excited just yet. Almost every IR question has multiple parts, and you have to answer all parts of the question correctly to be credited with a correct answer. When you consider the average number of sub-questions contained within each of those 12 questions, the actual number of IR answers you have to come up with in 30 minutes may be as high as 30. Therefore, you have to use your time wisely as you move through the section. You’ll likely feel the time crunch more fiercely in this section than the others. We provide some coping skills to help you through it: Conceal the timer. To maintain your sanity, refrain from constant clock-watching. Hide the timer on the computer by clicking on it. After you answer about three questions, reveal the timer by clicking on it again. It counts down from 30 minutes, so if you’re at 22 minutes, you’re cruising comfortably. If you’re at 21 or fewer, you may need to make some more calculated guesses to move through the section at a successful pace. Know when to move on. Discipline yourself to submit your best stab at an answer if you find yourself spending more than several minutes on any one question. You don’t want to sacrifice getting to an easy, less-time-consuming question because you’ve worked too long on a harder question. You can’t go back and revisit questions after you submitted your answers, so this practice may be difficult for you, especially if you tenaciously seek perfection. Take a deep breath, mark your best guess, and move on to what lies ahead. Write stuff down. Don’t be afraid to spend a little time upfront analyzing the loads of data in some IR questions. Unless you’re someone who can juggle a lot of details in your head, you should write on your noteboard as you think. A little note-taking may save you from reading information over again, which is a real time waster. Whisper to yourself. Studies show that processing information is easier if you speak out loud. Don’t be afraid to whisper your way through some of the more complex problems the IR section throws at you. You’ll likely take the test in a cubicle-like setting, so if you speak quietly, you won’t disturb anyone.

View ArticleArticle / Updated 01-31-2018

The Sentence Completion section on the GMAT consists of about 12 questions in the Verbal section. You are presented with a sentence that may contain a grammatical error in the underlined portion. The first answer choice presents the underlined portion as written, while the following answer choices make corrections in some way. Practice questions Alexander Graham Bell was a gifted inventor, but they did not know how his invention of the telephone would change the world. A. but they did not know how his invention of the telephone would change the world. B. but they did not know how his invention of the telephone would change the world back then. C. but he did not know how his invention of the telephone would change the world at that time. D. but neither he nor anyone else knew how his invention of the telephone would change the world. E. but not gifted enough to see his invention was going to change the world with the invention he made that was the telephone. Liu felt that the exhaust fan in the first examination room was more effective than the second. A. more effective than the second. B. more effective than the exhaust fan in the second examination room. C. more effective that she expected. D. the most effective exhaust fan. E. more effective than what she had noticed in the second examination room. Answers and explanations The correct answer is D. Alexander Graham Bell was a gifted inventor, but neither he nor anyone else knew how his invention of the telephone would change the world. This is a question about pronoun choices, so ignore those answers which do not address this, including Choice (B) and Choice (E). The sentence as is contains a pronoun error: they does not refer back to Alexander Graham Bell correctly. Choice (C) matches the pronouns correctly, but changes the meaning of the sentence, which refers to how Bell's invention would go on to change the world in the future. Choice (D) does the best job of matching the pronoun and making it clear (by the addition of the phrase nor anyone else) that the sentence is meant to show that no one, including Bell, foresaw how his invention would change the world. The correct answer is B. Liu felt that the exhaust fan in the first examination room was more effective than the exhaust fan in the second examination room. Of the choices provided, Choice (B) is the best. It clarifies that the comparison is between the exhaust fans in two examining rooms, whereas the original leaves it unclear as to what the second is referring to.

View ArticleArticle / Updated 01-31-2018

The Critical Reasoning section on the GMAT consists of about 12 questions in the Verbal section. In Critical Reasoning, you are shown a passage that presents an argument of some kind (often dealing with a business, government, or education topic). Some passages have multiple questions. You must choose the answer that best answers the question based on your understanding of the logic in the passage. Practice questions Both practice questions are based on the following passage. Dirk: I can't believe how long we've been waiting for them to bring us our food. Ellen: It's very busy in this restaurant, though. Dirk: Well, it's Saturday night! At 6:30 PM! Of course it's busy! They should have two times the number of servers working than what they have now. Ellen: That's ridiculous. It's impossible to predict how many customers will visit a restaurant on any given day for a particular meal. Which line of dialogue would most strengthen Dirk's case, if it were true? A. Dirk: Saturday night is traditionally a very busy night for restaurants, Ellen. B. Dirk: They should at least serve simpler foods, which would take less time to prepare. C. Dirk: You know as well as I have that we've eaten here every Saturday night for years, and usually there are twice as many employees working. D. Dirk: There's a motorcycle rally in town tonight, too, and that always draws a crowd. E. Dirk: If we had ordered the specials, they'd have been served by now. What line of dialogue, if true, could be added to Ellen's last statement in order to improve her logic? A. You know this, Dirk. You've been a bartender. B. We've eaten here before on a Saturday night at this time and been the only customers! C. The motorcycle rally brings a lot of extra people to town. D. It's important to order the correct amount of inventory without wasting much, too. E. None of the other customers look as angry as you do. Answers and explanations The correct answer is C. You want to complete the dialogue in a way that proves Dirk's point as logically as possible. If he has prior evidence that the restaurant is frequently busy on Saturday nights and usually has more staff at work, his case that they can plan for a particularly busy night is stronger. That's Choice (C). The correct answer is B. You want to improve Ellen's logic. Choice (B) does this best, by offering evidence that proves her thesis: that there is no way to predict how many people will visit the restaurant on a given Saturday night.

View ArticleArticle / Updated 01-31-2018

The Reading Comprehension portion of the GMAT is about 12 questions (more or less) in the Verbal section. In Reading Comprehension, you are shown a reading passage of one to three paragraphs, along with between two and six questions about each passage. You can refer to the passage while you answer each question about it. Practice questions Both practice questions are based on the following passage. The "morning star" isn't a star; it's always a planet. And sometimes two Morning Stars appear at once, such as Mercury and Venus. The same idea applies to the "evening star": You're seeing a planet, and you may see more than one. "Shooting stars" and "falling stars" are misnomers, too. These "stars" are meteors — the flashes of light caused by small meteoroids falling through Earth's atmosphere. Many of the "superstars" you see on television may be just flashes in the pan, but they at least get 15 minutes of fame. —Astronomy For Dummies by Stephen P. Maran Which of the following titles would be the most appropriate for the contents of this passage? A. 15 Minutes of Celestial Fame B. What Was That Flash? C. Explaining the Evening Star D. Don't Wish on the Morning Star! E. Some Stars Aren't What You Think! Which of the following situations is most similar to that described in the bolded section? A. A group of teenagers identifying the constellations in the sky based on what they learned in their freshman year science class. B. A couple looks through a telescope to try to see Jupiter's rings but the sky is too cloudy. C. A group of people on a boat spot what they think is a pack of dolphins in the ocean in the distance, but the captain informs them they're actually looking at buoys bouncing in the water. D. A man thinks he won the city marathon but he actually misread his time and came in second. E. A group of friends follow what they think is the sound of a band playing, and end up dancing the night away at a club. Answers and explanations The correct answer is E. The best title captures some understanding of the main point of the passage, which is that the Evening and Morning Stars are not actually stars at all. Choice (E) is the best of the answers here. The correct answer is C. The passage describes mistaking one thing for another, which is clarified by an expert (in that case, the author). Choice (C) describes a similar phenomenon.

View ArticleArticle / Updated 01-31-2018

Data Sufficiency questions on the GMAT will sometimes appear as word problems. These problems can cover a wide range of topics, including percentages, rate-time-distance, consecutive integers, ages, work rate, coins, mixtures, divisibility, factors, sequences, and equation setup. Each Data Sufficiency problem poses a question, followed by two statements. Your task is to evaluate the statements to determine at what point there is or is not sufficient information to answer the question. Unlike the Problem Solving questions, you do not actually have to answer the question posed. Instead, you select one of five fixed answer choices that offer different options about the sufficiency of the information provided in the two statements. Practice questions A retail store sent out a promotional offer to 300 former customers and 700 potential customers. What percent of the total number of people who received the promotional offer gave a favorable response? (1) The store received a favorable response from 30 percent of the former customers. (2) The store received a favorable response from 20 percent of the potential customers. 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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient to answer the question asked. 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. If a sequence A has 200 terms, what is the 100th term of A? (1) The first term of sequence A is . (2) Each term of sequence A after the first term is 15 more than the preceding term. 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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient to answer the question asked. 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. Answers and explanations The correct answer is C. Let F = the number of favorable responses from former customers and P = the number of favorable responses from potential customers. Then the percent of favorable responses is From (1), , which you can substitute into The value of this quantity can vary, so without additional information, you cannot determine an exact value of Thus, (1) is not sufficient. From (2), P = 20% (700) = 140, which you can substitute into The value of this quantity can vary, so without additional information, you cannot determine an exact value of Thus, (2) is not sufficient. Taking (1) and (2) together, Therefore, both statements together are sufficient, but neither statement alone is sufficient. The correct answer is C. Let a1 = the first term of sequence A, and a100 = the hundredth term of sequence A. From (1), a1 = –10. But without additional information, you cannot determine subsequent terms, including an exact value of a100. Thus, (1) is not sufficient. From (2), a1 = a1, a2 = a1 + 15, a3 = a1 + (2)(15), a4 = a1 + (3)(15), and so on. Hence, a100 = a1 + (99)(15). But without additional information, you cannot determine an exact value of a100. Thus, (2) is not sufficient. Taking (1) and (2) together, the exact value of the 100th term is a100 = (–10) + (99)(15). Therefore, both statements together are sufficient, but neither statement alone is sufficient.

View ArticleArticle / Updated 01-31-2018

The GMAT Quantitative section will contain problems that test your geometry skills, and some of these problems may appear as Data Sufficiency questions. You should be able to tackle lines, angles, two-dimensional shapes, three-dimensional solids, perimeter, area, surface area, volume, the Pythagorean theorem, and coordinate geometry. Each Data Sufficiency problem poses a question, followed by two statements. Your task is to evaluate the statements to determine at what point there is or is not sufficient information to answer the question. Unlike the Problem Solving questions, you do not actually have to answer the question posed. Instead, you select one of five fixed answer choices that offer different options about the sufficiency of the information provided in the two statements. Practice questions In the figure shown here, what is the value of z? (1) m = n (2) y = 88 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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient to answer the question asked. 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. The circumference of circle X is 1/2 the circumference of circle Y. What is the area of circle X? 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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient to answer the question asked. 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. Answers and explanations The correct answer is B. From (1), m = n implies x = z (because base angles of an isosceles triangle are congruent). However, without additional information, you cannot determine the value of x or z. Thus, (1) is not sufficient. From (2), because the measure of an exterior angle of a triangle equals the sum of the measures of the nonadjacent interior angles, 88 = 54 + z, which you can solve for z. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient. The correct answer is D. Recall that a circle with radius r has circumference equal to 2πr and area equal to πr2. From (1), in circle Y, so r, the radius of circle Y, is 10 feet. Then given that the circumference of circle X equals 1/2 the circumference of circle Y, the circumference of circle X is which implies the radius of circle X is 5 feet and its area is Thus, (1) is sufficient. From (2), you know from (1) that if the circumference of circle Y is known, you can proceed as in (1) to determine circle X's area. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

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