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Cheat Sheet / Updated 10-31-2023
When you take the Graduate Management Admission Test (GMAT), make sure you take the required items with you to the test. Use these guidelines to help you get through the integrated reasoning, data sufficiency, quantitative problem solving, reading comprehension, and critical reasoning questions — as well as for writing your analytical essay and conquering integrated reasoning questions.
View Cheat SheetArticle / Updated 10-05-2023
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. — From 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 FameB. 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 09-29-2023
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 09-29-2023
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.
View ArticleArticle / Updated 04-18-2023
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
Some Data Sufficiency questions in the Quantitative section of the GMAT will test your mettle with algebra. You should be ready to handle polynomials, linear equations and inequalities, quadratic equations, basic function concepts, and systems of linear equations. 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 grocer sells avocados for $1.50 each and pineapples for $2.00 each. How many avocados did the grocer sell today? (1) The number of avocados sold today is 20 more than twice the number of pineapples sold. (2) Today the grocer received a total of $155 from the sale of avocados and pineapples. 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. Is the sum of the roots of the equation, x2 + bx + c = 0, positive? (1) b < 0 (2) c < 0 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 A = the number of avocados sold today, and P = the number of pineapples sold today. From (1), A = 2P +20, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of A. For example, if P = 5, then A = 30. But if P = 10, then A = 40. Thus, (1) is not sufficient. From (2), 1.50A + 2.00P = 155.00, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of A. For example, if P = 1, then A = 102. But if P = 4, then A = 98. Thus, (2) is not sufficient. Taking (1) and (2) together, yields a system of two equations, A – 2P = 20 and 1.50A + 2.00P = 155.00, with two variables, A and P. The system has a unique solution because Thus, you can determine a unique value of A. Therefore, both statements together are sufficient, but neither statement alone is sufficient. The correct answer is A. Using the quadratic formula, the two roots of x2 + bx + c = 0 are Adding the roots yields Hence, the sum of the roots of x2 + bx + c = 0 equals –b. From (1) b < 0 implies –b > 0, so the sum of the roots is positive. Thus, (1) is sufficient to answer the question posed. From (2), c > 0 implies that the product of the two roots is negative, indicating that the two roots have opposite signs. However, without additional information, you cannot determine whether the sum is positive. For instance, the sum of the roots of x2 – 2x – 15 = 0, which has roots 3 and –5, is –2. This result yields an answer of No to the question posed. But the sum of the roots of x2 + 2x – 15 = 0, which has roots 5 and –3, is 2. This result yields an answer of Yes to the question posed. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.
View ArticleArticle / Updated 01-31-2018
Data Sufficiency questions in the GMAT Quantitative section will include problems involving probability and statistics. Be ready to tackle questions about counting techniques, permutations and combinations, basic probability, arithmetic mean, median, mode, and standard deviation. 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 The heights of a certain plant species are normally distributed. What height is 2 standard deviations greater than the arithmetic mean height of the plant species? (1) The arithmetic mean height is 32.8 centimeters. (2) The standard deviation of the heights is 2.4 centimeters. 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. Harper interviewed for a job with company A and with company B. What is the probability that Harper will get job offers from both companies? (1) The probability that Harper will get a job offer from exactly one of the companies is 0.6. (2) The probability that Harper will get a job offer from neither company is 0.1. 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 h = the height that is 2 standard deviations greater than the mean height. Then h = mean + 2(standard deviation). From (1), h = 32.8 cm + 2(standard deviation). Without knowing the standard deviation, you cannot determine an exact value of h. Thus, (1) is not sufficient. From (2), h = mean + 2 (2.4 cm). Without knowing the mean, you cannot determine an exact value of h. Thus, (2) is not sufficient. Taking (1) and (2) together, h = 32.8 cm + 2(2.4 cm), which you can calculate to determine an exact value of h. Therefore, both statements together are sufficient, but neither statement alone is sufficient. The correct answer is C. Let P(both) = the probability Harper will get a job offer from both companies, P(exactly one) = the probability Harper will get a job offer from exactly one of the two companies, and P(neither) = the probability that Harper will get a job offer from neither company. Given that one of these three events is certain to happen, then P(both) + P(exactly one) + P(neither) = 1, from which you have P(both) = 1 – P(exactly one) – P(neither). From (1) P(both) = 1 – 0.6 – P(neither). Without additional information, you cannot determine an exact value of P(both). Thus, (1) is not sufficient. From (2), P(both) = 1 – P(exactly one) – 0.1. Without additional information, you cannot determine an exact value of P(both). Thus, (2) is not sufficient. Taking (1) and (2) together, P(both) = 1 – 0.6 – 0.1 = 0.3. Therefore, both statements together are sufficient, but neither statement alone is sufficient.
View ArticleArticle / Updated 01-31-2018
Some of the Data Sufficiency questions in the GMAT Quantitative section will test your basic math skills, so you should brush up on your fractions, decimals, ratios and proportions, percent, and exponents. 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 garden contains 32 tomato plants. How many pepper plants does the garden contain? (1) The ratio of the number of tomato plants to the number of pepper plants is 8 to 3. (2) If the number of tomato plants is increased by 4, and the number of pepper plants stays the same, the ratio of the number of tomato plants to the number of pepper plants is 3 to 1. 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 what is the ratio of (1) 7x = 6y (2) x = 6 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 D. Let P = the number of pepper plants in the garden. Using the question information and (1) gives the proportion which you can solve for P. Thus, (1) is sufficient. Using the question information and (2) gives the proportion which you can solve for P. Therefore, each statement alone is sufficient. The correct answer is A. The ratio of From (1), 7x = 6y implies Thus (1) is sufficient. From (2), x = 6 implies The value of this expression varies depending on the value of y. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.
View ArticleArticle / Updated 01-30-2018
The Problem Solving questions in the Quantitative section of the GMAT cover a lot of ground, and on top of that, some of them will appear as word problems that you need to parse to find the answer. These word problems may involve percentages, rate-time-distance, consecutive integers, ages, work rate, coins, divisibility, factors, multiples, sequences, and equation setup. Practice questions Kyra and Sage, working together, can paint a room in 5 hours. If Melora helps Kyra and Sage paint the room, the three of them can paint the room in 4 hours. What amount of time (in hours) would it take Melora, working alone, to paint the room? A. 6 B. 8 C. 10 D. 15 E. 20 Ninety percent of a large field is cleared for planting. Of the cleared land, 50 percent is planted with blueberry plants and 40 percent is planted with strawberry plants. If the remaining 360 acres of cleared land is planted with gooseberry plants, what is the size, in acres, of the original field? A. 2,916 B. 3,240 C. 3,600 D. 4,000 E. 8,000 Answers and explanations The correct answer is E. Let t = the time (in hours) it would take Melora, working alone, to paint the room. The portion of the room Melora, working alone, can paint in one hour is 1/t. The portion of the room Kyra and Sage, working together, can paint in one hour is 1/5. The portion of the room the three of them, working together, can paint in one hour is 1/4. Therefore, Solve the equation: Melora would take 20 hours, working alone, to paint the room. The correct answer is D. Let A = the size (in acres) of the original field. Then The percent of the cleared land planted in gooseberry plants is Solve the equation: The size of the original field is 4,000 acres.
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