Master gmat 2010 part 59 pptx

QUANTITATIVE SECTION 37 QUESTIONS • 75 MINUTES Directions for Problem Solving Questions: (These directions will appear on your screen before your first Problem Solving question.) 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 infor- mation 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. Directions for Data Sufficiency Questions: (These directions will appear on your screen before your first Data Sufficiency question.) 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. practice test Practice Test 5 563 www.petersons.com 1. If a . b and c . d, which of the following is true? (A) b 2 c , a 2 d (B) a 1 d . b 2 c (C) b 2 d . a 2 c (D) a 1 c . b 1 d (E) a 1 b . c 1 d 2. Which of the following is nearest in value to = 664 1 = 414? (A) 16 (B) 33 (C) 40 (D) 46 (E) 68 3. In a group of 20 singers and 40 dancers, 20% of the singers are less than 25 years old, and 40% of the entire group are less than 25 years old. What percent of the dancers are less than 25 years old? (A) 20 (B) 40 (C) 50 (D) 60 (E) 80 4. How many ounces of coffee remain in a cup that has a 14-ounce capacity? (1) Originally, the cup contained 12 ounces of coffee. (2) The cup is currently filled to 50 percent of the cup’s capacity with coffee. 5. If 0 , N , 30, is N a factor of 30? (1) N is a factor of 12. (2) N is a multiple of 3. 6. A B C D 2 In the figure above, which shows rectangle ABCD tangent to a circle at each corner, AB is 2 units in length. Is rectangle ABCD a square? (1) The length of minor arc AB is exactly half the length of arc ABC. (2) The length of minor arc AD is p = 2 2 . 7. What is 150% of the product of 1 8 and 0.4? (A) 0.025 (B) 0.075 (C) 0.25 (D) 0.75 (E) 2.5 8. A recipe calls for 2 3 cup of butter to make a batch of cookies. How big is the batch? (1) If each of six people wanted to eat five cookies, 5 3 cup of butter would be needed. (2) Three batches would require 2 cups of butter. 564 PART VI: Five Practice Tests www.petersons.com 9. What is the sum of five numbers? (1) The arithmetic mean (simple average) of the five numbers is 9. (2) The difference between the greatest and least of the five numbers is 9. 10. Two square rugs, R and S, have a combined area of 20 square feet and are placed on a floor whose area is 112 square feet, as shown above. Measured east to west, each rug is placed the same distance from the other rug as from the nearest east or west edge of the floor. If the area of rug R is four times the area of rug S, how far apart are the rugs? (A) 1 foot, 6 inches (B) 2 feet (C) 2 feet, 8 inches (D) 3 feet (E) 3 feet, 4 inches 11. If p 5 (3)(5)(6)(9)(q), and if q is a positive integer, then p must be divisible, with no remainder, by all the following EXCEPT: (A) 27 (B) 36 (C) 45 (D) 54 (E) 90 12. = 10 = 2 3 = 5 = 2 5 (A) = 10 2 (B) 5 = 2 2 (C) 2 = 5 (D) 10 (E) 25 2 13. For all integers a and b, where b Þ 0, subtracting b from a must result in a positive integer if (A) |a 2 b| is a positive integer (B) (a 1 b) is a positive integer (C) S a b D is a positive integer (D) (ab) is a positive integer (E) (b 2 a) is a negative integer 14. In the figure above, m∠ACB 5 90°. What is the length of DB? (A) 3 = 21 2 8 (B) 8 (C) 5 = 7 2 8 (D) 5 = 5 (E) 18 2 5 = 6 15. If 3x 1 2y 5 5a 1 b, and if 4x 2 3y 5 a 1 7b, then x 5 (A) a 1 b (B) a 2 b (C) 2a 1 b (D) 4a 2 6b (E) 17a 1 17b practice test Practice Test 5 565 www.petersons.com 16. What is the equation of the line that is the perpendicular bisector of the line segment connecting points (21,1) and (3,5) on the xy plane? (A) y 5 2x 1 1 (B) y 5 x 2 2 (C) y 52x 1 4 (D) y 523x 1 2 (E) y 5 x 1 3 17. If 2x 1 1 is a positive multiple of 5, and if 2x 1 1 ≤ 100, how many possible values of x are integers? (A) 5 (B) 10 (C) 11 (D) 15 (E) 20 18. An empty swimming pool can be filled to capacity through an inlet pipe in 3 hours, and it can be completely drained by a drainpipe in 6 hours. If both pipes are fully open at the same time, in how many hours will the empty pool be filled to capacity? (A) 4 (B) 4.5 (C) 5 (D) 5.5 (E) 6 QUESTIONS 19–20 REFER TO THE FOLLOWING TABLE: WORLDWIDE SALES OF XYZ MOTOR COMPANY (2004–05 Model Year) Automobile Model Basic Standard Deluxe Purchaser Category U.S. institutions 3.6 8.5 1.9 U.S. consumers 7.5 11.4 2.0 Foreign institutions 1.7 4.9 2.2 Foreign consumers 1.0 5.1 0.8 Note: All numbers are in thousands. 19. Which of the following most nearly describes sales totaling 9000 automo- biles for the 2004–2005 model year? (A) All U.S. institution sales of the standard and deluxe models (B) All foreign sales of the standard model (C) All foreign-institution sales (D) All consumer sales of the basic model (E) All institution sales of the standard model 20. Of the total number of automobiles sold to the institutions during the 2004–2005 model year, which of the following most closely approximates the percentage that were NOT standard models? (A) 24% (B) 36% (C) 41% (D) 59% (E) 68% 21. What is Michael’s monthly salary? (1) If Michael’s monthly salary were cut by 25 percent while Sam’s monthly salary were raised by 25 percent, they would earn the same salary. (2) Michael’s monthly salary is $1000 more than Sam’s. 566 PART VI: Five Practice Tests www.petersons.com 22. In a room are five chairs to accommo- date 3 people, one person to a chair. How many seating arrangements are possible? (A) 45 (B) 60 (C) 72 (D) 90 (E) 120 23. N is 83 1 3 % of what number? (A) 6 5N (B) 7N 8 (C) 5N 4 (D) 6N 5 (E) N 1 50 3 24. Mona has $2.05 in quarters and dimes. How many quarters does she have? (1) She has more quarters than dimes. (2) She has a total of ten coins. 25. What number must be subtracted from the denominator of the fraction 7 16 to change the value of the fraction to 4 9 ? (A) 1 4 (B) 5 16 (C) 7 9 (D) 3 2 (E) 5 3 26. Four people plan to rent a summer cottage, apportioning the rent equally among themselves. What is the total amount of rent for the cottage? (1) If one additional person were to join in renting the cottage, each person would pay 20 percent of the total rent. (2) Three of the four people would pay a total of $2400 in rent. 27. 30 O 40 O 45 O x O In the figure above, what is the value of x? (A) 25 (B) 30 (C) 40 (D) 45 (E) 65 28. In a geometric sequence, each term is a constant multiple of the preceding one. If the first three terms in a geometric sequence are 22, x, and 28, which of the following could be the sixth term in the series? (A) 24096 (B) 21024 (C) 64 (D) 1024 (E) 2048 practice test Practice Test 5 567 www.petersons.com 29. How long does it take Sam to eat an entire large pizza? (1) Thomas can eat the same large pizza in 8 minutes. (2) Sam and Thomas together can eat the same large pizza in 6 1 2 minutes. 30. If x . 0, is x . y ? (1) 5x 2 4y 5 3 (2) 4y 2 5x 5 3 31. If x 5 2 and y 5 –2, then x 4 2 y 5 x 4 y 5 5 (A) 2 3 32 (B) 0 (C) 1 32 (D) 1 16 (E) 1 32. What is the one, unique value of x ? (1) x 2 2 4x 1 3 5 0 (2) x 2 2 2x 1 1 5 0 33. A B C D If the length of arc ACB in the circle above is 5p, is the length of AB greater than the length of CD ? (1) The length of AB equals the circle’s diameter. (2) The length of CD is 5. 34. A passenger train and a freight train leave from the same station at the same time. Over 3 hours, the passen- ger train travels 45 miles per hour faster, on average, than the freight train. Which of the following ex- presses the combined distance the two trains have traveled after 3 hours, where x represents the number of miles the freight train traveled per hour, on average? (A) 3x 1 45 (B) 6x 1 45 (C) 3x 1 120 (D) 3x 1 135 (E) 6x 1 135 35. If the total price of five grocery items is $6.05, what is the price of the most expensive of these items? (1) The price of the most expensive item is exactly 50 percent greater than the price of each of the other four items. (2) The price of each item (except the most expensive item) is $1.10. 568 PART VI: Five Practice Tests www.petersons.com 36. If s is an integer greater than 1, how many 1-inch cubes can be packed into a rectangular box having sides s, s 1 3 2 , and s 2 1, measured in inches? (A) s 3 2 s (B) s 3 1 s 2 2 1 s 2 (C) s 3 2 2s 1 s (D) s 3 1 s 2 2 s (E) s 3 37. A bag of marbles contains twice as many red marbles as blue marbles, and twice as many blue marbles as green marbles. If these are the only colors of marbles in the bag, what is the probability of randomly picking a blue marble from the bag? (A) 1 6 (B) 2 9 (C) 1 4 (D) 2 7 (E) 1 3 practice test Practice Test 5 569 www.petersons.com VERBAL SECTION 41 QUESTIONS • 75 MINUTES Directions for Sentence Correction Questions: (These directions will appear on your screen before your first Sentence Correction question.) This question presents a sentence, all or part of which is underlined. Beneath the sentence you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. This question tests correctness and effectiveness of expression. In choosing your answer, follow the requirements of Standard Written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error. Directions for Critical Reasoning Questions: (These directions will appear on your screen before your first Critical Reasoning question.) For this question, select the best of the answer choices given. Directions for Reading Comprehension Questions: (These directions will appear on your screen before your first group of Reading Comprehension questions.) The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all the questions following the passage on the basis of what is stated or implied in the passage. 1. Raising a child alone and holding down a full-time job require good organizational skills, not to mention a lot of support from friends and coworkers. (A) require good organizational skills (B) requires good organization skills (C) requires the skill of good organization (D) require a person to be well organized (E) requires good organizational skill 2. J. S. Bach’s The Musical Offering, long considered one of his minor works, but nevertheless a masterful composition, consisting of a series of canons, fugues, and other pieces based on the same musical theme. (A) but nevertheless (B) would instead be considered (C) but rather (D) and is nevertheless (E) is nevertheless 570 PART VI: Five Practice Tests www.petersons.com 3. A reliable survey indicates that college graduates change employers four times on average during the first ten years after college gradua- tion. Therefore, in order to avoid employee turnover, business adminis- trators in charge of hiring new employees should favor job applicants who obtained college degrees at least ten years earlier. The advice about how to avoid employee turnover rests on which of the following assumptions? (A) Employee turnover among businesses that hire employees without college degrees is greater than among businesses that hire only employees with college degrees. (B) Job changes within the same company are less common than job changes from one employer to another. (C) Employees who graduated from college at least ten years ago change employers less fre- quently on average than other employees. (D) Most employees who leave their jobs do so upon either request or demand of their employers rather than by their own initiative. (E) The survey excluded college graduates who interrupted their vocational careers to pursue advanced academic degrees. 4. Although residents of the north- central region of the United States are not known to have any accent, they nevertheless share certain distinctive utterances that help distinguish their speech from other regions. (A) distinguish their speech from (B) distinguishes their speech from those of (C) distinguish their speech from that of (D) distinguish the way they speak from (E) distinguishes their manner of speaking from 5. Driving excessively fast has been demonstrated to decrease the number of miles one can drive per gallon of fuel. Gary has recently been experi- encing a decrease in mileage per gallon of fuel while driving his car. This clearly proves that Gary has been driving excessively fast lately. Which of the following statements, if true, would most seriously weaken the conclusion about Gary’s driving? (A) Recently Gary’s speedometer has been indicating the speed of his car as lower than the car’s actual speed. (B) Recently Gary has been driving more miles per day on average than before he began experienc- ing a decrease in fuel mileage. (C) Other tests have shown that a car’s speed affects fuel mileage more than any other single factor. (D) Before Gary began driving excessively fast his speedometer over-represented his car’s actual speed. (E) Recently the tires on Gary’s car have been losing air pressure, and low tire air pressure is known to lower fuel mileage. practice test Practice Test 5 571 www.petersons.com 6. Expensive television advertising campaigns clearly help political candidates win elections, as evidenced by the fact that, in most political elections, the candidate with the most campaign money ultimately wins. Which of the following, if true, would provide most support for the argument above? (A) Endorsements from minor political office-holders generally have no effect on a candidate’s chances of winning an election. (B) In most cases, candidates who currently hold the office for which they seek re-election have more available campaign money than their competitors. (C) Expensive television advertising campaigns are waged most frequently by candidates who have more available campaign money than their competitors. (D) When it comes to choosing among candidates, the voting public tends to disregard how a candidate is portrayed in television advertisements. (E) Nearly any political candidate can afford to wage some type of television advertising campaign. QUESTIONS 7–9 ARE BASED ON THE FOLLOWING PASSAGE: Line The twentieth-century discovery of Archaeans, which did not fit into the kingdom classification scheme for biological life, led to the creation of the domain classification level, above the kingdom level. This new level included the new domain Archaean. Prior to the discovery of Archaeans, it had been generally accepted that no life could exist in temperatures much hotter than 60 degrees centigrade. This limit was set because it was thought that the molecular integrity of vital cellular components could not be maintained beyond such temperatures. The thermal capacity of cellular life, it was believed, was a fixture across all biological organisms. Archaeans, in recent decades, have repeatedly demonstrated that the previously maintained thermal threshold for life was far too low. So-called extremophilic Archaeans have been discovered to thrive in temperatures as high as 160 degrees centigrade. Such discoveries have required a broadening of biology’s conceptions concerning what environ- ments are hospitable to life. 7. The author of the passage implies that extremophilic Archaeans (A) are able to maintain molecular integrity of cellular components past what was formerly ac- cepted as the thermal threshold of life. (B) have been known to exist in moderate environments for some years, but their extremo- philic properties have only recently been discovered. (C) are able to live and thrive in temperatures higher than 160 degrees centigrade. (D) were responsible for the development of a distinct kingdom in the classification scheme for biological life. (E) are the oldest known form of multi-cellular biologic life. 8. The passage’s author suggests that the “thermal threshold” (line 21) is (A) the thermal capacity of extre- mophiles. (B) the critical point temperature at which the metabolic pathways of extremophiles become functional. (C) an environmental extremity indicator. (D) the temperature at which the molecular integrity of cellular components of an organism are compromised. (E) a biological constant across all of nature. 572 PART VI: Five Practice Tests 5 10 15 20 25 www.petersons.com . question.) This question presents a sentence, all or part of which is underlined. Beneath the sentence you will find five ways of phrasing the underlined part. The first of these repeats the original;. east or west edge of the floor. If the area of rug R is four times the area of rug S, how far apart are the rugs? (A) 1 foot, 6 inches (B) 2 feet (C) 2 feet, 8 inches (D) 3 feet (E) 3 feet, 4. closely approximates the percentage that were NOT standard models? (A) 24% (B) 36% (C) 41% (D) 59% (E) 68% 21. What is Michael’s monthly salary? (1) If Michael’s monthly salary were cut by 25