3. The figure above shows a rectangle intersected by a line. If b = 2a, then d + e + g + h = (A) 120 (B) 240 (C) 300 (D) 320 (E) 360 4. For all real numbers x where x ≥ 1, let . What is the value of f (100)? (A) 3 (B) 9 (C) 10 (D) 27 (E) 100 5. If 3 k+ m = 243 and 2 m = 8, then what is the value of 2 k ? (A) 2 (B) 4 (C) 6 (D) 8 (E) 10 fx x () =−1 a° b° c° d° e° f° g° h° 600 MCGRAW-HILL’S SAT 5 5 555 5 GO ON TO THE NEXT PAGE 6. If b varies inversely as the square of c, and if b = 8 when c = 3, then what could be the value of c when b = 2? (A) 2 (B) 5 (C) 6 (D) 25 (E) 36 7. In a certain soccer league, each of the five teams plays every other team in the league exactly three times each season. How many games are played in total in one season? (A) 15 (B) 24 (C) 30 (D) 60 (E) 120 8. Pump A, working alone, can fill a tank in 3 hours, and pump B can fill the same tank in 2 hours. If the tank is empty to start and pump A is switched on for one hour, after which pump B is also switched on and the two work together, how many minutes will pump B have been working by the time the pool is filled? (A) 48 (B) 50 (C) 54 (D) 60 (E) 64 CHAPTER 16 / PRACTICE TEST I 601 5 5 555 5 GO ON TO THE NEXT PAGE • Mark no more than one circle in any column. • Because the answer sheet will be machine-scored, you will receive credit only if the circles are filled in correctly. • Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately. • Some problems may have more than one correct answer. In such cases, grid only one answer. • No question has a negative answer. • Mixed numbers such as 3 must be gridded as 3.5 or 7/2. (If is gridded, it will be interpreted as , not 3 .) 1 2 31 2 31 2/ 1 2 • Decimal Answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid. For example, if you obtain an answer such as 0.6666 , you should record your result as .666 or .667. A less accurate value such as .66 or .67 will be scored as incorrect. Acceptable ways to grid 2 / 3 are: . . . . 201 102 0 2 3 4 5 1 0 2 3 4 5 1 0 2 3 4 5 1 2 3 4 5 1 . . . . 0 2 3 4 5 1 0 2 3 4 5 1 0 2 3 4 1 2 3 4 5 1 Answer: 201 Either position is correct. Note: You may start your answers in any column, space permitting. Columns not needed should be left blank. . . . . 7/12 0 2 3 4 5 6 7 8 9 1 0 2 3 4 5 6 7 8 9 1 0 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 Grid in result. Fraction line Write answer in boxes. Answer: 7 12 . . . . 2.5 0 2 3 4 5 6 7 8 9 1 0 2 3 4 5 6 7 8 9 1 0 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 Decimal point Answer: 2.5 . . . . 2/3 0 2 3 4 5 6 1 0 2 3 4 5 6 1 0 2 3 4 5 6 1 2 3 4 5 6 1 . . . . 66 . 6 0 2 3 4 5 6 1 0 2 3 4 5 6 7 1 0 2 3 4 5 6 1 2 3 4 5 6 1 . . . . 66 . 7 0 2 3 4 5 6 7 1 0 2 3 4 5 6 7 1 0 2 3 4 5 6 7 8 1 2 3 4 5 6 7 1 Directions: For student-produced response questions 9–18, use the grids at the bottom of the answer sheet page on which you have answered questions 1–8. Each of the remaining ten questions requires you to solve the problem and enter your answer by mark- ing the circles in the special grid, as shown in the examples below. You may use any available space for scratchwork. 602 MCGRAW-HILL’S SAT 5 5 555 5 9. If four times a certain number is decreased by 5, the result is 25. What is the number? 10. For every integer m greater than 1, let «m» be defined as the sum of the integers from 1 to m, inclusive. For instance, «4» = 1 + 2 + 3 + 4 = 10. What is the value of «7» − «5»? 11. If the circumference of the circle above is 10π, then what is the value of a 2 + b 2 ? A, B, C, D 12. How many different three-letter arrangements of the letters above are possible if no letter may be repeated? (An arrangement like ABC is dis- tinct from an arrangement like BCA.) 13. If 96,878 × x 2 = 10,200, then 14. Every term in a certain sequence is one less than three times the previous term. If the fourth term of this sequence is 95, what is the first term of the sequence? 10 200 5 96 878 2 , ,x × = a b P 15. If , what is the value of ? 16. Admission to a museum is $10 for each adult and $5 for each child. If a group of 30 people pays a total of $175 in admission, how many adults are in the group? 17. The perimeter of the isosceles triangle above is 24. If the ratio of a to b is 2 to 3, what is the value of b? Note: Figure not drawn to scale. 18. In the figure above, AB = 6, BC = 6, and CD = 2. What is AD? A B C D E a bb 4 − b 472+=b . STOP If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test. CHAPTER 16 / PRACTICE TEST I 603 1. The strange signal detected by the radio tele- scope, rather than being taken as evidence of a new cosmological phenomenon, was instead treated as merely of the equipment itself. (A) a malfunction (B) a bulwark (C) an anthology (D) a mutation (E) a transfer 6 6 666 6 SECTION 6 Time—25 minutes 24 questions Turn to Section 6 of your answer sheet to answer the questions in this section. Directions: For each question in this section, select the best answer from among the choices given and fill in the corresponding circle on the answer sheet. GO ON TO THE NEXT PAGE 2. The long-standing divisions among the indige- nous ethnic groups in the region have created an problem that may never be solved without international intervention. (A) impotent (B) intractable (C) evanescent (D) irate (E) insipid 3. The ease with which the army’s defenses were breached surprised the opposing general, who expected resistance to be far more than it was. (A) ephemeral (B) compatible (C) egregious (D) tolerable (E) imposing 4. Although dependence on electronic devices has in recent years, the increased effi- ciency of common appliances has the de- mand on the power grid. (A) abated . . decreased (B) surged . . attenuated (C) increased . . compromised (D) diminished . . reduced (E) flourished . . elevated Each sentence below has one or two blanks, each blank indicating that something has been omitted. Beneath the sentence are five words or sets of words labeled A through E. Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. EXAMPLE: Rather than accepting the theory unquestion- ingly, Deborah regarded it with . (A) mirth (B) sadness (C) responsibility (D) ignorance (E) skepticism A C D B 604 MCGRAW-HILL’S SAT 6 6 666 6 GO ON TO THE NEXT PAGE 5. Although persecution at the hands of landowners vanquished the will of many, it the dreams of revolution among the hardier insurgents. (A) despotic . . squandered (B) cruel . . destroyed (C) amenable . . bore (D) celebrated . . initiated (E) ruthless . . forged theory of morality. So impressed was Kant by the insights of Rousseau that he hung a picture of him on the wall of his study, convinced that Rousseau was the Newton of the moral world. PASSAGE 2 The roses we lay at Rousseau’s feet for this the- ory of Natural Rights tend to overwhelm the less fragrant of his ideas. He persisted in believ- ing in the nobility of the primitive state of nature, and that women’s nature was to serve men. His assertions about Natural Rights of Man laid the philosophical foundation of American independence, but his worship of emotion over reason and of “negative educa- tion” gave generations of parents permission to ignore the need to discipline and teach their children. 6. Passage 1 suggests that Goethe (A) was at the forefront of the Age of Reason (B) was a traditionalist (C) was influenced by Rousseau (D) opposed the Romantic movement (E) inspired much of Rousseau’s work 7. Passage 1 mentions Kant’s “daily walk” (line 16) in order to emphasize (A) Kant’s forgetfulness (B) Kant’s commitment to healthful practices (C) the dogmatic nature of Rousseau’s writ- ings (D) the effect of Rousseau’s philosophy on Kant (E) Kant’s close friendship with Rousseau 8. Unlike Passage 1, Passage 2 characterizes Rousseau’s emphasis on emotion as (A) insincere (B) innovative (C) harmful (D) temporary (E) necessary First passage: from “Rousseau: A Romantic in the Age of Reason,” from Socrates to Sartre, McGraw-Hill, 1999, p. 278 Second passage: Copyright 2005 Christopher Black. All rights reserved. Line 5 10 15 20 25 30 35 The passages below are followed by questions based on their content; questions following a pair of related passages may also be based on the relationship between the paired passages. Answer the questions on the basis of what is stated or implied in the passage and in any introductory material that may be provided. Questions 6–9 are based on the following passages. PASSAGE 1 The following is from a recent commentary on Jean-Jacques Rousseau (1712–1778), a French philosopher during the Enlightenment. Taken as a whole, Rousseau’s writings at- tacked the Age of Reason, gave impetus to the Romantic movement by emphasizing feeling (leading Goethe to say that “feeling is all”), revived religion even though he had doubts about some traditional teachings, provided a new direction for education (his book Émile was considered by some the best work on edu- cation since Plato’s Republic), inspired the French Revolution, made a unique impact on political philosophy, and, more than the writ- ing of any of his contemporaries, influenced several subsequent philosophers, especially Immanuel Kant. On one occasion, Kant was so absorbed in reading Rousseau’s Émile that he forgot to take his celebrated daily walk. While Kant admitted that it was David Hume who awakened him from his dogmatic slum- bers regarding the theory of knowledge, it was Rousseau who showed him the way to a new CHAPTER 16 / PRACTICE TEST I 605 6 6 666 6 GO ON TO THE NEXT PAGE 9. Both passages credit Rousseau with (A) attacking the Age of Reason (B) inspiring revolutionary thought (C) encouraging discipline (D) praising the primitive state of nature (E) establishing the Romantic movement This isn’t an idle example. India developed a pharmaceutical industry many years ago that could produce drugs very cheaply that would have saved tens of thousands of lives each year. In a free-market economy, the Indian pharmaceutical industry would have been allowed to make drugs and get them to the people who needed them. But that would mean that western pharmaceutical companies would make less profit. Of course, it’s not that the American pharmaceutical companies don’t care about Indian children dying be- cause they can’t get drugs; it’s just that their responsibility is to their stockholders. They must maximize profits. But the “free market” was getting in the way, so they simply changed the rules. Thus, in 1994 India “agreed” (that is, gave in to Western pressure) to “liberalize” its pharmaceutical industry by allowing its largest drug companies to be sold to Western interests, thereby reducing competition. Drug prices predictably shot up, putting them out of reach of people who needed them, but the Western corporations made more money. It was a big triumph for the “liberalization” of markets, but a great blow to free markets. In a free economy, businesses are also ex- pected to wager their own capital on success in the marketplace. The adventurous entre- preneur is a moral icon in the United States. The American pharmaceutical industry, how- ever, receives over half a billion dollars annu- ally in federal tax dollars in the form of research grants to develop medications and vaccines that they can then patent and sell back to consumers at monopolistic prices. The legislators who sponsor these grants know that their campaigns will likely receive reciprocal monetary benefit as a result. What is worse, most American voters accept this sys- tem happily because they believe that they are simply helping to find cures for diseases. The reality, however, is very different: by discourag- ing the competition that leads to real progress, this system of protectionism is actually a huge impediment to the elimination of disease. Questions 10–16 are based on the following passage. The following passage was written by an American essayist in 2003 about the status of capitalism. In response to a journalist’s question, “What do you think about Western civilization?” Mahatma Gandhi is said to have replied, “It would be a good idea.” Any honest person who values the concept of the free market, who believes in the promise of open economic competition, would say the same thing about capitalism. We hear our politicians, and of course the corporate news and entertainment media, speaking as if the United States were a model of free-market capitalism, as if anyone could start a business to create and sell a product or service without the obstruction of the government. The truth is quite different. Those we hear saying such things are quite often voices that are bankrolled by large cor- porations, which themselves are often pro- tected from competition by mutual agreement with the federal government. The concept of free trade is simple: if Company A can produce and distribute a prod- uct more efficiently and at a higher quality than Company B, it should be allowed to do so, and to charge any price for it that free consumers are willing to pay. Although Company B would likely suffer as a result, humanity would benefit from freer and cheaper access to high-quality goods. Sometimes free trade works nicely, as when Company A is in the United States and Company B is in India. Then, agreements are signed to “open up” India to the cheaper goods made by Company A, even if doing so crushes Company B because, we say, consumers have a right to cheap, high-quality goods. But if Com- pany A were in India and Company B were in the United States, the story would likely be very different. Line 5 10 15 20 25 Line 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 606 MCGRAW-HILL’S SAT 10. The quotation from Mahatma Gandhi (lines 3–4) suggests that Gandhi believed that Western civilization was (A) on the decline (B) the beneficiary of unfair economic practices (C) antithetical to progress in Asia (D) a great triumph (E) an unrealized concept 11. The “voices” mentioned in line 16 can be in- ferred to include all of the following EXCEPT (A) American politicians (B) leaders like Mahatma Gandhi (C) television journalists (D) some leaders of large corporations (E) those who believe that the United States is faithful to the capitalist ideal 12. The primary function of the second paragraph (lines 20–37) is to (A) illustrate a debate (B) provide a statistical analysis (C) explain a concept (D) give historical background (E) describe a popular viewpoint 13. By saying that “the story would likely be very dif- ferent” (lines 36–37), the passage suggests that (A) the rules of a free market are selectively applied (B) trade laws favor smaller countries (C) American companies produce the best products (D) Asian countries are moving away from the free market (E) American companies share the same interests as Indian companies 6 6 666 6 GO ON TO THE NEXT PAGE 14. The quotation marks around particular words in the fourth paragraph (lines 55–65) serve pri- marily to indicate that those words are (A) being used ironically (B) technical economic terms (C) adaptations of foreign words (D) recently coined (E) direct quotations from a document described earlier 15. The “triumph” described in line 63 is charac- terized as (A) a rare success for free markets (B) a legislative victory (C) a breakthrough in the development of inexpensive drugs (D) a tragic violation of the principle of free trade (E) a success that was based on luck 16. The passage suggests that the “entrepreneur” (lines 68–69) differs from executives in the pharmaceutical industry in that the entre- preneur (A) does not abide by free-market ideals (B) risks his or her own money (C) does not hire employees from overseas (D) works more closely with representatives in Washington (E) needs less money to start a typical business CHAPTER 16 / PRACTICE TEST I 607 6 6 666 6 GO ON TO THE NEXT PAGE Questions 17–24 are based on the following passage. The following passage is an excerpt from Mary Shelley’s Frankenstein, written in 1831. Natural philosophy, and particularly chem- istry, became nearly my sole occupation. I read with ardor those works, so full of ge- nius and discrimination, that modern inquir- ers have written on these subjects. I attended the lectures and cultivated the acquaintance of the men of science of the university. In M. Waldman I found a true friend. His gentle- ness was never tinged by dogmatism, and his instructions were given with an air of frank- ness and good nature that banished every idea of pedantry. In a thousand ways he smoothed for me the path of knowledge and made the most abstruse inquiries clear and facile to my apprehension. As I applied so closely, it may be easily conceived that my progress was rapid. My ardor was indeed the astonishment of the students, and my proficiency that of the mas- ters. None but those who have experienced them can conceive of the enticements of sci- ence. A mind of moderate capacity which closely pursues one study must infallibly ar- rive at great proficiency in that study; and I, who continually sought the attainment of one object of pursuit and was solely wrapped up in this, improved so rapidly that at the end of two years I made some discoveries in the improvement of some chemical instru- ments, which procured me great esteem and admiration at the university. When I had arrived at this point and had become as well acquainted with the theory and practice of natural philosophy as depended on the lessons of any of the professors at Ingolstadt, my residence there being no longer con- ducive to my improvements, I thought of returning to my friends and my native town, when an incident happened that protracted my stay. Whence, I often asked myself, did the prin- ciple of life proceed? It was a bold question, and one which has never been considered as a mystery; yet with how many things are we upon the brink of becoming acquainted, if cowardice or carelessness did not restrain our inquiries. I revolved these circumstances in my mind and determined thenceforth to apply myself more particularly to those branches of natural philosophy which relate to physiology. Unless I had been animated by an almost su- pernatural enthusiasm, my application to this study would have been irksome and almost in- tolerable. To examine the causes of life, we must first have recourse to death. I became acquainted with the science of anatomy, but this was not sufficient; I must also observe the natural decay and corruption of the human body. In my education my father had taken the greatest precautions that my mind should be impressed with no supernatural horrors. I do not ever remember to have trembled at a tale of superstition or to have feared the ap- parition of a spirit. Darkness had no effect upon my fancy, and a churchyard was to me merely the receptacle of bodies deprived of life, which, from being the seat of beauty and strength, had become food for the worm. I saw how the fine form of man was degraded and wasted; I beheld the corruption of death succeed to the blooming cheek of life; I saw how the worm inherited the wonders of the eye and brain. I paused, examining and ana- lyzing all the minutiae of causation, as exem- plified in the change from life to death, and death to life, until from the midst of this dark- ness a sudden light broke in upon me—a light so brilliant and wondrous, yet so simple, that while I became dizzy with the immensity of the prospect which it illustrated, I was sur- prised that among so many men of genius who had directed their inquiries towards the same science, that I alone should be reserved to discover so astonishing a secret. Line 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Excerpted from Frankenstein by Mary Shelley, public domain, edited for length 608 MCGRAW-HILL’S SAT 17. In the first paragraph, the narrator indicates that the instruction given to him by M. Wald- man was (A) haughty (B) challenging (C) easily understood (D) obscure (E) expensive 18. In line 15, the word “apprehension” most nearly means (A) fear (B) reservation (C) imprisonment (D) understanding (E) arrest 19. The narrator indicates that proficiency in an academic study requires which of the follow- ing? I. genius II. diligence III. financial resources (A) I only (B) II only (C) I and II only (D) II and III only (E) I, II, and III 20. The narrator indicates that he considered leav- ing Ingolstadt because he (A) had learned all he could from its instruc- tors (B) was acutely homesick (C) was offered another job (D) had a negative experience with a profes- sor there (E) had become ill 6 6 666 6 21. In saying that he was “animated by an almost supernatural enthusiasm” (lines 51–52), the narrator suggests that he (A) was easily influenced by superstition (B) loved lecturing at Ingolstadt (C) was passionate about studying the physi- ology of life and death (D) was excited about the prospect of return- ing home (E) wanted to learn more about the origin of certain superstitions 22. The “seat of beauty and strength” (lines 67–68) is a reference to (A) the churchyard (B) the human body (C) the worm (D) the university at Ingolstadt (E) the narrator’s studies 23. In line 71, the phrase “succeed to” most nearly means (A) inspire (B) thrive (C) replace (D) proceed to (E) promote 24. The final sentence of the passage suggests that the narrator feels (A) intimidated by the enormous task before him (B) grateful to those who instructed him (C) anxious about the moral dilemma posed by his work (D) baffled by particular scientific principles (E) privileged to be on the verge of a mo- mentous discovery STOP If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test. CHAPTER 16 / PRACTICE TEST I 609 7 7 777 7 GO ON TO THE NEXT PAGE 1. Which of the following integers is 2 greater than a multiple of 7? (A) 14 (B) 15 (C) 16 (D) 17 (E) 18 2. A store sells oranges for 20 cents each, but for every four oranges you buy, you may buy a fifth for only 5 cents. How many oranges can you buy from this store for $3.40? (A) 14 (B) 17 (C) 18 (D) 19 (E) 20 3. If r is a positive number and s is a negative number, all of the following must represent positive numbers EXCEPT. (A) −r + s (B) r − s (C) (D) rs 2 (E) (rs) 2 r s 2 SECTION 7 Time—20 minutes 16 questions Turn to Section 7 of your answer sheet to answer the questions in this section. Directions: For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding circle on the answer sheet. You may use any available space for scratchwork. 1. The use of a calculator is permitted. 2. All numbers used are real numbers. 3. Figures that accompany problems in this test are intended to provide information useful in solv- ing the problems. They are drawn as accurately as possible EXCEPT when it is stated in a spe- cific problem that the figure is not drawn to scale. All figures lie in a plane unless otherwise indicated. 4. Unless otherwise specified, the domain of any function f is assumed to be the set of all real num- bers x for which f(x) is a real number. The number of degrees of arc in a circle is 360. The sum of the measures in degrees of the angles of a triangle is 180. Notes Reference Information r A = πr 2 C=2πr ᐉ w A = ᐉw V = ᐉwh V = πr 2 h Special right triangles c 2 = a 2 + b 2 A = 1 / 2 bh h b ᐉ w h r h b c a 2x x x s s s 3 2 30° 60° 45° 45° . and enter your answer by mark- ing the circles in the special grid, as shown in the examples below. You may use any available space for scratchwork. 602 MCGRAW-HILL’S SAT 5 5 555 5 9. If four times. accepting the theory unquestion- ingly, Deborah regarded it with . (A) mirth (B) sadness (C) responsibility (D) ignorance (E) skepticism A C D B 604 MCGRAW-HILL’S SAT 6 6 666 6 GO ON TO THE NEXT. 1831. Natural philosophy, and particularly chem- istry, became nearly my sole occupation. I read with ardor those works, so full of ge- nius and discrimination, that modern inquir- ers have written on