820 MCGRAW-HILL’S SAT Detailed Answer Key Section 1 One particularly interesting exception to a rule is the orbit of Mercury. For hundreds of years, Sir Isaac Newton’s laws of motion and gravity stood as a testa- ment to the power of mathematics to describe the universe. Newton’s equations showed that the moon did not revolve around the earth because the gods willed it to, or because of the abstract perfection of a circular orbit. Rather, it circled the earth because doing so obeyed a simple mathematical formula: Newton’s Universal Law of Gravitation. It was a sin- gular achievement in the history of science. The equation was not only elegant, but enor- mously powerful. It was used to predict the existence of two new planets before they were even seen: Nep- tune and Pluto. Astronomers actually began to doubt the power of the Universal Law of Gravitation when they noticed that Uranus was not behaving the way the equation said it should. Its orbit was wobblier than Newton’s law predicted. Could the law be incor- rect? A few careful scientists noticed that the law could still be correct if another planet, further from the sun, were tugging at Uranus. Indeed, astronomers looked carefully and found a planet they called Nep- tune. As even further confirmation of Newton’s law, irregularities in Neptune’s orbit led astronomers to find Pluto exerting yet another tiny gravitational tug at the edge of the solar system. It seemed that New- ton’s equation could do no wrong. But it was wrong. When astronomers began to no- tice irregularities in Mercury’s orbit, they surmised, naturally, that another planet must be near the sun tug- ging at Mercury. They even went so far as to call the undiscovered planet Vulcan. But even the most careful observations revealed no such planet. How could this equation, so powerful and elegant, be wrong? It turned out that Newton’s equation broke down a bit as gravi- tational force became great, as it did near the sun. It wasn’t until the 20th century that Einstein’s theory of General Relativity tweaked Newton’s equation to make it explain the precession of Mercury’s orbit. The value of Mercury’s orbit, in fact, lies not so much in its ability to “prove” Einstein’s theory as in its ability to disprove Newton’s. It was the exception to a very powerful rule. It seems to suggest that, in sci- ence, nothing is truly sacred; everything must be ex- amined. If one of the most powerful and elegant equations in all of science—one that had been “proven” time and again by rigorous experiment—could turn out to be wrong (albeit only by a tiny bit, in most or- dinary circumstances), how much can we trust our own beloved “truths” about our universe? So many of us believe we know at least a few things that are “ab- solutely true.” But can we say that we are more in- sightful, intelligent, or rigorous than Isaac Newton? Perhaps we should be more like the scientists, and look for the holes in our theories. The following essay received 6 points out of a possible 6. This means that it demonstrates clear and con- sistent competence in that it • develops an insightful point of view on the topic • demonstrates exemplary critical thinking • uses effective examples, reasons, and other evidence to support its thesis • is consistently focused, coherent, and well organized • demonstrates skillful and effective use of language and sentence structure • is largely (but not necessarily completely) free of grammatical and usage errors Consider carefully the issue discussed in the following passage, then write an essay that answers the ques- tion posed in the assignment. We like to believe that physical phenomena, animals, people, and societies obey pre- dictable rules, but such rules, even when carefully ascertained, have their limits. Every rule has its exceptions. Assignment: What is one particularly interesting “exception” to a rule? Write an essay in which you answer this question and discuss your point of view on this issue. Support your position logically with examples from literature, the arts, history, politics, science and technology, current events, or your experience or observation. CHAPTER 16 / PRACTICE TEST 4 821 When we are children, everyone—parents, teachers and friends—tells us that we should never lie. It’s even one of the ten commandments in the Bible. This is a rule that many believe should have no exceptions. It is just something you should not do. Lying is bad, and being truthful is good. End of story. But I believe that this rule has its exceptions, as many rules do. Sometimes lying can even be consid- ered the right thing to do. It’s obviously not good to lie just because you don’t feel like telling the truth or just because you might look better if you lie. There has to be a good reason to deceive someone in order for it to be a valid action. For instance, sometimes telling the truth can really hurt a situation more than it helps. For example, my friend is in a dance company, and I went to see her in the Nutcracker dance performance this past week- end. Even though she was pretty good, the whole thing was long, boring, and a lot of the dancers were not very good. I know that she would not want to hear that. So instead of telling her the truth, I lied and told her how great it was. This is what is called a ‘white lie.’ Yes, I was deceiving her, but there was really very little to come from telling her the truth that the show was a disaster. What is the point of telling the truth there if it is only going to hurt every- one involved? Recently, I watched a documentary about the Vietnam War. The documentary focused on a troop of 25 soldiers and their experience in the war and how they grew closer together as a group as the time went by. One of the soldiers, a 16 year old boy who had lied about his age so that he could fight, died because he made a bad decision and chased after a Vietnamese soldier into the woods without anyone else to back him up. Part of the reasoning behind this action, they explained, was because he spent his entire life trying to prove to his parents that he was not a failure at everything and that he could be a hero. A fellow troop- mate knew what he had done, knew the struggle for respect he was going through at home, and wrote the formal letter home to the family telling them how their son had died in an honorable fashion saving sev- eral members of the troop with his heroism. Some might argue that it was bad to lie about his death, but I would argue that this was a valiant thing done by the soldier who wrote the letter because it allowed the family to feel better about the death of their young son in a war so many miles away. To summarize, in general, it is best not to lie. But there are in fact situations where it is better to tell par- tial truths than the whole truth. It is important to avoid lying whenever possible, but it is also important to know when it is OK to tell a slight variation to the truth. The following essay received 4 points out of a possible 6, meaning that it demonstrates adequate compe- tence in that it • develops a point of view on the topic • demonstrates some critical thinking, but perhaps not consistently • uses some examples, reasons, and other evidence to support its thesis, but perhaps not adequately • shows a general organization and focus but shows occasional lapses in this regard • demonstrates adequate but occasionally inconsistent facility with language • contains occasional errors in grammar, usage, and mechanics 822 MCGRAW-HILL’S SAT A lot of rules have exceptions because there are dif- ferent circumstances for everybody and also people grow up and the old rules don’t apply anymore. One afternoon back in elementary school, I got in trouble when I took my friend’s Capri-Sun drink out of his lunchbox and took a sip without asking his permis- sion. My teacher caught me in the act and yelled at me reciting the “Golden Rule.” She said: How would you feel if he took your drink and had some without ask- ing you? I guess I would have been pretty annoyed. I hate it when people drink from the same glass as me. It seemed like a pretty fair rule that I should only do things to other people that I would be OK with them doing to me. This interaction with my 3rd grade teacher stuck with me throughout my education experience and I heard her voice in my head many times as I was about to perform questionable acts upon others around me. It kept me from doing a lot of pranks like I used to do like tie Eric’s shoelaces together and putting hot pepper flakes in Steve’s sandwich one afternoon while he went off to get himself another cup of water. But this rule seemed to get a bit more difficult to follow as I got older and found myself in more com- plex relationships. Sometimes I wanted to be treated in ways that my friends did not want to be treated. I wanted my friends to call me each night so that we could talk and catch up on the day’s events so I would call each of them every night to chat. This annoyed my friends though who did not like talking on the phone. Or, I would always point out to my friends when something they were wearing did not look good because I wanted to be told such things so that I did not embarrass myself. This made a LOT of my friends very angry at me and cost me a few good friendships. “Do unto others” is a rule that requires a bit of thought and a lot of good judgment. Doing unto others things that I was hoping they would do to me some- times cost myself friendships. I think it is better to re- serve that rule for things that I might consider negative rather than positive. The following essay received 2 points out of a possible 6, meaning that it demonstrates some incompe- tence in that it • has a seriously limited point of view • demonstrates weak critical thinking • uses inappropriate or insufficient examples, reasons, and other evidence to support its thesis • is poorly focused and organized and has serious problems with coherence • demonstrates frequent problems with language and sentence structure • contains errors in grammar and usage that seriously obscure the author’s meaning CHAPTER 16 / PRACTICE TEST 4 823 Linear pair: z + x = 180 Substitute: 55 + x = 180 Subtract 55: x = 125 Since lines l and m are parallel: Corresponding: z = d = 55 x = c = 125 Alternate interior: z = a = 55 x = c = 125 a + b + c = 55 + 125 + 125 = 305 (Chapter 10, Lesson 1: Lines and Angles) 7. E Subtract 16: Divide by 7: Square both sides: x = 81 (Chapter 8, Lesson 4: Working with Roots) 8. D Work backwards with this problem. Each term, starting with the second, is 2 less than the square root of the previous term. So to work back- wards and find the previous term, add 2 and then square the sum: 2nd term = (1 + 2) 2 = 3 2 = 9 1st term = (9 + 2) 2 = 11 2 = 121 (Chapter 11, Lesson 1: Sequences) 9. C Before trying to solve this with geometrical formulas, analyze the figure. The rectangle is divided into 15 squares. Each of the 15 squares is split into 2 identical triangles, which means there are 30 trian- gles total. Of those 30 triangles, 15 of them are shaded in, or half of the figure. This means that half of the area, or 45, is shaded. (Chapter 10, Lesson 5: Areas and Perimeters) (Chapter 6, Lesson 2: Analyzing Problems) (Chapter 6, Lesson 4: Simplifying Problems) 10. C The long way: ★ 16 = 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 120 ★ 13 = 12 +11 +10 +9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 78 ★ 16 − ★ 13 = 120 − 78 = 42 More simply, this can be solved without actually calcu- lating the sums. Just focus on the terms in the sum of ★ 16 that are not “cancelled” by the terms in ★ 13 : ★ 16 − ★ 13 = 15 + 14 + 13 = 42 (Chapter 9, Lesson 1: New Symbol or Term Problems) x = 9 763x = 71679x += Section 2 1. C It does not matter how big each station is. All that matters is the total area and how many stations there are. (Chapter 10, Lesson 5: Areas and Perimeters) (Chapter 9, Lesson 2: Mean/Median/Mode Problems) 2. D Solve for a and b: 3a = 15 Divide by 3: a = 5 4b = 10 Divide by 4: b = 2.5 Plug in a and b: (Chapter 8, Lesson 1: Solving Equations) 3. A Pick the employee whose line has the largest positive slope. This is Employee 1. Her line has the largest “rise over run.” Her salary increases approxi- mately $20,000 in 8 years, or roughly $2,500 per year. (Chapter 11, Lesson 5: Data Analysis) 4. D Use unit analysis and solve: Total number of buckets = 20 + 20 = 40 (Chapter 7, Lesson 4: Ratios and Proportions) 5. B (5x − 3x + 4)(3x + 6x − 2) Combine like terms: (2x + 4)(9x − 2) FOIL: (18x 2 − 4x + 36x − 8) Combine like terms: 18x 2 + 32x − 8 (Chapter 8, Lesson 5: Factoring) 6. D 100 1 5 20 60 children b uc k et children buckets×= aadults bucket adults buckets×= 1 3 20 a b == 5 25 2 . average total pieces ft 6 stations 2 == = 3 600 600 , fft 2 55° 125° 55° 125° 125° 55° 125° 55° m l Detailed Answer Key 824 MCGRAW-HILL’S SAT 11. D Look at the right (units) column first. Y + X = X Subtract X: Y = 0 Look at the 10s column: 3 + Y = 3 Because Y = 0, we know there is no carried digit. Look at the left (1,000s) column: X + 5 = 13 Subtract 5: X = 8 (Chapter 9, Lesson 3: Numerical Reasoning Problems) 12. B Write out an equation given the average: Multiply by 3: x + y + 3y = 9x Combine like terms: x + 4y = 9x Subtract x: 4y = 8x Divide by 4: y = 2x (Chapter 9, Lesson 2: Mean/Median/Mode Problems) 13. C xy y x ++ = 3 3 3 15. E z° (z − 1)° (180 − x°) (180 − w)°y° x° w° (y + 1)° The simplest method is to use the Triangle External Angle theorem, which says that the measure of an “exterior angle” of a triangle equals the sum of the measures of the two “remote interior angles,” so x = y + z and w = (z − 1) + ( y + 1) = y + z. Therefore, w = x. Another, more involved method is to write an equa- tion for each triangle: Triangle on left: y + z + (180 − x) = 180 Subtract 180: y + z − x = 0 Add x: y + z = x Triangle on right: (y + 1) + (z − 1) + (180 − w) = 180 Subtract 180 and simplify: y + z − w = 0 Add w: y + z = w Substitute w for y + z: w = x (Chapter 10, Lesson 2: Triangles) 14. B Pick a value for r, like 19, that makes this statement true. (r must be 9 more than some multiple of 10.) If r is 19, then r + 2 is 21. When 21 is divided by 5, it leaves a remainder of 1. (Chapter 7, Lesson 7: Divisibility) The best way to solve this problem is to draw the lines. With each line you draw, attempt to create as many intersection points as possible. The maximum number of intersection points possible with 5 lines is 10, as shown above. (Chapter 6, Lesson 2: Analyzing Problems) 16. B The probability of selecting a king is 1/4, and the probability of selecting a queen is 2/7. To find the probability of randomly choosing a jack, add up the probabilities of choosing a king and a queen and sub- tract that sum from 1. 1 ⁄4 + 2 ⁄7 Find a common denominator: 7 ⁄28 + 8 ⁄28 = 15 ⁄28 Subtract from 1: 1 − 15 ⁄28 = 13 ⁄28 (Chapter 9, Lesson 6: Probability Problems) 17. E V U T Y X W 50° 60° 60° 60° 2x° x° 65° 65° Since ΔVXT is equilateral, its angles all measure 60°. Mark the diagram as shown. If WU = WY, then ∠WUY =∠WYU = 65°. ∠VWU (2x°) is twice as large as ∠VUW (x°). There are 180 degrees in a triangle: x + 2x + 60°=180° Combine like terms: 3x + 60°=180° Subtract 60°:3x = 120° Divide by 3: x = 40° The angles on one side of a line add up to 180°: 40°+65°+∠TUY = 180° Combine like terms: 105°+∠TUY = 180° Subtract 105°: ∠TUY = 75° (Chapter 10, Lesson 2: Triangles) CHAPTER 16 / PRACTICE TEST 4 825 18. A The question asks: what percent of m − 4 is n + 2? Translate the question: Multiply by 100: x(m − 4) = 100(n + 2) Divide by (m − 4): (Chapter 7, Lesson 5: Percents) 19. C Like so many SAT math questions, this has an elegant solution and a few not-so-elegant solutions. Most students will take the “brute force” path and start by evaluating the height function when t = 10: h(10) =−5(10) 2 + 120(10) + m = 700 +m. Then they will try to find the other solution to the equation: 700 + m =−5t 2 + 120t + m Subtract 700 + m:0 =−5t 2 + 120t − 700 Factor the quadratic (the tricky step): 0 =−5(t − 10)(t − 14) Apply the 0 product property: t = 10 or 14 Obviously, factoring a quadratic can be a pain, but in this problem you can make it easier by remembering that the equation must be true for t = 10, which means that you already know one of the factors: t − 10. The truly elegant solution, though, comes from rec- ognizing that the function is quadratic and using the symmetry of parabolas. Clearly, the height of the rocket is m when t = 0. When is the height next equal to m? The next time that −5t 2 + 120t is equal to 0. This is a much easier quadratic to solve: −5t 2 + 120t = 0 Factor: −5t(t – 24) = 0 Apply the 0 product property: t = 0 or 24 Since these two values of t give the same height, they must be reflections of each other over the parabola’s axis of symmetry. The axis of symmetry is therefore halfway between t = 0 and t = 24, at t = 12. (This is when the rocket is at its maximum height.) So when is the rocket at the same height as it is at t = 10? At t = 14, since 10 and 14 are both the same distance from 12. y t 0 m 12 10 14 24 x n m = + () − 100 2 4 x mn 100 42×− () =+ 20. C Work month by month with the price: Start of Jan: d After Jan: d − .2d = .8d After Feb: .8d + (.4)(.8d) = 1.12d After Mar: 1.12d − (.25)(1.12d) = .84d After Apr: .84d + (.25)(.84d) = 1.05d (Chapter 8, Lesson 7: Word Problems) (Chapter 7, Lesson 5: Percents) Or, more simply, remember that each percent change is a simple multiplication: d(.8)(1.4)(.75)(1.25) =1.05d. (Chapter 6, Lesson 6: Finding Alternatives) Section 3 1. A The bistro is world-renowned, so it is famous and successful. Both words should be positive. delec- table = pleasing to the taste; scrumptious = delicious; unpalatable = bad tasting; tantalizing = exciting be- cause kept out of reach; debilitating = sapping energy; savory = pleasing to the taste 2. D The first word represents something that could put a country on the brink of war. The second word represents something that could cause it to explode into destructive conflict. dissension = disagree- ment; harmony = concord; instigation = provocation; strife = violent disagreement; provocation = rousing of anger; unanimity = complete agreement; agitation = disturbance 3. B For over 500 years, art historians have argued about the emotion behind the Mona Lisa’s enigmatic (mysterious) smile. This would make the painting the source of much debate or discussion. assent = agree- ment; deliberation = discussion of all sides of an issue; concurrence = agreement; remuneration = payment for goods or services; reconciliation = the act of re- solving an issue 4. C Every year, crowds of people travel to Elvis’s hometown to pay tribute (respect). Therefore, he was a very well-respected or admired musician. satirized = made fun of, mocked; unexalted = not praised; revered = respected, worshipped; despised = hated; shunned = avoided 5. C The poker player uses tactics (strategies) to out- think his opponents, so his tactics must be intellectual. This is why he is called “the professor.” obscure = not well understood; cerebral = using intellect; transparent = easily understood; outlandish = bizarre, unusual 826 MCGRAW-HILL’S SAT 6. E Detractors are critics who would likely say something negative about the aesthetics of the build- ing, whereas its developers would likely claim that the project would be a great success. adversary = oppo- nent; enhancement = something that improves the ap- pearance or function of something else; gratuity = tip; embellishment = decoration or exaggeration; windfall = unexpected benefit; defacement = act of vandalism; calamity = disaster; atrocity = horrific crime; boon = benefit 7. B Poe wrote tales of cruelty and torture, so they must have been horrific. His tales mesmerized his readers, so they must have been hypnotizing. tenuous = flimsy; spellbinding = mesmerizing; grotesque = distorted, horrifying, outlandish; enthralling = capti- vating; interminable = never-ending; sacrilegious = grossly disrespectful; eclectic = deriving from a vari- ety of sources; sadistic = taking pleasure in others’ pain; chimerical = unrealistically fanciful, illusory; mundane = everyday, common 8. D The DNA evidence was vital to proving the de- fendant’s innocence. The missing word should mean to prove innocent or free from blame. perambulate = walk through; expedite = speed up; incriminate = ac- cuse of a crime; exculpate = free from blame; equivo- cate = avoid telling the whole truth 9. B Debussy is said to have started the breakdown of the old system (line 3) and then to have been the first . . . who dared to make his ear the sole judge of what was good harmonically (lines 6–7). Therefore, the old system did not allow this and was a rigid method for writing harmonies. 10. D The passage as a whole describes Debussy’s inventiveness as a composer of musical harmony. 11. B The hot-air balloon trip is an analogy for the difficulties involved in exploring the ocean. 12. A These are examples of the limited and rela- tively ineffective methods (lines 15–16) that make ocean exploration a difficult and expensive task (lines 18–19). 13. D This primal concept is revealed by the fact that the paintings of Stone Age artists are charged with magical strength and fulfilled . . . other functions be- yond the mere representation of the visible (lines 8–10). 14. E To be charged with magical strength is to be filled with magical strength. 15. A The stylistic change was from the naturalism based on observation and experience to a geometrically stylized world of forms discoverable . . . through thought and speculation (lines 45–48). In other words, artists were depicting ideas rather than just objects and animals. 16. B The sculptures are said to be ample witnesses (line 63) to the fact that art of this period contained elements of naïveté . . . side by side with . . . formalized compositions (lines 59–62). 17. A The passage states that Renaissance art is characterized by the discovery of linear and aerial per- spective (lines 80–81), that is, the ability to imply depth in painting, while the earlier art of the period of the catacombs (line 71) was averse to any spatial illu- sions (line 74) and contained action pressed onto the holy, two-dimensional surface (lines 75–76). 18. C Transitional forms (line 9) are described as fossils that gradualists would cite as evidence for their position (line 8), which is that evolution proceeds gradually. 19. E This case is mentioned as an illustration of the theory of punctuated equilibrium (lines 11–12). 20. B The passage says that one explanation for the extinction of the dinosaurs is that a meteorite created a cloud of gas and dust that destroyed most plants and the chain of animals that fed on them (lines 42–48). 21. D This sentence is discussing fossil evidence. The supportive structures are those bones that sup- port the weight of the body. 22. E The passage states in lines 35–38 that the biggest mass extinction in history happened between the Paleozoic era and the Mesozoic era, thereby im- plying that there were far fewer species in the early Mesozoic era than there were in the late Paleozoic era. 23. B In lines 66–71, the passage states that the probable key to the rapid emergence of Homo erectus was a dramatic change in adaptive strategy: greater reliance on hunting through improved tools and other cultural means of adaptation. 24. C The author presents several examples of mass extinctions and environmental changes that would likely lead to punctuated evolution but also describes species like Homo erectus, which remained fairly sta- ble for about 1 million years (lines 72–73). CHAPTER 16 / PRACTICE TEST 4 827 15. B This phrase lacks parallel structure. A good revision is a charismatic leader. (Chapter 15, Lesson 3: Parallelism) 16. B The sentence indicates two reasons, not one. (Chapter 15, Lesson 4: Comparison Problems) 17. D This phrase is redundant. Circuitous means roundabout. (Chapter 15, Lesson 12: Other Modifier Problems) 18. D Eluded means evaded, so this is a diction error. The correct word here is alluded, meaning hinted at. (Chapter 15, Lesson 11: Diction Errors) 19. B As it is written, the sentence is a fragment. Change clutching to clutched to complete the thought. (Chapter 15, Lesson 15: Coordinating Ideas) 20. E The sentence is correct. 21. C This is a comparison error. A grade point av- erage cannot be higher than her classmates, but rather higher than those of the rest of her classmates. (Chapter 15, Lesson 4: Comparison Problems) 22. B Both the emissary and the committee are sin- gular, so the pronoun their should be changed to its (if it refers to the committee) or his or her (if it refers to the emissary). (Chapter 15, Lesson 5: Pronoun-Antecedent Disagreement) 23. D The verb receive does not agree with the singu- lar subject each and so should be changed to receives. (Chapter 15, Lesson 1: Subject-Verb Disagreement) 24. E The sentence is correct. 25. B The subject of this sentence is genre, so the correct conjugation of the verb is encompasses. (Chapter 15, Lesson 1: Subject-Verb Disagreement) 26. C The proper idiom is method of channeling or method for channeling. (Chapter 15, Lesson 10: Idiom Errors) 27. C The sentence does not make a comparison, but rather indicates a result, so the word as should be replaced with that. (Chapter 15, Lesson 10: Idiom Errors) 28. A The word perspective is a noun meaning point of view. In this context, the proper word is prospective, which is an adjective meaning having the potential to be. (Chapter 15, Lesson 11: Diction Errors) Section 4 1. B The original phrasing is a fragment. Choice (B) completes the thought clearly and concisely. (Chapter 12, Lesson 8: Write Clearly) 2. A The original phrasing is best. 3. E This phrasing is concise, complete, and in the active voice. (Chapter 12, Lesson 9: Write Concisely) 4. D The participle pretending modifies Chandra and not Chandra’s attempt, so the participle dangles. Choice (D) corrects the problem most concisely. (Chapter 15, Lesson 7: Dangling and Misplaced Participles) 5. D The original phrasing contains a comparison error, comparing his speech to the candidates. Choice (D) best corrects the mistake. (Chapter 15, Lesson 4: Comparison Problems) 6. A The original phrasing is best. 7. C The original phrasing is not parallel. Choice (C) maintains parallelism by listing three consecu- tive adjectives. (Chapter 15, Lesson 3: Parallelism) 8. D The pronoun their does not agree with its an- tecedent, student. Choice (C) is close, but including the word also implies that the tests do indicate acad- emic skill. (Chapter 15, Lesson 5: Pronoun-Antecedent Disagreement) 9. B The original phrasing is a sentence fragment. Choices (C) and (D) are incorrect because semicolons must separate independent clauses. (Chapter 15, Lesson 15: Coordinating Ideas) 10. E The phrase requested that indicates that the idea to follow is subjunctive. The correct subjunctive form here is be. (Chapter 15, Lesson 14: The Subjunctive Mood) 11. A The original phrasing is best. 12. B The past participle form of to write is written. (Chapter 15, Lesson 13: Irregular Verbs) 13. D This phrase is redundant and should be omitted. (Chapter 15, Lesson 12: Other Modifier Problems) 14. E The sentence is correct. 828 MCGRAW-HILL’S SAT Since 7,000 out of the total of 14,000 items sold were CDs, 14,000 − 7,000 = 7,000 were DVDs. Since 4,500 of these DVDs were new, 7,000 − 4,500 =2,500 were used. (Chapter 11, Lesson 5: Data Analysis) 3. D Set up a ratio: Cross-multiply: 4x = 100 Divide by 4: x = 25 Set up a proportion: Cross-multiply: 40x = 400 Divide by 40: x = 10 bags (Chapter 7, Lesson 4: Ratios and Proportions) 4. E Divide this complex-looking shape into a square and two right triangles. Area square = (5)(5) = 25 Area triangle = 1 ⁄2(2)(5) = 5 Total shaded area = Area square + Area triangle + Area triangle = 25 + 5 + 5 = 35 (Chapter 10, Lesson 5: Areas and Perimeters) 1 44 bag 0 ounces bags 00 ounces = x 25 1 1 400pounds 6 ounces p ound ounces×= 5 400 2000 pounds pounds $ . $ . = x 29. D The list of camp activities should be parallel. The verbs should consistently be in the present tense, so will write should be changed to write. (Chapter 15, Lesson 3: Parallelism) 30. B This phrasing is concise and parallel and makes a logical comparison. (Chapter 15, Lesson 3: Parallelism) 31. C Chaplin’s mother’s mental illness is not perti- nent to the main ideas of paragraph 1. (Chapter 12, Lesson 7: Write Logically) 32. D In the original phrasing, the opening modi- fiers are left dangling. Choice (D) corrects this prob- lem most concisely. (Chapter 15, Lesson 8: Other Misplaced Modifiers) 33. E This choice is most parallel. (Chapter 15, Lesson 3: Parallelism) 34. A Sentence 11 introduces the idea that some were interested in more than Chaplin’s art. Sentence 9 expands on this fact with the specific example of Senator McCarthy’s interest in Chaplin’s political be- liefs. Sentence 10 extends the ideas in sentence 9. (Chapter 15, Lesson 15: Coordinating Ideas) 35. D This sentence provides the best transition from the idea that Chaplin’s films contained political messages to a discussion of their specific messages about domestic and international issues. (Chapter 12, Lesson 7: Write Logically) Section 5 1. B Eric earns a 5% commission on each $200 stereo, so he makes ($200)(.05) = $10 per stereo. So if he makes $100 on x stereos, 10x = 100 Divide by 10: x = 10 (Chapter 8, Lesson 1: Solving Equations) (Chapter 7, Lesson 5: Percents) 2. A Fill in the table: Jane’s Discount Music Superstore Holiday Sales New Used Total CDs DVDs Total 4,5003,000 7,500 2,500 7,000 4,000 6,500 7,000 14,000 y x 7 (5,5) 7 O 5 5 2 2 CHAPTER 16 / PRACTICE TEST 4 829 5. D If each of the small cubes has a volume of 8 cubic inches, then each side of the smaller cubes must be 2 inches long. So the dimensions of the box are 6, 4, and 4. To find the surface area, use the formula: SA = 2lw + 2lh + 2wh You are told that the volume of the prism is 300π. Since this is 1 ⁄4 of a cylinder, the entire cylinder would have a volume of 4(300π) = 1,200π. A C B D 50 10 2426 50 Plug in values: SA = 2(6)(4) + 2(6)(4) + 2(4)(4) Simplify: SA = 48 + 48 + 32 = 128 (Chapter 10, Lesson 7: Volumes and 3-D Geometry) 6. C Don't waste time doing the calculation: −15 + −14 +−13 +−12 +−11 +−10 +−9 +−8 +−7 +−6 +−5 + −4 +−3 +−2 +−1 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19. In- stead, think logically. The sum of the numbers from −15 to +15 is 0. They cancel out completely: −15 + 15 = 0, −14 + 14 = 0, −13 + 13 = 0, etc. Therefore, y must be greater than 15. With a little checking, it's easy to see that 16 + 17 + 18 + 19 = 70, so y = 19. The total number of integers from −15 to 19, inclusive, is 19 − (−15) + 1 = 35. (Chapter 9, Lesson 3: Numerical Reasoning Problems) 7. C The general strategy is to find out how many matches there are if each plays every other player once and multiply that by 2. Opponents: Player 1: 2, 3, 4, 5, 6, 7 6 Player 2: 3, 4, 5, 6, 7 5 Player 3: 4, 5, 6, 7 4 Player 4: 5, 6, 7 3 Player 5: 6, 7 2 Player 6: 7 1 Total head to-head-matchups: 21 Since they play each opponent twice, there is a total of 21 × 2 = 42 matches. (Chapter 9, Lesson 5: Counting Problems) 8. B The area of the base of the prism is 12.5π. Since this is one-quarter of a circle, the entire circle has an area of 4(12.5π) = 50π. πr 2 = area Substitute: πr 2 = 50π Divide by π: r 2 = 50 Take square root: r = 50 πr 2 h = volume of a cylinder Substitute: πr 2 h = 1,200π Divide by π: r 2 h = 1,200 Substitute : Simplify: 50h = 1,200 Divide by 50: h = 24 Finally, to find the distance from point A to point B, no- tice that AB is the hypotenuse of a right triangle with legs AD and DB. First you must find the value of AD: Simplify: 50 + 50 = 100 = (AD) 2 Take square root: 10 = AD Solve for AB: (AD) 2 + (DB) 2 = (AB) 2 Substitute: (10) 2 + (24) 2 = (AB) 2 Simplify: 100 + 576 = (AB) 2 Combine like terms: 676 = (AB) 2 Take square root: 26 = AB (Chapter 10, Lesson 3: The Pythagorean Theorem) (Chapter 10, Lesson 7: Volumes and 3-D Geometry) 9. 135 Set up an equation: x + (3y + 3) = 180° Substitute y + 1 for x: y + 1 + 3y + 3 = 180° Combine like terms: 4y + 4 = 180° Subtract 4: 4y = 176° Divide by 4: y = 44° Solve for 3y + 3: 3(44) + 3 = 135° (Chapter 10, Lesson 1: Lines and Angles) 50 50 22 2 () + () = () AD 50 1 200 2 () =h ,r = 50 . 820 MCGRAW-HILL’S SAT Detailed Answer Key Section 1 One particularly interesting exception to a rule is the orbit of Mercury contains occasional errors in grammar, usage, and mechanics 822 MCGRAW-HILL’S SAT A lot of rules have exceptions because there are dif- ferent circumstances for everybody and also people grow up. understood; outlandish = bizarre, unusual 826 MCGRAW-HILL’S SAT 6. E Detractors are critics who would likely say something negative about the aesthetics of the build- ing, whereas its developers would