Answer Key 5: Using Context Intelligently 230 MCGRAW-HILL’S SAT Concept Review 5 1. Parallelism is the grammatical and logical consis- tency in phrases that list or compare things in a sentence. 2. A modifier is a word or phrase that describes an- other word. A word that modifies a noun is called an adjective, and a word that modifies a verb, an adjective, or another adverb is an adverb. 3. Try to infer its meaning from its usage in the sen- tence, then look it up in the dictionary to see if you are correct, then make a flashcard for the word using the College Hill system described in Chapter 3. 4. Britain can hardly be considered an island, despite the fact that it is separated from the European continent both physically and linguistically. 5. Even while it maintains a deep respect, even rev- erence, for its history, Britain can hardly be con- sidered archaic. 6. Britain can hardly be considered an empire, hav- ing been reduced to a mere shadow of the vast do- minion it once was. 7. The speakers ran the gamut from the eloquent to the bumbling; some were articulate while others spoke with profound ineptitude. (You may have used different words, but be sure that the first word is positive in tone and corresponds roughly to articulate and that the second word is negative and corresponds roughly to ineptitude in meaning.) 8. I did not want to sit through another lecture that was rambling and mind-numbing; rather, I was hoping for one that was focused and engaging. (You may have used different words, but be sure that both words are positive in tone and that the first corresponds roughly to focused and that the second word corresponds roughly to engaging in meaning.) SAT Practice 5 1. E Something pedestrian and conventional is ordi- nary and uses methods that have been used many times before. Therefore it is not new. lucidity = clarity; analysis = examination of parts; articulation = expression; mediocrity = average- ness; innovation = novelty, creativity 2. B To raze something is to destroy it completely. If a historical building is not razed, it is preserved or, even better, made new again. renovated = made new again 3. C Brevity of expression is conciseness. vivid = full of lively forms or colors; concise = to the point; accessible = easily understood; concrete = perceived through the senses 4. D A melée is a fight. If the groups were fighting, they probably have disagreed with each other. Therefore the melée was not unexpected. 5. B A highway that has been devastated by the earthquake would be hard to travel through. impassable = unable to be travelled through 6. E Those who think they can write a novel if they simply sit down and type are probably unaware of how challenging such a task is. They are naive. amateur = nonprofessional; candid = frank and honest; renowned = reputable, well-known; skepti- cal = inclined to doubting; superb = exceptional; timid = shy; naive = lacking a sophisticated understanding 7. D If something cannot be tested with scientific rigor and is not a reliable method, it must be with- out a reasonable, scientific basis. intuitive = based on hunches rather than reason; ornamental = decorative 8. A Despite indicates contrast. Paranoia and extreme competitiveness are certainly bad things. Of course, cutthroat executives would claim that they help, but they can’t really be helpful to success in the business world. by-products = results of a process; conducive = helpful; detrimental = harmful; inequities = unfair situations 9. D If something is transformed into a menacing poison, then it must not have been so bad before. Perhaps it was only a little bit troublesome. epidemic = a broad outbreak; derivative = repetitive of previous works; rudiment = basic element; virulent = dangerous; nuisance = annoyance CHAPTER 5 / SENTENCE COMPLETION SKILLS 231 Lesson 6: The Toughest Sentences There are two ways to complete this sentence. Modern film directors might like or dislike the natural half- sentences and interrupted thoughts that characterize genuine human speech. If they like them, they would use them; choice (A) supports this reading. If they don’t like them, they would prefer more formal dialogue. Choice (B) gives formal and (D) gives stilted, which convey that idea. But if the directors use formal lan- guage, they wouldn’t assume imperfect dialogue, so (B) is out. Likewise, if they used stilted (formal) dia- logue, they wouldn’t adopt imperfect dialogue. So (A) is the correct response. Abstract vs. Concrete Tough Sentences Some sentences are tough not because they have tough vocabulary, but because they have a complicated or ambiguous logical structure. Negatives can easily complicate a sentence and are easily overlooked. Watch carefully for negative words like not, hardly, rarely, lacking, etc., because they are as important as the key words! When you encounter a sentence with negatives, it may help to paraphrase the sen- tence more “positively.” Some sentences are tough to work with because they are ambiguous; that is, they have more than one possible interpretation, usually one positive and one negative. Since there are usu- ally only two possibilities, just try them both. Concrete nouns, which usually represent peo- ple and objects, are typically easier to under- stand than abstract nouns, which typically represent quantities, qualities, or ideas. When we focus on the concrete nouns in a sentence more than the abstract ones, we can misread the sentence. Pay special attention to abstract nouns in sentences. Negatives Example: Their approach was not unlike that of the Neo- Darwinians, whose lack of respect for quasi- scientific methods was far from unknown in the University community. This sentence is easier to work with if it is first para- phrased without so many negatives: Their approach was like that of the Neo-Darwinians, whose support for the scientific method was well known in the University community. Ambiguous Sentences Example: The recent trend of using dialogue in films can be traced to directors who have the natural half-sentences and interrupted thoughts that characterize genuine human speech. (A) halting . . embraced (B) formal . . assumed (C) imperfect . . eschewed (D) stilted . . adopted (E) passionate . . endured Example: The dissent regarding the new restrictions on student parking was those who wanted to be able to drive freely to school. (A) spearheaded by (B) surprising to (C) troublesome to (D) disputed by (E) disregarded by This sentence is not about the parking restrictions, but rather about the dissent. It’s easy to misread if you don’t focus on the word dissent. (We overlook it be- cause it’s so abstract.) If you wanted to drive freely to school, how would you feel about the dissent regard- ing parking restrictions? You’d probably be one of the people dissenting! You may even initiate the dissent, which is why (A) is the best choice. Concept Review 6: The Toughest Sentences 232 MCGRAW-HILL’S SAT 1. What, other than tough vocabulary, can make a sentence hard to understand? 2. What are abstract nouns, and why should you pay close attention to them in sentences? 3. Circle the abstract nouns and draw boxes around the concrete nouns in the sentence below. The lack of interest among the voters ensured that the referendum about the new playground could sneak through, even though it contained some objectionable clauses. Paraphrase the following sentences to minimize negatives. 4. It is not uncommon to find people who refuse to deny that ghosts exist. 5. The council did not fail to block a single motion. Complete the following ambiguous sentences in two ways, with different tones. 6. Despite the ____________________ of the climb, the explorers were beginning to believe that the trek would soon become ____________________. Despite the ____________________ of the climb, the explorers were beginning to believe that the trek would soon become ____________________. 7. Far from being ____________________ on the issue of gun control, Will has ____________________ on the issue for many years. Far from being ____________________ on the issue of gun control, Will has ____________________on the issue for many years. CHAPTER 5 / SENTENCE COMPLETION SKILLS 233 SAT Practice 6:The Toughest Sentences 1. The country’s confidence, formerly sustained by an sense of power, was replaced by an equally exaggerated sense of following the hasty evacuation of its troops from three foreign capitals. (A) inflated . . weakness (B) overwhelming . . inviolability (C) erratic . . hysteria (D) unquestioned . . omnipotence (E) arbitrary . . resolution 2. According to their detractors, the leaders of the Union for Progressive Politics do not truly change, but simply rehash old and discredited theories of political philosophy. (A) admonish (B) censor (C) advocate (D) caricature (E) hinder 3. Dr. Cuthbert often his former associates for not continuing to support him; apparently he harbored great animosity because of their of him. (A) disparaged . . endorsement (B) excoriated . . abandonment (C) exonerated . . denunciation (D) extolled . . betrayal (E) venerated . . dismissal 4. Despite her gregariousness, Andrea seems to have been a woman who cherished her highly. (A) colleagues (B) friendships (C) privacy (D) integrity (E) humility 5. It is extremely rare to see a politician any opinion that is widely unpopular; it seems that, for them, public censure is more even than death. (A) conform to . . desirable (B) tolerate . . exciting (C) reject . . feared (D) espouse . . painful (E) manipulate . . natural 6. The cogency and animation he showed in private belied his reputation for a notably style of lecturing. (A) tepid (B) incisive (C) versatile (D) infrequent (E) fluent 7. The haiku, with its , its reduction of natural and everyday events to their mere essence, seems to economically depict the of even the sim- plest human experience. (A) casualness . . destructiveness (B) optimism . . barrenness (C) capriciousness . . rigidity (D) digressiveness . . precariousness (E) conciseness . . poignancy 8. Sadly, most people who say they want change in public schools will struggle to resist it, or at least its effects on them. (A) initiate (B) distort (C) palliate (D) defend (E) enhance 9. Despite the literature debunking the theory of ESP, a critical and rational awareness of the sub- ject continues to most of the public. (A) vivid . . pervade (B) voluminous . . elude (C) provocative . . captivate (D) ambiguous . . perplex (E) incomprehensible . . escape Answer Key 6: The Toughest Sentences 234 MCGRAW-HILL’S SAT Concept Review 6 1. Complicated or ambiguous logical structure. 2. Abstract nouns are nouns that represent ideas, quantities, or qualities; that is, they represent things that cannot be directly perceived. 3. The lack (abstract noun) of interest (abstract noun) among the voters (concrete noun) ensured that the referendum (abstract noun) about the new play- ground (concrete noun) could sneak through, even though it contained some objectionable clauses (ab- stract noun). 4. It is common to find people who believe in ghosts. 5. The council blocked every motion. 6. Despite the ease of the climb, the explorers were beginning to believe that the trek would soon be- come treacherous. (or some similar words) Despite the arduousness of the climb, the explor- ers were beginning to believe that the trek would soon become easier. (or some similar words) 7. Far from being passive on the issue of gun control, Will has pontificated on the issue for many years. (or some similar words) Far from being consistent on the issue of gun con- trol, Will has equivocated on the issue for many years. (or some similar words) SAT Practice 6 1. A What would follow a hasty evacuation of a country’s troops? A feeling of being overwhelmed and defeated, most likely. This feeling of weak- ness, we are told, is just as exaggerated as the sense of power just prior to the withdrawal. inviolability = invincibility; erratic = irregular; hyste- ria = irrational and exaggerated emotion; omnipo- tence = supreme power; arbitrary = based on whim and random power; resolution = determination 2. C If their detractors (critics) believe that they only rehash old and discredited theories, then they are suggesting that they do not really speak out for change. admonish = reprimand; censor = eliminate objec- tionable material; advocate = speak in favor of; caricature = exaggerate comically; hinder = get in the way of 3. B If his associates did not continue to support him, they must have abandoned him. If he har- bored animosity for them, he must have criticized them. disparaged = criticized harshly; endorsement = show of support; excoriated = criticized harshly; exonerated = proved innocent; denunciation = con- demnation; extolled = praised highly; venerated = honored 4. C Despite indicates contrast. Gregariousness is sociability. Its opposite is solitude, reclusiveness, or privacy. 5. D If public censure is like death, politicians must not like it. They must never openly adopt a widely unpopular opinion. conform = do what is expected; espouse = adopt publicly; manipulate = take control of 6. A Cogency is persuasiveness and animation is liveliness. To belie is to misrepresent, so he must not have a reputation for being lively and persua- sive, so people must think he’s dull. tepid = dull, lukewarm; incisive = keen and thoughtful; versatile = well-rounded; fluent = smooth, flowing 7. E The first word must mean something like re- duction to its essence, and the second word must mean something like essence. barrenness = starkness; capriciousness = whimsy, randomness; digressiveness = tendency to go off topic; precariousness = danger; conciseness = brevity; poignancy = sharpness of feeling 8. C If they resist it, then they want to prevent its effects on him, or at least minimize its effects on them. initiate = begin; distort = twist; palliate = make less severe; enhance = make better 9. B Despite indicates irony. If there is literature de- bunking the theory of ESP, it would be ironic if the public failed to develop a critical and rational awareness of the subject. What would make it even more ironic is if the literature were plentiful. vivid = full of vibrant imagery; pervade = fill com- pletely; voluminous = plentiful; elude = escape cap- ture or understanding; provocative = tending to elicit strong reactions; captivate = capture; am- biguous = unclear; perplex = confuse; incompre- hensible = beyond understanding 235 WHAT THE SAT MATH IS REALLY TESTING CHAPTER 6 ✓ 1. Mapping Problems 2. Analyzing Problems 3. Finding Patterns 4. Simplifying Problems 5. Connecting to Knowledge 6. Finding Alternatives 7. Thinking Logically 8. Checking Your Work Copyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use. 236 MCGRAW-HILL’S SAT What Is Mapping? Mapping a problem means orienting yourself to the problem and representing its information. It’s like pulling out a map before you start a trip. The map shows you where you’re going but not how to get there. On some tough SAT math problems, half the battle is “mapping”—orienting yourself to the problem and figuring out what it’s asking. Tips for mapping tough SAT math problems: • Write out any diagrams, equations, or tables that represent the key information in the problem. You don’t get neatness points on the SAT—good test-takers scribble all over the test booklet. Writing things down helps you to keep track of the information as well as your thought process. • Notice any restrictions on the unknowns. For instance, do they have to be integers or positive numbers or multiples of some number? Are they measures of angles or segments or areas in a figure? Underline key restrictions. • Know the definitions of special terms such as primes, integers, factors, multiples, perimeter, and so on, and underline these terms when you see them. • Notice whether any unknowns can take any values that you choose or have only one par- ticular value that you have to find. You can solve many complicated-looking problems by just choosing values for the unknowns! • Read carefully and notice exactly what the problem is asking for. Does it ask you to solve an equation? Find the value of an ex- pression? Find an area? Underline what the problem is asking you to find so that you don’t lose track of it. • Notice whether the question is multiple- choice, and if so, notice the range of the an- swer choices. If the answers are far apart, you might be able to just estimate an answer to zero in on the right choice. Also, notice how the choices are expressed. Are they frac- tions, decimals, radicals, algebraic expres- sions? Noticing this often helps you to see what you have to do to get the answer. Lesson 1: Mapping Problems Watch for the Common Mix-Ups Even the best students sometimes miss questions be- cause they misinterpret key terms in the problem. You can avoid this by underlining these key terms and thinking about the terms they are commonly confused with. •A perimeter is the distance around a figure. Don’t confuse it with area, which is the num- ber of square units that fit inside a figure. • The circumference formula for a circle is c = 2πr. Don’t confuse it with the area formula of a circle, which is a = πr 2 . To avoid confusing them, remember that area is always measured in square units, so its formula contains the “square.” • An odd number is any integer not divisible by 2. Don’t confuse it with a negative num- ber, which is any number less than 0. These two are commonly confused because both of these words have a “bad” tone. • An even number is any integer divisible by 2. Don’t confuse it with an integer in general, which is any positive or negative whole number. These two are commonly confused because when we talk of a number dividing another “evenly,” we really mean that it goes in an integer number of times, not necessar- ily an even number of times. •A product is the result of a multiplication. Don’t confuse it with a sum, which is the result of addition. Don’t Rush—Avoid Quick Gimmicks Always read the whole problem carefully before deciding how to solve it. SAT math questions—especially medium and hard-level ones—are designed to trap students who don't read carefully or who pigeon-hole questions too quickly. Getting an answer quickly doesn’t help if it’s the wrong answer. It’s important to be prepared for what you’ll see in the Math sections on test day. Visit our Online Practice Plus at www. MHPracticePlus/SATmath for more tools and resources to help. CHAPTER 6 / WHAT THE SAT MATH IS REALLY TESTING 237 Concept Review I: Mapping Problems 1. Describe what it means to “map” a problem. 2. Why is it important to consider the choices (in a multiple-choice question) as part of the problem? Define the following terms, and indicate what terms they are sometimes confused with. 3. Odd means and is sometimes confused with 4. Even means and is sometimes confused with 5. Perimeter means and is sometimes confused with 6. Integers are and are sometimes confused with Equations or inequalities are powerful “mapping” tools. Translate the following statements into equations or inequalities. Be sure to specify the meanings of any unknowns you may use. 7. The sum of two consecutive odd numbers is 28. 8. Ellen is twice as old as Maria. 9. Last year, Jennifer was twice as old as Brian is now. SAT Practice 1: Mapping Problems Map each of the following problems before solving it. Use the space for scratchwork, and underline any key words in the problem. Then solve each problem. 1. The product of five consecutive even integers is 0. What is the greatest possible value of any one of these integers? 2. The perimeter of a rectangle is 28 inches, and its area is x square inches. If x is an even integer, what is the greatest possible value of x? 3. Carlos begins with twice as much money as David. After Carlos gives $12 to David, Carlos still has $10 more than David. How much money did they have combined at the start? (A) $32 (B) $66 (C) $68 (D) $92 (E) $102 4. Corinne travels from home to work at an average speed of 50 miles per hour, and returns home by the same route at 60 miles per hour. It takes her 10 more minutes to get to work than it takes her to get home. How many miles is it from Corinne’s home to work? (A) 25 (B) 35 (C) 50 (D) 75 (E) 90 Do Your Scratchwork Here 238 MCGRAW-HILL’S SAT CHAPTER 6 / WHAT THE SAT MATH IS REALLY TESTING 239 Concept Review I 1. To map means to represent the general problem situation and goal, either mentally or on paper. 2. Because the choices tell you the range of values to consider, as well as the form of the numbers (in- tegers, fractions, etc.) and format (factored, deci- mal, etc.). 3. Odd means an integer not divisible by 2 and is sometimes confused with negative because of the “negative” tone of both words. 4. Even means an integer divisible by 2 and is some- times confused with positive because of the “posi- tive” tone of both words. 5. Perimeter means distance around a figure and is sometimes confused with area, which is the num- ber of square units that fit inside a figure. 6. Integers are whole numbers and negative whole numbers and are sometimes confused with count- ing numbers, which are the positive integers: 1, 2, 3, 4, . . . 7. Let n be the smaller of the two numbers. Then the next odd number is n + 2, so an equation that says that the sum of two consecutive odd numbers is 28 is n + n + 2 = 28. 8. Let e stand for Ellen’s current age and m stand for Maria’s current age. An equation that says that Ellen is twice as old as Maria is e = 2m. 9. Let j stand for Jennifer’s age now and b stand for Brian’s age now. Last year, Jennifer was j − 1 years old, so an equation that says that last year Jennifer was twice as old as Brian is now is j − 1 = 2b. SAT Practice 1 1. 8 If the product of a set of integers is 0, then one of the numbers must be 0. To maximize the value of any one of them, let 0 be the smallest of the integers. If they are consecutive even integers, they must be 0, 2, 4, 6, and 8. If your answer was 4, then you overlooked the fact that the numbers are even. 2. 48 Your first tool in mapping a geometry prob- lem is a good diagram. This one has no diagram, so you must draw your own. Draw a rectangle, labeling its width w and its length l: 3. E Let c be the number of dollars Carlos had to start and d be the number of dollars David had to start. The question asks for the value of c +d. If Carlos begins with twice as much money as David, then c = 2d. After Carlos gives $12 to David, he has c − 12 dollars, and David has d + 12 dollars. If Carlos still has $10 more than David, then c − 12 =(d + 12) +10. Simplify: c − 12 = d + 22 Add 12: c = d + 34 Substitute c = 2d: 2d = d + 34 Subtract d: d = 34 Plug back in: c = 2(34) = 68 So c + d = 34 + 68 = 102. 4. C To “map” this problem, you must know that distance = speed × time. You must find the num- ber of miles from Corinne’s home to work, so call that d. If she travels from home to work at an average speed of 50 miles per hour, then it must take her d/50 hours, or 60 × d/50 = 6d/5 minutes. If she returns home at 60 miles per hour, it must t ake her d/60 hours, or 60 × d/60 = d minutes. If it takes her 10 more minutes to get to work than it takes her to get home, then: Simplify: Multiply by 5: d = 50 d 5 =10 6d d 5 10−= Since the perimeter of the rectangle is 28 inches, you can set up an equation: 2w + 2l = 28. Divide both sides of the equation by 2 to get w + l = 14. Since the area is x, you can set up the equation lw =x. If x is even, then l and w can’t both be odd. (Can you see how we know that?) You should be able to see that the possible values for w and l are 2 and 12, 4 and 10, and 6 and 8. (Check them and see.) This means that x can have values of 2 × 12 = 24, 4 × 10 = 40, or 6 × 8 = 48. The greatest of these, of course, is 48. Answer Key I: Mapping Problems ᐉ w . Thinking Logically 8. Checking Your Work Copyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use. 236 MCGRAW-HILL’S SAT What Is Mapping? Mapping a problem means orienting yourself. many miles is it from Corinne’s home to work? (A) 25 (B) 35 (C) 50 (D) 75 (E) 90 Do Your Scratchwork Here 238 MCGRAW-HILL’S SAT CHAPTER 6 / WHAT THE SAT MATH IS REALLY TESTING 239 Concept Review. Answer Key 5: Using Context Intelligently 230 MCGRAW-HILL’S SAT Concept Review 5 1. Parallelism is the grammatical and logical consis- tency in phrases that list or compare things in a sentence. 2.