sat virtual reality ii explanations phần 4 doc

“verbal” (D) is out because you wouldn’t need to specify that a bunch of letters contained words B The sentence sets up a contrast between the woman’s opinion of the film and how she usually feels about such “dramatic stories.” You don’t know what either of these (her opinion or her general attitude) is, exactly; you just know that the two have to be roughly the opposite of each other Be careful, though This doesn’t mean that all you need are two opposite words for the blanks “Predictable spontaneity” (A) are rough opposites, but “spontaneity” doesn’t fit in the sentence How can someone have “spontaneity” towards dramatic stories? The words in (B), “poignant impassivity,” work the best “Poignant” means “touching” and “impassivity” is “being unresponsive emotionally.” Clearly it would be a surprise that a woman who normally has no emotional response to dramatic stories found a film “poignant.” (C) is wrong because it wouldn’t be surprising that someone with “animosity,” or “ill will,” towards dramatic stories would find the film “irrelevant.” “Anachronistic” (D) means “chronologically out of place,” while “perspicacity” means “shrewdness.” “Affected” (E) describes something that is faked in order to impress people, for example, a foreign accent E There’s no reason to get worried as soon as you see words in the sentence you don’t understand, like “epiphytic” in this one Usually you can either figure out what the word means or you don’t need to know what it means, as with “epiphytic.” What you need to see is that the semi-colon signals that the two halves of the sentence are related in meaning If epiphytic ferns can’t survive without constant moisture, then they can only live in tropical rain forests, which have a lot of moisture You can predict something like “only found in” for the blank “Endemic to” (E), which means “restricted to a region,” matches the prediction This is a tough word, but that’s to be expected, since we’re getting near the end of the set “Steeped in” (B) means “plunged into a liquid.” Tea bags are steeped in hot water to make tea “Inimical to” (C) means “hostile to.” D The word “despite” tells you that the scientist’s conviction about his hypothesis starkly contrasts with what he has been forced to Since he thinks his hypothesis is right, you can predict that he has been forced to “change” or “retract” it Only a “lack” of supporting evidence could have caused him to this (D) matches both predictions: the “dearth,” or “scarcity,” of supporting evidence forced him to “recant,” or “renounce,” the hypothesis “Revise” (A) fits in the second blank, but “surfeit,” which means “surplus,” is the opposite of the word needed in the first blank Both words in (B), “availability accept,” have meanings opposite to those of the predicted words (C) is out because although “lack” fits in the first blank, a “lack” of evidence wouldn’t force him to “print” the hypothesis Similarly, consistent “agreement” (E) of the evidence would not force him to “deny” it section five 10 SAT Virtual Reality II 36 E The adjective in the blank has to be related to “winning over many viewers who previously supported her rival.” A good prediction would be “persuasive.” The only word that comes even close is “disarming” (E), which means “capable of winning favor.” “Presumptuous” (A) means “overstepping bounds of propriety.” “Dogmatic” (D) means “acting as though one possessed absolute truth”; the candidate wouldn’t have won over many people speaking dogmatically 11 E SAT A GARAGE is a special place for parking CARS Likewise, a “hangar” is a special Virtual Reality II place for keeping “aircraft” If you didn’t know the word “hangar” you could have worked by process of elimination, since the bridge between the stem words is clear 37 You know that in (A), for example, a “highway” is not a place for parking “buses.” You could have done this down the list, until you were left with no choice but (E) 12 C The PROLOGUE, the introduction to a PLAY, whets your appetite for what’s to come An “appetizer” is similarly the introduction to a meal (A) and (E) may have looked good because they involve the same sort of subject matter—literature and writing—as the stem words However, a “chapter” is a division of a “novel,” not its introduction A “screenplay” is the script and shooting directions for a “movie.” 13 C To have CURIOSITY is to have a desire to KNOW, just as to have “greediness” is to have a desire to “possess.” (A) and (D) have bridges that are opposite to the stem bridge Someone who shows “chattiness” has no desire to “listen,” and someone using “deception” probably has no desire to “disclose” or give out information (E) doesn’t work because someone who has “boredom” does not necessarily have a desire to “entertain.” 14 D A MARATHON is a very long RACE The only choice that fits this stem bridge is (D): an “epic” is a very long narrative “poem,” like the “Iliad” and the “Odyssey.” (A) reverses the bridge that you want A “highway” can be thought of as a very long “street”; the order of the words in this choice is what makes it wrong In (B), a “sprint” is faster than a “jog,” but not usually longer In (E), a “vice” is a bad “habit.” 15 E 16 D Someone GULLIBLE is, by definition, easy to DECEIVE Likewise, something “combustible” is, by definition, easy to “burn.” (B), (C) and (E) don’t fit this model: in (B), someone “reputable” wouldn’t necessarily be easy to “blackmail”; in (C), something “liquid” is not always easy to “evaporate”; in (E), something “broken” may not be easily fixed (A) has things muddled Someone trusting, not “trustworthy,” might be easy to “cheat,” and even then the word pair would not be connected by definition 17 B If you REND something—like a piece of clothing—thoroughly, what will be left is TATTERS, or ragged shreds The only choice that has the same bridge is (B): if you “burn” something thoroughly, what will be left is “ashes.” A couple of the other choices, (C) and (E), contain pairs of words that are closely associated with each other, but the relationship between the two words is not the same as between the stem words 18 B CALLOWNESS means “a lack of sophistication.” Someone characterized by CALLOWNESS is not COSMOPOLITAN, which means “worldly and sophisticated.” Likewise, someone characterized by “uninventiveness” is not “original,” or section five The difference between DESIRE and COVET is a matter of degree To COVET something is to DESIRE it excessively Similarly, to “loathe” something it is to “dislike” it excessively (A) is tricky because “multiply” and “increase” have very similar meanings, but to “multiply” is not to “increase” excessively “Supplement” and “subtract” in (B) are opposites The SAT never uses strict opposites like the words in choice (B) as the stem pair or the right answer Likewise, strict synonyms are never the right answer or the stem pair on SAT analogies section five “inventive.” You can get rid of (E) easily because there is no link between “intelligence” and being “friendly.” The other three choices are wrong because they contain pairs of words that are strongly connected in a positive way, unlike the stem pair In (A), someone with “skepticism” does tend to be “cynical,” and in (C), someone in “ecstasy” is very definitely “happy.” “Despotism” (D) is a form of government that involves “tyrannical” rule C A common word is being used in an unusual way here A group of LIONS is called a PRIDE; a group of “geese” is called a “gaggle.” In (B), a group of “workers” may or may not be a “syndicate,” or “union.” Not all workers are unionized You might find “violinists” (A) in a “quartet” or “elephants” (E) in a “circus,” but groups of violinists are not necessarily quartets and groups of elephants not make a circus 21 A A PLUTOCRACY is a system of government in which the WEALTHY hold power Likewise, a “monarchy” is one in which the “sovereign,” the one possessing absolute power, holds power In (B), the “elite” don’t hold power in a “democracy,” at least not in theory “Anarchy” (C) means the “absence of government,” which means no one, not even the “populace,” holds power In (E), an “oligarchy” is a system in which a small group holds power, but the group isn’t necessarily the “military.” 22 E A CONSTELLATION is made up of STARS that are grouped together The Big Dipper is a constellation Likewise, in (E) a “range” is made up of “mountains” that have been grouped together The other choices don’t have this relationship In (A), a “play” usually involves “actors” but it isn’t made up of “actors.” In (B) a “hospital” is made up of more than just “doctors” In (C), a “garden” can have more than “flowers” in it, and they haven’t been formed into a group, necessarily In (D), a family doesn’t consist of only “parents.” 23 38 D The NAP of a piece of VELVET is its texture related to the direction in which the fabric goes—if you run your hand against the NAP, the VELVET will not feel smooth Similarly, the “grain” is the texture of wood related to the direction in which the wood grows None of the other choices possesses a similar relationship In (B), the “luster” of a “pearl” is its gloss or shine In (C), the “bouquet” is the odor or perfume of a “wine.” 20 SAT Virtual Reality II 19 E A MISANTHROPE hates and distrusts HUMANKIND Even if you weren’t sure of the meaning of the word MISANTHROPE, you could have figured out from the MIS prefix that it meant something negative: think of the words “misinformed” or “mistake.” And even if you didn’t know that a “xenophobe” hates and distrusts “foreigners,” you could have eliminated all of the other choices to get the right answer In (A), a “cynic” may sometimes distrust “kindness,” but he doesn’t by definition hate kindness A “martyr” (B) does not hate “punishment”; he dies as a result of it A “deserter” (C) is cowardly, not a hater of “cowardice.” An “optimist” (D) is full of hope Westerners and Arabs Passage The author of this passage is interested, as the introduction alerts you, in how Arabs and Americans respond differently to spatial relationships After introducing his subject, known as the study of proxemics, the author goes on to consider various examples of the differences between Arabs and Americans In the second paragraph he shows how Arabs and Americans have different expectations regarding body position during a conversation Arabs expect “involvement” when interacting with friends This notion of involvement extends to public domains, according to the third paragraph; involvement and even intervention is expected on levels ranging from business transactions to government SAT Virtual Reality II 39 The differences are not limited to public places, as the author establishes in the last two paragraphs Arabs arrange their homes to get large open spaces, thus creating “an environment where personalities are intermingled ” They feel socially and sensorially deprived in America This does not mean, however, that Arabs cannot attain privacy in their own homes; they so merely by not talking Since not talking has a completely different meaning in America, awkward situations—such as that of the Arab exchange student in Kansas—can arise out of miscommunication between members of the two cultures D The first question is fairly straightforward Reading the lines directly below the phrase “two conflicting sensations” will clue you in to what sensations the author has in mind Americans feel “compressed and overwhelmed” in public in the Middle East and “exposed” in the wide open spaces of the Arab home (D), “crowding and spaciousness,” sums up the sensations well (A) is wrong because Americans may experience “confusion” in the Middle East but the author doesn’t say there is any “understanding.” “Involvement and participation” (B) are not conflicting, nor is there any evidence to suggest that Americans feel either of the two in the Middle East The author does not mention “friendliness and hostility” (C) (E) may have been tempting because Americans experience high noise levels in Arab public places, but the author doesn’t talk about “silence” in the first paragraph 25 C The author uses the example of the difficulty of walking and talking with his Arab friend to highlight the difference in “position of the bodies of people in conversation from culture to culture.” In other words, the author is “demonstrat[ing] that Arabs respond differently from Americans to spatial relationships” (C) The incident with his Arab friend was not a breakthrough in his research (A) but rather one of his “earliest discoveries.” (B) is out because the author and his friend are certainly communicating with each other; the Arab is merely having difficulty doing so while walking alongside the author Although it took the author a little while to understand his friend’s behavior, he does not mention this to emphasize that it is difficult to learn foreign customs (D)—the scope of (D) is far too broad (a typical wrong answer type) Finally, (E) can be eliminated because the author never mentions “American cities” in the passage 26 E The work you in answering one question may help you answer another If you had re-read the second paragraph in order to answer the last question, you should have been able to pick out the correct answer here The author’s Arab friend was “unable to walk and talk at the same time” because, as the author learns, “to view another person peripherally is regarded as impolite.” The Arab doesn’t “wish to section five 24 section five seem rude” (E) Perhaps the most tempting wrong choice was (C); it’s wrong because the fact that the Arab is behaving according to his own customs and not according to Western customs does not mean that he is not familiar with Western customs There is no evidence for (A), (B) and (E) in the second paragraph or anywhere else in the passage D The author says that “the notion of privacy in a public place is a foreign concept” to Arabs In the next few lines, he supports this statement by discussing how everyone in a marketplace can participate in a business transaction, how grownups are expected to discipline other people’s kids etc This type of behavior would certainly not be common in America What the author means by the phrase “foreign concept,” then, is that Arabs “do not recognize a custom that is common elsewhere.” The author never says that Arabs “prefer not to conduct business transactions in public” (A)—this is an inference that goes too far Nor does the author say that the Arabs see the “right to privacy” as an American idea (B) or that Arabs behave towards friends and strangers in different ways Finally, (E) is wrong because there is no evidence in the passage that Arabs are adjusting their way of life at all 29 E 30 D The Arab attitude toward government policy is that when a government does not intervene “when trouble is brewing,” this is the same thing as taking sides The answer to this question lies in the next sentence: it is normal for Arabs to see the actions of other governments this way because they don’t understand the “cultural mold” of their own thoughts (D) is the best paraphrase of this idea The author does not make the judgment that not taking sides is “an effective strategy” (A) or that the Arab approach is simplistic (C) (B) has things backwards: the author is talking about how Arabs misunderstand the actions of Western governments, not the other way around Finally, (E) is out because it is too broad and sweeping (remember that wrong answer type?); the author isn’t making any global statement about Middle Eastern politics 31 40 B 28 SAT Virtual Reality II 27 Beware of the obvious choice, (A) “apprehended”, which is the most common use of the word “arrested.” “Arrested” has a completely different meaning as it is used in the passage From the context of the passage, it is clear that the Arab is stopping, or “delaying” (B), the progress of the two of them walking together by insisting on facing the author while they talk D You don’t have to go very far in paragraph to realize that the word “space” keeps appearing again and again This is indeed what the author is talking about here: the use of space inside Arab homes and how different it is from what you find in American homes If you had a good grasp of the Big Picture, perhaps you didn’t even need to re-read the paragraph, for you would know that the use of space inside of the Arab home was its general topic All of the other choices are things that the author never mentions at all The example of intervening when two men fight is presented in the third paragraph, where the previous question also came from Since the author is discussing the Arabs’ emphasis on public participation in this paragraph as a whole, (E) should have jumped right out (A), (B), (C) and (D) are all reasonable-sounding answers that don’t reflect the context of the passage, which just goes to show that you should always go back to check the context before picking an answer 32 A Several of the possible answers to this Vocabulary-in-Context question are definitions of the word “value,” but only one fits in the context of the passage: “belief ” (A) The statement that the word “value” refers to in the passage, “if one is not with people and actively involved in some way, one is deprived of life,” is a belief E 34 C In the author’s story, the Arab exchange student does not realize that his hosts are mad at him because silence does not mean the same thing to him as it does to them As you know from the fifth paragraph, “silence is not considered unusual in Arab households” (C ) Although it may be true that Arabs visiting the U.S often experience homesickness (A) and that ignoring other people is rarely an effective punishment (B), the author doesn’t tell his story to make either of these points Sense of humor isn’t discussed in the passage at all, so (D) is out Finally, the story does show that it can be difficult to recognize anger in foreign cultures (E), but once again, this isn’t what the author is trying to illustrate 35 41 A few lines into the fifth paragraph, the author says that the Arabs’ “way to be alone is to stop talking.” Silence doesn’t mean that “anything is wrong or that [the Arab] is withdrawing, only that he wants to be alone with his thoughts ” The best paraphrase of this among the answer choices is (E); silence is a way for Arabs to “obtain a psychological form of privacy.” The dangerous choices to be avoided are (B) “indicate displeasure with guests” and “express unhappiness within families,” (C) both of which are ways that silence can be used in American culture (B) especially may have been tempting because of the author’s story at the end of the passage Always be sure to read the question stem carefully D The author mentions at the end of the first paragraph that Americans “rattle around” in Arab homes because there is too much space It stand to reason, then, that an Arab would feel just the opposite, “crowded” (D), in an American home There is no reason given in the passage that an Arab would find an American home “noisy” (A), “empty” (B), or “quiet” (E) (C) is wrong because paragraph indicates that Arabs prefer spacious homes section five 33 SAT Virtual Reality II Section (Verbal) Writer Pair section six Just a reminder about general strategy: read the first passage and the questions relating to it (questions 1-5 in this case), then read the second passage and the rest of the questions These two passages are not that difficult to get through, and the authors’ points of view on the process of writing contrast clearly and sharply The author of Passage believes that the writer experiences his writing as an “act of discovery” which is not in his power to control When the writer finds the proper tone of voice for his writing, he enters some sort of magical state in which “sentences mysteriously shape themselves” right before his eyes After he is finished, he will feel “that there is an order to things, and that he himself is part of that order.” The author of Passage 2, on the other hand, approaches his writing “as if it were a job like any other.” He ascribes “dangerous” notions like that of the author of Passage to the influence of the nineteenth-century Romantic movement Writing to him is “hard labor with no guaranteed reward.” Although being a good writer takes talent, it also requires a lot of difficult learning and, for him at least, “an enormous amount of bruising self-questioning.” C In lines 16-25, the author describes his vision of what happens when the writer finds the right tone of voice for his writing: he sits and watches as sentences and paragraphs mysteriously form themselves, etc What is being conveyed here is the writer’s sense of “wonder at the seemingly magical process of creation” (C) You probably could have picked out (C) without going back to the passage, simply by eliminating the other choices The author of Passage never talks about “frustration at the unpredictability of writing” (A) or about “discovering an unsuspected talent” (D) A writer is driven by a “dim vision” and does not seem to need to plan a project (B) Writing is “hard labor” (E) to the author of Passage 2, not the author of Passage 42 E SAT Virtual Reality II C The author of Passage says that unless a writer is “writing mechanically,” he experiences his writing as an act of discovery “Mechanically” is used here in the sense of “unimaginatively” (C) None of the other choices works in the context of the sentence A Reading a few lines up from the reference to “unlocking the floodgates,” you find the author asserting that creative writing is “not within the power of [the writer’s] will to summon forth” or to resist When he talks about how to “unlock the floodgates,” then, he is suggesting that creative writing is “in part beyond the writer’s conscious control” (E) The author of Passage never says that almost anyone can be a writer (A), that writing derives its power from depicting dramatic events (C), or that it requires a rigid sense of structure and form (D) He does suggest that writing can be very difficult (B), but not until the end of the passage Look at the context in which “dim” appears The author is poetically describing what happens during creative writing: “ paragraphs begin to shape themselves into an organically coherent pattern that corresponds only better, much better to the dim vision which had driven him to his desk in the first place.” Cutting through the SAT flowery language, you see that the writer only has a vague idea of what he wants to write when he sits down, but things get much clearer once he starts to write “Dim” Virtual Reality II is used in the sense of “vague” (A) 43 A Re-reading the sentence at the end of the third paragraph should be enough to enable you to pick out the right choice It is “the writer’s search for order,” according to the author, “ which exists not only in poems and stories, but in any form of writing, however humble or trivial.” (A) paraphrases this nicely The other choices may seem to be plausible general reasons for referring to different forms of writing, but they don’t work in the context of Passage B As with the previous question, all of the choices here seem like plausible reasons for adopting a “professional attitude to writing.” Only one can fit what the author actually says, though–which is that the only way he can “ensure a consistent output is to approach writing as if it were a job like any other.” He wants to “maintain a high level of productivity” (B) D In lines 50-68, the author of Passage attacks the “dangerous misconceptions” that many people have about the creative process of writing The problem, he states, is that we still believe the “fanciful notions” of the Romantic movement “Fanciful” clearly has a negative connotation here, which makes “unrealistic” (D) the best choice B D The author of Passage compares writing to “breaking rocks to look for gold” in emphasizing that writing is hard work with no guaranteed reward Looking through the answer choices, the one that echoes this sentiment most reasonably is (D) The author does think that writing requires unusual talent (A), but that has nothing to with his analogy (B) is far too extreme, while (C) is out because the author is not considering here what other people think of writers Nor is he concentrating on the possible rewards of writing (E), although such rewards do, no doubt, exist 10 D When he says that “writers are born rather than made,” the author means that some people feel compelled to write by their “response to narrative sensitivity towards language, and curiosity about human nature.” These are “innate abilities” that “play an important role in determining who will become a writer” (D) (A) contradicts the author’s continual stress on writing as hard labor (B) is reasonable but does not explain the author’s statement (C) and (E) both contradict the idea that writers are born, not made; if childhood experiences make someone a writer, then a writer would be made, not born section six As we saw in the last question, the author of Passage launches an attack on the Romantics and their fanciful notions about artistic creativity His main target is Coleridge, whose work led to the belief “that the creation of art is unlike every other form of human productivity”–an idea the author doesn’t agree with at all The author is suggesting, therefore, that Coleridge’s writings “propagated erroneous ideas about artistic creativity” (B) The author himself, not Coleridge, emphasizes the “role of maturity in an artist,” so (A) is out (C) is wrong because the author thinks that Coleridge spread false ideas about art, not that Coleridge “exaggerated the importance of the arts.” Furthermore, there is no suggestion in the passage that Coleridge ignored how long it takes to learn writing skills (D) or that he exalted experience over talent (E) SAT Virtual Reality II 44 A Several of the choices here look good, especially (E), until you re-read the last paragraph of Passage The author criticizes the publishing world for overlooking “craft and maturity of vision” in favor of “novelty and originality.” (A) is therefore the right answer None of the other choices, plausible as it may seem to be, is mentioned by the author in his criticism of the publishing world 12 A The second paragraph of Passage has been the subject of several questions so far It’s the description of creative writing as a kind of blissful mystical experience in which sentences and paragraphs form before the writer’s eyes Look through the choices to see which one jumps out–you know enough at this point to predict what Passage 2’s author would say He would see this description of the writing process as overly romantic, and point out that it “does not reflect the hard work that writing involves” (A) The author of Passage doesn’t give an opinion about the musicality of words (B) or the structure of a work (E) His idea that writers are “born, not made” (C) is not his main concern; the true nature of writing is As for (D), this criticism simply doesn’t apply to the description of the writing process in Passage 13 section six 11 E The author of Passage spends his last paragraph discussing the terror that a writer faces staring a blank page, and the fact that a writer has to be willing to risk suffering in the process of writing The author of Passage talks about the “enormous amount of bruising self-questioning” he had to undertake before he started to write Judging from this, the two authors would agree that writing entails a lot of “emotional pain” (E) The author of Passage 2, but not the author of Passage 1, stresses the importance of “life experience” (A), “background reading” (C) and “maturity” (D) Only the author of Passage emphasizes the importance of “inspiration” (B) Section (Math) SAT Virtual Reality II 45 C If a car needs 15 gallons of gas to travel 300 miles, it will need a lot more to travel 500 miles, certainly more than 16, so one thing you can here is eliminate choice (A) Let’s call the number of gallons you need to go 500 miles x To solve, the best thing to is set up a proportion: x gallons 15 gallons ᎏᎏ = ᎏᎏ 300 miles 500 miles x 15 ᎏ = ᎏ 300 500 300x = (15)(500) x = 25 D This one is certainly solvable by multiplying × 27 × 64 on your calculator and then finding the cube root of the result, but it’s just as easy to on paper If × 27 × 64 equals r cubed, then the logical thing to is to try to put 8, 27, and 64 in the form “something cubed.” is 23, 27 is 33, and 64 is 43 The equation can be rewritten as 23 × 33 × 43 = r If you remember all the rules of exponents you’ll know that 23 × 33 × 43 can be rewritten as (2 × × 4)3 Even if you didn’t remember that, you could figure it out by just multiplying out and shifting terms around: 23 × 33 × 43 = × × × × × × × × =2×3×4×2×3×4×2×3×4 = (2 × × 4)3 × × is 24, so 243 = r and r = 24, choice (D) Here we’ve got equations, one with variables and one with variable Let’s start with the equation that has only variable If 2a = 10, then dividing both sides by gives us a = If a = 5, then a2 – 16 = b can be written 52 – 16 = b 2, or 25 – 16 = b 2, or = b If b is 9, then b must be or –3, and choice (E), 3, could be a value for b A The sequence that you’re given has numbers, of which are odd and of which are even You want to know how the sum of those numbers would change if the individual numbers changed by various amounts You don’t need to start adding up the numbers in the sequence — you’re only concerned with how the sum would change, not what its value is There are odd numbers in the sequence The question stem tells you that each odd-valued term will be increased by How much will the sum of a group of numbers change when terms in the group are each increased by 3? Right, the sum will increase by × 3, or 12 If each evenvalued term is decreased by 2, that’s the same as decreasing of the terms by each, or the entire sequence by × 2, or So the sum of the sequence will increase by 12 and decrease by That’s like adding 12 and then subtracting 8, which is the same as adding 12 – 8, or 4, so the sum will increase by 4, choice (A) section seven E section seven C This is a tricky multiple figures problem You’ve got a rectangle in the middle of a triangle The only thing you know about the rectangle is that its perimeter is 12 What you know about the triangle? One angle is a right angle and another angle is labeled 45˚, so the third angle, XYU, must also be 45˚ Since RSTU is a rectangle, all its interior angles are right angles Two of its interior angles, SRU and STU, lie on straight lines That means that angles SRX and STY are also right angles Now you have small right triangles next to the rectangle Each of these right triangles has an angle that measures 45˚, so the third angle in each of these triangles must also measure 45˚ Now you know the measure of every angle in the figure, and you should have them all labeled appropriately Since RSTU is a rectangle, let’s call line segments ST and RU , for length Notice that line segment ST is not only a side of the rectangle, but also a leg of triangle YST Since YST is a 45-45-90, or isosceles right triangle, its legs must be equal in length So if ST is , then YT is also If ST and RU represent the length of the rectangle, then SR and TU must represent the width of the rectangle, so you can call those line segments w Since SR is one leg of isosceles right triangle SXR, then XR must also have length w Now we know the relationship between all the line segments Back to the perimeter The perimeter of RSTU is 12, so 2(w + ) = 12 That means that w + = Notice that the sides of the larger triangle, XU and YU, are also equal to w + XU is made up of XR and RU, which have lengths w and , respectively, and YU is made up of YT, or , and TU, or w Since each of the legs of triangle XYU have length w + , and w + = 6, the legs of triangle XYU each have length The area of a right triangle is ᎏ the product of the lengths of the legs, or ᎏ × × 6, or 18, answer choice (C) E We’ve got a bunch of lines and angles here, with a triangle in the middle One of the interior angles of the triangle is 60˚ The other interior angles of the triangle are unknown, but the one on the right and the angle marked 115˚ make up a straight line or 180˚ That means the interior angle on the right measures 180˚ – 115˚, or 65˚ The interior angles of a triangle add up to 180˚, so the third interior angle of the triangle, the one on the left, must measure 180 – 60 – 65, or 55˚ That 55˚ interior angle of the triangle is on the same side of the straight line as the angle labeled r˚, so r must be 180 – 55, or 125˚ The 55˚ angle and the angle labeled s˚ are vertical angles, so they are equal and s = 55 Therefore, r – s = 125 – 55, or 70, answer choice (E) A The date of the second Friday in December depends on what day the first of the month falls on If the first of the month is a Friday, then the 8th of the month is also a Friday since + is If the first of the month is a Tuesday, then the first Friday is the 4th, and the second Friday is the 11th If you try putting the first of the month on each of the days of the week, you’ll find that the latest possible date for the first Friday occurs when the first of the month falls on a Saturday In that case, the first Friday falls on the 7th, and the second Friday falls on the 14th, choice (A) SAT Virtual Reality II 46 C We want to find the ratio of the length of a side of the square to the length of a side of the triangle We’re told that the square and the triangle have equal perimeters The perimeter of any polygon is the sum of the lengths of its sides In an equilateral SAT triangle, all three sides have the same length Let’s call the length of each side of Virtual Reality II the equilateral triangle t Then the perimeter of equilateral triangle E is 3t In a 47 square, all four sides have the same length Let’s call the length of each side of the square s Then the perimeter of square S is 4s The perimeter of the triangle and the square are equal, so 3t = 4s Since we want the ratio of the length of a side of the square to the length of a side of the triangle, let’s solve the equation 3t = 4s for 4s s ᎏ Dividing both sides of 3t = 4s by t results in = ᎏ Dividing both sides by t t 3 s s gives us ᎏ = ᎏ So ᎏ = ᎏ and the ratio is 3:4 t t B For this question you have to know not only how to read graphs but how to find a percent decrease If you weren’t sure about how to either one of these things, you might want to some review in your Math Reference Book The population in 1986 is 500,000, since the bar above 1986 reaches to on the graph and the graph is in units of 100,000 The population in 1988 is 400,000 What’s the percent decrease in population if it goes from 500,000 to 400,000? It’s ΂ ΃ 500,000 – 400,000 100,000 just ᎏᎏᎏ × 100% = ᎏ × 100% = ᎏ × 100% = 20% If the 500,000 500,000 percent decrease in population from 1988 to 1990 is the same as the percent decrease from 1986 to 1988, then from 1988 to 1990 the population also decreased by 20% 20% of the 1988 population was 20% of 400,000, or 80,000, so the 1990 population was 400,000 – 80,000 = 320,000, answer choice (B) If the sum of the integers is negative and their product is positive, then both integers must be negative If their product is also odd, then both integers must be odd since odd or even × even = even Analyze your answer choices (A) is wrong because both integers must be negative (B) is wrong because both integers must be odd (C) is wrong because -63 = -216 which is even (D) is wrong because all prime numbers are positive section seven 10 E ... multiplying out and shifting terms around: 23 × 33 × 43 = × × × × × × × × =2×3? ?4? ?2×3? ?4? ?2×3? ?4 = (2 × × 4) 3 × × is 24, so 243 = r and r = 24, choice (D) Here we’ve got equations, one with variables... first of the month falls on a Saturday In that case, the first Friday falls on the 7th, and the second Friday falls on the 14th, choice (A) SAT Virtual Reality II 46 C We want to find the ratio... it takes to learn writing skills (D) or that he exalted experience over talent (E) SAT Virtual Reality II 44 A Several of the choices here look good, especially (E), until you re-read the last