sat virtual reality ii explanations phần 2 doc

SAT Virtual Reality II 12 section two Section 2 (Verbal) 1. C The important idea in this sentence is that the woman “lost herself in her work,” which means it must have been “inspiring” (A), “complex” (B) or “absorbing” (C), not “exhausting” (D) or “repetitive” (E). If she were really involved in her work, she would have been ignorant of the noise around her. This rules out (A) and (B); if the work were “inspiring” or “complex” she wouldn’t be “annoyed by” or “involved in” the noise. (C) works: her work was so “absorbing” that she was completely “oblivious to” the noise. 2. C “In contrast to” is the signal; that there is the difference between the piranhas’ image and the reality that many species of piranha are vegetarian. The word in the blank has to emphasize the piranha’s image as a carnivore. (C), “voracious,” or “greedy, ravenous, having a huge appetite,” works best. “Nomadic” (A) means “moving from place to place”; “lugubrious” (B) means “mournful”; (D) “covetous” means “eagerly desiring something belonging to someone else.” (E) might have been tempting, but the fact that piranhas seem “exotic” has nothing to do with their diet. 3. A This sentence has quite a bit of verbiage that you can ignore. The important thing to see is that there is a contrast between the “modern, subway stations” and the “graceful curves” of the old buildings. The word in the blank, therefore, has to be something like “rectangular.” (A), “rectilinear,” which means “characterized by straight lines” is the only one of the choices that provides the necessary contrast. 4. B The structural clue “while” alerts you that vetiver does not have a disruptive impact on the local ecology like kudzu does. A good prediction for th blank would then b “negative,” because vetiver has “no negative effects.“ The only good match for this prediction among the choices is (B), “adverse,” which means “unfavorable.” Vetiver clearly has “foreseeable” (A) and “advantageous” (E) effects because it controls soil erosion, so these choices are wrong. (C), “domestic,” doesn’t make sense in the sentence. Since you don’t know whether kudzu’s impact on the ecology is permanent, (D) doesn’t fit either. 5. E Concentrate on the second blank first. It stands to reason that Douglass would pattern his autobiography after Equiano’s own “autobiography” or “life story.” The only choice that has a second-blank word coming even close to this prediction is (E), “consciously narrative,” “Consciously” fits well into the first blank, too; Gates think that Douglass patterned his autobiography after Equiano’s narrative “consciously,” or “on purpose.” (E) is the correct answer. “patronizingly” (A) means “condescendingly.” An “epitaph” (D) is the “inscription on a tomb or grave.” 6. D The first blank has to be consistent with “lived a lonely life”; you can predict a word like “uncommunicativeness.” This rules out (B) “career” and (E) “gregariousness,” which means “sociability.” SInce Houseman did let a few close friends into his life, these friends must have been able to “get past” the “uncommunicativeness.” The choice that matches these predictions is (D), “reserve penetrate.” “Reserve” is restraint in one”s words and actions.” (A) is out because close friends would not “spurn,” or disdainfully reject,” Houseman. “Seclusion” works in (C), but “observe” doesn’t make any sense in the second blank. section two SAT Virtual Reality II 13 7. B Narrowing your focus helps with this sentence. Look at the phrase “patriotic and other cliches.” The first blank has to be a word for a category that “patriotic” falls into, such as “ideological” (B). For the second blank, you can infer that in an impersonal world, relief will come from occasional “displays” of emotion. (B), “ideological manifestations,” has what you need to fill the blanks. “Pragmatic,” which mens “practical,” doesn’t work in the first blank, and “absences” is the opposite of what we want in the second blank. “Ephemeral” (D) means “lasting a very short time,” while “vestiges” (E) means “trace or makes left by something.” 8. C The semi-colon in the middle of the sentence tells you that the two halves of the sentence have similar meanings. If a plan has “caused widespread resentment,” then it has few elements that will “make the party popular” with the electorate. We need a word that means “make popular.” “Ingratiate” )C) means “to gain favor or acceptance”; it’s the only choice that has the predicted meaning. To “consolidate” (B) is to “join together into one whole or to strengthen,” and the party doesn’t want to merge with the electorate, so (B)’s out. “Involve” (A) gives you a strange sentence when you plug it in. A political party is always involved with the electorate. “Deprecate” (D), to “express disapproval,” doesn’t make sense in the context of the sentence. (E) “impeach,” “to charge with a crime, especially the crime of misconduct in a public office” might have tricked you because it’s a word that fits in with the political subject matter of the sentence. But it doesn’t fit in with the meaning of the sentence. 9. C This is particularly difficult question, which you can anticipate because it comes at the end of the set. Several of the choices look good at first, which is why you have to look carefully at the sentence. You need an adjective describing the students who founded the literacy movement. They all had come from French-speaking colonies to live in France; so they were “expatriate” students, (C), which means “exiled from or living outside of one”s country.” The word “expatriate” derives from the root PATER, or “father” which is also found in “paternal.” And the prefix “EX” means “out.” So to move out from your “fatherland” or native country is to “EX- patriate.” “Laconic” (B) means “not talkative” and doesn’t fit the context. The students may have been “radical” (D) or “sophisticated” (E), but the evidence in the sentence that they were “expatriated” is much stronger. 10. C The WRIST is the joint that attaches the HAND to the rest of the body, in the same way that the ANKLE is the joint that attaches the FOOT to the rest of the body. None of the other pairs of words int he choices fits into the stem bridge. 11. E A good stem bridge here is “to REVERE someone is to ADMIRE that person intensely.” Analogously, to “scrutinize” something is to “examine” it intensely. “Think” and “ponder,” in (C), are synonyms; there is no difference in degree of intensity. In (B), to “delay” something a great deal is not to “cancel” it. 12. A A HEDONIST is primarily occupied with the pursuit of PLEASURE; a “philosopher” is primarily occupied with the pursuit of “knowledge.” In (B), a “stenographer,” knows “shorthand” and in (C), a “physicist” studies “energy,” but they are not, by definition, primary occupied with these things. In (D) a “progressive” wants social improvement through government action, not necessarily “liberty.” SAT Virtual Reality II 14 section two 13. E When something is being UNEARTHed, the process is called EXCAVATION (digging something out and removing it). Similarly, “imprisoning” someone is the process of INCARCERATION. In (A), the process of “addition” does not always involve “constructing.” In (D), “imposition” is “the act of imposing.” “Demanding” something is not imposing something on someone, so this pair of words doesn’t work. 14. C Something that is ABSTRUSE is by definition difficult to UNDERSTAND. Likewise, something that is OBSCURED is difficult to SEE. Things that are “unusable” (A) can still be changed; things that are “faulty” are not always difficult to “fix” (B); things that are “irrelevant” (D) may be easy to “prove.” None of these has a bridge that matches the stem bridge. “Tepid” (A) means “lukewarm,” not “difficult to heat.” 15. B To SULLY is to damage a person's REPUTATION. Similarly, to MAR is to damage an object's FINISH. Leatherback Turtles Passage If you are particularly averse to science, you could have gone on to the next passage, the fiction piece, and then returned to this one after you got through the questions there. But take a look at the introduction to this one: this passage is about turtles, not quantum electrodynamics — not too tough. Just be sure that with a passage like this one, you don’t let yourself get bogged down in the details. The overall sense of the passage is that the author, a scientist who is fascinated by the deep-diving of leatherback turtles, is reporting what he and his wife have learned about the turtles’ behavior. He tells of recording—at least, partially—the dive of a female leatherback in the first paragraph. In the second paragraph, the author discusses the difficulty of studying leatherbacks: they can’t be kept in captivity. An instrument known as the time-depth recorder has been designed to measure turtle-diving at sea. Using this instrument, the author found that female leatherbacks dive almost continuously. Why do the turtles dive? This is the question the author attempts to answer in the final three paragraphs. It seems that the turtles are following the movements of a group of organisms known as the deep scattering layer; this is where jellyfish, the turtles’ food source, are. The author has two main pieces of evidence for this hypothesis: 1) the turtles’ pattern of diving seems to match the movement of the deep scattering layer, and 2) turtles do not lose weight between bouts of nesting. Don’t worry about the details — you can always go back to the passage to get the details you need when you’re answering the questions. 16. B When you go back to the passage and locate the lines cited in a question stem, be sure to read for the context. The author says in lines 18-23 that it is impossible to keep leatherbacks in captivity because they constantly swim against the walls of the tank. Now, if you only read these lines, you’ll be tempted to select (E), keeping an animal in captivity can have negative consequences, or perhaps (A), larger facilities have to be constructed. Neither is, however, the point that the author is trying to make in the context of the passage. The author is explaining why “researchers have been developing methods of studying [the turtles] at sea.” The best paraphrase of section two SAT Virtual Reality II 15 this is (B). (C) is far too broad a generalization to be correct; furthermore, the author doesn’t say anything about scientific understanding of the turtles being “limited.” As for (D), the author never mentions other species of reptile in the passage. 17. A The “specific behavior” that the author describes in the cited lines is the continuous diving of the turtles. The author at this point is relating how astonished he and his wife were when they first recorded the turtles’ diving. He is conveying a sense of “how impressive the diving activity of the leatherbacks is” (A). The author has not yet talked about the deep scattering layer, so (B) is out. Leatherback breeding (C) is never even mentioned in the passage. (D) is wrong because the author is not suggesting that the turtles’ behavior is “unpredictable.” It may be unexpected and astonishing because the scientists didn’t know much about the turtles, but that doesn’t mean the turtles behave unpredictably. Finally, you may get an insight into the life of a marine biologist from this part of the passage, but the author’s purpose is to describe the leatherbacks, not his lifestyle. 18. C Several of the choices are possible definitions of “gradual.” Remember that with all Vocabulary-in-Context questions, you need to check how the word is used in the context of the passage. Approach this question in the same way as you would a Sentence Completion. Put a blank in the sentence in place of “gradual” and you see that the word in the blank has to have a meaning opposite of “vertical.” In other words, “gradual” and “vertical” have opposite meanings here. The only word among the possible answers that has a meaning opposite of “vertical” is “sloping” (C). 19. B The question “Why the incessant diving?” serves to lead the reader into a discussion of the author’s attempts to explain the turtles’ diving behavior. The author is using the device of asking a question and then answering it in order “introduce a new topic for discussion” (B). Although the turtles’ diving may be an area requiring “further research” (A), the author does not pose the question to make this point. Nor is he making a statement about the limitations of the time-depth recorder (C); you already know from the previous paragraph what the instrument can and cannot do. There is no suggestion here that the turtles were “behaving in a novel way” (D). How would the researchers know if the behavior were novel or not? This was the first time time they ever monitored the turtles. Finally, (E) is far too broad to be the right answer — watch out for this common kind of wrong answer type. 20. C Read the lines surrounding lines 56-57. The deep scattering layer “migrates to the surface at night to feed on phytoplankton, then gradually retreats from daylight A leatherback’s dives seem to follow the movements of the deep scattering layer.” The reason turtles make shallower dives as dusk approaches is that their food source is getting closer to the surface (C). Clearly turtles can locate their prey at night, so (A) is out. (B) can be eliminated because turtles feed on jellyfish, not phytoplankton. (D) and (E) may seem to be reasonable choices, but they don’t work in the context of the passage. SAT Virtual Reality II 16 section two 21. E You can answer this question without reading all of the final paragraph. The author says that they “have not been able to directly observe leatherbacks feeding, but we have collected some additional circumstantial evidence.” It stands to reason, then, that the additional evidence will support what the author has been claiming in the previous two paragraphs, that “female leatherbacks find most of their food in the deep scattering layer” (E). Choices (A), (B) and (D) have little to do with the information in the passage. (C) may have been distracting because the author does mention that female leatherbacks come ashore repeatedly during each nesting season, but this is not the circumstantial evidence the author uses nor is it what the author is trying to prove. 22. D The author’s hypothesis is that “female leatherbacks feed between bouts of nesting.” You also know from working through the last few questions that the leatherbacks apparently get their food (jellyfish) by following the deep scattering layer as it moves. The author admits, though, that he has not been able to observe the leatherbacks feeding when they dive. This is what would support his hypothesis the most—information about “the activity of diving female leatherbacks” (D). (E) is a tricky wrong choice. The average weight of the turtles doesn’t matter at all; it’s how much each individual turtle gains or loses that will show whether they are feeding between bouts of nesting. 23. E The correct answer to this Big Picture question should jump right out at you now that you’ve done the other questions and re-read quite a bit of the passage in the process. The author doesn’t say much about leatherbacks’ nesting patterns (A) or about “misconceptions” concerning the leatherback’s feeding activity (B). His description of the time-depth recorder (C) is a detail, not his primary objective. (D) is wrong because the author never encourages others to study leatherbacks. Instead, he is “offer[ing] his own findings about the behavior of leatherbacks.” A shortcut to answering this question would have been to take a look at the verbs in the answer choices first. Does the author “dispute” anything or “encourage” in the passage? No, so these two choices could have been eliminated right away, leaving you with only three to examine more closely. Marc and Camilla Passage With this fiction passage, you really needed to read the introduction (something you should always do, in any case). If you didn’t, you wouldn’t have had any idea what caused the extremely uncomfortable situation to arise between Marc and his friends, and you’d be confused throughout the passage because the author never specifically mentions what has upset Camilla and Karen. The first paragraph centers on Camilla’s reaction to Marc’s bragging and Marc’s realization that he has offended her once again. In the second paragraph, the author airs Marc’s opinion on Camilla’s tendency to “overreact.” She gets “emotional when it isn’t warranted, from Marc’s point of view, as a consequence of her intelligence and the fact that she cares strongly about certain things. Marc’s attention and thoughts turn to Karen in the third paragraph when he sees that he has offended her also, even though they’ve been friends for a long time. The final paragraph depicts Marc’s initial, awkward attempts to smooth the situation over. This is approximately the level of information you should retain from a good-enough reading. The question stems will direct you to specific details you need to answer the questions. 24. A In line 22, Marc’s view is that “you had to watch your mouth” around Camilla. The author goes on to explain that there were “certain things she cared strongly about,” things about which she would get emotional. ”The most innocuous (harmless) remark would set her off ” (lines 27-8). Therefore, “to watch you mouth” in this context means to “avoid sensitive topics” in conversation (A). It was clearly not Marc’s failure to observe grammatical rules (B) or the fact that he used profanities (D) (you don’t know if he did or not) that upset Camilla. (C) “behave in a polite fashion” is too broad to be the correct answer. (E) is far-fetched; Camilla would not demand that you have to “talk eloquently” in her presence. 25. D Marc thinks that Camilla has a tendency to get emotional when it isn’t “warranted.” You get a clue about what “not warranted” means in the next sentence: “the most innocuous remark would set her off.” In other words, she has no good reason, in Mark’s eyes, to get so upset; she tends to get emotional when it isn’t “justified” (D). It may be true that Camilla gets upset when she doesn’t “intend” (B) to or when Marc doesn’t “expect” (E) it, but these are not possible meanings of the word “warranted.” 26. C Marc compares having a conversation with Camilla to walking in a minefield: “one minute you’d be strolling along admiring the view, and the next, you’d have tripped her wire ” This analogy emphasizes “the unpredictability of Camilla’s reactions” (C). The author never mentions “Marc’s fear of offending other people” (A), “Camilla’s discomfort at upsetting others” (B) or “the close understanding between Marc and Camilla” (D). As for (E), Marc may be annoyed at Camilla’s behavior—the author says he suppresses a momentary impulse to get angry—but this doesn’t have anything to do with the minefield analogy. 27. B Choices (B), (C) and (E) are all possible meanings of the word “dissecting,” so you have to go back to the passage to find the meaning of the word in context. Karen and Marc had spent whole summers “dissecting each other’s private lives.” So “analyzing” (B) is the right meaning of dissecting here; “criticizing” (C) has too sharp a connotation and “cutting” (E) is too literal (remember to watch out for the most common meaning of the word — usually it’s not the correct choice). 28. B In the line immediately following the description of Marc’s summers with Karen, the author says that “Marc couldn’t think of a single woman who knew him better.” The summers spent with Karen show the “longstanding nature of their friendship” (B). This choice should have stood out because it’s the only one that fits in the context of the third paragraph, which is all about the fact that Marc has offended Karen also even though they’ve been friends for a long time. Nowhere does the author mention that Marc has “few close women friends” (A), that Marc has to overcome many obstacles in his private life (D), or that Marc regrets not having pursued a relationship with Karen further (E). (C) is based on a misinterpretation of the line that says “Marc used to justify the relationship to his father ” This does not mean that Marc had to seek his father’s approval; “justify” means “rationalize” here. section two SAT Virtual Reality II 17 29. C Marc’s feeling that he’d “really done it now” comes right on the heels of his realization that he has offended Karen, his closest friend, in addition to upsetting Camilla. Reading a few lines up from the phrase quoted in the question stem makes this clear. Marc doesn’t feel that he’s “really done it now” because he’s lost the ability to talk (A)—it’s the other way around. (B) is wrong because there is no reason to think that Karen is not loyal to him. She is simply annoyed at him right now. (D) and (E) can be eliminated quickly because they don’t make sense in the context of the passage. 30. C The author says that Marc was the “statesman of the class people joked about how much money he was going to make ” However, Marc is “groping for his words now ” You can make the inference that the author talks about Marc being the statesman of the class in order to show that he is “generally an articulate speaker” (C), but he’s floundering now. It’s true that being the statesman means that Marc is also probably “noted for his diplomacy” (A) and a “a popular student on campus” (D). These do not, however, touch upon the contrast the author is making between Marc’s usual articulate self and his current awkwardness. There is no evidence in the passage that people resent Marc’s success (B) or that his “ambitions are not realistic” (E). SAT Virtual Reality II 18 section two Section 3 (Math) 1. B In the QC section you’re supposed to compare, not calculate. Plugging all these numbers into your calculator is too time-consuming. If you look carefully at the numbers in the 2 columns, you’ll see that each number in Column B is slightly larger than a number in Column A, so you can compare piece by piece. 2 is greater than 1.7, 3.1 is greater than 3, 4.5 is greater than 4.1, and 5.4 is greater than 5.2, so the correct answer is choice (B). 2. A These angles lie on a straight line, so together they measure 180˚. You can turn this into an algebraic equation and then solve it: a + 20 + a + 10 + a = 180 3a + 30 = 180 3a = 150 a = 50 So a is greater than 45, Column A is greater than Column B, and the correct answer choice is (A). 3. C In this question you’re given 2 equations. Since one equation contains one variable, x, and the other equation contains 2 variables, x and y, let’s start with the easier one, the one with only one variable. If = 3, you can multiply both sides of the equation by 2 to get x = 6. Now you know the value of x and you can plug that into the 2nd equation like this: 2x – y = 7 Plug in 6 for x. 2(6) – y = 7 Multiply 2 × 6. 12 – y = 7 Subtract 7 from both sides. 5 – y = 0 Add y to both sides. 5 = y Now you’re ready to compare the columns. Since x = 6, Column A is 6 – 1, or 5, and since y = 5, Column B is also 5, so the correct answer is choice (C). 4. B The only thing you’re given here is that x is positive. In Column A you’ve got a percent, and in Column B you’ve got a fraction. Remember the strategy “Make one column look like the other”? That strategy is very useful here. You should either change the percent to look like a fraction or change the fraction to look like a percent. 10% is the same as and since is less than , of x is less than of x (as long as x is a positive number). If you wanted to change the fraction to a percent, you’d have to remember (or use your calculator to figure out) that is approximately 11%. Either way you do it, Column B is larger and choice (B) is correct. 1 ᎏ 9 1 ᎏ 9 1 ᎏ 10 1 ᎏ 9 1 ᎏ 10 1 ᎏ 10 x ᎏ 2 SAT Virtual Reality II 19 section three 5. A If you subtract 13 from both sides of the equation that’s given to you the result is a + b = c + d + 1. The average of a and b is and the average of c and d is . You can make the equation a + b = c + d + 1 look more like the averages by dividing both sides by 2, which gives you = , or = + . Another way of writing this equation is “the average of a and b is one- half more than the average of c and d”. That means that the average of a and b is greater than the average of c and d, so choice (A) is correct. 6. C The best way to do questions like this is just to pick a number for the variable. Since y is a positive even integer, let’s say that y is 2. Then Column A becomes the remainder when 3 is divided by 2, which would be 1, and Column B becomes the remainder when 7 is divided by 2, which is also 1. (In fact, y + 1 and y + 5 must both be odd since y is even, and an even number plus an odd number is an odd number. Any odd number divided by 2 has a remainder of 1.) Since the columns are equal, the correct answer is (C). 7. A Here you are told that a circle has radius 5. That means that its circumference is 2π(5) or 10π. You’re also given that angle AOC is 60˚. That means that it is , or of the entire circle. If you cut the circle into 6 identical wedges (pieces like pie slices), each one would be 60˚. Each one would also have the same area, and the same arc length. The 6 equal arcs make up the entire circumference of the circle. So the length of arc ABC must be of the circumference. of the circumference is of 10π, or ( )π, which is π. Now π is a little greater than 3, so π is a little greater than 5. Column A is greater. 8. B The slope of a line is the change in y divided by the change in x. (If that doesn’t sound familiar to you, you might want to check out your Math Reference Book.) Point D’s y-coordinate is 1 and point E ’s y-coordinate is 6, so the change in y is 6 – 1, or 5. Point D’s x-coordinate is 0 and E ’s is 4, so the change in x is 4 – 0, or 4, and the slope is . Notice that you could have written the change in y as 1 – 6 and the change in x as 0 – 4. It doesn’t matter which point’s coordinate you put first, 5 ᎏ 4 5 ᎏ 3 5 ᎏ 3 10 ᎏ 6 1 ᎏ 6 1 ᎏ 6 1 ᎏ 6 1 ᎏ 6 60 ᎏ 360 1 ᎏ 2 c + d ᎏ 2 a + b ᎏ 2 c + d + 1 ᎏᎏ 2 a + b ᎏ 2 c + d ᎏ 2 a + b ᎏ 2 SAT Virtual Reality II 20 section three as long as you’re consistent and put the same point’s coordinate first when you do both the change in y and the change in x. You can find the slope of the line passing through D and F the same way. That slope is = . You have in Column A and in Column B, so B is greater and the answer is choice (B). 9. D If there were less than 60 students at the lecture and 60% of them were female, how many were female? It’s probably a good idea to try picking numbers here. There might have been 50 students, in which case there were 60% 50 = .6 50 = 30 female students. On the other hand, there might have been only 20 students at the lecture, in which case there were 60% 20 = .6 20 = 12 female students. Since you get 2 different relationships depending on exactly how many students were there, the correct answer must be choice (D). 10. A Compare, don’t calculate. If T is greater than S, the result of the subtraction problem would be negative. Think about it logically. If T and S were 1 and 2, respectively (they’re not), then ST – TS would be 12 – 21 = -9. Don’t do the math; just think logically. 11. B Inequalities are easy to solve if you remember that you can usually treat them the same as you do equations. Just be careful if you multiply or divide by a negative number — in that case you have to switch the direction of the inequality sign. There’s more information about inequalities in your Math Reference Book. Here you can solve pretty easily: 3 + 2c < –5 Now just subtract 3 from both sides. 2c < –8 Divide both sides by 2. c < –4 That’s what you need to answer the question! Notice that you didn’t have to change the direction of the inequality sign because you divided by a positive number. Since c < –4, Column A is less than Column B and choice (B) is correct. 12. D If you got this one wrong, you did not read the question carefully. If apples cost 79 cents a pound, then the cost of one pound of apples is 79 cents, the cost of two pounds of apples is $1.58, etc., but how do you figure out the cost of a certain number of apples? Well, you have to know how big the apples are, in other words how many apples are in a pound. If they’re really big apples, they could weigh half a pound each, but if they’re really small apples there might be 4 or 5 or 6 or even more per pound. Since you have no way of knowing how many apples there are in a pound, the only possible answer to pick is (D). 13. D The only thing you’re given here is the inequality a > 0 > b; in other words a is positive and b is negative. That means that is a positive number divided by a negative number, which is a negative number. It also means that is a negative b ᎏ a a ᎏ b × × × × 5 ᎏ 2 5 ᎏ 4 5 ᎏ 2 6 – 1 ᎏ 2 – 0 SAT Virtual Reality II 21 section three [...]... the same numerator, CE, as Column B, but ED SAT Virtual Reality II 22 a different denominator How do AE and ED compare? Well AE = ED because the centered information tells us that E is the midpoint of AD So we can substitute AE SAT Virtual Reality II CE AB CE AB for ED in the equation ᎏ = ᎏ , resulting in ᎏ = ᎏ The columns are equal BD ED BD AE 23 1 16 ᎏ or 5 2 You’re given that the whole line segment,... DE is 1 ᎏ AD is made up of 2 2 three small line segments, all of which are equal in length That means that each 1 1 1 one must measure one-third of 1 ᎏ , which is ᎏ So AB has length ᎏ , and you can 2 2 2 1 put ᎏ or 5 into your grid 2 17 70 If you notice that there is a triangle on the right side of the figure with 2 labeled angles, you can probably solve this one The 2 labeled angles are 60˚ and... such as ᎏ If b = ᎏ , then 2a + 4 8 8 So pick a number for b that is 1 7 1 ᎏ = 1, 2a = ᎏ , and a = ᎏ , 8 8 16 which is greater than 0 and therefore meets the only other requirement you’re given for a 11 20 ᎏ or 5.5 2 If the area of a circle is 36π its radius is 6 and if the area of a circle is 25 π its radius is 5 Therefore if a circle’s area is less than 36π but greater than 25 π its radius must be less... than 5 Since the diameter of a circle is twice the radius, that means that the diameter is less than 12 but greater than 10 There is only one integer that is less than 12 and more than 10, 11, so the diameter must be 11 The 11 1 1 radius of the circle must be ᎏ of this which is ᎏ of 11 or ᎏ 2 2 2 4 21 ᎏ or 1.33 3 This one seems confusing, since you’re given the value of x + y over x – y and x asked... because you’re given 3 that a > 0 and that b > ᎏ Since a and b are both positive and 2a and b sum to 1, 4 3 1 represent? Well, suppose b were equal to ᎏ Then 2a would have to equal ᎏ 4 4 1 1 3 3 since ᎏ + ᎏ = 1 You’re given that b is greater than ᎏ , so 2a must be less than ᎏ 4 4 4 4 1 1 in order for 2a and b to sum to 1 If 2a is less than ᎏ then a is less than ᎏ a is 4 8 1 also a positive number, so any... sides by y : y x + y = 7(x – y) Divide both sides by y 7 x ᎏ + 1 = ᎏ (x – y) y y Multiply out 7x x ᎏ +1 = ᎏ –7 y y Add 7 to both sides x 7x ᎏ +8 = ᎏ y y x Subtract ᎏ from both sides y 6x 8= ᎏ y SAT Virtual Reality II 24 Divide both sides by 6 x 8 ᎏ = ᎏ 6 y Switch & reduce the fraction x 4 ᎏ = ᎏ y 3 That’s the answer! ... such a triangle is 1:͙3 :2 In particular, the ratio of the length of the shorter leg to the length of the longer leg 15 C 6 is 1:͙3 Here the longer leg is 6, so the shorter leg must be ᎏ Now that we ෆ ͙3 ෆ 1 know the lengths of both legs we can say that the area of triangle ABC is ᎏ × BC × 2 1 6 18 18 ෆ AC = ᎏ × 6 × ᎏ = ᎏ Since ͙3 > 1, ᎏ < 18 So the area of the triangle in 2 ͙3 ෆ ͙3 ෆ ͙3 ෆ 18 Column... d = 180 That means that 40 + 2d = 180, 2d = 140, and d = 70, so grid in the number 70 17 18 ᎏ , 1.88, or 1.89 9 Since 17 is prime, its only factors are 1 and 17 Therefore, a must be 17 and c must 1 c 1 be 1, since 1 is not prime Substitute 1 for c in the equation ᎏ = 9 ᎏ = 9 b = ᎏ b b 9 1 17 ab = 17 × ᎏ = ᎏ or 1.88 9 9 1 19 0 < a < ᎏ 8 This one requires some thought If 2a + b = 1, what kind of numbers... number Do you know anything else about the quantities in the 2 columns? No, all you know is that section three they’re both negative so the correct answer choice must be (D) 14 B We want to compare the area of a right triangle in Column A with 18 in Column B 1 The area of a right triangle is ᎏ × Leg1 × Leg2 We know the length of leg BC, 2 that’s 6 We still need to find the length of leg AC Angle C . first, 5 ᎏ 4 5 ᎏ 3 5 ᎏ 3 10 ᎏ 6 1 ᎏ 6 1 ᎏ 6 1 ᎏ 6 1 ᎏ 6 60 ᎏ 360 1 ᎏ 2 c + d ᎏ 2 a + b ᎏ 2 c + d + 1 ᎏᎏ 2 a + b ᎏ 2 c + d ᎏ 2 a + b ᎏ 2 SAT Virtual Reality II 20 section three as long as you’re consistent and put. correct. 1 ᎏ 10 1 ᎏ 8 1 ᎏ 8 1 ᎏ 4 1 ᎏ 4 3 ᎏ 4 3 ᎏ 4 1 ᎏ 4 1 ᎏ 4 3 ᎏ 4 3 ᎏ 4 1 ᎏ 8 17 ᎏ 9 1 ᎏ 9 1 ᎏ 9 1 ᎏ b c ᎏ b 17 ᎏ 9 1 ᎏ 2 1 ᎏ 2 1 ᎏ 2 1 ᎏ 2 1 ᎏ 2 1 ᎏ 2 1 ᎏ 2 CE ᎏ AE AB ᎏ BD CE ᎏ ED AB ᎏ BD SAT Virtual Reality II 23 section three You could also have picked numbers the CE ᎏ ED AB ᎏ BD CE ᎏ ED AB ᎏ BD AB ᎏ BD AB ᎏ BD AB ᎏ BD 18 ᎏ ͙3 ෆ 18 ᎏ ͙3 ෆ 18 ᎏ ͙3 ෆ 6 ᎏ ͙3 ෆ 1 ᎏ 2 1 ᎏ 2 6 ᎏ ͙3 ෆ 1 ᎏ 2 SAT Virtual Reality II 22 section three centered information tells us that E is the midpoint of