Now look at the answer choices. The only one that is true is (E), which states that the median of the scores is equal to the mean. 11. C Check the statements one at a time. Start with Statement I. The sum of the measures of the angles of a triangle is 180 degrees, and the small triangle has angles measuring a, b, and 90 degrees. Therefore, a + b + 90 = 180. Subtracting 90 from both sides leaves you with a + b = 90, so I is true. Move on to Statement II. Because lines 3 and 4 are parallel and d and a are corresponding angles, you know that d = a. Now you need to decide whether the sum of the measures of d and c equals 90 degrees. Notice that d and c are part of a large right triangle. Therefore, as with Statement I, d + c + 90 = 180, so d + c = 90. Since a = d, you know that a + c = 90 and that Statement II is also true. Now try Statement III. There is no information that tells you that b is equal to either a or d, or that any of the line segments are of equal length. Therefore, there is no way of knowing whether b and d are equal. They may be, but it is also possible that they are not. Therefore, only I and II must be true and the answer is (C). 12. C If there are 200 mattresses in the store, you can subtract the sum of the twin-, full-, and king-sized mattresses from 200 to find the number of queen-sized mattresses currently in stock: There are 70 queen-sized mattresses. When there are 70 mattresses of each size, there will be 70 × 4 = 280 mattresses total. There are currently 200 in stock, so you need 80 more. 13. D The best way to do this problem is to use common sense. If there were 4 chairs at all 25 tables, there would be 100 total seats. If there were 1 table with 2 chairs and 24 with 4 chairs, there would be (24 × 4) + 2 = 96 + 2 = 98 chairs. Therefore, for every 1 table with 2 chairs, you lose 2 chairs from the sum. The total of 86 chairs in the restaurant is 14 less than the 100-chair maximum. 14 ÷ 2 = 7, so there are 7 tables with 2 chairs and 18 tables with 4. Double-check this by computing (18 × 4) + (7 × 2) = 72 + 14 = 86. Another way to do this problem is by backsolving. Plug the answer choices into the following equation: 4t + 2(25 – t) = 86 Start with choice (C) since it’s in the middle: 4(15) + 2(25 – 15) = 60 + 20 = 80 That’s too few chairs. You have to try a bigger choice. Try (D): x = 200 −(39 + 67 + 24) = 200 −130 = 70 section five SAT Virtual Reality III 34 4(18) + 2(25 – 18) = 72 + 14 = 86 It works! Either way you approach this problem, the answer is (D). 14. D The most important part of this question is knowing which of the coordinates are positive and which are negative. Look at the diagram again: Remember that the x values are the first coordinates in a pair and the y values are the second coordinates. Values for x are positive if they are to the right of the y-axis and are negative if they are to the left. Values for y are positive if they are above the x- axis and are negative if they are below it. Following these rules, the positive values must be d, b, and a. The negative values must be c, e, and f. Now all you have to do is go through the answer choices and find two variables with the same sign that are multiplied together. The only such choice is ef, choice (D). 15. C First figure out how many miles will be traveled at each price. There are 100 miles total, and the first 10 cost a flat rate of $5.00. That leaves 90 miles, 40 of which cost $0.25 per mile. The last 50 miles cost $0.10 per mile. Now find out how much each segment costs and add them together: 16. C The formula for the area of a triangle is the following: Area = Base × Height In this problem, you are told that the area of the triangle is 24 and that the height is 6. You can also tell from the diagram that the base is equal to x + (x + 2). Now substitute these values into the area formula: 24 = 1 2 (x + x + 2)(6) 48 = (x + x + 2)(6) 8 = (x + x + 2) 8 = 2x + 2 6 = 2x x = 3 1 2 $5.00 + 40($0.25) + 50($0.10) = $5.00 + $10.00 + $5.00 = $20.00 section five SAT Virtual Reality III 35 ( c , d ) ( a , b ) ( e , f ) x y 17. A Begin with Statement I. Look at the inequality that states x – y > 0. Adding y to both sides gives you x > y, so Statement I must be true. Move on to Statement II, which states that x and y are both positive. Now look at the first inequality, x + y < 0. If the sum of x and y is less than 0, it is impossible for both numbers to be greater than 0. Therefore, Statement II cannot be true. Now try Statement III. This says that x must be positive and y must be negative. The best way to test this statement is to pick numbers. If x = 2 and y = –3, x + y = –1, which is less than 0, and x – y = 5, which is greater than 0. In this case, Statement III is true. But what if x and y are both negative? What if x = –2 and y = –4 ? Using these values, x + y = –6, which is less than 0, and x – y = 2, which is greater than 0. Since x can be either positive or negative, Statement III is not necessarily true and the answer is (A). 18. B All you need to do in this problem is plug a = 6 and b = 4 into the expression and evaluate it: 19. E This problem is a bit more involved than the last one using the same operation, but still uses the same concepts. Instead of simply substituting one set of values into the expression and computing, you must substitute 2 sets of values into the expression, set them equal to each other, and solve for a. Substituting the given values into the expression and setting them equal to each other gives you: 20. B The first step to solving this problem is getting both ratios into a form that has the same value for a. If a : b = 4 : 5 and a : c = 2 : 7, you can make both values of a 4 by multiplying the entire a : c ratio by 2. The new form of the ratio becomes 4 : 14. Now you can compare b and c. Be careful, however, because the question asks for c : b, not the other way around. Therefore, the ratio is 14 : 5 or , choice (B). 21. A The easiest way to do this problem is to try some values for x and see which is the greatest power of 4 that is less than 250. Since you have to calculate 4 3 to raise 4 to higher powers, you should start there. 4 × 4 × 4 = 64, which is less than 250. Multiply this number by 4 to find 4 4 . 64 × 4 = 256, which is greater than 250. The greatest power of 4 which yields a number less than 250 is 3, choice (A). 14 5 a 2 − a a = 10 2 − 2 2 a(a − 1) a = 100 − 2 2 a − 1= 98 2 a − 1= 49 a = 50 a 2 − b b = 6 2 − 4 4 = 36 − 4 4 = 32 4 = 8 section five SAT Virtual Reality III 36 22. D To figure out how many tiles are needed, you must break up the L-shaped floor into sections. This will allow you to work with rectangular areas instead of an odd shape. Break the room up like this: Now you must find how many tiles are needed to cover each rectangle. Since you have the dimensions of each tile in terms of x and y, you can figure out how many tiles are needed by picking numbers for x and y. To make life easier, use x = 25 and y = 20. Now calculate the dimensions of a tile and of the room and relabel the diagram: Now the tile is 1 by 1 and the room’s two areas are 5 by 25 and 15 by 5. Find the areas of the 2 sections of the floor, add them together to get the total area of the bathroom floor, and, since the area of a tile is 1, you have your answer: You would normally divide this number by the area of one tile, but since the area of a tile is 1, 200 ÷ 1 = 200 and the answer is (D). 23. D The first thing you need to do is find what the tens’ digit can be. You are given that the sum of the other two digits must equal the square of the tens’ digit and that the hundreds’ digit must be 3, 2, or 1. Therefore, the greatest possible sum of the hundreds’ and tens’ digits is 3 + 9, or 12. The square of the tens’ digit must be 12 or less, and the only perfect squares less than 12 are 0, 1, 4, and 9. Since there is no way the hundreds’ digit can equal 0, you can eliminate 0 as an option. The tens’ digit can either be = 1, = 2, or = 3. Now count the combinations of numbers 9 4 1 Area = (5 × 25) + (15 × 5) = 125 + 75 = 200 5 5 25 15 section five SAT Virtual Reality III 37 x y 4 x 5 3 y 4 between 100 and 400 in which the sum of the hundreds’ digit and the units’ digit equals 1, 4, or 9. The easiest way to do this is to list the possibilities: 110 123 222 321 138 237 336 There are 7 possibilities, choice (D). 24. B Use algebra to find the solution to this problem. First, find the numerical values for b and c. Since 2b = 7, divide both sides of the equation by 2 and you get b = . Do the same thing with 3c = 7, giving you c = . Now plug these values into the first equation: Now solve for : 25. D This one is hard to draw. Think logically and try to visualize the orange. The first cut breaks the orange into 2 pieces. If you cut the orange so that you cut the 2 halves into equal pieces, you have 4 equal quarters. Your next cut can cut the quarters into 8 equal pieces. Therefore, 3 cuts can yield a maximum of 8 pieces, choice (D). x 7 2 − 7 3     − x = y x 7 2 − 7 3 − 1     = y x 21 6 − 14 6 − 6 6     = y 21 6 − 14 6 − 6 6 = y x y x = 1 6 y x x 7 2 − 7 3     = y + x 7 3 7 2 section five SAT Virtual Reality III 38 Section 6 (Verbal) Medical Pair Although these two passages discuss issues in medical research, don’t be intimidated by the subject matter. Read through the passages once to get a general feel for them. The question stems will direct you back to the specific sentences you’ll need to understand to get the answers. Also, it’s a good idea to read through Passage 1 and do the questions that refer to it, and then read through Passage 2 and do the rest of the questions. Passage 1 talks about the difficulty of reconstructing or replacing certain bones in humans. A recent advance has been the creation of bone substitutes from muscle using the protein osteogenin. While osteogenin can’t be used directly on a defect, it can be used to prefabricate bones in molds implanted in an animal’s abdomen. The process hasn’t been tried in humans, though, because osteogenin is scarce, and because it has to be tested on larger animals first. Passage 2 has a distinctly different tone. The author is not objective and impartial; he’s taking a stand on an issue: he argues that testing on humans is necessary in order to make improvements in artificial organs. Using animals, he says, isn’t good enough: there are no good animal models for human bones and joints. Moreover, testing on humans gives doctors crucial experience. The author concludes that there’s no point in developing new designs for artificial organs until present ones have been evaluated on people. 1. D Remember to read the sentences before and after the line reference. At the end of paragraph 1, the author talks about the difficulty of reconstructing and replacing bones. This is the “challenge” that’s further explained in paragraph 2—(D) is the answer. The author doesn’t mention tissue development in the human embryo until paragraph 3 (A). (B) contradicts the passage: the author states that it ’s impossible to reconfigure bones. It’s currently possible to replace joints with plastic or metal substitutes, but the author never says anything about designing better types of them (C). She never identifies “the causes of diseases that lead to bone losses” (E) either. 2. E The stem contains no line reference, but the only place the author talks about future experiments in making bone from muscle is the last paragraph. She says there that surgeons “have not yet tried the process in humans” and that it “must first be tested on larger animals.” The author expects, therefore, that future experiments will “involve larger animals and perhaps humans” (E). There’s no evidence that future experiments will “encounter no serious problems” (A), that they will be hindered by surgeons (C), or that they “face enormous technical obstacles” (D). And despite the fact that all experiments have so far been limited to smaller animals (B), it’s clear that this isn’t what the author expects in the future. 3. C An example of the all/EXCEPT question type. Information about osteogenin is spread over the last three paragraphs, so scan through the choices to see if one jumps out before you start digging through the passage. (C), “its application can section six SAT Virtual Reality III 39 be easily controlled,” should strike you as false because the author says in paragraph 4 that osteogenin is hard to control—it might turn an entire area to bone if sprinkled on a defect. If you didn’t spot (C), you had to confirm the other choices. “Current supplies [of osteogenin] are limited” (A) is indicated in paragraph 6. This is also where the author says that “tests of its effectiveness have been limited” (B) to small animals, and that osteogenin’s “safety for human use is undetermined” (D). The fact that “some surgeons hesitate to use it” (E) because it’s hard to control is stated in paragraph 4. 4. A Yo u ’ve already had to go back and read through the last paragraph a couple of times by now, so glance through the choices. “A review of current knowledge” (A) looks good right away, because the author points out in the last paragraph how far surgeons have gone in experimenting with and learning about the new process. There’s no “qualification of an earlier remark” (B). (C) is out because the author never mentions, no less challenges, a contradictory view. The final paragraph presents new facts and ideas rather than a “summary of previous ideas” (D). As for (E), the author’s call for testing on larger animals is a demand not “for an alternative approach” but for a guarantee of safety and effectiveness before the process is tried on people. 5. D The phrase “to die young at a ripe age” doesn’t make much sense until you understand its context. The author’s discussing the eventual benefits of artificial organs: ordinary people can live longer or, even better, they can die young at a ripe age. “Dying young at a ripe age” does not mean “living longer” (E). Nor does it mean “dying prematurely” (A), “dying young of an illness” (B), or “extending one’s life despite being ill” (C)—none of these is a positive thing—the author’s talking about the benefits of artificial organs. “Dying young at a ripe age” means dying at a normal old age after having enjoyed a relatively young body during your life; in other words, it means “maintaining a healthier body into old age” (D). 6. C In paragraph 2 of Passage 2, the author accuses medical ethicists of hampering the activities of human volunteers. He declares that the ethicists are “well- intentioned” but “their standards are inappropriate.” Clearly, the author is “disapproving” (C) of them. None of the other words comes close to describing the author’s attitude. 7. E Looking down through the choices, you can see that the only one that can be eliminated right away is “slogans” (A), which is not a synonym for standards. To pick the right one, go back and locate "standards" in its context. The author says that the “standards,” or “principles” (E), of the medical ethicists are inappropriate. “Measurements” (B), “examples” (C), and “banners” (D) don’t make sense in the context of the sentence. 8. A Another vocabulary-in-context question. Checking the sentence, “critical” is used to mean “decisive“ (A): the author’s stating that the need to use humans leads to a decisiv e or very significant “bottleneck in the experimental process.” Critical isn’t used to mean “aggressive” (B), “skeptical” (C), “perceptive” (D), or “fault-finding” (E). 9. A The author discusses the use of artificial heart devices in paragraph 4. The design of the devices is not a problem, he says; rather, it’s the lack of experience SAT Virtual Reality III 40 section six section six SAT Virtual Reality III 41 researchers have had using them with human subjects. He points out that heart devices may work in one patient and not in another, depending on age, health and the quality of postoperative care. He repeats his point at the beginning of the next paragraph: what’s lacking in coronary care is simply more experience (A). The author isn’t “praising scientists’ ability to fight coronary disease” (B); he’s saying it could be much better if human testing were done. The author never mentions any “lingering doubts” about artificial heart implants (C). (D) contradicts the passage directly: the author says that “engineering design is not currently the main obstacle.” Finally, (E) is wrong because the author never discusses “several new treatments now available to heart patients.” 10. C The author poses the questions in the last paragraph in order to identify information that scientists still lac k. He’s showing that their knowledge of coronary disease is incomplete (C)—that’s why human testing is so essential. He’s not illustrating the value of any new devices (A)—he’s opposed at present to new devices. Nobody else’s arguments are being refuted here (B). (D) turns the author’s ideas around: he suppor ts human testing. As for (E), “widely publicized areas of research” misses the point. The point is simple: these are questions that need to be answered. 11. B The answer here has to be fairly general, because the connection between the two passages is indirect. Take the answer choices one by one and evaluate each one using evidence from the passages. For example, (A) is wrong because the author of Passage 1 doesn’t disagree with anyone or cite any views different from hers. (B), though, is accurate: the author of Passage 1 talks about the difficulty surgeons have in reconstructing and replacing bones, and the author of Passage 2 laments surgeons’ lack of experience in using artificial organs. (C) and (D) are wrong because only the author of Passage 2 demands mentions cultural values as a barrier to research. As for (E), neither author advocates a more rapid development of new implant procedures. 12. B Passage 2 is devoted to arguing for the testing of artificial organs on humans, because restrictions on human testing are a major obstacle to improved devices. Before checking the choices, predict what the author of Passage 2 might say about the wider use of osteogenin. No doubt he’d say that gaining experience with the use of osteogenin on humans would be difficult—exactly what (B) says. (A) and (D) cite valid obstacles to the wider use of osteogenin, but they’re wrong because there’s no reason to think that the author of Passage 2 would stress them. (C) and (E) are out because they aren’t obstacles to the use of osteogenin at all. 13. D The last paragraph of Passage 1 states that the process of bone prefabrication has not yet been tried on humans—that it needs to be tested on large animals first. The last paragraph of Passage 2 features questions about coronary care that can only be answered through human testing. In other words, both authors are stressing the need to “gather information that’s relevant to the treatment of human patients” (D). (A) is out because neither author sees the need to “develop new and improved devices for human implantation.” The author of Passage 1 suggests that experiments should next be carried out on larger animals, which rules out (C), while the author of Passage 2 wants testing on humans, which eliminates (B). As for (E), neither author advocates “curbing the growing use of animals in testing.” section seven SAT Virtual Reality III 42 Section 7 (Math) 1. D If Thomas wound up in debt, it means that he spent more money than he actually had — a situation that we’re all familiar with. So, the correct answer must be greater than the amount of money he had, which was $15, so eliminate choices (A), (B), and (C). If he has a debt of $5, then he must have spent all the money he had, or $15, and then borrowed another $5 and spent that also. So he spent a total of $15 + $5, or $20, choice (D). 2. D Here, the angle marked x ° is in a triangle with 2 other unknown angles. However, one of those unknown angles of the triangle, the one just above the x ° angle, lies on a straight line with an angle measuring 98°. Therefore that angle must measure 180° – 98° = 82°. The third angle in the triangle is opposite a 54° angle that is formed by the intersection of 2 straight lines. So the third angle of the triangle must also measure 54°. The 3 angles of a triangle add up to 180°, so 54° + 82° + x ° = 180°, and x = 44, choice (D). 3. E Since something happens every 5 minutes at this party, let’s look at each five-minute interval. At first there are 256 people. After 5 minutes half of them leave. That means that 128 people leave and 128 people are left after 5 minutes. 5 minutes after that, or 10 minutes after we started, half the remaining people leave. That means that half of 128, or 64, people leave and 64 are left after 10 minutes. At 15 minutes after the start, half the remaining 64, or 32, people leave and 32 people are left. At 20 minutes after the start, half of 32, or 16, people leave and so finally only 16 people are left to eat all those ham and cheese sandwiches from section 2. Answer choice (E) is correct. 4. A Remember, in a symbolism problem you shouldn’t worry that there’s a strange symbol you’ve never seen before. It’s just a made-up symbol that is always defined by mathematical concepts that you’ve seen before. Here, an x with a circle around it just means to plug x into an equation. If x = 5x – , then 8 = 5(8) – , or 40 – 4, which is 36, answer choice (A). 5. C You have 6 chairs and 4 people. Go through your rules one at a time and make deductions accordingly. You'll want to start with the following sketch: 1 2 3 4 5 6 8 ᎏ 2 x ᎏ 2 Rule 1 - Ruth occupies Chair 2 Rule 2 - No one sits next to Quincy. Deduction - Quincy does not sit in chair 1 or 3. Rule 3 - Peter sits between Ruth and Sarah 6. B If a rectangle has a perimeter of 12 then 2(W + L) = 12, where W is the width of the rectangle and L is its length. If 2(W + L) = 12, then W + L = 6. If the width is 2 less than the length, then W = L – 2. You can plug L – 2 for W into the equation W + L = 6, so W + L = 6 becomes (L – 2) + L = 6, and so 2L – 2 = 6, 2L = 8, and L = 4. If the length is 4, then the width, which is 2 less, must be 2. The area of a rectangle with length 4 and width 2 is 4 × 2 = 8, answer choice (B). 7. C The easiest way to do this one is to just draw lines from each point and then add up the number of line segments drawn. From point A, draw one line to each of points B, C, D, and E. From point B, you already have a line to point A, so just draw a line to each of points C, D, and E. From point C you have already drawn lines to A and B, so draw in a line to point D and one to point E, and finally draw a line from point D to point E. (You’ve drawn a star inside a pentagon - very artistic!) Can you see any point that is unconnected to any other point? No, so just add up the number of lines you’ve already drawn — there are 4 + 3 + 2 + 1 or 10 of them, answer choice (C). 8. B Whenever you have a word problem that doesn’t give you a definite amount and asks you a question like “What fraction of the total ?”, you should pick a number for the total. Since you’re dealing with percents here, a good number for the total is 100. So let’s say that 100 people were polled. 80% of the 100 people were registered voters, so 80 people were registered voters. 75% of the registered voters voted in the last election, so 75% × 80, or 60 people voted in the last election. If 60 of the 80 registered voters actually voted in the last election then 80 – 60 = 20 of the registered voters didn’t vote in the last election. The fraction of the people surveyed who were registered but didn’t vote is , or , answer choice (B). 1 ᎏ 5 20 ᎏ 100 1 P 2 R 3 4 5 S 6 1 2 R 3 P 4 S 5 6 1 2 R 3 4 5 6 section seven SAT Virtual Reality III 43 [...]... its diameter, which is twice the radius, is 2 × 2 or 4 Since the side of the square is 4, its area is its side squared or 42 which is 16 The area of the square is 16 and the area of the circle is SAT Virtual Reality III 44 4 , so the area outside the circle and inside the square is 16 – 4 So the area of 1 the shaded region is ᎏ (16 – 4 ) = 4 – π 4 ... ᎏ , which is just an 4+ x 3 algebraic equation that can be easily solved: 4 2 ᎏ = ᎏ 4+ x 3 2 (4 + x) = 4 × 3 8 + 2x = 12 2x = 4 x=2 Cross-multiply Multiply out the left side Subtract 8 Divide both sides by 2 That’s the amount of alcohol left If there are 2 ounces of alcohol left after starting with 16 ounces, then 16 – 2 = 14 ounces must have evaporated, so the correct answer is 14, choice (E) 10 B The... with 4 ounces of iodine and 16 ounces of alcohol, and we end with 4 ounces of iodine and an unknown quantity of alcohol, which we can call x ounces That means that in the end the whole solution has a total of 4 + x ounces, since the solution is made up of only iodine and alcohol The final quantities of iodine and total solution are in the ratio of 2 to 3 That means that the 4 2 ratio of 4 to 4 + x... this difference We must 4 first find the area of the circle and the area of the square To find the area of the circle, we must know its radius We’re told that the circumference of the circle is 4 We also know that the circumference C of a circle is related to its radius r by the formula C = 2πr So here, 4 = 2πr and r = 2 The area of the circle is πr 2 which equals π(2)2 or 4 To find the area of the . choice (B). 1 ᎏ 5 20 ᎏ 100 1 P 2 R 3 4 5 S 6 1 2 R 3 P 4 S 5 6 1 2 R 3 4 5 6 section seven SAT Virtual Reality III 43 section seven SAT Virtual Reality III 44 9. E. Mixture problems are very tricky is 3, choice (A). 14 5 a 2 − a a = 10 2 − 2 2 a(a − 1) a = 100 − 2 2 a − 1= 98 2 a − 1= 49 a = 50 a 2 − b b = 6 2 − 4 4 = 36 − 4 4 = 32 4 = 8 section five SAT Virtual Reality III 36 22. D To figure. in paragraph 4. The design of the devices is not a problem, he says; rather, it’s the lack of experience SAT Virtual Reality III 40 section six section six SAT Virtual Reality III 41 researchers