## Cracking the SAT with 5 Practice Tests, 2014 Edition (2013)

### Part VI. Answer Key to Drills

**CHAPTER 5**

__Drills 1 and 2__

__1.__ **C** Since the journalist’s description was *devoid of any bias or emotion*, a good word for the blank would be *unemotional*. The only word that matches with that is answer choice C, *dispassionate*.

__6.__ **B** The candidate’s response was *long-winded and rambling*, so a good word for the blank would be *rambling*. Answer choice B, *meandering*, is the only answer that matches with *rambling*.

__7.__ **B** Lots of triggers in this one. First, *but* tells us that we are looking for a contrast between the first blank and *technically slick*, therefore we want a word like *unsophisticated* or *simplistic*. Eliminate A, C, and D. The sentence also states that the films should be filled with *poignancy*, the best opposite of which is *vacuous*.

__Drill 3__

__2.__ **A** A good clue for the first blank is *simplify the procedure* and the trigger is *instead of*; a good word for the first blank would have to do with being *not simplified.* Eliminate B and D. For the second blank, officers are trying to do something that will simplify the procedure, so a good word for the blank is *help.* The answer is A.

__5.__ **C** For the first blank, think what type of person rescues the victim in a novel. It is often the hero. *Hero* is a good word for the first blank. Eliminate A, B, D, and E. The best answer is C.

__6.__ **D** The clue for this sentence is *intended to teach particular morals*. Because of this, the novel probably had a *instructive* or *teacher-y* tone. The only word that matches with *instructive* is *didactic*. The answer is D.

__7.__ **D** The clue is the second half of the sentence, starting with *courageously.* So we’re looking for a word that means “supportive and devoted.” The best answer is D.

**CHAPTER 6**

__Drill 1__

__14.__ **C** Babe Ruth’s personality and appearance captured the imagination of people of all ages, which includes children. Choice B is too extreme, and choice E goes too far. We are not given specific information to support choice A. The reference in choice D to “rules” makes it wrong; baseball was revitalized, but that doesn’t mean rules were changed. The best answer is C.

__12.__ **B** Like food, the early erasers tended to rot quickly. Although we are told that the erasers were popular within the Continent, there’s no information about shipping costs to support choice A. Choices C and D find no support in the passage. Choice E refers to the 70-year period between the invention of the eraser and the invention of the curing process. However, the answer choice states that the curing process itself takes 70 years. The best answer is B.

__10.__ **E** The author writes about the fame of Mendelev, Darwin, and Einstein, but the question asks why the author mentions them. The remainder of the excerpt discusses three other scientists who, according to the author, made significant discoveries, and yet are essentially unknown. The author believes that these other scientists should be famous as well. Choices A and C relate to a specific discovery and theory; the author did not mention the famous scientists in order to discuss such particulars. Because there is no trend or pattern discussed in the passage, choices B and D are not supported. The best answer is E.

__17.__ **D** The author explained that for a time “there was no commercially viable way to extract hyaluronan,” but that later a method was developed and sold to a pharmaceutical company. Choice A is not supported; just because physicians now use hyaluronan does not mean veterinarians are prohibited from doing so. Choice B is contradicted. Choice C is contradicted; we are told that hyaluronan is extracted from rooster combs. Choice E is extreme and not supported. The best answer is D.

__24.__ **C** In context, *omits* means *forgets*. C is the best answer.

__19.__ **B** The author has a positive attitude towards *Star Wars*. Choices C, D, and E are *not* positive. Choice A is extreme. The best answer is B.

__21.__ **A** The author mentions a variety of telescopes to show that “all telescopes do not ‘see’ in the same way.” While choice B might be a true statement, the author didn’t mention other telescopes to make this point. Choice C is incorrect because the author isn’t showing the *importance* of explaining how telescopes have different ways of seeing long distance. Choice E is incorrect because it is never stated in the passage that mirrored telescopes are *outdated*. Choice D is extreme and does not state the correct purpose. The best answer is A.

__15.__ **C** The author wrote that the terra-cotta rough drafts “often created more interest than the finished works.” We are not told that terra-cotta works *always* created more interest or that finished works stopped being of interest. Choice A goes too far; some collectors believed the terra-cotta revealed talent more accurately, but they did not claim that talent previously had gone unrecognized. Choices B and E, however logical, are not supported by the text of the passage. Choice D is not supported and is extreme. The best answer is C.

__11.__ **E** The author writes that a “monastic chant that relies solely on the human voice and an orchestral symphony utilizing multiple instruments are both classical, yet neither sounds remotely like the other.” Choice A is not supported and is arguably contradicted. Choices B, C, and D are contradicted. The best answer is E.

**CHAPTER 7**

__Drill 1__

__9.__ **C** Passage 1 contains several metaphors, including referring to certain art as “lifeless” and “soulless,” and referring to a particular artistic process as “aping.” Although Passage 2 does contain a limited use of metaphor, metaphors are featured more substantially in Passage 1. Both passages use historical references and artistic analysis, so choices A and E are wrong. Neither passage mentions specific dates, so choice B is wrong. Passage 2, but not Passage 1, uses visual description; choice D is wrong. The best answer is C.

__10.__ **D** Although the authors disagree about the artistic merit of using older forms, both authors agree that it is technically possible to do so. Choice A is wrong because the authors are in disagreement about the point in the answer. Choices B and C relate to factual differences between the passages, but not issues on which the authors are in agreement or disagreement. Choice E is not supported by the text of either passage. The best answer is D.

__11.__ **A** The point of Passage 2 is that an artist can use older forms in a new way so as to create his or her own vision. The author of Passage 1 does not discuss this possibility. Choice B is wrong as it is consistent with Passage 1, not Passage 2. The information in choice C is discussed in both passages, while the information in choice E is discussed in neither passage; both choices are wrong. Choice D erroneously refers to “contemporaries.” The best answer is A.

__12.__ **B** The author of Passage 2 disagrees that borrowing artistic forms from the past must be bad. To the contrary, Passage 2 states that the old forms *can* be used in new ways. Choice A is extreme. Choices C, D, and E are not supported by the text of Passage 2. The best answer is B.

__13.__ **C** Although the authors address the issue from different perspectives, they agree that humans are creating problems for chimpanzees. Choice A goes too far; the authors do not claim that the reason chimps should be valued is their genetic closeness to humans. The remaining answer choices clearly do not reflect the primary purpose. The best answer is C.

__14.__ **C** The author of Passage 1 states that “chimpanzees must nurse for five years.” Choice A is extreme. Choices B, D, and E are not supported by the text of the passage. The best answer is C.

__15.__ **A** The author mentions population growth as part of a lengthy explanation about how this growth affects chimpanzees. The author does not offer a solution or demand a reaction, so choices B and E are wrong. The author does not criticize the growth, which wouldn’t be called a policy anyway, so choice D is wrong. The author does not praise the population growth, of course, so choice C is wrong. The best answer is A.

__16.__ **D** Answer choices A, B, C, and E are all supported by the text of the passage. Answer choice D is the only one that is not mentioned. The best answer is D.

__17.__ **D** The author tells us that poachers take baby chimpanzees. The author does not call for logging restrictions and even explains why logging is important to the African poor, so choice A is wrong. The author does not discuss whether logging or poaching is worse, so choice B is not supported. Choice C is not supported because the author discusses only chimpanzees. Choice E is extreme. The best answer is D.

__18.__ **A** The author of Passage 2 tells us that chimpanzees “suffer greatly as a consequence of their genetic similarity with humans” and that their “appealing demeanor” leads people to believe they can fit into a household. Choices B, C, and D are not supported by the text of the passage. Choice E may reflect the author’s belief, but it does not represent how the author would respond to the text referenced in the question. The best answer is A.

__19.__ **B** The author of Passage 2 tells us that the “appealing demeanor” of chimpanzees leads people to believe the animals can fit into a household as pets. The remaining answer choices do not provide a reason for the author’s comment, even if some of the answer choices are mentioned in the passage. The best answer is B.

__20.__ **C** In context, *check* means *stop*. The best answer is C.

__21.__ **C** The author believes that the fate of chimpanzees is poor for several reasons, including the lack of sanctuary slots. Even assuming choices A, B, D, and E to be true (as required by the question), none of these choices relates directly to the author’s stated reasons for the poor fate of the chimpanzees. The best answer is C.

__22.__ **B** The phrase “given the opportunity” is used to describe the lengthy life-span of chimpanzees in the wild. Choices A and C might contain true statements, but they do not relate to the author’s use of the quoted phrase. Choices D and E are contradicted. The best answer is B.

__23.__ **E** The principal difference between the two passages is that Passage 1 concerns chimpanzees in the wild, while Passage 2 concerns chimpanzees in captivity. The author of Passage 1 mentions legal restrictions briefly, but that does not amount to a major difference, so choice A is wrong. Both passages are concerned with actions of humans, so choice B is wrong. Both passages discuss chimpanzees of all ages, so choice C is wrong. The author of Passage 1 does not discuss ways to help chimpanzees, so choice D is wrong. The best answer is E.

__24.__ **B** The authors of both passages discuss how the actions of people are negatively affecting chimpanzees. However, the author of Passage 1 does explain that poor people in Africa need deforested land to live and look to the logging industry as a means to survive. Thus, the author of Passage 1 is more understanding. The best answer is B.

**CHAPTER 11**

__Drill 1__

__1.__ 109

__2.__ 38

__3.__ –3

__4.__ 10

__5.__ 15

__Drill 2__

__1.__ 6(57+13) = 6 × 70 = 420

__2.__ 51(48 + 50 + 52) = 51(150) = 7,650

__3.__ *ab* + *ac* – *ad*

__4.__ *x*(*y* – *z*)

__5.__ *c*(*ab* + *xy*)

__Drill 3__

__1.__

__2.__

__3.__

__4.__

__5.__

__Drill 4__

__1.__ 3

__2.__

__3.__

__4.__

__5.__

__6.__

__7.__

__Drill 5__

__1.__ 0.3741

__2.__ 1,457.7

__3.__ 186

__4.__ –2.89

**CHAPTER 12**

__Drill 1__

__4.__ **A** For this question, we should try Plugging In The Answers. Starting with C, we can plug in 10 for the number. First, we can take 10 and multiply it by 2, then add 4. This gives us 24. To check if this is right, we can take 10 and subtract 6. This gives us 4. So C is not the correct answer. Since the two results came out to be 24 and 4, we can try a smaller number to try and narrow it down. If we plug in choice B, we get 2 × 2 = 4. Adding 4 to this gives us 8. Does this equal 2 – 6? No. So let’s try A. We first get –10 × 2 = –20. Adding 4 gives us –16. Is this equal to –10 – 6? Yes. The answer is choice A.

__6.__ **E** With a “must be” question, we should plug in. Let’s make *n* = –2. We then plug into the answer choices. Choices A, B, and C don’t give us a positive integer and can be eliminated. Since we have two choices left, we need to plug in again. Let’s try *n* = –3. Using this number eliminates D, leaving us with E.

__7.__ **E** Plug in a number for *c*. If we say that *c* = 5, we can calculate that Ashley is 15. That means Sarah is 15 + 7, which equals 22. This is our target. Plugging 5 into the answer choices for *c* gives us E as our answer.

__8.__ **D** The words “must be” mean this is a good place to plug in. Let’s plug in values for *r* and *s*. We can make *r* = 3 and *s* = 5. Using these numbers in the answer choices, the only choice that gives us an even integer is D.

__9.__ **D** Here, we can plug in our own number for *y* dollars. Let’s make *y* = 80. That makes each sack of flour cost 2 dollars. Then, 12 sacks of flour would cost 12 × 2 = 24. This is our target answer. When we plug 80 in for *y* in the answer choices, we get D as our answer.

__11.__ **A** A problem with variables means using the technique of Plugging In! Let’s first plug in for *x*. If we say that *x* = 10, then 10 percent of 50 gives us 5. Now, we can figure out what *y* is. To solve, we can use our percent translation terms. If 5 is 20 percent of *y*, this becomes 5 = *y*. Solving for *y* gives us 25. When we plug in 25 for *y* in the answer choices, the only choice that works is A.

__12.__ **C** Two variables tells us this is a great place to plug in. Let’s pick numbers that make the math easy. We can try *x* = 30 and *y* = 2. So in 2 hours there are 4 periods of 30 minutes each: 12 × 4 = 48. Alex can fold 48 napkins in 2 hours. 48 is our target. Plugging into our answer choices gives us C as the only answer.

__13.__ **C** Since the problem is asking for a specific amount, this is a good place to PITA. Starting with C, if we say that Alice read 200 pages on Saturday, we can figure out how many she read on Sunday. We take 200 and divide it by 2. This gives us 100. Now, we add 50 to it. This gives us 150 pages that Alice read on Sunday. To check to see if we’re right, we add 200 for Saturday and 150 for Sunday. Do these add to 350? Yes. The correct answer is C.

__14.__ **B** Here, the words “must be” again indicate a good place to plug in. We need numbers for *x* and *y* that will give us a negative product. Let’s try *x* = 1 and *y* = –2. If we plug these into the statements in the roman numerals, we find that I is false, but II and III are true. We can eliminate any answer choice that contains I. This leaves B and D. Let’s try different numbers and see if we can eliminate another choice. If we try *x* = –1 and *y* = 2, we find that II is false and III is still true. This leaves us with B as the only correct answer.

__15.__ **A** This problem is asking for a specific amount, so we should probably PITA. Starting with choice C, if we assume that Mark pays $160 dollars, then Fred pays twice that, or $320, and Alan pays $360. To check if this is correct, we add the three values together. This gives us $840, which is too much. We can eliminate C and also D and E. If we try B, the sum of all three becomes $740, which is still too much. Choice A is the only one left, but even when we check it, the sum of the three is $540.

__16.__ **D** The easiest way to do this question is with PITA. Let’s start with choice C. If Allie has 5 coins, that means that Jonathan has 4 coins. To check if this is the right answer, we add 2 coins to Allie and subtract 2 from Jonathan. This gives us 7 for Allie and 2 for Jonathan. Since 7 is not three times as much as 2, we can eliminate C and anything less. When we try D, it gives us the correct answer.

__18.__ **C** With multiple variables, we should definitely plug in. To try and make the math easy, let’s plug in first for *r*. We can make *r* = 3. To make the fraction easier to work with, let’s make *s* = 6. That means that *t* = 1. So our target is 6. We plug in 3 and 1 for *r* and *t*, respectively, in the answer choices. We get our target answer in choice C.

**CHAPTER 13**

__Drill 1__

__1.__ 0.5 50

__2.__ 3.0 300

__3.__ 0.005 0.5

__4.__ 33

__Drill 2__

__5.__ **A** Variables in the answers? Plug in! Make up a value for *x*. Let’s say that *x* is 3. The list of numbers then becomes 20 – 2(3), 20 – 3, 20, 20 + 3, 20 + 2(3), so the list is 14, 17, 20, 23, and 26. To find the average, make an average pie: We know the number of things (5) and the total (14 + 17 + 20 + 23 + 26 = 100), so the average is 100 ÷ 5 = 20, answer choice A.

__8.__ **C** Henry has two spaces on his lawn for statues, so draw two boxes. For the first box, he has 9 options of statues to choose from. He chooses one statue out of the 9, and now he has only 8 statues to choose from for the other statue. So there are a total of 9 × 8 = 72 total arrangements of the 2 statues.

__9.__ **D** Since we know the time that Amy walked and the distance she walked are directly proportional, we can set up a proportion to show her distance ÷ time. We want to know how many miles she’ll walk in two hours, so put in 120 (60 × 2) minutes in the section half of the ratio: . To solve, cross multiply, and you’ll get 50*x* = 2.5 × 120; 50*x* = 300; *x* = 6 miles, answer choice D.

__10.__ **C** Since this is a ratio question, let’s draw a ratio box. We know the ratio for the votes for Skinner and Whitehouse, and the total number of votes cast. Fill in the total by adding the ratio (4 + 3 = 7), and then find the multiplier by seeing how many times 7 goes into 140,000 (140,000 ÷ 7 = 20,000).

The question wants to know how many votes Whitehouse received, which is 60,000, answer C.

__14.__ **D** Start out by finding 1/4 of 18 percent of 616 by translating to math: × 616. Plug that into your calculator (remember to use parentheses for your fractions) and you’ll get 27.72. That’s the number we’re looking for. Convert each answer to math and plug in to your calculator to see which one gives you 27.72. D, 18% of 154, is 27.72.

__16.__ **E** Start by figuring out what percent of the houses do not have two-car garages. Since 60% of the houses with garages have two-car garages, 40% of the houses with garages do not have two-car garages. In other words, 40% of 80% of the houses do not have two-car garages. Translate that into math to get = 0.32, or 32% of the houses. The problem tells us that 56 houses do not have two-car garages, which means 32% of the houses equals 56. Translating into math gives us × *x* = 56. Solve for *x*, and you’ll get 175, answer choice E.

__18.__ **E** Let’s try out the answers, and see which one works. Start with C. If the watchmaker made 21 watches on Tuesday, then he must have made 17 watches on Monday. We know that he should have made 16% more watches on Tuesday than on Monday, so let’s use the Percent Change formula (difference ÷ original) and see if we get 16%: 23.5%, which is too big. Eliminate answer choice C. We want the 4 watches to be a smaller percent of the total, so we need a bigger total. Try a bigger answer choice, like E. If he made 29 watches on Tuesday, then he made 25 watches on Monday. Now the percent change is = 0.16 = 16%, which is exactly what we wanted.

**CHAPTER 16**

__Answers and Explanations to Putting It All Together…__

__13.__ **13** Use the common quadratic: (*x* − *y*)^{2} = *x*^{2} − 2*xy* + *y*^{2}. So, *a*^{2} − 2*ab* + *b*^{2} = (*a* − *b*)^{2}. That means (*a* − *b*)^{2} = 169. Take the square root of both sides to find *a* − *b* = 13 or −13; but don’t forget *a* > *b* and *a* − *b* > 0, so *a* − *b* = 13.

__15.__ **E** Since you are never told what *x* is, and there is no way to find it, Plug In for *x*. Say that *x* = 100. 63% of 100 is 63, and of 100 is 37.5. The ratio of *a* to *c* is . So, = 1.68. To save time, you can ballpark the answer, since *a* > *c* and E is the only choice greater than 1.

__11.__ **C** Draw out the triangle. If it’s a right triangle, and the two other angles are equal, then this is a 45°-45°-90° triangle. That tells us sides *BC* and *AC* are both the same, and that *AB* is the hypotenuse. Using the Pythagorean theorem, we know that *a*^{2} + *b*^{2} = *c*^{2}. Since *a* and *b* are the same, and *c* = 4, *a*^{2} + *a*^{2} = 4^{2}. Solve, for *a* = 2. The perimeter is therefore , answer C.

__18.__ **E** There are 5 cyclists that could be first. Then, once you use one for the first spot, there are 4 that could be second, then 3 that could be third and that is all. Remember: Who cares about fourth or fifth place, since they’re not getting a medal? So, there are 5 × 4 × 3 = 60 places in which the cyclists finish.

__12.__ **D** Plug in the answers for the value of *b* to find the values of *a* and *b* that work in both equations. Plugging in choice D, if *b* = 4, then *a* + 2(4) = 10; so, *a* = 2. Plug these values into the second equation: Does 4 − 2 = 2? Yes, so D is correct. Alternatively, rewrite the second equation as −*a* + *b* = 2. Then, add the two equations together. This yields 3*b* = 12. Divide by 3 to get *b* = 4.

__8.__ **B** The perimeter of a square is 4*s*. So, 28 = 4*s*. Divide by 4 to find *s* = 7. The diagonal of a square divides the square into two 45:45:90 triangles, with sides in the ratio of *x*:*x*:*x*. If the side is 7, the diagonal is 7.

__17.__ **D** The angles in quadrilateral *ABCD* (or any other quadrilateral) must add up to 360°. Since *A* and *C* are tangent points, we know that ∠*BAD* = ∠*BCD* = 90°, so we get ∠*ABC* + ∠*ADC* = 180°. the question, ∠*ABC* = ∠*ADC*. We can substitute and solve: ∠*ADC* + ∠*ADC* = 180°, so ∠*ADC* = 180°, so ∠*ADC* = 140°.

__10.__ **D** There are 5 pictures that could be first. Then, once you use one for the first spot, there are 4 that could be second, then 3 that could be third, then 2 that could be fourth, then 1 that could be fifth. So, there are 5 × 4 × 3 × 2 × 1 = 120 ways to arrange the photographs.

__19.__ **B** Rewrite these statements as equations, where *a* = the price of an apple and *c* = the price of a cherry: 3*a* + 5*c* = 1.25 and 15*a* + 100*c* = 9.25. Add the equations together to get 18*a* + 105*c* = 10.50, then divide everything by 3 to get 6*a* + 35*c* = 3.50.

__7.__ **A** If *n* represents the number of people that are added to the number of people already on the bus (42), you know that the new total on the bus is *n* + 42. Since that number is not *over the limit* of 66, but *could be equal to* the limit, you know that *n* + 42 ≤ 66.

__18.__ **17.5 or** The trick is to recognize that *ABC* is a 30-60-90 right triangle. ∠*ABC* must equal 90° since a tangent line must be perpendicular to the radius of a circle drawn to the point of tangency. Only a 30-60-90 has a hypotenuse (*AC*) equal to double the length of one of the sides (*AB*). (You can also use the Pythagorean theorem to show this.) This means that ∠*BAC* = 60°, so the shaded region has a central angle measure of 360° – 60° = 300°. To get the area, use the proportion . Reduce, cross-multiply, and solve to get *s* = 17.5.

__14.__ **E** First, find *g*(1) by plugging in 1 for *x* in *g*(*x*) = *x* − 3. So, *g*(1) = (1) − 3 = −2. Next, find *f*(−2) by plugging in −2 for *x* in *f*(*x*) = |*x*| + 1. So, *f*(−2) = |−2| + 1 = 2 + 1 = 3. (The bar marks are absolute value, which is the distance from zero on a number line.)

__15.__ **C** Because −3 is less than 0, find *f*(−3) by plugging in −3 for *x* in *f*(*x*) = *x*^{2} + 2. So, (−3)^{2} + 2 = 9 + 2 = 11. Because 8 is greater than 0, find *f*(8) by plugging in 8 for *x* in *f*(*x*) = . So, *f*(8) = . *Sum* means to add. So, 11 + 3 = 14.

__6.__ **B** Since you have numbers in the answers, PITA. Start with answer choice C. If Katey purchased 3 hardcover books and 6 books total, then she must have purchased 3 paperback books. 3 hardcover books cost (3*x*)3 = 9*x*dollars, and 3 paperback books cost (2*x*)3 = 6*x* dollars. In that case, Katey spent 15*x* dollars total. However, the problem says that she only spent 14*x* dollars. Eliminate answer choice C. Since Katey spent too much money, she must have purchased fewer hardcover books and more paperback books, which are cheaper. Try answer choice B. If Katey purchased 2 hardcover books for (3*x*)2 = 6*x* dollars, and 4 paperback books for (2*x*)4 = 8*x*dollars, then she spent 14*x* dollars total, and the answer is B.

__16.__ **D** Start by finding the volume of a sphere with radius 2 cm, to find how much metal is in one sheet. Using the formula supplied by the problem, you find that *V* = π(2)^{3} = π × 8 = 33.5 cubic centimeters. Now find the volume of a sphere with radius 6: *V* = π(6)^{3} = π(216) = 904.3 cubic centimeters. Since each metal sheet has a volume of 33.5 cubic centimeters, you need to know how many sheets it would take to make a volume of 904.3 cubic centimeters. 904.3 ÷ 33.5 ≈ 27, answer choice D.

__17.__ **4** Plug 5 and *d* into the equation: *f*(5, *d*) = 9. So, (5)^{2} – (*d*)^{2} = 9. So, 25 – *d*^{2} = 9. Subtract 25 from both sides, and then multiply by negative 1 to find *d*^{2} = 16. So, *d* = ±4. The question asks for the positive value of *d*. So, *d* = 4.

__13.__ **90** 6^{2} + 8^{2} = 10^{2}. Since this triangle works in the Pythagorean theorem, it is a right triangle, meaning it has a 90-degree angle. (You can also recognize that the sides are in a ratio of 3-4-5.) Since the three angles in any triangle add up to 180 degrees, the right angle must be the largest angle.

__20.__ **C** Factor *x*^{2} – 6*x* + 5 into (*x* – 5)(*x* – 1). Factor 2*x*^{2} – 7*x* + 3 into (2*x* – 1)(*x* – 3). So if their product is equal to zero, that means (*x* – 5)(*x* – 1)(2*x* – 1)(*x* –3) = 0, or *x* = 5, 1, , or 3. Eliminate A, B, D, and E. Alternatively, you can plug the answer choices into the equations and multiply, but that could take some time.

__12.__ **24** For problems in which you choose one item each from different sources, multiply the number of items in each of the sources together. So, Jon has 3 × 4 × 2 = 24 ways to make omelets.

__17.__ **20** The sum of the angles in triangle *ABD* must be 180. So, 3*a* + 2*a* + ∠*ABD* = 180. Thus, ∠*ABD* = 180 – 5*a.* The sum of the angles in triangle *BCF* must be 180. So, *a* + 60 + ∠*CBF* = 180. Thus, ∠*CBF* = 120 – *a*. Because is a line segment ∠*ABD* + ∠*CBF* = 180. Plug in the angles in terms of *a*: (180 – 5*a*) + (120 – *a*) = 180. Combine like terms to find 300 – 6*a* = 180. Subtract 300 to find –6*a* = –120. Divide by –6 to find *a* = 20.

__18.__ **D** Find the smallest and largest values for *n*. Although *n* has to be an integer, doesn’t have to be an integer. The smallest value for *n* is 26, because 5 < . The largest value of *n* is 80, because < 9. The sum of 26 and 80 is 106, answer choice D.

__12.__ **A** Because angles that are opposite sides of equal length are equal, ∠*ABC* = ∠*BCA* = 45. Because ∠*ADC* is 90 and ∠*BCA* = 45, triangle *ADC* is a 45:45:90 triangle, with sides in the ratio of *x*:*x*:*x*. The side across from the 90-degree side is 4, so *x* = 4. Divide by to find that

__7.__ **A** Since you have variables in the answers, Plug In. Make *n* = –2. In that case, the list is: –2, –4, –6, and –8. Remember that for negative numbers, numbers that are farther from zero are smaller than numbers closer to zero. So, the list in order from least to greatest is –8, –6, –4, and –2. The greatest therefore –2. Plug in *n* = –2 to each answer choice to find which answer gives you –2. The answer is A.

__20.__ **D** Draw a line through or close to the points given: (0, 0), (1, 5), (2, 10), (3, 15), (4, 20). Then use POE. The line is linear, not quadratic, so you can eliminate E. It is also clear that the line begins at the origin, so the *y*-intercept will be 0. This will eliminate A and C. A slope of 25 is far too big—ballpark—so we can eliminate B, leaving D.

__17.__ **A** Since we’re dealing with averages, let’s draw some Average Pies. First off, we know the total number of days (20) and the average (15), so the total number of computers fixed over the first 20 days is (20 × 15) 300. After another 10 days, the average goes up to 18, so draw another Average Pie: The average is 18, and the number of days is now 30, so the total number of computers fixed over 30 days is (18 × 30) 540, meaning that in the last 10 days there were (540 – 300) 240 computers fixed. Draw one last Average Pie, and you’ll find there were an average of (240 ÷ 10) 24 computers fixed over the last 10 days.

__20.__ **C** We’ve got variables in the answer choices, which means this is a perfect Plug In problem. Let’s make up an easy value for *x*, such as 2. 9^{x} + 3^{x+1} then becomes 9^{2} + 3^{2+1} = 81 + 27 = 108. We plugged in *x* = 2, so let’s use that to find *y*: *y* = 3^{x}, so *y* = 3^{2} = 9. Now plug in *y* = 9 to each answer choice, and see which one gives you 108. Answer choice C is *y*(*y* + 3), which is 9(12) = 108, which is the answer.

**CHAPTER 17**

__Drill 1__

__1.__ to

__2.__ of, for

__3.__ by, for

__4.__ of

__5.__ about

__6.__ by

__7.__ over

__8.__ to

__9.__ from

__Drill 2__

__1.__ **D** The correct idiomatic phrase is “responsible for.”

__2.__ **D** The pronoun *it* is ambiguous: Are environmentalists pleading to change how people fish, or the dwindling of certain fish species?

__3.__ **D** The phrase *has started* is in the wrong tense. It should be *started.*

__4.__ **C** In the case of *neither … nor* the verb must agree with the word after *nor*. In this case that is *snow,* which is singular.

__5.__ **D** When comparing, the phrases should be parallel. So *running a marathon* should be *to run a marathon.* Changing *to box* to *boxing* would also be correct, but this is not an option.

__6.__ **D** When using the phrase *not only … but also* the phrases following those terms must be parallel. Since *improving* is the wrong form of the verb when it’s in the future perfect tense (when combined with the word “will”), you must change *improving* to *improve.*

__Drill 3__

__1.__ **B** The word *blind* modifies *stumbled.* Since adjectives modify only nouns and adverbs modify everything else, *blind* should be *blindly*.

__2.__ **E**

__3.__ **E**

__4.__ **D** The phrase should be “between you and me.”

__5.__ **B** The word *clear* modifies *think.* Again, adjectives modify only nouns, so you need an adverb here. *Clear* should be *clearly*.

__6.__ **B** The verb *was completed* must agree in number with *all*, which is plural. So *was completed* should contain the plural form of the verb: “were completed.”

__7.__ **D** The simplest, most straightforward answer is D.

__8.__ **B** The tense in the verb *would have soon become* is incorrect. The best answer is B.

__9.__ **C** The conjunction *since* doesn’t work within the sentence. It should be *but*. Answer B is unnecessarily long. Answer E contains an -ing word, which is incorrect—and one of ETS’s favorite kinds of wrong answers. The best answer is C.

__10.__ **B** The sentence as is contains a run-on. *It was used only in rural areas at first* can stand alone as a sentence. Answer C changes the meaning of the sentence. Answer D contains an ambiguous pronoun (*it*). Answer E also changes the meaning of the sentence. The best answer is B.

__11.__ **B** When using the phrase *either … or* the phrases after each word should be parallel. B is short, direct, and has a correct parallelism.

__12.__ **E** *They* is a pronoun that refers to the term *mach,* which is singular. Eliminate A, B, and D. Eliminate C because it contains an incorrect comparison: it compares the *speed of sound* to the *craft* rather than to the speed of the craft. The best answer is E.

__Drill 4__

__1.__ **B** The current sentence is incorrect because *they are called graphic novels* can stand alone as a sentence. C, D, and E are all in the wrong tense; C is also unnecessarily wordy. B is the clearest, best answer.

__2.__ **E** The first paragraph talks about comic books and starts off by mentioning kids. So the best topic for a previous paragraph would be one that includes both of those things. The best answer is E.

__3.__ **C** Sentence 3 talks about comic books in Europe while Sentence 4 talks about comic books in the United States. This is a good break. The best answer is C.

__4.__ **E** The first sentence talks about those who dismiss comic books. So the *you* would best refer to those who dismiss them. The best answer is E.

__5.__ **D** The word *birth* refers to comic book characters. The best word to replace it is *creation*. The best answer is D.

__6.__ **A** Since the comic books are what generates the money, answer A is the shortest and clearest way to combine those two sentences.