Cracking the SAT

Part VII

SAT Practice Tests and Explanations

Chapter 22

Answers and Explanations for Practice Test 2

  1.  E  The blank in this sentence is a word that describes the wastes produced by nuclear power plants. What do you know about the wastes? The wastes are radioactive materials that have to be stored in protective containers, which means they must be dangerous, so “dangerous” would be a good word for the blank. E, noxious, is the best match for dangerous.

  2.  D  Let’s start with the second blank. The clues for this blank are living specimen and thought to be no longer. If a living specimen was found, and it affects the scientific community, then the creature must have been thought to be no longer living—a good word for the second blank. Only D and E have second blank words that match living. For the first blank, a word that means “surprised” is needed, because you’d certainly be surprised if something you thought was dead turned out to be alive. There is nothing in the sentence to indicate disappointment, so E, dismayed, can be eliminated. Astounded comes closest to the meaning of surprised.

  3.  E  The clues here are third trip overseas and voters complained. Why would the voters complain about the governor taking a lot of trips abroad? If he’s always away in a foreign country, then he probably isn’t paying a lot of attention to the affairs of his own country. So you can put “his own country” in the blank. Looking to the answer choices, domestic is the best match; it means the opposite of foreign.

  4.  E  For this question you need to figure out the relationship between the blanks. Claudius was viewed one way by generations of historians, until newly discovered evidence changed everyone’s mind. So the words in the blanks must be somewhat opposite in meaning. You can get rid of A, B, and D because the words aren’t opposites. In C and E, the first word is negative and the second is positive, so they are both possibilities. To narrow it down, let’s look at the second blank, which describes Claudius’s ability as an administrator. Would it make sense to call him an eageradministrator? Not really, so get rid of C.

  5.  C  The clues in this sentence are scarce and nutrition. In these primitive areas, something is scarce, so they have to be resourceful to find nutrition. What is scarce? It must be nutrition; that’s why they have to be resourceful to find it. So you can recycle the clue and put nutrition in the blank. Looking at the answer choices, sustenance is the best match for nutrition.

  6.  A  Let’s start with the first blank. The first clue in the sentence is division between. Morgan wants to do something with the division between theory and empiricism. In the second part of the sentence, you learn that she thinks doing something with philosophy and applied science is possible and necessary. If doing something with both things together is possible and necessary, then she must be against the division, so the word in the first blank must mean “against.” Eliminate B and C. Because Morgan is against the division, she must be convinced that a combination is possible and necessary, so you can put “combination” in the second blank. Eliminate D and E, neither of which contains a second word meaning “combination.”

  7.  D  The colon is a same-direction trigger telling you that the clue for the blank is vivid colors and mixture of bold patterns and center of attention. A good word to use for the blank is “showy.” Flamboyant comes closest in meaning to “showy.”

  8.  A  Let’s start with the second blank. The clue in this sentence is disagreeable, and the trigger word for the second blank is although, which means that the word in the second blank is the opposite of disagreeable. Therefore you can put “agreeable” in the second blank. Looking at the answer choices, the only word that matches “agreeable” is complaisant, and contentious is close in meaning to disagreeable.

  9.  C  Hurston consciously wrote about the lives of African Americans. In A, although Hurston did participate in the Harlem Renaissance, the term deconstructed refers to her writing, not her participation. B is too literal: Hurston’s writing is not about actual scientific experimentation. D is incorrect because there is no evidence that Hurston was cut off from Harlem. Finally, E is too extreme; there’s no support for Hurston trying to make sweeping changes.

10.  B  This is the only statement that is not stated in the passage: Although she was indeed an anthropologist, widely acclaimed is too extreme and makes this statement inaccurate. All the other choices are supported by information in the passage and therefore are the incorrect answers.

11.  C  C is correct, because it says that the author merely relates the arguments of both sides without adding his own opinion. This also explains why A and B are incorrect. D is too broad and not discussed in the passage, and E is only partially correct. While the passage does touch upon some arguments of opponents to SURTASS LFA, he also discusses the views of proponents, and thus this is not the author’s main point.

12.  D  D is correct because the example demonstrates how harmful sounds at 150 decibels can be, and this allows the reader to appreciate how dangerous sounds at 215 decibels would be. A is incorrect because the author is comparing different sound levels, not humans and whales. B and C are both incorrect because the author neither supports nor attacks either side in the argument. E is unsupported by the text.

13.  C  According to the first paragraph, early man viewed … healing as purification, and this notion is apparent in the origin of our word “pharmacy.” The passage then gives the meaning of the Greek word pharmakon, which is purification through purging. Therefore, the literal definition is cited to give an example of how early man thought of healing as purging, or internal cleansing, as is paraphrased in C. Remember: The answer to most specific questions will be an exact paraphrase of what the passage says. Choice A doesn’t make any sense. Did ancient civilization have an advanced form of medical science? No way. Don’t forget to use your common sense. B doesn’t answer the question, and it is irrelevant. You’re talking about ancient medicine, not ancient beliefs in general. D is wrong because the passage doesn’t say anything in the first paragraph about the mental and physical causes of diseases. This is mentioned much later in the passage. Make sure you’re reading in the right place. E is too extreme, and it actually contradicts the passage. In lines 32–33, the passage says that the Greeks had adopted a sophisticated mind-body view of medicine, so they were certainly not primitive.

14.  E  The lead words in this question are early Sumerian drugs, which should lead you back to the second paragraph. According to lines 9–13, the first drug catalog, or pharmacopoeia, was written at that time by an unknown Sumerian physician. Preserved in cuneiform script on a single clay tablet are the names of dozens of drugs to treat ailments that still afflict us today. So it was possible to identify a number of early Sumerian drugs because somebody back then wrote them all down, which is exactly what E says. A is wrong because the passage doesn’t say anything at all about traces of the drugs being found in archeological excavations. If it’s not in the passage, then it’s not ETS’s answer. B is wrong because the passage says in line 14 that the Egyptians added to the ancient knowledge of medicine. The passage doesn’t say that they used the same medications as the Sumerians. C is wrong because the passage doesn’t say anything at all about Sumerian religious texts. D is way off the topic. The passage is about ancient civilizations, not about Europe. Modern Europe didn’t even exist back then. Read the answer choices carefully.

15.  C  This question asks about Sumerian drugs again, so you need to go back to the second paragraph. This time the question is looking for a similarity between Sumerian drugs and modern drugs. According to lines 6–8, the Sumerians in the Tigris-Euphrates Valley had developed virtually all of our modern methods of administering drugs. So the similarity between Sumerian and modern drugs is in the methods of administering drugs, which is paraphrased in C as the delivery of drugs. The answer to most specific questions will be an exact paraphrase of what the passage says. A is wrong because the passage says that the Sumerians had the same methods of administering drugs, not that they used the same chemicals. Besides, it doesn’t make any sense to say that an ancient civilization had the same chemicals that you do now. They didn’t have penicillin, or anything like that, did they? Don’t forget about common sense. B is wrong because the passage doesn’t talk about mental and physical disorders until much later in the passage. Use the lead words to make sure you are reading in the right place. D doesn’t make any sense at all. Were ancient Sumerian drugs the products of sophisticated chemical research? No way! Use common sense. E is wrong because a hierarchy of drug producers was part of Egyptian society, not Sumerian society.

16.  D  For this question, you should read before and after the word hierarchy to give yourself some context. In the fourth paragraph, the passage talks about the hierarchy of ancient drug preparation. In lines 22–31, the passage describes the different people involved in the process of making drugs, including the chief of the preparers of drugs, the collectors of drugs, the preparers, the preparers’ aides, and the conservator of drugs. With all these different jobs, the hierarchy must be an example of a division of labor. A is wrong because the fourth paragraph doesn’t say anything about superstitious practices. B is wrong because the passage doesn’t say anything about the severity of ancient diseases. C is close, but the fourth paragraph is about the people who made drugs in ancient Egypt, not the doctors who administered the drugs. E is also wrong because the fourth paragraph is about the people who made the drugs, not the recipes for the drugs themselves. Read carefully.

17.  B  The best answer is B. Ointments are mentioned in the passage as a characteristic of Sumerian, not Egyptian, medicine (line 9). Each of the other answer choices is cited as a characteristic of Egyptian medicine: anesthesia (lines 20–21, in which ethyl alcohol is used to numb the pain of tooth extraction), ingredients derived from animals (line 30), use of trial-and-error (lines 16–17), and a workplace hierarchy (lines 22–31).

18.  D  Go back to the passage, find the word holistic, and cross it out. Then read the sentence and come up with your own word. The paragraph is talking about how the Greeks had a mind-body view of medicine, meaning they believed it was important to treat the mind as well as the body. Because they believed in treating the whole person, that means they emphasized an approach to health that included everything. So you use “included everything” in place of holistic. The best match in the answer choices is comprehensive. A and C are wrong because holistic doesn’t just describe the psychological perspective or just the physiological perspective, but both together. B gets the time frame wrong. The Greeks were ancient, not modern. E is easy to eliminate.

19.  C  The best answer is C. Seventh-century Greek medicine is discussed in the fifth paragraph. The author contends that the seventh-century Greeks had a mind-body view of medicine (line 33) in which mental maladies were interpreted as curses from displeased deities (lines 40–41). Evidence that a seventh-century Greek doctor’s prescription urged a patient to pray to a Greek deity would support this contention. A is incorrect because in the passage, the author discusses the Egyptian, not Greek, use of antacids. In the fifth paragraph, the author states that the suspected “mental” causes of disease were not [emphasis added] recognized as stress (lines 39–40), so B is incorrect. There is no discussion in the passage of the Egyptian influence on Greek medicine, or of Greek use of the term pharmacology, so choices D and E are incorrect as well. Note that most of the incorrect answer choices for this question contain a word or phrase that is used in the passage (e.g., sophisticated). Remember that the use of a word or phrase from the passage in an answer choice does not ensure that the choice is correct. In fact, such an inclusion is often a trap! The right answer often contains a paraphrase of material in the passage, instead of the exact wording.

20.  B  The lead words in this question are the seventh-century Greeks, which should lead you to the fifth paragraph. The question asks how the view of medicine differed between the Greeks and the Sumerians. According to lines 32–33, By the seventh century B.C., the Greeks had adopted a sophisticated mind-body view of medicine. If this view were newly adopted by the Greeks, it must have been different from what the Sumerians thought. So the difference is that the Greeks had a mind-body view. “Mind-body” is paraphrased in B as the mental and physical roots of illness. A is wrong because the passage doesn’t say anything about advanced chemical applications. Read carefully. C contradicts the passage. The Greeks believed that it was necessary to treat the mind and the body. That is the point of the fifth paragraph. Go back and read it again. D is wrong because a hierarchy of drug producers was part of Egyptian society, not Greek society. E is wrong because the word most makes it an extreme answer. The Greeks didn’t develop most of the precursors of modern drugs. What about the Egyptians and the Sumerians?

21.  E  The best answer is E. Lines 42–43 identify the sixteenth century as having the first major discoveries in chemistry. A is an extreme statement that is not supported by the passage. B is wrong because of the word prove. C is wrong because, according to the passage, a modern head pharmacist is analogous to the Egyptian chief of preparers of drugs (lines 23–24), not to the conservator of drugs. D would be correct if you substituted the word some for most. As written, however, it is an extreme answer choice that is unsupported by the passage.

22.  A  The lead words in this sentence are modern era of pharmacology, which should lead you to the sixth paragraph. This paragraph talks about how the modern era of pharmacology began, but the question asks what delayed advances in medical science during the modern era. So you need to keep reading into the next paragraph to find the answer: physicians, unaware of the existence of disease-causing pathogens such as bacteria and viruses, continued to dream up imaginary causative evils. So the problem was that doctors didn’t really know what caused diseases, and that is exactly what A says. The other answer choices are wrong because none of them is mentioned anywhere in the passage. Go back and read the second to last paragraph carefully.

23.  B  To answer this question, you just need to read the final paragraph and find out what the passage says about scientific discovery. According to the last paragraph, many of the latest sophisticated additions to our medicine chest shelves were accidental finds. In other words, many modern drugs were discovered by accident. B paraphrases the idea of accidental finds as chance events. A doesn’t make any sense. Are discoveries in biochemistry uncommon? Most biochemists would probably disagree. Don’t forget to use common sense. C may actually be true, but the passage doesn’t mention it, so it can’t be ETS’s answer. ETS’s answers come right out of the passage. You don’t need any outside knowledge. D is wrong because the word best makes this a must answer. How do you know that trial and error is the best way to make scientific discoveries? The passage never says that it’s the best way. E is wrong because it is also a must answer. Is it really true that most of the important scientific discoveries have been accidents? Besides, you’re talking only about drugs here!

24.  A  According to the last paragraph of the passage, many drugs common in modern times were accidental finds; this supports A. Not only is B a bit wacky, but it’s also unsupported by the passage. C and D use deceptive language—they quote directly from the passage, but they don’t answer the question. Neither choice refers to drugs used in 1987. D is especially tricky, because the modern era of pharmacology (line 42) began in the sixteenth century, which does not necessarily mean that any modern drugs were created then. E may well be true, but this idea is not discussed in the passage and therefore it is not correct.

  1.  E  If you divide 12 by 4, you’ll see that x = 3. When you plug x = 3 into the term, you’ll see that 4(3) + 2 = 12 + 2 = 14.

  2.  B  The shaded region lies in the quadrant where x is positive and y is negative. Given this, you can get rid of A, C, and E. If you plot answers B and D, you’ll find that (1, –2) is inside the shaded region, while (5, –4) is not.

  3.  A  You need to take this question one step at a time. First, figure out how many batches there are in 12 jars of cookies. If one jar holds 1.5 batches, then 12 jars will hold 12 × 1.5, or 18 batches. Now you need to figure out how much flour is needed for 18 batches. If you need 6 cups of flour for 1 batch, then for 18 batches you will need 18 × 6, or 108 cups.

  4.  B  There are variables in the answers, so this is a question for the technique of Plugging In. If n = 2, then answer choice B is the only answer choice that gives you an odd integer: 3(n + 1) = 3(2 + 1) = 3(3) = 9. Plugging In makes this problem much easier.

  5.  A  Use the midpoint formula : Take the average of the x-coordinates of the two points to get the x-coordinate of the midpoint, and do the same for the y-coordinates. The midpoint between (3, 4) and (0, 0) is therefore = (1.5, 2).

  6.  C  This question is much easier if you work out the square roots first. You know that = 2 and = 3, so you can rewrite the question like this: 2x – 3x = –x.

  7.  B  Use average pies:

In the first pie you have the number of red parrots sold, which is 5, and the average weight, which is 2. That gives you a total weight of 10 pounds. In the second pie you have the number of blue parrots, which is 4, and the average weight, which is 3. That gives you a total weight of 12. To find the average weight of all the parrots, you need to find the total weight of all the parrots. This is simply the total of the red plus the total of the blue. In the last pie you have the total number of parrots, which is 9, and the total weight of all the parrots, which is 22. This gives you an average weight of .

  8.  C  Remember that the perimeter is the sum of all the sides. FCDE is a square, so all the sides are equal. Because = 3, each side of the square is 3, so you know that , , and are all 3. ABDE is a rectangle, which means that the opposite sides are equal. = 2, so = 2 also. Along the same lines equals 3, so that means the opposite side, , also equals 3. Add up all the sides of ABDE to find the perimeter: 2 + 2 + 3 + 3 + 3 + 3 = 16. To find out how much smaller the perimeter of FCDE is, just subtract: 16 – 12 = 4.

  9.  D  The sides of a 45°-45°-90° triangle have a special pattern, which you can find in the gray box at the beginning of every Math section. Each leg of a 45°-45°-90° triangle is equal to the hypotenuse divided by . Because the hypotenuse in triangle ABC is 8, must be equal to . You can’t have a square root on the bottom of a fraction; so multiply the top and the bottom by . That gives you . Meanwhile, you can use Ballparking to eliminate A and B. Because the hypotenuse of a right triangle is always the longest of the three sides, must be less than 8.

10.  D  Multiply both sides by 2 to get . Square both sides to get x = 162. Therefore, x = 32. You could also have plugged in the answer choices. For D, put 32 in for x and ask, does ? Then does ? Square both sides to find that it does, so D is correct.

11.  D  If there are variables in the answer choices you should … plug in! First, cross out that phrase in terms of b, because you don’t need it. Next, let’s plug in a number for a. This is a percent question, so let a = 100. Because b is 40% of a, that means b = 40. If a = 100, then 4a = 400. Use your calculator to find 40% of 400, which is 160. That’s your target answer. When b = 40, D gives you 160.

12.  D  According to the function, f(x) = 2x2 + 4. To find the value of f(4), just substitute 4 for x: f(4) = 2(4)2 + 4 = 32 + 4 = 36.

13.  B  To find the value of f(3) + f(5), find the values of f(3) and f(5) separately: f(3) = 2(3)2 + 4 = 22 and f(5) = 2(5)2 + 4 = 54. So f(3) + f(5) = 76. You already know that f(4) = 36 from question 12, so you can cross out A. C is the Joe Bloggs answer because Joe simply adds 3 and 5, and it can’t be that easy. If you ballpark D and E, putting 10 or 15 in the function will give you a number bigger than 100, and you’re looking for 76, so D and E are too big. That means the answer is B by POE.

14.  C  The formula for the area of a circle is , so you need to find the radius, r, of the circle. You know that the diameter is 9, and the radius is half of the diameter, so the radius is . Because there are fractions in the answer choices, you might as well keep the radius as a fraction. Now you replace r with in the formula for area of a circle: .

15.  D  Lines that are parallel have the same slope. In the form y = mx + b, m is the slope. So, the slope is −3. Find the line that has a slope of −3 when you rewrite it in the form y = mx + b. Only D works when you rewrite it: Subtract x from both sides to get y = 5 − x, then multiply both sides by 3 to get y = 15 – 3x or y = –3x + 15.

16.  C  If |x| = |2x – 1| this means that either x = 2x – 1 or –x = 2x – 1. The solutions to these equations are 1 and , respectively. However, the only thing you need to recognize is that the equation has two different solutions to establish that the answer is C.

17.  A  Variables in the answer choices? Plug in! This is a percent question, so make k = 100 and d = 40. If 40 out of the 100 gallons have been pumped, that equals 40%. So 40% is your target answer. When you plug k = 100 and d = 40 into the answers, only A gives you 40. Plugging In turns a hard question into a much easier question.

18.  C  For this question you need to know the distance formula: d = r × t. There are two good ways to solve this question. One is Plugging In The Answers. The question asks how far Ray and Jane will be from Ray’s house when they meet. Start with C: If they are 56 miles away from Ray’s house, and Ray traveled from home at 30 miles per hour, then you can figure out the time he traveled using the d = r × t formula (and your calculator): 56 = 30 × t, t = 1. In this case Ray has traveled for 1 hours. If Jane has traveled 93 miles and Ray has traveled 56 miles, then they have traveled a total of 150 miles when they meet. Bingo! You’re done. An even easier way is to think about how fast Ray and Jane are traveling put together. You can simply add the rates. Together they are traveling at 80 miles per hour. Therefore you can figure out the time by setting 150 miles = 80 × t. The time is 1 hours. To find how far Ray has traveled, use the formula one last time: .

19.  D  To figure out probability, you need to work with fractions; the total number of possible outcomes goes on the bottom, and the number of desired outcomes goes on the top. To figure out the probability of selecting three blue hammers, you need to figure out the probability of getting a blue hammer each time a hammer is selected. The first time, there are a total of 20 hammers and 10 of them are blue, so the probability of getting a blue hammer is . When the second hammer is selected, there are only 19 hammers left, and only 9 of them are blue. So the probability of getting a blue hammer the second time is . When the third hammer is selected, there are a total of 18 hammers left and 8 are blue, so the probability of getting a blue hammer on the third try is . To find the probability of selecting three blue hammers, you need to multiply the three separate probabilities: . By the way, A and C are Joe Bloggs answers because he doesn’t consider how the probability changes with each event.

20.  D  Don’t forget that you can plug in on geometry questions. Let’s make b = 70° and a = 30°. So the third angle in the triangle is 80°. You know that c would be 80°, because it is opposite an 80° angle. Your target answer is a = 30°, so plug in 80° and 70° to find it. The only possible answer is D.

  1.  E  The clue in this sentence is they hoard water in their leaves. If the plants are hoarding water, they must be doing it to survive long periods without water. So you can put “without water” in the blank, in which case the best match is aridity.

  2.  E  The clue for this sentence is eloquence and logic. If Liam is eloquent and logical, he must speak “very well”; therefore, you can eliminate A, C, and D because they’re negative. Liam’s eloquence and logic probably made it difficult for his most bitter opponents to contradict his opinions. The best match for “contradict” is disagree with, in E. It also makes sense that Liam’s eloquence and logic made him speak cogently.

  3.  D  The clue in this sentence is first deduced from eccentricities in other planets’ orbits. If subatomic particles are being compared to the outer planets, then these particles must have been deduced through their effects on other particles. If you put “deducible” (recycle the clues!) in the first blank, you can get rid of A. What was deduced about the outer planets and subatomic particles? That they existed. So you can put “existence” in the second blank, which means D must be the answer. Notice that it would not make sense to talk about the outer planets’ proximity, or theircreation; they are not close by and you really can’t deduce creation.

  4.  D  The clues in this sentence are foster and in tense situations. Because foster is a positive word, meaning to care for or nurture, a good phrase for the first blank must be positive; you can get rid of C because dissension is a negative word and E because discourse is neither positive nor negative. If Miranda wants to foster something good, then in tense situations she is probably compelled to give in to others. You can use “give in” for the second blank, which means you can eliminate A. Between B and D, you can eliminate B because fortitude doesn’t make any sense in the first blank. Remember: It’s often easier to figure out which answer is wrong than to figure out which one is right.

  5.  C  The clue in this sentence is helped bring about a period of prosperity in the United Kingdom, and the trigger word is although, which means the blank must be the opposite of helped. If you put “harmful” in the blank, the best match is regressive.

  6.  C  I and II are both true. The author tells you that the war was fought for several reasons. The reasons that are mentioned are a desire for Florida and Canada on the part of the United States—i.e., expansionist tendencies—and as a response to British actions taken against the United States.Statement III is mentioned as an unexpected result of the war, which means it couldn’t have been a reason for starting the war.

  7.  B  Choice B is the best answer. Passage 1 states that the war was in effect a second War of Independence. Passage 2 states that American confidence and nationalism increased after the war. A is wrong because Passage 2 mentions battles that each side won. The passage does not give you any information to support C. D may be true, but neither passage speaks about other international conflicts. E is more closely related to Passage 1 than Passage 2.

  8.  A  In the first passage, the author says the war lacked a clear winner. Passage 2 says that there was no clear victor. B, while perhaps true, is incorrect because the impact on British citizens is not mentioned in the passages. C can’t be supported anywhere in Passage 2. D is more relevant to Passage 2 than Passage 1. E is incorrect because the second passage doesn’t mention how well known the war is in either the United States or Britain. A is the best answer.

  9.  E  Choice E is the best answer. Passage 2 states that although the war was over, Jackson’s victory contributed greatly to American confidence and nationalism. A contains information from Passage 1 and so is incorrect. B is not clearly supported by Passage 2 because no other battles are mentioned. C is incorrect because Jackson’s victory took place after the treaty was signed. D is directly contradicted by the passage which says that the Americans defeated the British at the Battle of the Thames.

10.  C  C is correct because the passage states that since he took his job very seriously, he would in the end go over all the figures himself. Choice A may be appealing, as the passage states that Poseidon could have hired more people, but there is no mention that he does not have enough people. The remaining answers have no support in the passage.

11.  B  This is an EXCEPT question, so it will probably be time consuming to answer. You need to know why Poseidon is unable to change his job. The passage mentions A in lines 24–25: he had been appointed God of the Sea in the beginning, and that he had to remain. C is in lines 17–18:when a job away from the water was offered to him he would get sick at the very prospect. D is in lines 11–12: nothing suited him quite as well as his present position, and E is in lines 16–17: Poseidon could in any case occupy only an executive position. Therefore B must be the answer.

12.  B  In lines 33–35, the passage says, Thus he had hardly seen the sea—had seen it fleetingly … and he had never actually traveled around it. If you read further, you also learn that Poseidon was waiting for the fall of the world so he would have a quiet moment to make a quick little tour of the sea. From that you can infer that Poseidon is too busy to see his own kingdom. A gets it backward. The passage says that Poseidon’s trips to visit Jupiter are the only break in the monotony of his job, so if anything, he prefers the trips to his duties, not the other way around. C is wrong because the passage doesn’t say anything about Poseidon needing silence. D contradicts the passage. Poseidon is waiting for the fall of the world so that he can finally get out and make a quick little tour of his domain, which he has never had a chance to see. E is wrong because the passage doesn’t say anything to suggest that Poseidon is inefficient.

13.  D  The lead word for this question is dissatisfaction, so you should go back to the passage and find where it mentions Poseidon’s dissatisfaction. Lines 26–29 describe what is chiefly responsible for his dissatisfaction. He does not like to hear the conceptions formed about him: how he was always riding about through the tides with his trident. According to the passage, Poseidon doesn’t actually get out much at all, so people have the wrong idea about what he actually does. This is exactly what D says. A contradicts the passage. Poseidon was so irritated by the false idea people had that he was always riding around with his trident. B is a trap. The question asks what is primarily responsible for Poseidon’s dissatisfaction. Although something similar to B is mentioned earlier in the passage, it’s not chiefly responsible for his dissatisfaction (lines 26–27). Use the lead words to make sure you are reading in the right place. C contradicts the passage. Poseidon does the exact same thing every day. That’s why he’s so bored and unhappy. E is incorrect because the passage says that Poseidon actually did most of the bookkeeping tasks himself, leaving little for his assistants to do (lines 4–6).

14.  E  The best answer is E. This is a Vocab In Context (VIC) question, so you should work it like a sentence completion. Go back to the passage, cross out the word described, and fill in your own word based on the context of the passage. In this case, a good word to put in the blank is “formed.” The only answer choice that is close to “formed” is traced, in E. Choice A is tempting, because it seems to describe something that a gull would do, but it does not make sense in context. (Is it possible to soar circles? Nope.) B is also tempting, because it refers to a more common meaning of the word described, but that is not the meaning that is used in the passage. Remember: When a VIC question asks you about a commonly known word, such as described, the primary meaning of the word is almost always a trap. Eliminate it! C is wrong, because the gull was notimagining circles. (This passage is not about the inner lives of animals!) There is no evidence in the passage to support choice D, which does not match up with “formed.”

15.  A  This is a general question, so you need to know only the main idea of the passage. The passage portrays Poseidon as someone who sits around working out figures all day and doesn’t go out much. Poseidon is also clearly unhappy (as you learned in questions 10 and 11), so he is best described as a dissatisfied bureaucrat. The other answer choices are wrong because they don’t fit the main idea of the passage. Poseidon may be a deity, but the passage doesn’t characterize him as being powerful. Poseidon is definitely not a vagabond, and he’s definitely not a tyrant. D is half-wrong, which means that it’s all wrong. Although the description of Poseidon’s duties make him sound like an accountant, the passage focuses on his unhappiness, not his capabilities as an accountant.

16.  E  Based on the blurb and the passage, E is the best answer. The passage lists the role of women in Frankish society, giving information on the queen, the working class, and the religious population. A can be eliminated because there is no dispute in the passage. B cannot be correct because no other societies are mentioned. C is too extreme and, additionally, no other societies are presented. D is incorrect because there is no indication that the passage provides new information.

17.  D  The lead words in this question are Frankish law, which should lead you to the beginning of the passage. According to lines 1–3, the laws and customs in lands under Frankish domination emphasized the biological function and sexual nature of women.… These lines are perfectly paraphrased in D, which says that women were defined in physical or biological terms. A contradicts the passage. Frankish society did not deprive women of opportunities to find personal fulfillment in a variety of roles (lines 3–4). B completely contradicts the second half of the passage, which is all about women in religious communities. Always keep in mind the main idea of the passage. C contradicts lines 7–8, which tell you that Frankish society did not exploit women’s labor to the extent that primitive tribal societies did. E is wrong because lines 8–24 say that women had access to power in several different ways.

18.  B  The lead word in this question is marriage, which should lead to lines 16–18. According to these lines, in Frankish society people either contracted a formal union or entered into a quasi-marriage. B paraphrases this sentence by saying that marriage could be entered into formally or informally. A is wrong because the word only makes this a must answer, and not likely to be right. Besides, does it make sense to say that marriage was the only means of exchanging wealth? C implies that marriage always raised women to positions of power, which is definitely not the case. D is wrong because there is no comparison made in the passage between marriage in primitive society and marriage within Frankish society. Read carefully. E is wrong because the passage doesn’t say anything about whose mother—the bride’s or the groom’s—arranged a marriage.

19.  E  Go back to the passage, find the word instrumental, and cross it out. Then read the sentence and come up with your own word. According to the passage, women were instrumental in bringing about the merger of the free and slave elements in society (lines 23–24); therefore, they werevital to the process. C is a trap answer because it refers to the word instrument and because instruments remind you of harmony. The other choices are wrong because they don’t make any sense in context.

20.  D  D is supported by lines 30–33. A is contradicted by the passage, which states that widows were also able to participate. B is incorrect. The passage states that monasteries were a refuge for married women, but doesn’t say that many women sought refuge or why. C is not stated. The writings of medieval nuns are mentioned, but not as a model for life in a monastery. E is beyond the information in the passage.

21.  C  C is the best answer because the passage states that women were freed from the need to compete for the attention of men. The passage does not explicitly make the links suggested by A and E. Choice B is backwards. There is no support for D.

22.  A  The only answer choice that comes from something stated in the passage is A. According to lines 40–43, women outside the communities must have had to compete for the attention of men. B doesn’t make any sense. How can it be true that women outside the religious community were not inclined to any religious feeling at all? Just because they weren’t nuns doesn’t mean they weren’t religious. C is wrong because it makes no sense to say that women outside the religious community had less economic power. If anything, the opposite would be true. D is too extreme and offensive. ETS would never say that women outside religious communities did not contribute to Frankish culture. E is wrong because ETS would never suggest that women had to rely on men for emotional support. Besides, the passage never says that. Read carefully.

23.  C  This is an EXCEPT question. ETS is asking how Christianity allowed women to escape from male-dominated society, so you have to go back to the passage and find where that is discussed. You are looking for the answer choice that is not mentioned. A is mentioned in line 48; B is mentioned in lines 33–36; D is mentioned in lines 40–43; E is mentioned in lines 25–28. That leaves C.

24.  A  Lines 8–24 detail the different rights and roles of queens, the wives of magnates, and the wives of members of the working classes. B, C, and D are wrong because they do not answer the question. They all refer to specific classes of women, not women in Frankish society. E is never mentioned. A is the best answer.

  1.  A  Subtract 10 from both sides to find 2x = 6, then substitute 6 for 2x. 6 – 10 = –4. You could also solve for x, and then plug that into the expression. If 2x = 6, then x = 3. So, 2(3) – 10 = 6 – 10 = –4.

  2.  C  If he bought 3 boxes of muffins at $4.50, he would have 3 × 6 = 18 muffins. That’s not enough muffins. So, he needs to buy 4 boxes of muffins. Each box costs $1.50; so, the cost is 4 × $1.50 = $6.00.

  3.  E  From 1 to 100, there are 50 even integers. If you don’t include 2 and 100, then there are only 48.

  4.  B  Fill in the angles of the small triangle. The lower left angle is 70° and the lower right angle is 80°. Because the angles in a triangle must add up to 180°, a = 180 – 70 – 80 = 30.

  5.  E  Plug 3 into each answer choice, and try to get 6. Eliminate C and D. Now plug 4 into each remaining answer choice, and try to get 13. Eliminate A and B.

  6.  B  This is a right triangle with two equal sides, so it is a 45°-45°-90° triangle. must be the hypotenuse, so the legs are each . The legs are also the height and base of the triangle. A = bh, so .

  7.  B  This question has several steps, so don’t try to do it all at once. Take it one step at a time. Andrei starts out with 48 baseball caps. In the first step, Andrei gives away 13 caps, so he has 35 left. In the next step, he buys 17 new caps, so now he has 52. Then Andrei gives Pierre 6 caps (46 left) and gets 8 caps in return. In the end, Andrei has 54 baseball caps, which is 6 more caps than he had originally. The percent increase is . You can also change to a percent by typing it into your calculator and multiplying by 100.

  8.  D  Draw a line straight up from D to divide the shape into a rectangle and a triangle. The area of a 5-by-10 rectangle is 50. To get the area of the triangle, find the length of the base; you already know the height is 5. Use the Pythagorean theorem, or to save time, recognize that this is a 30°-60°-90° triangle because the hypotenuse is twice as long as the shortest side. The base is therefore 5. The area of the triangle is therefore . The total area of ABCD is therefore 50 + 12.5.

  9.      100
Use a Ratio Box:

You need to work out only the total column to figure out the total number of garments that the store sold, which is 100.

10.      81
The formula for the volume of a box is length × width × height. But the question gives you the area of the base of the crate, so you already know that length × width = 18. The volume of the crate, then, is simply the area of the base times the height: 18 × 4.5 = 81.

11.      .75 or
All you have to do is solve for x:

12.      8 Using 3b = 2, solve for b by dividing both sides by 3 to get b = . That means . Fractional exponents tell you to use the denominator as the root and use the numerator as a regular exponent. So, . First, cube both sides to find a2 = 43 = 64. Next, take the square root of both sides to find a = 8.

13.      5, 7, or 11 First, think of a prime number that will make 3b greater than 10. How about 5? To see if that fits the other side of the inequality, you need to find the value of which is less than 10, so 5 is one possible value of b. Remember: You need to find only one possible value of b.

14.      21
Let’s say you have seven dancers: A, B, C, D, E, F, and G. How many different ways can you pair them up? This is a combination question, because A and B is the same pair as B and A, and you don’t want to count them twice. Start by finding the number of possible permutations: 7 × 6 = 42. Finally, divide this number by 2 × 1 = 2 (we’re looking to fill 2 positions) to eliminate redundant combinations. There are 21 possible combinations.

15.      96
You know that arc BC is a semicircle, which means it’s half a circle. So the circumference of the entire circle would be 6π × 2 = 12π. Therefore, the diameter of that circle is 12. Because is also a side of the rectangle you know that the length of rectangle ABCD is 12. You can also use the same method to find the width. If the length of semicircle CD is 4π, then the circumference of the entire circle would be 8π and the diameter is 8. Because is the width of the rectangle, you can find the area: length × width = 12 × 8 = 96.

16.      5
f(6) = 62 – 5 = 31. f(4) = 42 – 5 = 11. So f(6) – f(4) = 20. You then find y such that y2 – 5 = 20. y2 = 25, so y = 5 or –5, and the absolute value of y = 5.

17.      282
This is a hard question, so you have to stay on your toes. If the owner buys 3 pounds of each spice, that means she pays the following amounts for each spice:

So she pays a total of 24 + 27 + 21 + 30, or $102 for 12 pounds of spices. She then sells the spices per ounce, so you have to figure out first how many ounces of spices she has. If 1 pound is 16 ounces, then 12 pounds is 12 × 16, or 192 ounces. She sells all the spices at $2 per ounce, so she makes 192 × $2, or $384. To figure out her profit, subtract the amount she paid for the spices from the amount she made selling them: $384 – $102 = $282.

18.      .375 or
Because the question doesn’t give you a figure, you should draw one. Then plug in some values.

If EG = EF, then you can make EF = 3 and EG = 5. That means FG must be 2. If HF = 5FG, then HF = 5(2) = 10. If HF = 10 and FG = 2, then HG = 8. So or .375.

  1.  A  The question is essentially asking which of the answers cannot be a value of x. So just try each answer one at a time by plugging the number into each of the two inequalities in the question, and see which one doesn’t fit. If x = –6, is –6 + 6 > 0? No, because zero is not greater than zero. So –6 is the exception.

  2.  D  Whenever there are variables in the answers, you should always plug in. Let’s say x = 20, which means there are 20 ounces of root beer in the pitcher. Next, let’s make y = 3 and z = 4. That means Elsa pours 3 ounces into each of 4 glasses, so she pours a total of 12 ounces. The question asks how much root beer remains in the pitcher, so your target answer is 20 – 12, or 8. Go to the answer choices and plug in x = 20, y = 3, and z = 4. In answer choice D, xyz = 20 – (3)(4) = 20 – 12 = 8.

  3.  E  Remember that the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. POE! The line in the graph has negative slope, so you can eliminate A and B, and it has a positive y-intercept, so you can eliminate C and D.

  4.  E  Start by writing out the pattern: Blue is the 1st light, orange is 2nd, green is 3, purple is 4, red is 5, and yellow is 6. Then the pattern starts over again, so the 7th light is blue, orange is 8, green is 9, purple is 10, red is 11, and yellow is 12. Notice that the yellow lights go by multiples of 6? The 18th light will also be yellow, as will the 24th, 30th, and so on. We want to know the 53rd, so the closest light we know to 53 is the 54th light, which is yellow. If the 54th is yellow, then the light immediately before is the 53rd, which must be red, answer E.

  5.  C  Whenever there are variables in the answer choices, you should plug in. Because x = y + 1 and y ≥ 1, you can make x = 5 and y = 4. In that case, x2 – y2 = 25 – 16 = 9, so 9 is your target answer. When you plug x = 5 and y = 4 into the answer choices, only C gives you 9. Plugging In turns a hard question into a much easier question.

  6.  B  The “Third Side Rule” states that any side must be less than the sum of the other two sides, and greater than the difference between the other two sides. In other words, if the sides are a, b, and c, |bc| < a < b + c. Find the smallest possible value of a. If a = 1, then b + c = 9. For example, b = 4 and c = 5. This is illegal, as |bc| = a. If a = 2, then b = 4 and c = 4, so 2 is okay. The largest a can be is 4, because if a = 5, then a = b + c and you have violated the Third Side Rule. Thus, the difference between the largest possible value of a and the smallest possible value of ais 4 – 2 = 2.

  7.  C  The Joe Bloggs answer is E because Joe simply chooses the greatest number. If you draw three straight, intersecting lines through the center of the triangle, you get 6 regions, so you know that you can have at least 6. Therefore, you can eliminate A. But that was too easy. That means the answer must be 7 or 8. If you don’t have time, you can guess between C and D. Here’s how you can actually get 7 regions:

  8.  B  To find out what numbers a could be divisible by, you need to try different values of b. If b = 1, then a = 4(1) + 26 = 30. In this case, a is divisible by 2, 5, and 6, so you can cross out A, C, and D. If b = 4, then a = 42, which is divisible by 7, so cross out E. That leaves only B, which must be the answer.

  9.      2
First, solve for x. Divide both sides of the equation by 3, and you get x = 4. Then divide 8 by 4, which gives you 2.

10.      270
The trick here is that ETS is not asking for the value of a, b, or c. It just wants to know what they add up to. ETS is testing only the Rule of 360. All the angles in the figure make up a circle, so they all add up to 360. The right angle is 90 degrees, so 90 + a + b + c = 360. Therefore a + b + c = 270.

11.      7
It would definitely help to draw out this question:

XY = XZ, which means Y is the midpoint of . So XY = YZ, and therefore YZ = XZ.

If YZ = 4a + 6 and XZ = 68, then 4a + 6 = (68). Now just solve for a:

12.      3
You can solve this question using simultaneous equations because you have two equations with two variables. First, you need to rearrange the equations a bit: 4x + 2y = 24 divided by 2 on both sides becomes 2x + y = 12. , multiplied by 2x on both sides, becomes 7y = 14x. This, divided by 7 on both sides, becomes y = 2x, which can be manipulated into 2xy = 0. Now you can add the equations:

13.      9
Factor the numerator and the denominator into . The (x – 2) cancels out of the top and bottom to leave . Multiply both sides by (x – 6) to get x + 3 = 4x – 24. Subtract x from both sides: 3 = 3x – 24. Add 24 to both sides: 27 = 3x. Divide by 3 to get x = 9.

14.      .4 or
You can solve this question by setting up a proportion. There are 8 liters in 20 bottles of juice, and you need to find out how many liters are in one bottle. Here’s what the proportion looks like: . Solve for x, and your answer is or 0.4.

15.      120
There are a total of 6 women to choose from and the company needs 3, so you would calculate 6 × 5 × 4 = 120. However, because order doesn’t matter, we need to get rid of duplicates. Mathe-matically this is done by dividing your answer by the factorial of the number of spaces you need to fill. Because we need 3, we divide by 3!, or 6, which leaves us with 20. Now, on to the men. There are 6 men to choose and we need only 1. So there are 6 ways to choose that. Now we have to count our women (20) and our men (6). Remember in probability that and means multiply. 20 × 6 = 120, which is the answer.

16.      288
We can’t figure out how many rabbits there were after 7 years until we know the constant a. To find it, let’s use one of the data points that we’re given. We know that after 3 years (t = 3) there were 192 rabbits (P(t) = 192). Plug both of those into the equation and we get 192 = a(3) + 120, which we can solve to find a = 24. Now plug that into our original equation, and we have P(t) = 24t + 120. To find out how many rabbits there were after 7 years, plug in t = 7: P(t) = 24(7) + 120 = 288.

17.      18
To answer this question you have to set up an equation. If the radius of C is r, then the radius of B is 2r and the radius of A is 4r. The formula for the area of a circle is πr2. Because 84π is the sum of the areas of the circles, this is your equation:

If r = 2, then the radius of C is 2, the radius of B is 4, and the radius of A is 8. consists of the radius of A, the diameter of B, and the radius of C, so AC = 8 + 4 + 4 + 2 = 18.

18.      50
You don’t know how many cars are in the parking lot, so you can plug in a number. Let’s say there are 40 cars in the parking lot. Now read through the question; if of the cars are blue, there are 8 blue cars. If of the blue cars are convertibles, there are 4 blue convertibles. If of all the convertibles are blue, and there are 4 blue convertibles, that means there are 16 convertibles all together. The question asks what percent of the cars are neither blue nor convertibles. At this point, the question becomes a group question, and you have a formula for solving such questions: total = group 1 + group 2 – both + neither. In this question, the total is 40 cars, group 1 is the 8 blue cars, and group 2 is the 16 convertibles. You also know that 4 cars are both blue and convertibles. Now just plug those values into the formula: 40 = 16 + 8 – 4 + n. Then solve for n, which equals 20. So 20 out of the total 40 cars are neither blue nor convertibles: .

  1.  A  Take care of the answers one by one for this sentence. B is not a complete sentence. C uses the ambiguous pronoun their, D uses the ambiguous pronoun it, and E changes the meaning by suggesting rotary phones are unknown in general.

  2.  C  C correctly modifies the verb related with the adverb distantly. A is incorrect because in general, anyone is a “who” and not a “that.” In B and D, to modify relationships (a noun) you need distant (an adjective) and not distantly (an adverb). In E, to modify related (a verb) you needdistantly (an adverb) and not distant (an adjective).

  3.  C  The pronoun you refers to the person viewing the paintings, and so the next pronoun which refers to that person should also be you rather than people, as in B or one, as in A, D, and E.

  4.  E  In the original sentence A, and does not imply the contrast between the two types of fat; you need the conjunction but, which is used in E. B and D, each missing a conjunction, are run-on sentences. C uses the -ing form of the verb, which is not the first choice for a clear sentence.

  5.  B  Knoll isn’t clearly singular or plural, so look for its verb: sells. Because sells is singular, so too is Knoll (neither is underlined). Eliminate A, D, and E because all are plural. Between B and C, B is much more concise and clear.

  6.  D  Because there is a semicolon in this sentence, there should be a complete sentence on each side of it. Eliminate C because it is not a complete sentence. B unnecessarily uses the word being, so eliminate it. E uses the word those, but because it is referring to something in the same sentence it should have been these. Between A and D, A is redundant, using both because and is why.

  7.  B  A singular noun needs a singular verb (Increase … has), so this eliminates choices A and C. In D, the word which follows the name of the rest home, implying that the home caused the nurses to threaten. In E, angered the nurses … to have a walkout sounds awkward and makes little sense.

  8.  E  Galleons is plural, so eliminate anything that tries to describe them singularly: A, B, and C. D also uses the singular pronoun its, and so should be eliminated.

  9.  D  In both B and the original sentence, the pronoun he is unclear in its reference: It could mean either Evan or Ken. Only D and E correct this error, but E needlessly uses the -ing form of the verbs.

10.  B  Both the original, choice A, and the option in E use the incorrect construction neither … or. E also puts the final verb in the awkward -ing form. C and D unnecessarily add the word other. B uses the correct parallel structure: requires … assigns … does expect.

11.  A  There is no error in this sentence as written. The idiom, regardas, is the proper construction.

12.  D  The pronoun in D disagrees with the noun it replaces: King is singular; them is plural.

13.  A  Traveled is in the wrong tense. The rest of the sentence describes the plot in the present tense, so it should read travels.

14.  B  The verb should be claim or have claimed. There is no reason to use the past perfect, as there is no action occuring after it to warrant this tense.

15.  E  There is no error in the sentence as it is written.

16.  B  The phrase “more than” is the wrong idiomatic phrase here. The correct phrase is “prefer something to something.”

17.  A  This sentence has an idiom error: The phrase comply to should be comply with.

18.  E  There is no error in the sentence as it is written.

19.  A  The subject field is singular and the verb have is plural. Watch out for prepositional phrases that follow nouns: The phrase of consumer electronics is only a description of field. It is the field that has never been fixed, not consumer electronics.

20.  D  The pronouns shift from one to you. Correct this error by changing both words to one or changing both words to you.

21.  D  When comparing two people, you must always use the comparative form the more rather than the superlative form the most, which is used only with three or more things.

22.  E  There is no error in the sentence as it is written.

23.  C  To correct the verb-tense problem in this sentence, change spent to spend because target is in the present tense.

24.  E  There is no error in the sentence as it is written.

25.  C  This sentence contains an error in verb tense: C should say had ridden. The simple past tense, rode, is always used without a helping verb (has, had, is, was, for example).

26.  B  You cannot compare other sculptors to Rodin’s creations. It should be “unlike other sculptors’ creations” or “unlike those of other sculptors.”

27.  B  When making a contrary-to-fact statement (Jason did not, in fact, plan ahead), never use a would in an if clause. Thus, if he had planned,…he would not have had to write.

28.  A  The subject is words, which is plural, so the verb needs to be plural, as well. Trim the fat—cross out the inessential words, such as prepositional phrases—to find the basics of the sentence: words … have … meanings.

29.  E  There is no error in the sentence as it is written.

30.  E  If you try to remove the words production of in A and actually did in B, you will see that the sentence makes no sense without these words. Likewise, if you remove agreed to in C, the sentence loses an important verb. Removing when in D creates a run-on sentence. E is the only available choice.

31.  D  The sentence uses a list of items and all items in that list should be parallel. Only D does this correctly. B changes the meaning. C is in the passive voice, and E is awkward with the use of be building.

32.  B  The tense was ever wearing is used incorrectly in the original sentence. In C, the use of could makes no sense in context. Likewise, in D, the uses of would ever be makes no sense and is awkward. E is also awkward and makes no sense.

33.  C  The last paragraph talks of the opening night, and only C uses a transition word, finally, and introduces the topic of the paragraph.

34.  B  With addition questions, always stick to the main topic. Only B does so by discussing the author’s responsibilities during the rehearsal. This goes well with the discussion of the production and opening night. In A, the author’s other activities are not applicable to a passage about a theater production. C is too broad as this is a personal account of a production. Likewise, D and E are too broad.

35.  A  The sentence is acceptable as it is now, and therefore A is the best choice. B and C are inferior because the words being and having are rarely the verb forms found in the best version of an SAT sentence. D and E each create a sentence that lacks a verb.

  1.  C  To solve for y, begin by adding y to both sides of the equation, which gives you 6 = 3y – 6. Then add 6 to both sides, which gives you 12 = 3y. Now divide both sides by 3, and you find that y = 4. You can also plug in the answer choices for any question that asks you to solve for a variable: 6 – 4 = 2(4) – 6.

  2.  B  This is what is called a visual perception problem. It’s like a maze. Just put your pencil on a and see which other letter you can connect to a without crossing any lines. The only letter you can reach directly is w, all the way in the middle.

  3.  C  This is a perfect calculator question. Just add the morning shift and the afternoon shift for each day and see which total is the greatest. The total for both Tuesday and Wednesday (the greatest) is 575 + 595 = 1,170.

  4.  A  For this question, you need to know that volume equals length × width × height. You know that the volume is 16,500, the depth, or height, is 10, and the length is 75. Just put those numbers in the formula: 16,500 = 75 × w × 10. Use your calculator to solve for w, which equals 22.

  5.  D  The idea of the rest in this question can save you from doing unnecessary arithmetic. If 40% of the records are jazz, then the rest, or 60%, are blues. Because there are 80 records, just use your calculator to find 60% of 80, which is 48.

  6.  D  Use a Ratio Box:

There are 20 girls and 15 boys, so there are 5 more girls than boys.

  7.  B  Try plugging in some values for x and see if the graphs include that point. If x = 0, then y = 0, so, (0, 0) should be a point on the graph. Unfortunately this doesn’t eliminate anything. If x = 1, then y = 2, so, (1, 2) should be a point on the graph. Eliminate A, C, D, and E.

  8.  C  Plug in the answers starting with C. If the length is 16, the width is half of that. 16 ÷ 2 = 8. Area is length × width. So, does 128 = 16 × 8? Yes, so C is correct. Alternatively, write an equation. The equation is area = w × 2w. So, 128 = 2w2. Divide by 2 to get 64 = w2. Take the square root of both sides to find w = 8. The length is twice this width, so length = 2 × 8 = 16, so the answer is C.

  9.  C  Plug in! Let’s make T = .5 and S = –.8. Because a positive number divided by a negative number is negative, eliminate D and E. .5 ÷ –.8 = –.625, which is closest to C.

10.  A  Once again, plug in: Let’s say x = 50. Now you can translate the question:

If you work this out on your calculator, you should get 50 as your target answer. If x = 50, the only answer that works is A.

11.  E  Because A is the center of one circle and B is a point on the circumference, is r. and are also r. Whenever a line is tangent to a circle, the radius drawn to the point of tangency is perpendicular to the line. So, and are perpendicular to . That means ABCD is a square. Plug in for the radius, say r = 6. The area of a square is the square of a side, so the area is 36. Plug 6 into the answer choices to see which agrees with 36. Only E is 36!

12.  E  This is a perfect question for PITA (Plugging In The Answers). The question asks for the greatest possible number of 20-ounce boxes. Start with C. If there are twenty-five 20-ounce boxes, then there are twenty-five 8-ounce boxes because a total of 50 boxes were purchased. In this case, the twenty-five 20-ounce boxes weigh 500 ounces, and the twenty-five 8-ounce boxes weigh 200 ounces; the total is 700 ounces. This is too big because the question says the total weight was less than 600. If C is too big, A and B must also be too big; eliminate all three. If you try D, the total weight is 604 ounces, which is still too big. So the answer must be E.

13.  D  Here’s yet another chance to plug in because of the variables in the answer choices. In this case, you have several variables. You should start by plugging in values for x and y, and then work out c. Because x > y > 0, let’s say x = 6 and y = 3. Therefore, , which equals . The question asks for the value of , which is the reciprocal of , or 2. This is your target answer. If you plug x = 6 and y = 3 into all of the answer choices, you’ll find that only D equals 2.

14.  D  Test the answer choices. The first number in each pair represents x, and the second number represents y. The ordered pair should work in both functions. Try C in the first equation: Does 0 = (1) + 2? No. So, C is not the answer. Try D in the first equation: Does 4 = (2) + 2? Yes. So, try D in the second equation: Does 4 = (2)2 + 2 – 2? Yes. Because D works in both equations, it is the correct answer.

15.  A  This a great opportunity to Plug In The Answers! Start with C, and plug into g(x) first: |22 – 10| = 6. Now plug that value into f(x): + 2 = 5. Cross out C. Now the tough decision is whether or not a bigger or smaller value of a is needed. If you aren’t sure which way to go, then just try another answer. For instance, plug D into g(x): |62 – 10| = 26. Now into f(x): + 2 = 15. You got a lot further away from the answer, and using D resulted in a number much too big! Cross out E as well, and try one of the first two answers. Plug A into g(x): . Now into f(x): + 2 = 6! A is the correct answer.

16.  E  There are variables in the answer choices, so plug in. However, you can’t plug in a value for all the variables at once because you must follow the rules of geometry. (Makes sense, right? It’s the last question in the section.) Let’s start by saying a = 70 and b = 60. Because PQRS is a parallelogram, angle Q must equal angle S, so angle S also equals 60. If you look at the big triangle that contains a and c, you already know that two of the angles are 60 and 70, so the third angle, c, must be 50. You know that PQ and SR are parallel and, you can see that x is a big angle and a is a small angle. So a + x = 180. Because a = 70, that means x = 110. Therefore, your target answer is 110. Plug your values for a, b, and c into the answers and you’ll find that E equals 110.

  1.  C  In this sentence, the clue is cover a broad array of subject matters and range of historical eras. A good word or phrase to use for the blanks would be “varied” or “all different.” Diverse comes closest to this meaning. Remember to use word roots to help you eliminate answers.Meritorious shares the same root as merit, and merit means something of worth. So meritorious probably means something similar and does not match our word for the blank.

  2.  C  The clues in this sentence are apparent and deceptive. Professional skiers descend the slopes with apparent “ease,” but this apparent ease is deceptive. Therefore, it must actually be difficult to ski well. The best way to complete the second part of the sentence is to say that skiingrequires great effort and intense concentration. So you can put “great” in the second blank. That gets rid of E. Then you have “ease” in the first blank, and the best match among the remaining answers is nonchalance.

  3.  C  The missing word here needs to describe the role of famous singers in popular culture. Therefore “famous people” would fit well here. C is the best choice, because an icon is an idol or person who is the object of great attention.

  4.  C  The clues here are unnecessarily, trivial information, and did not need. A good word for the blank is “wordy.” A is incorrect as winsome means “charming.” B is incorrect as terse means “concise.” E is incorrect as deafening means “loud.” D is incorrect as fallacious means “wrong.” So the best answer is C, which means “complicated.”

  5.  D  The blanks here are related to each other, but the clues tell you in what manner. The clues enjoyed visiting New York and did not like all the traveling indicate that Cecilia had two contradictory feelings—one good, one bad. Look for a contradictory relationship between the blanks. A and C include two similar words. Cross them off. B and E have answers that are not really related at all. Only D includes two answers that are contradictory, involving both rest and work.

  6.  D  In this sentence, putting a word in one blank affects the word in the other blank, so the relationship between the blanks should be determined first. The trigger despite suggests that the two blanks have an opposite relationship. A, B, C, and E can be eliminated because the words in those choices do not comply with the trigger, thus D is the best answer.

  7.  E  Because this question involves both passages, you should definitely do it last. The easiest way to answer this question is to use POE. A is about Passage 1 only, so you can eliminate it. Newton certainly received credit for his theories, so you can eliminate B. C is wrong because the passages discuss the contribution of the three scientists mentioned, so you can eliminate it. Between D and E, choice E is better because it’s a may answer, and ETS likes wishy-washy answers.

  8.  E  Go back to the passage, find the word promulgated, and cross it out. Then read the sentence and come up with your own word. The first part of the sentence is saying something very positive about Democritus’s ideas, so you need a positive word. That means you can eliminate A, B, and D. It doesn’t make sense to say that Democritus’s ideas were protected, so you can cross out C. E is the only choice left.

  9.  A  A is correct because Democritus was one of the first to perceive that nature may include what he called the atom (line 15). This concept was forgotten (line 7) until the twentieth century (line 14). B says that Democritus was known more for his work in politics, but this is not mentioned anywhere in the passage. C says that his ideas were incompatible with those of Galileo and Newton, which contradicts lines 30–32. D says that Democritus was unduly credited, but the passage is all about giving him proper credit. E says that Democritus was known for his discovery of calculus, which is not said anywhere in the passage.

10.  D  The obsession referred to in Passage 1 (lines 18–23) is the search for a level of stark simplicity underlying all the complex richness, texture, and variety of our everyday life. This idea is paraphrased perfectly in D, which says that scientists are on a quest for a simple unifying property of everyday matter. The passage is talking about something that is today almost an obsession, so A and E are wrong because they are not about modern science. B and C are wrong because they aren’t mentioned anywhere in the passage. If it’s not in the passage, then it’s not the right answer.

11.  B  Democritus’s ideas were way ahead of his time but now few physicists can imagine any other approach, making B a good answer. You can also use POE on this question. A is wrong because the word dismay is extreme and the author never says that the early scientists were narrow-minded. You can get rid of C because the author does not tell you he is surprised or confused by the modern acceptance of Democritus’s ideas. Eliminate D, because the passage does not go on to talk about the uses of atomic theory. E is close, but not close enough. The author does not say that they are unwilling to explore other theories, but rather that they cannot even think of them.

12.  C  This is an inference question, because it uses the word suggests, which tells you that the author did not directly state the right answer but gave you enough information to draw a conclusion. On inference questions, look for an answer that you can definitely say is right. C is supported by the paragraph, because you know that both chemists and physicists dealt with it and its implications. There is no support in the passage for A, B, D, or E.

13.  A  A is correct because the author states that Newton, and others, should have realized the concept and it is odd that no one thought of it before. B is wrong because it says that Newton should have realized, not that he did. C isn’t right because the idea was discovered, and is still accepted, by modern physicists. You can eliminate D because it contradicts the passage. E is too extreme.

14.  C  Go back to Passage 2 and find where Newton is mentioned. According to lines 48–51, With hindsight, it is easy to wonder why no one had thought of it before. Newton, and others, should have realized that a static universe would soon start to contract under the influence of gravity. So the passage uses Newton as an example of a scientist who might have come up with the idea of an expanding universe before it was actually discovered in the twentieth century. This idea is paraphrased in C. A is wrong because ETS would never suggest that many physicists are ignorant. Remember: ETS has great respect for scientists. Newton wasn’t a proponent of the expanding-universe theory, so you can discount B. D contradicts the main idea of the passage. According to the author, the universe is expanding. Go back and read the first sentence of the passage. E is wrong because Newton didn’t disregard the expanding-universe theory. There was no such theory back then!

15.  B  According to lines 54–58, if the universe was expanding at more than a certain critical rate, gravity would never be strong enough to stop it.… This is a bit like what happens when one fires a rocket upward from the surface of the earth. So the rocket is being used as an example of how the force of gravity applies to the idea of an expanding universe. B paraphrases this nicely. A is wrong because the rocket example is not an implication of the expanding universe. The rocket is simply an example used to illustrate the implications of gravity on the expanding-universe theory. C makes no sense. Is the energy released by a rocket similar to the energy released by an entire universe? No way! D and E contradict the main idea of the author, that the universe is expanding.

16.  B  The lead words for this question are Einstein’s general theory of relativity, which should lead you back to lines 67–70. According to these lines, Even Einstein, when he formulated the general theory of relativity in 1915, was so sure that the universe had to be static that he modified his theory to make this possible. So the passage is showing you that, among modern scientists, even Einstein wanted to maintain the idea that the universe is static. He even changed his famous theory of relativity to make this possible. This idea is perfectly paraphrased in B. A is wrong because the expanding-universe theory is not the author’s theory. C is incorrect because the passage says nothing about Einstein’s creativity. The point is that Einstein disagreed with the expanding-universe theory. D is wrong because the passage never suggests that the expanding-universe theory may not be valid. Just because Einstein didn’t agree with the theory doesn’t mean it’s wrong. E strays too far from the main idea. Remember: The passage is about the expanding-universe theory, not about Einstein’s relation to Newton.

17.  A  According to lines 66–77, Einstein wanted so much to maintain the idea of the static universe that he modified his theory [of relativity] to make this possible. The change he made was to introduce the so-called cosmological constant. That is exactly what A says. B is wrong because Newton didn’t have any ideas about the expanding-universe theory. The theory didn’t exist back in Newton’s time! C is off the mark because the cosmological constant is part of Einstein’s theory of relativity, not an idea developed by his opponents. Read more carefully. You can’t pick D, either, because Newtonian physics has never been disproved, and this is not suggested anywhere in the passage. The passage is about the expanding-universe theory. Don’t forget the main idea. E is incorrect because the passage is not about the mass of all matter. Again, everything in the passage relates to the expanding-universe theory.

18.  D  Go back to Passage 2, find the word static, and cross it out. Then read the sentence and come up with your own word. According to the passage, Einstein and many other modern scientists were against the idea of an expanding universe. That means they must have believed in a universe that wasn’t expanding. So you can put “not expanding” in place of static. The best match for “not expanding” in the answer choices is unchanging. The other answers are wrong because they don’t make any sense in context.

19.  A  According to the passages, Democritus, an ancient Greek scientist, first came up with the theory of atomism, while the expanding-universe theory was first put forth in the twentieth century. That is one clear difference between the two theories, and it also happens to be exactly what A says. B is wrong because the passages never suggest that atomism is easier to understand than the static universe theory. The comparison is never made. C is way off base. There is no mention of politics anywhere in either passage. D is too extreme. The passage never says that the theory of atomism had been proven. Remember that it’s just a theory. E contradicts the main idea of the passage. Modern science has rejected the static universe theory in favor of the expanding-universe theory.

  1.  A  Always check the answer choices to determine if any work with the part of the sentence that is not underlined. B is wordy and choppy because of all the phrases that are set off by commas. The phrase because of complying in C would be stronger if it were because they comply. D usescomplied by, which is not the correct idiom. E is a run-on. A is the strongest choice.

  2.  E  Collective nouns, such as audience, are singular, so make sure to use singular pronouns and verbs with them. A and C use are—a plural verb. D uses the plural they. B contains a plural verb, aren’t.

  3.  C  There are two idioms at work in this sentence and the answer choices: distinguish … from and between … and. A, B, and D all use the idioms incorrectly. E is wordier than C and fails to maintain parallelism in comparing the two things.

  4.  C  As written, the sentence creates a faulty comparison. It states that something is unlike the Asian people. Only another people can be contrasted with the Asian people. But this sentence says that the settlements were unlike the Asian people, so A is incorrect. B and E have this error as well. D fixes the faulty comparison by placing the Ainu right after the comma, but as Caucasians makes no sense here.

  5.  D  An introductory phrase (in this case, A Mongol emperor associated with ancient Chinese splendor) must directly precede the noun to which it refers. Only D does this by placing Kublai Khan’s name right after the comma. C is deceptive because it uses his name as a modifier: The noun is actually army. In the other three answer choices, the noun is fleet, which is not what the introductory phrase is referring to.

  6.  A  The sentence is correct as it stands. B turns the sentence into a fragment. C unnecessarily changes the verb tense by adding had. D incorrectly changes the comma to a semicolon, which is used only when the word group on each side of it expresses a complete thought. In this case, the phrase following the semicolon is missing a subject. In E, and it is redundant. Therefore, A is the best answer.

  7.  A  This sentence is correct as it stands. The word each is singular, and is therefore correctly referred to by the pronoun its. In B and E, the word their is plural and therefore incorrect. C says each kitten has personalities (plural), and D unnecessarily adds the word which. Thus, A is the best answer.

  8.  B  B is the best answer. The clause that precedes the comma and the one after the comma can stand as complete sentences and must therefore be separated by a period, a semicolon, or a comma followed by a conjunction. B correctly uses this last option. Both A and D create comma splices, while C and E add unnecessary words that change the meaning of the sentence.

  9.  E  E correctly uses the word that to introduce a description of what the storm did. The semicolon is incorrect in A because the words following it are missing a subject and therefore express an incomplete thought. In B, and it is an unnecessary addition. Answers containing -ing verbs, such as C and D, are rarely the best choice, leaving E as the best answer.

10.  D  The best choice is D. The subject is effects, so the verb must be plural (were). A uses the past perfect for no reason; the simple past tense in D is sufficient here. The verb in C is singular and so does not agree with the subject. The word being in choice B makes the sentence a fragment. E uses the wrong pronoun, thereby changing the meaning of the second part of the sentence.

11.  B  B is the best answer. Mr. Peters has to follow the comma, because the opening modifier describes him, not the observation, as in A and E, or the act of observing, as in C. Choice D doesn’t actually contain a main verb.

12.  C  The best answer is C. A, B, and E are passive. C also correctly uses the construction not only … but also, while D incorrectly says not only … and … too.

13.  B  The original sentence, A, and the sentence in D are written in the passive voice. In C, the verb is in the past tense but needs to be in the future. E uses the future progressive tense, which unnecessarily adds –ing. Only B is clearly worded.

14.  D  The pronoun them is incorrect in the original, A, and in B. The pronoun those should refer to the streets in Belgium: This appears in both C and D, although C unnecessarily adds the word when. E is a comma splice, a form of run-on sentence.