## Cracking the SAT

# Part VII

# SAT Practice Tests and Explanations

# Chapter 20

# Answers and Explanations for Practice Test 1

## SECTION 2

1. **A** Answer this question in bite-sized pieces. The first step is to use your calculator to compute the sum of the subscriptions: $68.80. The down payment was half that amount, leaving $34.40 to be paid in 4 installments of $8.60 each. If you answered D or E, you may have misread the question.

2. **C** Try Plugging In The Answers. Starting with C, put in for *x*:

Cross-multiply: . So C is correct. Another way would be to cross-multiply first to get 2*x*^{2} + 4*x* = 2*x*^{2} + 2. Subtract 2*x*^{2} from both sides to get 4*x* = 2. Divide by 4 to get *x* = .

3. **C** This is an excellent time to turn on your calculator. If 48,000 people live in Town *X* and each household has 3.2 people, you can determine the number of households: 48,000 ÷ 3.2 = 15,000. And since each household has 1.2 televisions, you can now determine the number of televisions: 15,000 × 1.2 = 18,000.

4. **B** From the statement, you know that flour is necessary to make the cookies. You don’t know that flour is the only thing necessary to make the cookies. For example, you may also need sugar and eggs. You cannot conclude A or E, because there may be other reasons for not making the cookies (maybe you didn’t feel like it, or maybe you were out of sugar). Choice C is not necessarily true because there may be other things necessary besides flour. Answer choice D contradicts the original statement. Choice B must be true because you couldn’t have made the cookies without the flour.

5. **B** Start by plugging in what you know into the function given. If *f*(*x*) = *x*^{2} – *c*, and *f*(–2) = 6, then plug in –2 for *x* in the function: *f*(–2) = (–2)^{2} – *c*. Solve and replace *f*(–2) with 6: 6 = 4 – *c*; 2 = –*c*; and *c* = –2. If you picked answer choice A, you forgot that (–2)^{2} is positive 4, and if you picked answer choice E then you forgot about the minus sign in the original function.

6. **A** First solve for *b*. If 9*b* = 81, then *b* must equal 9. Insert 9 for *b* into :

7. **A** The formula for the circumference of a circle is *C* = 2π*r* or *C* = *d*π. (If you forget the formula, you can look it up at the beginning of the section.) The circumference of the circle is 5, so 5 = π*d.* Now, just solve for *d*, which equals .

8. **D** If you got this question wrong, you either misread it or forgot the correct order of operations. Remember to do parentheses first. Translating the information to an equation, you’d get the following:

9. **E** Approach the problem in bite-sized pieces. = 2^{3}, so = 4. Square both sides to get *x* = 16.

10. **B** We’re solving for shirts and pants, which constitute 60% of total sales. Because shoes ($12,000) account for 15%, shirts and pants would be four times that amount, or $48,000. Another way to solve this is to find out the total value of sales and find 60% of that. If $20,000 represents 25% (or ) of sales, then the total must be $80,000. Using translation, you’ll find that × $80,000 = $48,000.

11. **D** You should have noticed several things about this question. First, the figure was not drawn to scale. So a good first step would be to redraw the figure to comply with the condition ( > ). Second, the question asks which of the following *must* be true. *Must* is an important word—if it were *which of the following could be true,* you’d change your analysis completely. So, redrawing the figure, you’d get something like this:

In this figure, is clearly larger than . Because plugging in numbers makes the distance more concrete, you might have made *AB* = 3 and *CD* = 2, for example. Because you don’t know the length of *BD*, however, you’d have to leave it alone. Now, let’s check the conditions. Option I: Well, this could be true, but it doesn’t have to be. So, option I is out. This allows you to eliminate A and E. Option II: If you let *AB* = 3 and *CD* = 2, *AC* = 3 + *BC* while *BD* = *BC* + 2. No matter what *BC* is, *AC* > *BD*. Option II is true. This allows you to eliminate C, which does not include Option II. We still need to check one more. Option III: If *AB* > *CD*, and *AC* > *AB*, then *AC* > *CD*. Option III is true; therefore, D is the answer.

12. **D** Absolute value, a number’s distance from zero on a number line, is always expressed as a positive number. Cross out A and B since both are negative. Solve the function with *x* = 1: *f*(1) = |(|1| − 3)| = 2.

13. **D** This geometric sequence can be expressed as 6 × 2* ^{x}*, where

*x*is the number of hours. So, after 9 hours, there will be 6 × 2

^{9}= 6 × 512 = 3,072. Alternatively, you could just work out the problem each hour by doubling. So, after the first hour, there are 6 × 2 = 12. Then, after the second hour, there are 12 × 2 = 24, and so on, until you get to the ninth hour.

14. **E** Because any value squared must be 0 or positive, the least possible value for *x*^{2} is 0. This means the least possible value of *x*^{2} + 2 is 2. So, A, B, C, and D are not possible values for *f*(*x*). Only E is a possible value because when *x* = 0, *f*(*x*) = 2.

15. **E** Once again, the way *not* to solve an SAT question is to reason algebraically. Instead, use your calculator to start cubing integers and stop when you find an integer cubed that is greater than 200. 1^{3}, 2^{3}, 3^{3}, 4^{3}, and 5^{3} are all less than 200. 6^{3} is 216, so that’s too large. Thus there are 5 numbers.

16. **B** Plug in! Because the values you choose for *x* and *y* must satisfy the equation, let *x* equal 6 and *y* equal 9. The perimeter *p* would then equal 6 + 6 + 9 + 9, or 30. The target is *y*, which is equal to 9. Plugging in 30 for *p* in each of the choices, you’d get B as the answer. Although some of you might have answered this question correctly by using algebra, doing so might have caused you to make a mistake without realizing it. Trust us. Plugging In is always the safer method for this type of problem. The Joe Bloggs choice, by the way, was C.

17. **C** And yet again, the slow way to solve a word problem like this is to set up equations. Letting *w* and *l* represent the number of wins and losses, respectively, the slow method of setting up equations would yield the following:

Then you’d have to substitute for in the second equation and solve for *l* and then go back to solve for *w*.

We can also plug in the answer choices, starting in the middle, C, and see which one works:

Bingo! We found the answer on the first try! If C didn’t work, you’d move up or down depending on whether the result was too small or too big.

18. **A** This is a great opportunity to plug in. Make up a value for *x*—let’s say 40. Then name the two other angles created by the lines that meet at vertex *P*— let’s call the one to the left of *x* (within the same triangle as the angle labeled *a*°) angle *y* and the one to the right of *x* (within the same triangle as the angle labeled *b*°) angle *z*. Now make up values for these two angles so the sum of *x, y,* and *z* is 90. Let’s say that *y* = 30 and *z* = 20. Because both of these triangles are right triangles, *a* = 180 – 90 – 30 = 60, and *b* = 180 – 90 – 20 = 70. Thus *a* + *b* = 130, which becomes our target. Only A yields this answer.

19. **C** First a little error avoidance: Because 5 is one of the numbers you see, 5^{2}, or 25, is not going to be the answer. It’s a Joe Bloggs answer. So, eliminate A. Next, let’s estimate the area before you try to solve directly. The length of the square’s side is a little more than 5, so the area is going to be a little more than 5^{2}, or 25. E is too large, so before solving the problem, you’ve eliminated A and E. If you couldn’t calculate the area exactly, you could guess from among the remaining choices. To determine the area, let’s begin by assigning the variable *s* to indicate the length of the square’s sides. The area is given by this formula: *A* = *s*^{2}. Notice the triangle formed by side and the *x*- and *y*-axes. The base of that triangle is 1 and the height is 5, so you can use the Pythagorean theorem to find the length of side or *s*:

20. **B** Probability is the chance of something happening. In this case, to find the probability, find the area that is in the circle but not the square, divided by the area of the circle (which represents all possibilities). Plug in for the radius of the circle. Let’s say *r* = 5. So, the area of the circle is π × 5* ^{2}* = 25π. The area that is in the circle but not the square is the area of the circle minus the area of the square. Find the area of the square. The diagonal of the square is equal to the diameter of the circle: 2 × 5 = 10. The diameter creates a 45°-45°-90° triangle from the square. So, the side of the square is . That means the area of the square is . Therefore, the area within the circle but not the square is 25π – 50. That means the probability is . This is the target. Only B matches. After you’ve plugged in and realized that the probability is , you can also solve algebraically:

Another, even more complicated, approach would be to call the area of the circle π*r*^{2}, the diameter 2*r*, and the area of the square . The probability would be . This is simplified: . It’s much more confusing when you don’t plug in numbers!

## SECTION 3

1. **A** The clues *to prevent household fires* and *flammable liquids* make *flammable* a good word to recycle for the blank. A comes closest to this meaning. B, C, and D are unrelated. E means the opposite of the word needed.

2. **E** The semicolon is a same-direction trigger. Because Mark hates mistakes, he will review his papers “carefully.” We can immediately eliminate B, C, and D. E means “very carefully.” If you weren’t sure what A meant, you had to guess. Give yourself a pat on the back if you guessed rather than leaving the question blank. Even if you got the question wrong, you did the right thing. And in the long run, that’s how your score goes up.

3. **B** The clue for the first blank is *defends* and the trigger word is *nor*. A good word to use for the first blank will be one that is the opposite of *defends*, such as “disagrees with.” This eliminates D and E. Now look at the second blank. According to the first part of the sentence, Jenkins doesn’t do anything positive or negative, so a good word for the blank is “neutrality.” This eliminates A and C.

4. **A** *Great thinkers* must have “great” *insights*, so the first blank is a positive word. The clues here are *voiced so often* and *mere,* which indicate something trivial or unimportant. Things that are voiced often can be called “repetitions,” or some related negative word. The word *ironic* also suggests that the first and second blanks contrast in meaning. The only choice that has a positive word followed by a negative word is A. Remember to use POE to avoid words you don’t know. Because *beliefs* is not negative, you can eliminate B, even if you do not know what *banal* means.

5. **A** The clue is *been taught to communicate*, and the trigger word *but* indicates that the *skeptics* doubt this. So the skeptics must be arguing that the apes have *not really been taught*; they may be “mimicking” (aping!) their trainers. A is the best choice. Even if you don’t know what A, B, or E means, you should be able to use POE on C and D, and then guess.

6. **C** The clue is *technical difficulty and challenging counterpoint*, so good words for the blanks are *difficult* and *complex,* which agree with each other. This eliminates B and D, as both contain answers that disagree with each other. You can eliminate A because *diminutive* means small. Although *inscrutable* in E means “difficult to understand,” the word *classical* does not mean “difficult” or “complex.”

7. **D** Both **t**he first and second blanks are somewhat negative words. E is the only bad guess, since it doesn’t make much sense to view a situation as *political* and be *perplexed* by it. A, B, C, and D are all good guesses because at least one of the words is somewhat negative. Guessing one of these choices would have been better than leaving the question blank. If you look closely, you’ll notice that the trigger *since* tells you that the two blanks must be similar to each other. Eliminate A, as there is no evidence for how *obscure* or “little known” their situations are. B is close, but*bellicose* means “prone to fighting,” which is not supported by the sentence. Eliminate C, as *sanguine* means “confident and positive,” which does not agree with *acute* and is not negative.

8. **D** The clues in this sentence are *ancient ruins of marvelous bygone civilizations* and *sad*. What is sad about looking at the ruins of ancient civilizations? Seeing that, you can gather that human greatness doesn’t last. This idea is reinforced by the time trigger—if an ETS sentence completion compares past and present, it is usually to show a change. Therefore, you can put “doesn’t last” in the blank, and the best match is *transience*.

9. **C** After the second sentence, the passage shifts into information about *hypergraphia* and also suggests that if the cause of writer’s block is found to be *neurological*, then different treatment techniques might be appropriate. Therefore, we need an answer referring to a shift in meaning. A is not supported by the passage, which is not critical. B is too vague and doesn’t really refer to anything, and D is too broad. E refers to two problems, although only one, *writer’s block*, is mentioned in the passage.

10. **B** After a discussion of treatments for writer’s block in the first half of the passage, the second half of the passage develops the idea that writer’s block may have a *neurological* cause. A is incorrect because no comparison takes place. C is incorrect because some information is provided, but it is not detailed. D is incorrect since the passage doesn’t question *current techniques*. E is incorrect because only one side effect of *temporal lobe epilepsy* is mentioned.

11. **C** C is correct because the passage states that there are 20 arrondissements, but only 12 were *laid out* by 1795. A is wrong because we are not told why the Romans inhabited the islands. B is wrong because no information is given as to the Romans’ preference for architectural forms. D is likewise wrong because the we are not told when and why the Romans lost control of Paris. The comparison in E is not made.

12. **C** The passage states that Paris was protected by a wall. *New walls were built* that became the site of today’s streets. The protective walls determined the shape of the city. A is incorrect, because an increase in population required expansion of the city’s walls. There is no evidence for B or D. Although the passage mentions Romans, there is no reference to improving upon their architecture, making E incorrect.

13. **D** D is the best answer. A majority of the passage discusses the Zambesi River and its tributaries. Very little information is given on people, making A wrong. B is incorrect; color is mentioned in line 12 *(yellowish-green tinge)* but not again. No mention is made of C. E is mentioned only in the last line.

14. **C** C is the best choice. The first paragraph gives some details about the beginnings of the journey, which is later described in greater detail. A is not correct because Livingston’s private life is not described. B is wrong because no mention is made of characteristics or skills. D is incorrect; Livingston was not trying to determine how safe the waterway was. E is wrong, because it doesn’t actually explain why he was in Africa.

15. **D** The best choice is D. In lines 8–11, the passage states that Livingston explored the Zambesi and its tributaries in order to find if they could be used *for commerce*. A is not the primary reason for the expedition. Although refugees from Portuguese slavery are mentioned in passing at the end of the passage, contacting Portuguese settlers, B, is not mentioned at all in the passage. C is incorrect because it is not known if the way is safe or not. E is incorrect, because it is not stated that Livingston was the first to survey the land.

16. **E** The fish *screen* themselves from the *rays* of the *sun*—thus, E is the best answer. A is too positive; fish would not *screen themselves* from a *pleasant* sun. B is not supported by the passage. C is one definition of *torrid*, but it doesn’t fit in this context. D does not refer to the sun but rather to the fish.

17. **D** In lines 32–34, the author says that the Kongone is the safest because the water is deep even at low tide. A is incorrect, because the current and wind can make it more difficult to travel on the Kongone. B is mentioned in the passage, but is not given as a reason that Livingston decided that the river was the “best” course for a boat. C is also not stated as a contributing factor. E is wrong; there is no beacon on Pearl Island.

18. **A** The passage states that the Kongone is the *safest* branch for travel, because of the straight course and the depth of the water. The passage states that boats should not attempt the bar when the wind is from the south and south-east though. Thus, A is the best answer. B cannot be inferred since it is unknown if and when the beacon would be built. C is deceptive; the passage states that if the wind is from the *east or north* the bar would be smooth. D is too extreme; of the three rivers that Livingston explored, the Kongone is the best route. But that is not the same as being the best of all rivers in Africa. E is a misstating of the passage. East Luabo should not be attempted unless the wind is from the northeast, not the Kongone.

19. **A** Although the Kongone is mentioned throughout the third paragraph, the passage describes the effects of the current in lines 39–41. B is too strong. The change of water level is not attributed to the current, eliminating C. D is not supported by the passage. E refers not to the Kongone, but refers instead to the situation on the Zambesi.

20. **A** A is the best choice, because lines 43–44 state that the East Luabo is the easiest to spot. B is mentioned, but not as reason that East Luabo is favorable to navigators. C is contradicted by the passage, as the river is safe only when the wind is east or north-east. D is beyond the information given in the passage since no mention is given of *European navigators*. E is also not supported. The passage makes it clear that Livingston is not certain whether East Luabo is the same as the river described by de Gama.

21. **C** Livingston indicates that the river he is charting may be the river described by de Gama. A is incorrect, because Livingston isn’t certain that the river is the same one that de Gama referred to. B is not supported by the passage. D doesn’t make any sense; mentioning de Gama does not explain the lack of Portuguese settlers. E is wrong; there is no pillar at the river. C is the best answer.

22. **B** Lines 56–60 indicate that the natives had no interest in making contact with Livingston. A is extreme. No information is given about *most* of the inhabitants of Africa. C is not supported by the passage. Although Livingston saw few people, many people might have lived there. D is beyond the information given in the passage. E is incorrect because the reference to venison relates to Livingston’s men.

23. **E** E is the best answer; the passage presents factual information in an objective tone. A is incorrect; an author is not indifferent to his subject. B and C are too strong. D is wrong, as little personal information about Livingston is revealed.

24. **B** B is correct because the passage explicitly states that the natives *were probably fugitives from Portuguese slavery*. A is too strong. C is not stated. The comparisons in D and E are not made.

## SECTION 4

1. **B** This simple equation should present you with little difficulty, but beware: It is on precisely such questions that your guard might come down and you can become careless! Using Plugging In The Answers is safest. Only B works:

2 + (0) = 2 – (0)

2 = 2

2. **B** As the directions at the beginning of every math section remind us, the area of a triangle is given by this formula: *A* = *bh*. If the base is 4 and the height is 1, the area is 2. *A* = × 4 × 1 = 2.

3. **E** If the area of square *A* is 16, the length of each side is 4, and the perimeter is 16. You are told that this is of *B*’s perimeter, which you can calculate:

Now that you know the perimeter of *B*, you can calculate the perimeter of *C*:

If the perimeter of *C* is 36, each side is 9, and the area of *C* is 9^{2}, or 81. If you chose B, you need to read the question more carefully.

4. **E** According to the ratios given, you know that the mixture contains more wheat than rye; there must be more than 5 pounds of wheat. So let’s eliminate A and B. Use the Ratio Box.

Because there is a total of 5 pounds of rye, the multiplier is 2.5. This allows you to solve for 12.5 pounds for the wheat.

5. **C** Because 135° is one of the middle angles of the circle, the triangles must each have a 45° angle, and are therefore both identical 45°-45°-90° triangles. Remember (or check the front page of the test) that the ratio of the sides in such a triangle is *x*:*x*:*x*. You know that the diameter of the circle is 12, so the hypotenuse (which is equal to the radius of the circle) of each triangle is 6. If 6 is the long side, the other side of each triangle must be . Now you can find the area of one of the triangles and double it. The area of a triangle is *bh*, and both the base and height are equal to . So = 9. You have found the area for one of the triangles, so double it to get 18, or C. Another way to solve this is to use the side of your answer sheet as a ruler and ballpark. If *XZ* = 12, the hypotenuse of each triangle is 6. Now mark off the length of 6 with your homemade ruler and compare that to a side of one of the triangles. You can guesstimate that the side is about 4. Using that approximation, calculate that since the base and height of both triangles is 4, the area of each triangle is × 4 × 4 = 8. The area of both triangles together is 16, which is closest to 18, or C. ETS wants you to do complicated geometry, but all you care about is finding the answer.

6. **A** Translate each statement, piece by piece. The first part tells us that “ the product of *x* and *y* is 76.” Since *product* means multiplication, then the first equation must be *xy* = 76, so you can eliminate answers C and D. The second part says that “*x* is twice the square of *y*,” which translates to *x* = 2*y*^{2}, so eliminate answers B and E, and A is the only answer left. Notice that only the *y* needs to be squared, which is why B is wrong. The second equation for B would be written as “the square of twice *y*,” which is not what the problem stated.

7. **A** Try roughly plotting the data points, and then look at your graph. Find the answer that best fits your graph. Alternatively, notice that the number of customers increases as the temperature increases. The line of best fit will go up as you follow the graph from left to right, so eliminate B, D, and E. Notice that the number of customers does not increase by the same number for each 10-degree temperature increase. This is an exponential increase, not a linear increase. So, the graph will be curved. Eliminate C. Only A fits the data in the chart.

8. **E** Plug in 6 for *c*. The question is now asking what percent of 18 is 9. The answer would be 50. Which-ever choice gives you 50 when 6 is plugged in for *C* is the answer. Therefore, E is the answer. Remember: Plugging in good numbers will make your life much easier!

9. **D** Draw the missing figures. When you sketch this out, you’ll see that it’s a right triangle with legs of lengths 4 and 5. Use the Pythagorean theorem: 4^{2} + 5^{2} = *c*^{2}. Now solve for *c*. *c*^{2} = 41 and *c* = . Remember that the question asked for perimeter, so add up the sides: 4 + 5 + = 9 + , which is choice D.

10. **B** If 20% of the coins are either nickels or dimes, 80% are neither. 80% of 220 equals 176. Use your calculator or write it out and solve:

11. **D** Take out your calculator:

216,000 + 20% of 216,000 = 259,200

204,000 + 20% of 204,000 = 244,800

259,200 – 244,800 = 14,400

Another route to the answer is to take the difference immediately (216,000 – 204,000 = 12,000) and then increase that by 20%.

Watch out for partial answers. E is 20% of Springfield’s population, and A is the difference between 20% of Springfield’s population and 20% of Rockville’s population.

12. **E** With algebraic answer choices, you should plug in numbers. Let’s let *x* = *y* = 2, which makes *z* = 4. Plugging these values into the choices, you’d get the following:

(A) 2(2) + 2(2) = 2(4) [Yes]

(B) 2 – 2 = 0 [Yes]

(C) 2 – 4 = 2 – 4 [Yes]

(D) 2 - [Yes]

(E) 4 – 2 = 2(2) [No]

The correct answer is E. Don’t forget the EXCEPT!

13. **A** Do NOT try to figure out the seven numbers in the original list! The median is the middle number in a list of numbers. Because 8 is lower than every other number, and 43 is higher, they won’t change the value of the median. This means that option II is wrong, so you can eliminate B, D, and E. Because A and C both include I, you know it must be true without even checking it. Let’s focus on option III. The mode is the number repeated most often. Because 8 and 43 weren’t in the original list, they can’t change the mode. Eliminate C and pick A.

14. **D** There are variables in the answer choices, and the question asks you what *must be* true. This indicates that you will need to plug in values for *x*, possibly more than once. Try both –2 and 3. Only D remains true for both. Remember that the square of any nonzero number, either positive or negative, is always positive.

15. **E** Here’s the relationship: The smaller the shoes, the greater the difficulty. This is an inverse relationship. So, look for an inverse function. Only E is an inverse function. If you weren’t sure, try plugging in 8 and 10 for the *s*. The function should yield a greater *D* for 8 than it does for 10. Only E has *D*(8) > *D*(10).

16. **D** Note first that this is an EXCEPT question. Now, since *a*^{2}*b* = 12^{2}, and *b* is an odd integer, let’s see what you can come up with. Let’s make *b* equal 1, so you get the following: *a*^{2} × 1 = 12^{2} = 144, so *a* = 12. If *a* equals 12, it is divisible by 1, 2, 3, 4, 6, and 12. The only choice that remains is D.

17. **D** Since each side is a mysterious “*x* long,” let’s make up a value for *x* to make our lives a little easier. Let’s use 10, just because it’s nice and round. To find the area of the first triangle, you’ll have to find the height, which is the middle side of a 30°-60°-90° triangle. If the entire base is 10, then the height is 5. The area is then *A* = *bh* = 10(5) = 25. The second triangle has side lengths of 2*x*, which means each side is 20 long. We can find the area in the same way as the first one. We’ll end up with a height of 10, and the area is 20(10) = 100. Since the area of the second triangle is four times the area of the first one, the answer is D, 1 : 4.

18. **A** Keep in mind that this figure is not drawn to scale. Because , you know that the following angles are equal: ∠*DCE*, ∠*CEA*, ∠*BCA*, ∠*CAE*. Because triangle *ACE* has two equal angles, it is isosceles and the sides opposite those angles are also equal. Therefore, *CE* = *AC* = 3.

19. **C** Plug in numbers. If *a* = 10 and *b* = 10, then the inequality doesn’t work: (10 – 5)(10 + 5) = (5)(15) = 75, which is larger than 0, so eliminate answers D and E. If *a* = –5 and *b* = –10 then the inequality also doesn’t work: (–5 – 5)(–10 + 5) = (–10)(–5), which is larger than 0, so eliminate answers A and B, and C is the only answer left.

20. **D** Because 61 is the value of the *second* term in the sequence, plug in 2 for *n*: *a*^{3(2)} – 3 = 61. Therefore, *a*^{6} = 64, and *a* must be equal to ±2. Make sure you read carefully; III would work if 61 were the value of the *first* term.

## SECTION 5

1. **C** All versions of the underlined phrase except C are wordy or awkward.

2. **B** If something has been happening for the last two thousand years, it shouldn’t be discussed in the present or future tense. Eliminate A, D, and E for that error. *Building technologies* continue to change, so it would be better to use *have changed* rather than *had changed*. *Had changed*implies that the technologies will no longer change.

3. **A** The sentence is correct as it is written. B and E rewrite the verbs in *-ing* form, not the first choice for a clear sentence. C eliminates the cause-and-effect relationship present in the original. D adds the word *it*, which makes the sentence a run-on.

4. **D** D uses the correct idiom, *belief that*. Both A and E use an incorrect idiom, *belief of*. In B, the first *is* is unnecessary and makes the sentence awkward. C adds another unnecessary word, *which*.

5. **A** There is no error in the sentence as it is written.

6. **E** The beginning of the sentence is in the past tense, so get rid of anything that uses present tense in the underlined portion: A and C. B changes the meaning by using *second* in a different context. D changes the wording to *a miracle is what he needed*, which isn’t parallel with the rest of the sentence.

7. **B** As written, A contains nonparallel structure. C misplaces the word *careful*; D mistakenly implies a cause-and-effect relationship; and E uses the word *yet*, implying a contradiction which does not exist, and splits the infinitive *to document*. Only B correctly uses the parallel structure *you should gather … and document*, without adding other errors.

8. **E** The sentence should compare the soil of Pennsylvania with the soil of the Rhine. Only E does so correctly: The phrase *that of* helps draw the proper comparison. Each of the other choices creates a faulty comparison.

9. **D** An -*ing* form of a verb cannot be the main verb of a sentence, as in A and C. Also, to avoid a misplaced modifier, the phrase *as one of the forward-looking, enlightened monarchs of Europe* should follow the word *reputation* as it does in D. B adds the word *however*, which is unnecessary, and E says *always,* which changes the meaning.

10. **D** Watch out for switches from the pronoun *you* to the pronoun *one*. Stick with one or the other. Both A and B switch between the two. C isn’t a complete sentence, and E is awkward and somewhat changes the meaning.

11. **C** This sentence contains the ambiguous pronoun *it,* leaving the reader unsure which design movement *instigated* the paradigm shift. Eliminate A and B for this error. Both D and E use *and* instead of *however*. Because the second half of the sentence shows a difference between the two schools of design, and the first half shows a similarity, *however* is better, so eliminate D and E.

12. **B** Plural nouns must refer to plural nouns. There are two *characters* so they cannot be *an orphan*; they would be *orphans*.

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

14. **A** This sentence confuses subject with object. Because the speaker is the subject, *me* should be changed to *I*.

15. **A** An adverb, *completely*, is needed to modify the verb *exhausted*.

16. **A** To correct the error in subject-verb agreement, change *is* to *are* because *benefits* is plural.

17. **D** D creates an error in verb parallelism. The verbs in the list, *listening* and *reading,* do not agree with *she practiced*. It should be *practicing*.

18. **D** This sentence misuses an incorrect comparison modifier. Because more than two *jingoists* are mentioned (*all*), change *more* to the superlative *most*.

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

20. **C** The verbal phrase *brushing your teeth* acts as a singular noun (you could replace this phrase with *it*), which requires the singular verb *promotes*.

21. **C** In this sentence, the *trends* discussed *seem* to do two things: *show* and *indicating*. The verbs need to be parallel in form but are not. C should read *indicate* instead.

22. **D** The semicolon indicates that both clauses must be independent, so *being* creates a fragment. The correct form should be *was*.

23. **C** In C, *it* is a singular pronoun, which doesn’t agree with the plural subject *species*. The sentence should read “they swing.”

24. **C** This adjective should be in comparative form (*higher*) to parallel *shorter, lighter, or tighter.*

25. **C** This is a verb tense error; the father performed the action in the past tense, but not so far in the past as to require the past perfect tense. Therefore, *exercised* is better than *had exercised*.

26. **B** This sentence uses the wrong conjunction. Because the sentence contrasts two unlike things, replace *and* with *but* for greater logic and clarity.

27. **C** The sentence should read as follows: “Saif knew that the other applicants weren’t as good as he”; using *him* isn’t correct. Some may even write the sentence like this: “Saif knew that the other applicants weren’t as good as he was”; however, the verb *was* isn’t necessary.

28. **D** *She* is ambiguous in this sentence; it could refer either to Natalie or to Noelle. It should read *Natalie*.

29. **D** In D, *Branagh* sets up a faulty comparison. *Olivier’s* performance should be compared to *Branagh’s* performance, not to *Branagh* himself. It should read *to Kenneth Branagh’s*.

30. **B** Although there are no big errors in the original version, it is longer and less straightforward than B. C and E change the meaning of the sentence, and D is as awkward as the original.

31. **A** B and C introduce a casual tone that doesn’t flow with the rest of the passage. Deleting the word *another,* as D suggests, and deleting the entire sentence, as E suggests, would confuse the meaning and flow of the sentence and passage. A is best because it creates a transition between two examples that both support the author’s main point.

32. **E** Only E retains the correct meaning of the sentence while using correct grammar. The original version, as given in A, uses a run-on sentence. B does not fix this original error just by adding a semicolon. Both C and D suggest that the employees will invest in the stock, the stock will plummet, and their savings will disappear. You need to retain the original meaning—that this is a possibility and not a definite occurrence.

33. **C** The first paragraph discusses one side of an issue: Protective legislation may limit freedom and be unnecessary. The second paragraph shows the other side of the debate: Some laws may be helpful. The third paragraph concludes that a compromise is best. Thus, sentence 10 should be the concluding sentence of the second paragraph, making C the best answer. B would upset the chronology of the second paragraph. A improperly creates a contrast with the preceding ideas. D destroys the agreement between *their* and *people*. Similarly, E’s lack of noun agreement illogically implies that the employees all share one retirement account.

34. **E** Only E correctly uses the parallel construction *some people will think … others will complain.*

35. **D** With omission questions, read the sentence with the sentences immediately before and after it, then read those two sentences without the sentence in question. You are looking for a sentence with a piece of information that is not relevant to the passage. Sentences 3, 7, 11, and 15 are all necessary parts of the passage; therefore you can eliminate them and choose D.

## SECTION 6

1. **B** The best way to approach this problem is to plug in the answers. Start with C. When 6 is subtracted from 10, the result is 4. Divide 4 by 2 to see if it equals 3. It does not, so C can’t be correct. Because our answer was too small, you need to subtract a smaller number from 10. Try B. When 4 is subtracted from 10, the result is 6. Divide by 2 to get 3; this is correct.

2. **C** The number of degrees in a line is 180. Therefore, *b + c* = 180. And since *a* + 90 = 180, *a* = 90. So *a + b + c* = 270. Note that E is the Joe Bloggs choice—“it cannot be determined” is rarely the correct answer.

3. **E** Use the formula for distance: *distance = rate* × *time.*

Steve runs 12 miles at 8 miles per hour, which means that he runs for 1 hours (or 1.5 if you’re using your calculator). Adam runs the same 12 miles at 6 miles per hour, which means that he runs for 2 hours. Adam takes half an hour longer to complete the race, and half an hour is 30 minutes.

4. **D** Because there are variables in the answers, try Plugging In! If *a* = 2, then . Plug *a* = 2 into the answers to find that only D is 32. Another option is to rewrite the problem as . Reduce before you multiply by dividing the denominator of the first term and the numerator of the second term by 3 to get .

5. **E** To solve this problem, you need to figure out the ratio between the *x*- and *y*-values on line segment . Looking at the figure, is the hypotenuse of a right triangle with a side of 12. You can see this is a multiple of one of ETS’s favorite right triangles: 3:4:5. This is a 9:12:15 triangle, and the coordinates of point *B* are (9, 12). All the points on line segment are in a ratio of 9:12. Only E has a similar ratio.

6. **B** Because you aren’t given the cost of any book, you can plug in your own values. Let’s say that the average cost of the textbooks, excluding the anatomy textbook, is $10. You can make all the books cost $10 each to make the problem easier. The anatomy textbook would cost $30. The total cost of all the textbooks would be $130. The anatomy textbook would be of the total cost.

7. **A** The trick is to notice that this parallelogram is actually made of two equal triangles. By finding the area of the triangles, you can find the area of the parallelogram. The triangles are both right triangles, and the two sides given in the figure follow the 3:4:5 pattern. If you look at triangle*ACD* with as the base, the base is 3 and the height is 4. Now use the formula for area of a triangle:

That means the parallelogram is 2 × 6 = 12.

Also, if you estimate the area, the base is 5 and the height is less than 3, so the area is less than 15. The only answer less than 15 is A!

8. **D** Plug in a value for *b*, the number of minutes the pie is baked. Let’s say 52 minutes, because 52 is greater than 50, less than 60, and not 55 (which is in all the answer choices). The only answer choice that works is D: |52 – 55| = |–3| = 3, which is less than 5.

9. **2**

Just simplify and solve for *x*:

Remember that the first grid-in question returns the difficulty meter to easy!

10. **19, 39, 59, 79, or 99**

The simplest way to solve this problem would be to find values of *n* that satisfy the first condition, and then to check which of those also satisfies the second condition. So, let’s find some numbers that leave a remainder of 4 when divided by 5: {9, 14, 19, 24, 29}.

That should be enough. Now let’s check which of these leaves a remainder of 3 when divided by 4:

9 ÷ 4 = 2 *R*1

14 ÷ 4 = 3 *R*2

19 ÷ 4 = 4 *R*3

19 is one acceptable response.

11. **145**

Because the two lines are parallel, 110 + 2*x* = 180. Solving this equation for *x,* you get *x* = 35. Looking at the triangle, the missing angle (*m*) can be found by solving the equation 110 + *x* + *m* = 180. If *x* = 35, *m* = 35. If *m + y* = 180 and *m* = 35, *y* = 145.

12. **36**

If *x*^{2} = 16 then *x* = ± 4. If *y*^{2} = 4 then *y* = ± 2. To maximize (*x – y*)^{2}, you need to maximize the difference. The greatest difference is (–4) – 2 = –6 or 4 – (–2) = 6, and both 6^{2} and (–6)^{2} equal 36.

13. **130**

First use a Ratio Box to find the number of males and females. If the ratio is 2 to 3, the total ratio is 5. The actual is 250, so the multiplier is 50. That means there are 50 × 2 = 100 males and 50 × 3 = 150 females. Set up a group grid (the bolded numbers are information from the problem):

You find that 20 females must be taking French, and because there 150 females total, 130 must be taking Spanish.

14. **8**

In the diagram, you can assume that the shorter ticks are evenly spaced, so each one must be 0.25 units long. Plugging the coordinates of the points into the given expression gives you . As you can see, canceling works well: The two negatives cancel each other out, and two of the numbers in the numerator are double the size of two of the numbers in the denominator. This leaves you with . You can also just plug the whole thing into your calculator, but make sure you use enough parentheses: You need to enclose the entire numerator in parentheses, and then the entire denominator in parentheses.

15. **12**

Start with the most restricted spots. There are 2 tools that can go in the first spot. Once you put 1 there, only 1 tool can go in the second spot. Once you’ve used these 2 tools, there are only 3 that can go in the third spot, then 2 in the fourth spot and 1 in the fifth spot. So, there are 2 × 1 × 3 × 2 × 1 = 12 ways to arrange the tools.

16. **4**

This question looks tough, so work it one step at a time, and start with what you know. Sector *AOB* is a quarter-circle (it covers an angle of 90 out of 360 degrees), so multiplying its area (π) by 4 gives you the area of the whole circle (4π). Plugging this into the equation for the area of a circle,*A* = π*r*^{2}, gives you 4π = π*r*^{2}, and the radius must be a positive value, so *r* = 2. This means that the coordinates of point *A* must be (−2, 0). Because *A* is on both the circle and the parabola, you can plug its *x*- and *y*-coordinates into the given equation of the parabola, *y* = *x*^{2} – *b*. This becomes 0 = (–2)^{2} – *b*, so *b* = 4.

17. **3**

The first step is to draw a diagram:

You should notice that *BD* is part of one of ETS’s favorite right triangles: a 3:4:5 triangle. So *BD* = 3.

18. **or 1.2***Inversely proportional* means *x*_{1}*y*_{1} = *x*_{2}*y*_{2} where *x* represents hours of sleep and *y* represents the number of errors: (2 hours)(3 errors) = (5 hours)(*y* errors). 6 = 5*y,* so *y* =

## SECTION 7

1. **D** Because *morality* is being linked with *religion*, you need a word along the lines of *erosion*; *collapse* is the only choice that fits.

2. **A** The clue in this sentence is *anarchy*, which means lack of order. If people have been shaken by the lack of order, they must be ready to buy “order” at any price. A comes closest to this meaning.

3. **B** You may have had trouble coming up with your own words on this question. This is because there is a relationship between the blanks. The phrase *external factors* is a clue. On the one hand, if animal behaviors are inherited, they would be relatively unaffected by external factors. On the other hand, if the animal behaviors are learned, they would be affected by external factors. B is the only one to preserve this relationship.

4. **C** We know the general’s civilian life is simple, dignified, and *stoic*. The only blank that fits is C; B and D miss the clues. A and E, if you weren’t sure what they mean, are good guesses, but incorrect.

5. **A** The clue is *cruel severity of some criminal penalties*. A judge (at least one that ETS likes) would probably want to avoid or to lessen *the cruel severity of some criminal penalties*. B and D miss the point completely. If you know what *condone* means, it also misses the point; if not, it’s not a bad guess. E is a Joe Bloggs trap that contradicts the clue.

6. **A** *Hutton* and *Darwin* are used as examples of different scientists who contributed to geology. B is incorrect because the last sentence states that controversy surrounds many geologic theories and they are *constantly challenged*. C is incorrect because biological evolution expanded upon, rather than disproved, the theory of Uniformity. D is too negative an answer; though the science may be relatively new, it is not *inexact*. E is incorrect, because the passage mentions *seventeenth-century* attempts to date the earth.

7. **B** The best answer is B. Passage 1 does not attempt to *prove*, *contradict*, or *criticize* a theory. Therefore A, C, D, and E can all be eliminated.

8. **A** Both passages refer to Geological Evolution as a theory, which implies that it has not yet been proven to be a fact. B and D are mentioned only in Passage 2 whereas E is mentioned or implied only in Passage 1. C is not correct because the age of the theory is not discussed in Passage 2. A is the best answer.

9. **E** The best answer is E. *Confirmation*, *exception*, and itemization are too extreme or demanding to be accomplished in a short reading passage. Therefore, A, B and C can all be eliminated. D does not take into account the example of Heart Mountain, which appears to disprove the Geological Evolutionary theory.

10. **C** According to lines 14–18, *An attempt to harmonize the imbalances in my character by means of strict discipline at a boarding school … nearly led to the same ignominious end*. Even if you don’t know what *ignominious* means, it should still be clear that the attempt to straighten out the author had the same result as it did before—it didn’t work. This idea is paraphrased in C, which says that *the tactics were failing*. A is extreme. Perhaps the author was a bit unstable, but there is nothing in the passage that suggests the author was a *danger to others*. Remember: If an answer choice is half bad, it’s all bad. B is a trap. Maybe the author did poorly in school partly because the schools were too difficult. Or maybe not. The passage tells you nothing about the difficulty of the schools. All you know is that the author was having a really hard time. D is another trap. You have no way of knowing from the passage how well the author got along with his peers. In E, you know that his academic career is in bad shape, but does that mean he’ll never finish school?

11. **B** The best answer is B. You are told that the author’s people were once subjects of the Austro-Hungarian Empire. In a parenthetical aside he tells you that they still regard Austria as their cultural homeland. This is attached to the sentence in which you are told that he was sent to school in Styria, presumably a place in Austria.

12. **D** Go back to the passage, find the word *ignominious*, and cross it out. Then read the sentence and come up with your own word. According to lines 19–20, the author just barely escaped *final ostracism from the privileged ranks*. If he was about to get thrown out of the privileged ranks, the word that best describes that situation is *disgraceful* or something strongly negative. The other answers are incorrect because they don’t accurately describe the author’s situation as it is described in the passage.

13. **A** The lead words in this question are *the author’s parents*, who found him hopeless. The author mentions his parents again in lines 24–26: *My parents … agreed with the schoolmasters*. A paraphrases the answer well (*frustrated*). B is incorrect because the author’s parents clearly knew that he had a problem. How could they be oblivious to the fact that he was expelled from several schools? C has nothing to do with the passage. You might be able to infer that the author’s parents were wealthy because they sent him to a boarding school, but you cannot know their attitude toward the poor from the passage. D confuses several unconnected ideas mentioned in the passage. There is nothing in the passage to suggest that the author’s parents were schoolmasters. The first paragraph states that the author’s family lived together *in Bukovina*, so E is incorrect.

14. **B** Your first clue to the author’s attitude toward the aphorism is that he calls it *trivial*. After he quotes the aphorism, the author says, *this optimistic notion results more from wishful thinking than from practical experience*. The author clearly has a very negative opinion of it. B gives a perfect paraphrase of *wishful thinking* by saying that the author found the aphorism *unrealistic*. You can get rid of A as it is positive. D can be eliminated because the author wasn’t amused, and you can eliminate E because it refers to his *faith in it*; the author clearly has no faith in the aphorism. C is incorrect because the author doesn’t say anything about the aphorism working for others.

15. **C** This is a general question, so you need to know only the main idea of the passage. You know that the author was not happy in the passage, because he says he felt *skushno*, a word that means *more than dreary boredom*. You can get rid of A and E because they’re positive. D is too extreme; it is highly unlikely ETS would ever suggest that someone was suicidal. B is incorrect because the passage never says that the author had trouble with his friends.

16. **C** This is a general question, so you need to know only the main idea of the passage. In simple terms, the passage talks about the different behaviors of cats and dogs. This is exactly what choice C says. Notice that the author presents both sides of the issue and doesn’t advocate one animal over the other. That’s why B and D are wrong. A is way too extreme. If you don’t know what *enmity* means, look it up and you’ll see. E covers only one section of the passage, not the primary purpose of the passage as a whole.

17. **E** According to the passage, the cat treats its human owners as *pseudoparents* because they took over from the real mother at a sensitive stage of the kitten’s development. That means the human owners are obviously not the kitten’s real parents, but rather like adoptive parents that took over from the kitten’s real mother. E says exactly that. A is wrong because *pseudo*- doesn’t mean part-time. Human owners can be full-time parents to a cat, but that doesn’t make them the cat’s real parents. B misses the mark because the passage is talking about the parents of cats, not the parents of adults. C is wrong because the passage doesn’t say anything about neglect. D makes no sense. How can someone have the characteristics of both humans and cats?

18. **D** The lead words in this question are *difference between dogs and cats*, which should lead you right to the beginning of the second paragraph. According to lines 27–33, the adult *pet dog sees its human family both as pseudoparents* and *dominant members of the pack*.… On the other hand, cats *never hunt in packs*, and most of their day is spent in *solitary stalking*. So while dogs see their owners as leaders of the pack, cats do not, because they’re solitary. This is paraphrased in D. A directly contradicts the passage. According to lines 30–31, *cats do have a complex social organization*. Read carefully. B has it backward. Dogs are obedient, not cats. C comes out of nowhere. Where does it say that cats are creative? E also contradicts the passage. According to lines 31–32, cats spend most of their time in solitary stalking, which means they’re probably good hunters.

19. **B** According to the lines 23–25, *dogs live in packs with tightly controlled status relationships among the individuals*. *There are top dogs, middle dogs, and bottom dogs*.… This describes a social structure that is *hierarchical*. (If you don’t know what hierarchical means, look it up!) The other answers are incorrect because none of them accurately describes the social structure in the lines quoted above. There is nothing abstract (C) or flexible (A) about tightly controlled status relationships, nor is there any mention of male domination in the passage. And exclusivity (E) is certainly not the issue.

20. **C** The lead words in this question are *the domestic cat*, which should lead you to the first paragraph. According to lines 11–12, *the young cat becomes bimental. It may be a cat physically, but mentally it is both feline and human*. To be both feline and human is definitely a contradiction. Common sense kills A because cats don’t have two feet. B and D are incorrect because domestic cats are tame by definition. Otherwise, they would be wild. E doesn’t make any sense. Do cats dominate humans? No way!

21. **B** According to the passage, an *ambitious Yuppie* is an example of someone who is *not a typical cat-owner*. Because *cat-owners are solitary* people, this means the *ambitious Yuppie* must be *a group-oriented person*. Accordingly, B is the answer. A and D are insulting to Yuppies, and ETS wants to avoid controversy. C might be tempting, but ETS likes to avoid stereotypes. E is not mentioned in the passage.

22. **B** Eliminate A because it’s the opposite of what is said in the passage. According to the fifth paragraph, the differences between the roles of prehistoric men and women *contributed to a human male “pack mentality” that is far less marked in females.* This idea is paraphrased in B. Keep this one for now. C is partially correct since the passage says that women gathered food, but it says nothing about the strength of women. Eliminate C. Neither D nor E is supported in the passage. The correct answer is B.

23. **C** To answer this question, you have to know what *caricature* means. A caricature is an exaggerated drawing, so the author is saying that he exaggerated in the passage. He is thus qualifying some of the generalizations he has made in the passage. A is too extreme. ETS would never suggest that the author of one of its passages made a futile argument. B misses the point of these lines, which refer to generalizations, not contradictions. D goes in the wrong direction. In the lines cited in the question, the author admits that he exaggerated in order to make his point, so he’s trying to ensure that readers don’t overestimate what he said in the passage. E sounds like psychobabble; it also has nothing to do with what the author is saying at the end of the passage.

24. **C** This is a general question, but it is also an EXCEPT question, so do it last. The only way to answer this question is to search through the passage for each of the answer choices. Remember: You’re looking for the answer choice that is not there. The passage refers to findings in lines 59–60, makes a parenthetical statement in line 38, restates an argument in lines 70–73, and makes generalizations throughout the passage. C is the only one left.

## SECTION 8

1. **D** Use the first equation to solve for *x*: 3*x* – 5 = 4, so *x* = 3. Plug in 3 for *x*: 9*x* – 15 = 27 – 15 = 12.

2. **E** This is an excellent calculator question. Here are the costs per unit for each color:

The red buttons are the most expensive.

3. **C** Plug the answers into the equation starting with C. The (*x*, *y*) point is (7, 8), so plug in 7 for *x* and 8 for *y*. Because 8 = 2(7) – 6, C is the correct answer.

4. **B** Before you reach for your calculator, reduce the expression.

Then simply try each choice; At –1, B has the least value. If you selected E, you didn’t work out each choice.

5. **B** One way to solve this problem is to Plug In. First, simplify (*a* + *b*)^{2} = 49 by taking the square root of both sides to find *a + b* = 7. Now, brainstorm some values for *a* and *b* that make *a + b* = 7 and *ab* = 10. Let’s say *a* is 2 and *b* is 5. So, find the answer that yields 5 when you plug in *a* = 2. Only B works. The second, more complicated, way is to FOIL out (*a* + *b*)^{2} = 49 to get *a*^{2} + 2*ab* + *b*^{2} = 49. Plug in 10 for *ab* to get *a*^{2} + 2(10) + *b*^{2} = 49. That means, *a*^{2} + 20 + *b*^{2} = 49. Subtract 20 from both sides to get *a*^{2} + *b*^{2} = 29. Subtract *a*^{2} from both sides to get *b*^{2} = 29 – *a*^{2}. Take the square root of both sides to find *b* = .

6. **C** First, you can estimate. Because square *ABFE* has an area of 25, *EF* equals 5 and *EC* looks to be a little less than twice *EF*, or in the 7–9 range. Thus, since *CE* = *ED,* because they are the legs of a 45˚-45˚-90˚ triangle, you can eliminate D and E. You also know that the area of Δ*BCF* is 10, and that its base (*BF*) is 5. Using the formula for area, you can calculate *FC*, the height of the triangle: 10 = (5) × (*h*), *h* = 4. So 5(*FE*) + 4(*FC*) = 9, which is the length of and .

7. **C** Stack all three equations and add them together to get 3*x* + 3*y* + 3*z* = 51. Factor out a 3 to get 3(*x + y + z*) = 51. Divide both sides by 3 to get *x + y + z* = 17.

8. **D** Translate into algebra. *The sum of two numbers is 10* means *x + y* = 10. Next, *one number is equal to the sum of 6 and twice the other number* means *x* = 6 + 2*y*. Rearrange the second equation into *x* − 2*y* = 6. Subtract the second equation from the first to find 3*y* = 4. Divide by 3 to find*y* = . Plug that into the first equation to get *x* + = 10. So, *x* = 8. *The larger number minus the smaller number* is .

9. **D** Go through this problem one piece at a time. We know that of the $45,000 goes to the sanitation department. Remember that “of” in math questions means to multiply, so × 45,000 = $9,000. He now has (45,000 – 9,000) $36,000 left. He spends of that $36,000 remaining on the police department, which is ( × 36,000) = $24,000. He now has (36,000 – 24,000) $12,000 left to spend, so the answer is D.

10. **A** Let’s begin by drawing a parallelogram and plugging in a number for *y*, say 50, and calling the other two angles *x*:

Because there are 360 degrees in a quadrilateral, you know that 2*x* + 100° = 360°, which means *x* = 130°. So, you’re looking for the choice that gives you 130 when *y* = 50°. You simply plug 50 into all of the answer choices to find that A is the only one that works.

11. **D** This is a parabola, because one of the two variables is squared. Eliminate A, B, and E, which are not parabolic graphs. Because the smallest possible value of *mx*^{2} is 0, the smallest possible value of *mx*^{2} + *b* is *b*, so all of the curve must be above the *x*-axis. Only D works.

12. **C** First, you need to compute all possible values of *n*:

Now, be careful! The median value for is 5, but the median value for *n* is 25.

13. **C** Draw a picture! Look at triangle *CJK*. ∠*CJK* is 90° because the radius of a circle is always perpendicular to a line tangent to that circle. Use the Pythagorean theorem, (*CJ*)^{2} + 24^{2} = 26^{2}, or your knowledge of right triangles (this is a multiple of a 5:12:13 triangle) to get *CJ* = 10, which represents the radius of the circle. So the circumference of the circle = 2π × 10 or 20π.

14. **D** This is a tricky question. Let’s draw a picture:

Because 1 centimeter equals 6 kilometers, 4 centimeters equals 24 kilometers:

The area of this region is 24^{2} or 576. In case you were wondering, B is the Joe Bloggs answer because 16 × 6 = 96.

15. **E** Plug In values for *m* and *n* and use translation to solve this percent problem. You’re working with a small percent, so plug in a big number for *m.* Let’s say *m* = 2,000. 0.1% of . Therefore, 10% of *n* is 2; rewrite this as . Solving for *n,* you get *n* = 20. Now translate the rest of the problem: *m* is what percent of 10*n* can be written as . Solving for *x,* you get *x* = 1,000, so the answer is 1,000%.

16. **E** Remember your transformation rules. Whenever a parabola faces down, the quadratic equation has a negative sign in front of it. It always helps to plug in! Let’s take an example. If your original equation was (*x* + 2)^{2}, putting a negative sign in front, –(*x* + 2)^{2}, would flip the parabola. If you expand out that equation, you get –*x*^{2} – 4*x* – 4. Notice that *a* in this equation is –1. Also, notice that *c* in the equation is just the *y*-intercept, because if you plug in 0 for *x* you get *y* = *c*. On the graph, the *y*-intercept is negative. And a negative number times a negative number is always positive. Again, plug in if you like it better: (–1)(–4) = +4. The best answer is E.

## SECTION 9

1. **B** The best choice is B. The clue is *unconventional*, which tells you that “out of the ordinary” is a good phrase for the blank. *Eccentric*, B, is closest in meaning. Even if you are not sure what B means, you can eliminate A as it is opposite from the meaning of the blank. C has to do with the order of events in time, not with a person’s behavior; D, “friendly,” and E, “hardworking,” have nothing to do with behaving in an unusual manner.

2. **C** We can recycle the clue *swollen* into the blank, and immediately eliminate A and B, which have the opposite connotation. D and E do not mean *swollen*, so only C, *distended*, is left, making C the best answer.

3. **A** The best answer is A. The idea of human carelessness causing changes tells you that the blank should mean “bound to happen.” You can eliminate B and E because “wishing evil” and “being honest” are human attributes. C, “equally shared,” and D, “sluggish,” do not mean “bound to happen,” so you are left with A, *inevitable.*

4. **D** The clue *unrealistically* tells you that Tyler expected to improve his score greatly right away, so you can save B, D, and E, all of which could describe a great rise in his score. Thus you can eliminate A, “repeating,” and C, “unimportant.” Looking at the finalists, since the second blank should mean “slow and steady,” you can cross out B, “endless,” and E, “fast.” You are left with D, which is the best answer.

5. **C** The clue is *invoke a serenity that is otherwise lacking in her frenzied existence.* A good word for the blank is “relaxed.” Only C agrees with our word. If you guessed A because the root *eu*- means “good” as in *euphoria*, don’t feel bad. That was a smart guess, and smart guesses mean more points overall.

6. **E** The clue for the second blank is *appreciated his specialized knowledge*, and the trigger word is *but*, which tells you that the second part of the sentence must mean the opposite of the clue. If some students didn’t appreciate the specialized knowledge, then the *disappointed* students had “non-specialized” interests. The only word in the answer choices that means “non-specialized” is *eclectic*. The other word in E also makes sense because it fits the clue. You know that the professor *has specialized knowledge*, so if his lecture focused *utterly* on something, then it was very specialized.

7. **E** E is correct because Passage 1 states in the beginning of the second paragraph that philosophers shifted from theology to *intellectual exercises*. A is incorrect given the information in the passage. B is not supported, because there is not mention of angels anywhere in the passage. C is not supported because there is no mention of law-abiding citizens. D is a trap answer because the mention of *classicists* may make this look like an attractive answer choice.

8. **C** C is the credited choice because of lines 16–18 in Passage 1. A is incorrect because deviant behavior is a criminal act, not the result of one. B is incorrect because that would be according to the *demonic perspective*. D is not supported in the passage and E is incorrect because deviant behavior is the result of rationale that maximizes pleasure and minimizes pain, not the opposite.

9. **E** E is a close paraphrase of lines 37–38 in Passage 1, *each deviant act arises from a rational calculation of pleasure versus pain*.… Every other answer choice contains expressions found in the passage, but not as a cause for avoiding arbitrary, tyrannical punishment. B might seem like an attractive choice, but the belief that punishment could be *meted out precisely and mathematically* is not cited as a reason for avoiding overly severe punishment.

10. **B** A, C, and E are incorrect because the author is not revealing, describing, or explaining the emergence of deviant behavior to the individual. The author says that it is wrong to attribute the behavior solely to the individual; D does not reflect this meaning, but B does.

11. **A** A is the credited choice because of the phrase that follows the semicolon: *society that produces the individual*. B is not in the passage. C is the opposite of what is said in the passage. D is a stretch from line 43 and does not answer the question. E is extreme.

12. **E** The author states in line 58, *deviant behavior would have no role in this utopia*. A is too broad; while the author does place emphasis on having an organized society, the point of doing so was to show how the relationship between the individual and society produces deviant behavior. B is the opposite of what is stated by the passage, as it says that the utopia does not exist. C and D are extreme.

13. **B** B is correct. Despite the subject matter of this passage, the author’s approach is an objective analysis of deviance. The author does not express nostalgia (A), criticism (B and D), or praise (E).

14. **E** A is a trap answer, because it relates gender to sexuality. B and D do not make sense. C means “allows.” Between C and E, though, E is the better answer, because the disorganization in society is causing the deviance (lines 68–70).

15. **B** With constant change, there cannot be harmony and organization. A, C, D, and E can all result from change, but remember that the question asks which is the least likely to occur.

16. **A** According to both the third paragraph of Passage 2 and the main discussion in Passage 1, deviance is a choice made by an individual. B is not supported, since both authors discuss the individual causes of deviance. C is wrong because severe punishment is never advocated. D is true for 2 but not for 1. E is wrong because it contradicts information in Passage 1. The Enlightenment did not cause deviance; it only viewed it differently.

17. **B** Rationality is a central focus of Passage 1, but is not mentioned in Passage 2. A is not important in either. C is not the focus of 1 and is not mentioned at all in 2. D is important in the second passage, not the first. E is mentioned in the first, but as an act of deviant behavior, not an aspect of it, and even so, it does not matter a great deal to the passage.

18. **D** D is correct because the author of the first passage provides an objective historical overview of deviance, while the author of passage B provides a thesis on why deviance exists. The remaining choices are inaccurate.

19. **A** Passage 1 discusses the intellectual evaluation made by the individual, and Passage 2 discusses how deviance would not increase if it weren’t for disharmony in society. The remaining choices are inaccurate.

## SECTION 10

1. **D** *Weather vanes* is plural, so it’s important to use a plural pronoun later in the sentence. Get rid of A. B unnecessarily uses the word *being*, so eliminate it. Only D matches the sentence structure of the beginning of the sentence. The phrase *weather vanes* comes first, so in the second half*they* comes first.

2. **B** This sentence is a fragment. By eliminating the word *which,* the sentence becomes complete. In B the sentence says correctly, *horrors … and experiences … are … chronicled.* In C, D, and E, the verb is missing, so these versions of the sentence are also fragments.

3. **A** There is no error in this sentence as it is written.

4. **E** As written, A includes several words that make the sentence unnecessarily wordy. Because E omits the words *is, he is,* and *and he,* this version of the sentence becomes streamlined and correct. B is a run-on. C and D add *because* and *although*, changing the meaning of the sentence.

5. **E** Only E uses the correct idiom *responded … by*. In addition, the original sentence is a run-on. B is needlessly wordy. C and D both create fragments: C needs a conjunction to be correct; in D, the phrase that follows the semicolon lacks a grammatical subject.

6. **A** The original sentence is concise and uses the past tense required by *could* and *after* in the non-underlined portion. B and D use the present tense. C and E are wordy and redundant.

7. **E** The construction *not only … but also* achieves parallelism in E, since the noun *an inspiring teacher* matches *a great surgeon* in form. A unnecessarily uses the word *being*. B, C, and D violate parallelism.

8. **B** A is unnecessarily wordy. E is wordy and contains a noun agreement error. C changes the meaning of the sentence, suggesting that they switched plans after their payments were reduced, which is not correct. D also changes the meaning, suggesting that the new plan’s payments were being reduced from a higher price point to a lower one.

9. **D** Choices A and B are wordy and unidiomatic. C and E warp the intended meaning by (among other things) implying that *the expression*, C, or *the face,* E, *plays games*. Only D correctly and concisely expresses the idea that *the squirrel … plays games*.

10. **C** Only *the designers* can logically be modified by the phrase *learning from recent tests*, so eliminate A, D, and E. B changes the intended meaning, illogically saying that an *engine* can be based on an increase in efficiency.

11. **B** Parallelism requires a noun such as *a failure* to follow *a lack of training*, making B the only possible answer. Also, *which* in C is inappropriate, because you must use the pronoun *who* when referring to people. C also changes the intended meaning by implying that the *people*, rather than*a failure*, caused the crash. *Because,* in choices D and E, is redundant with *caused by* in the non-underlined portion of the sentence.

12. **E** Because the pronoun *we* is not underlined and therefore must remain in the sentence, beginning the sentence with *Rory and I* will make it a run-on. Kill A, B, and C. D ends with *Rory and I*, making the *we* that follows it unnecessary and incorrect. E provides a properly constructed subordinate clause and is correct.

13. **C** Always watch out for unnecessary use of the word *being*. It shows up incorrectly in both A and D, so eliminate both of those. The sentence should set up an opposite, since it starts with a way in which the two are similar, and ends with a way in which the two are different. E uses *and*, which doesn’t accomplish this. Between B and C, C is more concise.

14. **C** Watch out for misplaced modifiers. The phrase *better known for* The Foreigner should describe *Larry Shue*, but in A, B, and D the phrase incorrectly describes something else. E incorrectly uses the word *like* instead of *such as*. *Like* should be used to compare two nouns; *such as* should be used to give an example.