Cracking the SAT
SAT Practice Tests and Explanations
Answers and Explanations for Practice Test 3
1. A To solve for y, you should start by moving all the y’s to one side of the equation. If you subtract 4y from each side, you get 8 = 8y + 24. Now subtract 24 from each side of the equation, to give you –16 = 8y. Finally, you should divide each side by 8, which gives you –2 = y.
2. E Let’s plug x = 2 and x = 4 into the answer choices, and see which choice makes f(2) = 10 and f(4) = 44. If you plug 2 into A, you get 10. B gives you 20. C gives you 18, and D gives you 8. E gives you 10; leave it in. Now plug in x = 4 into the choices that remain. A gives you 14, so eliminate it. E gives you 44. Only E works for both of our numbers, so it must be the answer.
3. A If the probability of picking a blue jelly bean is , then you know that of the beans in the jar are blue. Let’s try Plugging In The Answers. If there are 78 blue jelly beans, then you would have a total of 58 + 78 + 78 = 214 beans in the jar. Is 78 equal to of 214? Nope, so C cannot be right. Let’s try B. If there are 56 blue jelly beans, then you would have a total of 58 + 78 + 56 = 192 beans in the jar. Is 56 equal to of 192? Nope. So let’s try A. If there are 34 blue jelly beans, then there will be a total of 58 + 78 + 34 = 170 jelly beans. Is 34 equal to of 170? Yes, so A is our answer.
4. D To find the 10th term of 3 × 2n, plug 10 in for n: 3 × 210 = 3 × 1,024 = 3,072.
5. B Whenever you see variables in the answer choices, you should plug in. Start by plugging in a number for x. If x = 10, then 3 more than x is 13. Now you know that 13 is 2 more than y, so y = 11. When you plug in 11 for y in all of the answers, B is the only one that gives you the answerx = 10, your target answer.
6. E Don’t assume that the figure ABCD must be a rectangle; it doesn’t have to be. All you need to do here is follow the rules: You know that AB = BC and that BC = 12, so you now know two of the four sides (sides AB and BC) are equal to 12. You know that AD is going to be one quarter of AB, so AD must be equal to 3. Finally, you know that AD is one half of CD, so CD must be equal to 6. This makes the total perimeter 12 + 12 + 3 + 6, or 33.
7. A Because it is much easier working with numbers than with variables, let’s plug in some consecutive multiples of 5. Let’s say that a = 5, b = 10, c = 15, and d = 20. The question then asks for the value of (a – c)(d – b). Using the numbers you just plugged in, this becomes (5 – 15)(20 – 10), or (–10)(10), which equals –100.
8. A Let’s take this one step at a time. First, just concentrate on the right side: 3b + 3 ≤ 18. You can simply treat this like an equation: If you subtract 3 from each side, you get 3b ≤ 15. Now you can divide each side by 3 to get b ≤ 5. This will allow you to eliminate B and E. Now let’s focus on the left side: –9 ≤ 3b + 3. Again, let’s subtract 3 from each side, which gives you –12 ≤ 3b. By dividing each side by 3, you get –4 ≤ b. This will eliminate C and D, so our answer must be A.
9. E Let’s start by finding the amount per bulb when bought in a pack of 6: If you can buy 6 bulbs for $30, then each bulb will cost $30 ÷ 6, or $5. In a box of 12, each bulb will cost $48 ÷ 12, or $4. Now you need to figure out the percentage difference between $5 and $4. The formula for percentage difference is . In this case, a reduction from $5 to $4 is a difference of $1 over an original price of $5. So the percentage difference is = 20%.
10. D Start by drawing out the towns. Let’s call the towns V, W, X, Y, and Z. The problem states that the towns can’t all be in a straight line, so draw them in a pentagon. Now connect the towns together. From the first town, V, the cartographer would have to measure 4 distances: VW, VX, VY,and VZ. From town W, she would have to measure only 3 distances, because she has already measured the distance from V to W: WX, WY, and WZ. From town X she would have to measure 2 distances: XY and XZ, and from town Y should have to measure the last distance, YZ. In total, she measured 10 distances between towns.
11. A Remember that the mode is the number that appears most often in a list. The number that appears most often (17 times) in the rainfall chart is 0.
12. D If you add up the amount of rainfall accounted for in the chart, you get the following figures:
5 days of 1 inch = 5 total inches of rain
3 days of 2 inches = 6 total inches of rain
3 days of 3 inches = 9 total inches of rain
2 days of 4 inches = 8 total inches of rain
for a grand total of 28 inches. If you expect 200 inches in a year, what percent of 200 is 28 inches? Translate this into algebra as , and you get x = 14%.
13. B First, find the slope of line l by using the slope formula: . A line perpendicular to line l must have a slope that is the negative reciprocal of l’s slope. So, its slope should be −. In the standard line equation y = mx + b, m is the slope. Only B has a slope of −. If you didn’t remember the rule about the slope of perpendicular lines, you could have sketched out each of the lines and looked for the answer that looked perpendicular to l.
14. C Choices B and D have negative values, so you can eliminate them right away. Start with the area of the whole figure. The square has sides of 2, so its area is 4. Now let’s remove the area of the two semicircles (which is the same as the area of one whole circle). These semicircles have a radius of 1, so the area of one whole circle will be π. So the area of the shaded region will be 4 – π.
15. E Let’s plug in the answer choices, starting with C. Twenty minutes is of an hour, so (using rate × time = distance) Jennifer ran 6 × = 2 miles to school. If she returned at 4 miles per hour, you can find the time for her return trip using the formula 4 × t = 2. Her return time is hour, or 30 minutes. Her total time is supposed to be one hour, but here it’s only 50 minutes. Eliminate A, B, and C because they’re too small. Let’s skip to E; that multiple of 6 looks like it will work better with time units than 22. Twenty-four minutes is of an hour, so Jennifer ran 6 × = 2.4 miles to school. If she returned at 4 miles per hour, you can find the time for her return trip using 4 × t = 2.4. Her return time is of an hour, or 36 minutes. Her total time is indeed one hour, so E is the answer.
16. C Because and are each radii of the circle, you know they are equal in length. This means that the triangle ABC must be isosceles, and the base and the height are equal. What base and height would give the triangle an area of 18? The base and height would each have to equal 6, because × 6 × 6 = 18. Because the circumference of the circle is equal to 2πr, the circumference will be equal to 12π.
17. B Plugging In The Answers is the easiest way to solve this problem. If the radius is 4, then the area, πr2, is 16π, and the circumference, 2πr, is 8π. The area using the value in C is twice the circumference, not half. In order to make the area smaller, try B. If the radius is 1, then the area is π and the circumference is 2π. This is what the problem asks for! B must be the correct answer.
18. E The statement tells you that Marta will get the project completed on time. You don’t know if other people could get the project done on time. You cannot conclude A, B, C, or D because there could be other people that also get projects completed on time. Also, for B, Marta could be assigned to both Project B and Project A. You can conclude E: If the project is not on time, then Marta could not have been assigned to it because if Marta were assigned to it, the project would be on time.
19. D You know that any two sides of a triangle must add up to be larger than the third side. This means that whatever the third side of the triangle is, its value + 5 must be larger than 7. This means that the third side must be larger than 2. Because the question specifies that the third side has an integer value, the smallest integer larger than 2 is 3. So the third side will measure 3, and the perimeter will be 3 + 5 + 7 = 15.
20. C Here’s a good rule of thumb for the SAT: If it looks like a quadratic equation, try to make it into a quadratic equation. If you try to solve for x, the best way is to move 12 to the same side of the equation, and then factor. x2 – x – 12 = 0 will factor as (x – 4)(x + 3). This means that x could be 4 or –3. You can factor for y in the same way, so y could also be 4 or –3. The greatest value for x – y will be if x = 4 and y = –3, which is a difference of 7.
1. A For the second blank, a good clue is rather quiet combined with the trigger while. This tells you that whatever comes in the second blank must mean that she was the opposite of rather quiet; in fact, she must have liked being around people. You can eliminate B, C, D, and E, leaving only A.
2. D Even if you can’t find an exact word for the first blank, you can probably tell that it’s going to be a negative word because of the clues serious and natural weather patterns cannot. This makes it likely that the first blank is discussing a problem with meteorology. This will allow you to eliminate A, C, and E. What might be a problem with meteorology? Probably if natural weather patterns cannot be “studied” or “created” in a lab. This will eliminate B, and makes D our best answer.
3. A In this sentence the second blank has a better clue, so you should start there. The clue is imaginary and the trigger or tells you that the blank is the opposite of imaginary. A good word for the blank is “real” or “not imaginary.” You can eliminate B, C, and D. For the first blank, what kind of word would describe what a playwright could do to make the audience uncertain? That playwright might combine realism and fantasy. Conversely, if the playwright exposed realism and fantasy, why would you be unable to tell fantasy from reality? Therefore, eliminate E; A is our best answer.
4. B The key to this question is the semicolon; this trigger tells you that whatever follows the semicolon describes the word in the blank. What follows says that the exterior of the car is different but the interior is the same. A good phrase for the blank is “on the surface.” B is the closest.
5. C This sentence may seem to lack a good clue. That is because the clue is the relationship between the two blanks. In this case, virtually disregarding the idea that indicates that they need to be opposites; either educators view it as bad while it actually has the power to be good, or educators view it as good while ignoring the fact that it can be bad. Knowing this, you can eliminate any answer pairs whose words are not strongly opposed—choices such as A, B, D, and E. The only answer that contains two strongly opposed words is C.
6. E In this sentence, the clue is convincing her readers to believe. This means that she must be able to create extremely “believable” characters. E comes closest to this meaning.
7. C From the clue that more recent works … introduce fewer problems, you know that the first blank should describe a problem of seventeenth-century literature—a word like “difficult” for readers. This eliminates A and E. For the second blank, you will need to say that the more recent works are not difficult for readers. B and D don’t really have anything to do with reading, so our best answer is C.
8. D The clue in this sentence is who gave generous holiday bonuses and often overlooked minor lapses in judgment. A word to describe someone like this is “kind” or “generous.” This easily eliminates A, B, and C, which are negative words. Gregarious and munificent come close, as both are positive words, but gregarious means social and munificent means generous, making D the best choice.
9. C C is correct because the author states that the theory about a particular meteor has been challenged and cites studies that suggest, instead, a second, later meteor. Thus, the author is skeptical about the challenged theory. B is too strong. The remaining answers do not reflect the author’s skeptical attitude.
10. E Before answering a main idea question, always state the main idea in your own words. The author’s main point is that there is a flaw in the current theory of dinosaur extinction leading to a revised theory. A and C are too narrow and not about why the dinosaurs died out. Eliminate them. D is too extreme; you do not know if this conclusively explains what caused the extinction of the dinosaurs. Eliminate it. You now have two choices, B and E. When you have it down to two, look for what makes one of the answers wrong. The author never says that the original theory is totally wrong, but rather that there is a flaw in it. This makes B extreme because it says that the passage thoroughly disproves the current theory. Eliminate B and choose E.
11. B The author introduces Jefferson and Franklin as examples of famous American figures whom you might have thought had written the Pledge of Allegiance, whereas the Pledge’s true author is not well known. A is close, but says that Jefferson and Franklin could have written a betterpledge, and the author never says that. Eliminate it. C, D, and E are not supported by the passage and were not the point of the sentence that mentions Franklin and Jefferson.
12. B Remember that in an inference question you need to find an answer that is supported by the passage. B is supported by the sentence that mentions that there were later revisions that added the words “under God.” You have no information on A, C, or E, so eliminate them. D is true, but is never mentioned in the passage. Don’t use outside information to answer the questions on this test.
13. E This is a line reference question, so you should read these lines in context to find the answer. You know that Penfield believed brain studies … would lead inevitably to an understanding of the mind. The correct answer is a paraphrase of this idea. E says exactly this.
14. B In paragraph 4, Dr. Penfield changes the solid line connecting the spirit and brain into an interrupted one. A, C, and E were all painted on the rock mentioned in D but did not signify his doubts. B is the best answer.
15. B The best answer is B, as stated in lines 32–34. The wordings in answer choices A, prove, C, fully explained, and E, concrete evidence, are too extreme. D is incorrect because these scientists are in agreement, not in contrast, with Penfield.
16. B B is correct because line 34–37 states that Pribram and Bohm are investigating the mind with ideas drawn from quantum physics, rather than study of the brain. A is wrong: they are not trying to understand quantum physics but to use it. C is wrong because, although Eccles and Popper are mentioned in the same paragraph, the passage does not state that Pribram and Bohm are investigating theories of Eccles and Popper. Neither D nor E finds any support.
17. A For a vocab-in-context question like this one, you should cross out the word bent, reread the sentence, and put your own word in the blank. In this sentence, you would probably insert a word like “belief” or “inclination.” The word that best fits this idea is A.
18. A After the sentence in question, the author states why that sentence is false. Because there is no indication that anyone raised the issue stated in the first sentence, the author raises the issue to counter a response to a question that might be asked. This is similar to asking a rhetorical question that will be answered in the negative. Thus, A is correct. The remaining answers find no support in the passage.
19. C The best answer is C. If you replace the word waxing with a blank, the sentence says a small number of them end up ------- philosophical and “becoming” is the only choice that fits sensibly into the sentence. The other words all relate to the word waxing but do not make sense in this context.
20. E Brain-injured patients such as those in A are not mentioned in the passage, nor are the type of questions patients asked Penfield. Impulses in the passage refers to electrical impulses applied to parts of the brain, C, not to actions. Patients reported experiences that were not happening at the time, not ones that had never taken place, D. The best answer is E.
21. D Peter Pan school of neuroscience is mentioned in paragraph 8. If you read the rest of the paragraph for context, you see that the point of the paragraph is that researchers become disillusioned with claims that the mind can be explained in terms of brain functioning. Which choice best paraphrases this idea? D does.
22. B Line 66 refers to all these scientists, so it is necessary to look at prior paragraphs. As we saw in question 16, some scientists look to quantum physics, while line 51 indicates a look at neurosurgical explorations. Thus, these unorthodox scientists look to alternative sources of research into the mind, making B the correct answer. A is not supported. While there is a reference to mystical phenomena in the passage, not all unorthodox scientists are interested in such phenomena, making C wrong. D is too strong. The phrase from literature makes E wrong.
23. A A is correct because the passage states that scientists such as Penfield have been comfortable sharing their findings and ideas with specialists in other fields. The comparison in B was not made. The author did not criticize Penfield, making C wrong. D is wrong because there an important development is not described. E is the opposite of what the passage states.
24. E The best answer is E. The wording in this choice is too extreme and thus appropriate for a NOT answer; the passage focuses on scientists who came to believe that brain studies could NOT explain fully the mind’s workings. A appears in lines 73–75, and in B, not unwilling means willing; the passage focuses on scientists willing to adapt innovative attitudes as well as pursue unorthodox lines of inquiry. In C, the five scientists mentioned in the first half of this article are brain researchers [who] have a change of heart late in their careers. D appears in lines 24–27.
1. A There are no errors in the sentence as it is written. B, C, D, and E all introduce pronouns that are incorrect: In B, its is singular but families is plural; in C, they’re has the wrong meaning; in D, it’s has the wrong meaning and is singular; and in E, there isn’t even a pronoun.
2. E The original sentence is in the passive voice, rarely the best choice. B, C, and D are also in the passive voice; B and D are also rewritten awkwardly. E is the most streamlined version of the sentence, and avoids having a misplaced modifier.
3. D The original sentence contains an idiom error. D avoids the unidiomatic phrasing of the original by linking an appropriate prepositional phrase with breeding to the verb credited.
4. C Because the subject is classical composers, the examples must be the composers themselves; not Haydn’s credit, but Haydn. That eliminates all but B and C. B does not use the from … to construction that describes a range and it changes the meaning by eliminating mention of credit.
5. B A cause cannot be where, as in A and C, or when, as in D. E is a very awkward passive phrase, the management by seniors of.
6. D The original sentence would be fine if the word which was just taken out, which D does. The word which makes this sentence a fragment, as does that in B. And in C simply does not make sense as a sentence. E incorrectly uses the future tense; the sentence should be in the present.
7. A This sentence is correct as it stands. Adding which in B makes it a fragment. Both C and D are wordy, and E, with the addition of -ing, makes little sense.
8. B B is the clearest, most concise choice. As written in A, she was is redundant. C is awkward. D changes the verb tense so it no longer agrees with the non-underlined part of the sentence. E uses the word being, which on the SAT usually indicates unnecessary wordiness.
9. C This sentence contains a misplaced modifier: In addition to having more natural resources should be describing the United States. This eliminates A, B, and E. C and D both properly place the United States directly after the comma, but D moves the words also and significantly,changing the meaning.
10. E The original sentence contains an ambiguity error. We don’t know who doesn’t have her wallet. Eliminate A and B. Only E fixes the error without adding other errors to the sentence.
11. E The original sentence is awkward and wordy, as are C and D. B contains an unnecessary and awkward pronoun, it. E provides the most clear and concise phrasing.
12. C C, which uses the -ing form, creates a problem in verb construction. Has become is the correct phrasing.
13. D Weakly is describing the appearance of the paintings, not the painting’s sense of vision, and so it should be an adjective (describing a noun), not an adverb. It should read look weak.
14. D Parallelism is the problem in this sentence. To keep the list parallel, omit to.
15. C Because rock is a verb, the modifying word slow should be an adverb. Change slow to slowly.
16. E There is no error in the sentence as it is written.
17. D In D, more is redundant; healthier, all by itself, is the proper phrasing.
18. E There is no error in the sentence as it is written.
19. D This is a verb tense error. Because realized is in the past tense and the sentence mentions the previous summer, wear should be the past tense wore.
20. E There is no error in the sentence as it is written.
21. A The pronoun refers to people, and thus should read, the students who; the word which is appropriate in this context for anything else except humans.
22. B There is a pronoun agreement error here. Because the subject is you, change yourself to you.
23. B The sentence contains a pronoun agreement error. The word one doesn’t agree with himself.
24. B This sentence has an idiom error; independent from should be independent of.
25. A To correct this ambiguous pronoun, name the people who make this statement or, if none exist, remove they say.
26. C In C, it is an ambiguous pronoun; it is unclear whether it refers to the barn, the property, or where he had intended.
27. E There is no error in this sentence as it is written.
28. B Because viewers is plural, preference should also be plural. It should read their preferences.
29. D The sentence contains a faulty comparison. The phrase use of can’t be compared to fluorescent bulbs.
30. D The use of the word however in D best reflects the shift in the meaning of the two sentences. The first sentence discusses Graham’s hope of becoming a lawyer and the second sentence shows a change in this plan. None of the other answers emphasizes this transition.
31. B The first two sentences make it clear that you are discussing the past. The use of the present tense verb is in sentence 3 is therefore incorrect, and needs to be changed to the past tense.
32. A The original sentence is a fragment. A is short and correctly uses the past tense. B incorrectly uses the verb were relying, which is not in the simple past tense. C is unnecessarily wordy and subtly changes the meaning. D also changes the meaning by saying that it is Graham and not thejobs that relied on his keen insight. E incorrectly uses the verb were relying.
33. E When combining two sentences, determine how their content should be linked. The first sentence discusses what you would expect of most people, while the second sentence discusses how Graham’s behavior differs. Only E shows that contrasting relationship between the two sentences.
34. A There is no reason to include the phrase of course at the beginning of the last sentence, as the passage does not give you a reason to think this is an obvious fact. Eliminate B. C and D would make the end of the passage awkward, and E does not agree with the author’s opinion of Graham’s accomplishments as expressed throughout the passage.
35. C C is the best bridge between the two sentences, linking Graham’s success with his compassion. A and E are fragments; B and D are not indicated in the passage.
1. A If both x and y are integers, it doesn’t matter if they are positive or negative, odd or even; when the absolute value of their product is taken, by definition, it will be positive. (None of the other answer choices need necessarily be true, although C, D, and E could be.)
2. D If you draw the lines from the center of a hexagon to its six vertices, you create six equilateral triangles. All the interior angles must add up to 360. ∠FOD comprises two of them. The answer is 120, or D.
3. A The easiest way to find the lengths is to create triangles and use the hypotenuses. A becomes about 2.12; B is (or 1.4); C is .5; D is 1; and E is 2.06. The distance farthest from the origin is 2.12.
4. D The easiest way to solve this problem is to get to a common rate. You know that one packer packs 15 boxes every 2 minutes, and the other packs 15 boxes every 3 minutes. If you put these in terms of 6-minute intervals, the first packer will pack 45 boxes in 6 minutes, while the other packs 30 every 6 minutes. This means that together they will pack 75 boxes in 6 minutes, 150 boxes in 12 minutes, and 300 boxes in 24 minutes.
5. E One of the safest ways to solve this problem is by Plugging In The Answers. While you normally start with C, you don’t want to forget that this is an EXCEPT question, so let’s just start with A and go straight through to E. Assume x = 20. Is the remainder when 20 is divided by 5 the same as the remainder when 20 is divided by 4? Sure, the remainder is 0 in each case. So you can cross off A. (This is an EXCEPT question, don’t forget!) How about B? If x = 21, is the remainder the same? Yes, the remainder is 1 when 21 is divided by 4 and when it is divided by 5. How about C? If x = 22, the remainder is 2 when divided by 4 and when divided by 5. How about D? If x = 23, then the remainder is 3 when divided by 4 and when divided by 5. If x = 24, however, the remainder when 24 is divided by 4 is 0, while the remainder when 24 is divided by 5 is 4. Therefore, E is our answer.
6. E Plug in numbers for the base and height of triangle ACD. For example, AC = 10 and AD = 8. The area of ACD is therefore (10)(8) = 40. The area of ABE is (5)(4) = 10. The area of the shaded region is therefore 40 – 10 = 30, so the fraction of ACD that is shaded is .
7. C Let’s multiply out what you have in parentheses using FOIL. This gives you , or 9 – x. So our equation now reads 9 – x = 7. This makes x = 2.
8. A Let’s try plugging in some numbers for this problem. Start by choosing 18 for x and 2 for y. This makes their product 36, which is divisible by 36. You also made sure to pick a value for x that is divisible by 6. Using these numbers, let’s look at statements I, II, and III. Are they true? Statement I is not true, because 2 cannot be evenly divided by 18; because statement I is not true, you can eliminate B and D. Now what about statement II? It’s also false, so you can cross off C and E. This means our answer must be A.
Negative exponents mean to take the reciprocal and raise it to the power. So . Now find what power of . Because 34 = 81, , and x must be 4.
If the area of the circle is 400π, then you can figure out its radius. A = πr2 so 400 = πr2, and the radius is 20. The diameter of the circle is twice the radius, or 40. Because this circle is inscribed in the square, you know that the diameter of the circle is equal to one side of the square, so you know that each side is equal to 40. The area of the square is 40 × 40 = 1,600.
You know that the total number of students is 320. Because you know that there are 60 more juniors than seniors, the easy way to find out how many of each there are is to take half of 320 (which is 160) and then add half of 60 to get the number of juniors, and subtract half of 60 to get the number of seniors. This means that the number of juniors is 190 and the number of seniors is 130. (Their difference is 60 and their sum is 320.) Therefore, there are 190 juniors. Knowing that there are 30 more female juniors than male juniors, you can find the number of male juniors the same way—take half of 190 (which is 95) and subtract half of 30: 95 – 15 = 80.
If a rectangle has a width of 5 and a diagonal of 13, this means that its other side must be 12, because 5:12:13 is a Pythagorean triple. Therefore, the perimeter of the rectangle will be 5 + 12 + 5 + 12 = 34.
Let’s begin by using our Average Pie. If Jeanette’s average on 6 tests was 92, then you know that her total score on all six tests must be 92 × 6 = 552. Two of those test scores add up to 188; if you remove those two tests, the other four tests must have a sum that adds up to 552 – 188, or 364. So the average of these four tests will be 364 ÷ 4, or 91.
The best way to approach this problem is to set up an equation. There is some price such that if you add 3% of the price to the price itself, you get $56.65. This means that you can set up an equation: x + 3% of x = 56.65, or x + 0.03x = 56.65. Now you can just solve for x, and you get the original price, which was $55. Subtract this from $56.65 to get the tax $1.65.
15. or .36
Probability in this case is the number of prime numbers divided by the total number of possibilities (25 numbers). The prime numbers between 1 and 25 are 2, 3, 5, 7, 11, 13, 17, 19, and 23. So, there are 9 prime numbers. The probability is .
To solve this problem, it is important to remember the formula distance = rate × time. Here, to get the overall average speed, you need to know the total distance and total time. The total distance is found by adding all of the distances given: 0.3 + 0.3 + 0.5 + 0.24 = 1.34. To find the time for each, rewrite the rate formula as follows: time = , thus time = hours for both Alan and Ben. For Carla, time = hours, and for Debby, time = = 0.02 hours. The total time is 0.04 + 0.04 + 0.05 + 0.02 = 0.15 hours. Thus the average rate is miles per hour.
Absolute value is the distance from zero to the number on the number line, or in other words, the positive version of the number. So, . A fractional exponent means the denominator is used as a root, so this is . Next, use the distance formula: distance = . Thus, . Square both sides: 17 = (2 – 1)2 + (6 – b)2. So, 17 = 1 + (6 – b)2. Subtract 1 from both sides to get 16 = (6 – b)2. Take the square root of both sides to get 4 = 6 – b. Subtract 6 from both sides to find –2 = – b. So, b = 2.
This looks suspiciously like a quadratic equation, and if you multiply it out, its equivalent is b2 – a2. You want to make this as large as possible, so you want b2 to be large and a2 to be small. If b = –3, b2 = 9; if a = 0, a2 = 0. So b2 – a2 can be as large as 9.
1. E The clue here is almost as if it were the middle of the day. This tells you that the second blank must be a term such as “lit up” and the first word something like “light.” This makes E our best choice.
2. B A good clue for the first blank is haughty. You know that the first blank has to be a negative word that goes along with haughty—a word like “stubborn” or “arrogant.” This will eliminate D and E. The second blank needs to be an opposing idea, something like “willing to listen.” This eliminates A and C, which leaves you with B.
3. B In this sentence you have a punctuation trigger (the semicolon) that tells you that the word in the blank will mean rarely suggest radical new ideas. B, conservative, fits the bill.
4. A The trigger word although tells you that the words in the blanks should have opposite meanings. B, C, D, and E are all pairs that have similar meanings, so they can be eliminated. This leaves you with A.
5. E The trigger word while combined with health-conscious individuals have stopped eating eggs means that the word in the blank must be a word that means “healthful” (or at least “not unhealthful”). E means exactly this.
6. C The statements about Jane Doe demonstrate the author’s assertion that For many consumers, these two issues (right to privacy and copyright rules) create a surprising paradox (lines 4–5). C best summarizes this. A is incorrect because no controversy is clearly identified in the passage. B is an almost word-for-word paraphrase of the first sentence. However, the statements about Jane Doe demonstrate the paradox (or conflict), not the legal and ethical questions. Be wary of choosing answers that seem to come straight from the passage. The sentences do not contradict the paradox mentioned in the first two sentences, making D incorrect. Finally, E sounds okay until you look at it closely. First, the previous two sentences provide you with an assertion or statement about the Internet and its users, not a theory. Second, Jane Doe is an example of the average user mentioned in the second sentence, not a real, specific case.
7. D D is the best answer. Because “not averse” means willing, you see that in Jane Doe’s case, she is willing to download others’ creations at no cost, and likewise, the “pirates” of Victorian times “cribbed” what they could of new operettas and produced them on their own without paying the creators. The subjects of A and C do not appear in both passages. B and E would impede the copying that Ms. Doe and the pirates did or would like to do.
8. B Although copyright laws regarding intellectual property have existed for years, evolving technology makes it possible for individuals to circumvent the protection they offer, so the laws are not always effective or immediately enforceable. A says the opposite of what the Gilbert and Sullivan passage says. C is not correct because respect for laws and organizations is not mentioned in either passage. D cannot work because while the Jane Doe passage says that she pays for her downloads in unusual currency, the passage does not imply whether she or the author thinks this is a fair exchange. Neither passage implies that artists should be more self-protective as in E. The best answer is B.
9. E If you cross out the word draconian and fill in your own word, in the context of the sentence (imposing ------- punishments), the blank should mean something like “harsh.” Severe, E, is closest to this meaning. There is a similarly spelled word (dragonian) which means “dragon-like,” as in B, but it is not the same as draconian. The concepts in A, C, and D all appear in the passages, but they are not used to describe punishments. Therefore, E is the best answer.
10. C From the introductory blurb, you know that the passage is about the art and recreation of Southeastern Indians. A is too extreme and slightly offensive. Eliminate it. B isn’t the main purpose of the passage. D doesn’t mention art and recreation; eliminate it. For E, the Cherokee Indians were mentioned only as a detail. This makes our best choice C.
11. B If you read about the problem in context, the passage says that you need to view the art and games as the outward expressions of their belief system. That is, you need to understand their beliefs to understand their art and recreation. B states this best. A is extreme and offensive. The passage never states that the belief system is impossible to understand. Eliminate it. C and E are never mentioned in the passage so you can safely eliminate them. Finally, D isn’t mentioned and contradicts the passage. You do have some understanding of the beliefs of Southeastern Indians. Eliminate it.
12. B B is correct because the author states that because of the materials used, the art and architecture did not survive and is irretrievably gone. Thus, the author provides an explanation (the materials used) for a problem (the non-survival). A is wrong as the author does not criticize past Indians for their choice of materials. C, D, and E find no support in the passage.
13. E In lines 33–34 the passage says that the words of a gifted speaker … could move contentious men to reach consensus. E is a paraphrase of these lines. None of the other answers are supported and D twists the reference. It says that timid, not skilled, speakers could soothe anxious tempers.
14. D In lines 40–43 the author says even though we know much about the Southeastern Indian ball game, we do not know the precise nature of the social and political forces that led them to play it with such ferocity. This best supports D. There is no support for the other four answers.
15. C The author states in lines 39–40 that we thought often wish that we knew more about underlying social issues. Thus, the author is thoughtful in a regretful way, which is wistful. Thus, C is the answer.
16. E The purpose of the passage is to highlight the complexity of jazz and to discuss influences on jazz, particularly the brass band and the blues. Thus E is the correct answer. The remaining choices are too specific and, in the case of C and D, too strong.
17. E E is correct because lines 6–8 state that jazz performances differ from player to player. The remaining answers find no support in the paragraph.
18. A In lines 13 and 15 the passage states that jazz contains elements that derive from older musical traditions. A is a paraphrase of this idea.
19. C C is correct: lines 27–29 state that the addition of saxophones suggests the influence of the syncopated dance orchestra. The comparison in A was not made. C, D, and E find no support in the passage.
20. B B is correct because the author states in lines 30–32 that the “tradition of the brass band” was an influence in early jazz bands. There is no support for A or D. The comparison in C was not made. E is too strong.
21. A A is correct because lines 51–52 state that soloists approximate the voice with their instructions.
22. D For a vocab-in-context question, cross out the word you’re being asked about, reread the sentence, and come up with a word you think fits the blank. You’ll probably pick a word like “interesting” or “distinctive.” Which choice comes closest to this idea? D does.
23. C The lead words here are exotic sound. You can find these in the beginning of the final paragraph of the passage, which says that the kinds of instruments used and the manner in which intonation is used are characteristic of jazz. Choice C is the best paraphrase of this idea. A, B, D, and E are too specific and do not paraphrase the reference.
24. D Because this question will take a lot of time, you may want to go for easier, quicker questions first. You can find evidence in the second paragraph that jazz was heavily influenced by ragtime, brass bands, and dance orchestras. In the next-to-last paragraph you see evidence that it was heavily influenced by blues. This allows you to eliminate A, B, C, and E, which leaves D as our best answer.
1. C The clue is entirely implausible. A good word for the blank might be “falsehood.” Only C means falsehood.
2. A This sentence starts with the trigger while. So you know that the two blanks need to be contrasting ideas. The only pair that has a strong opposite relationship is A.
3. A The clue is exchange players of comparable talent. Therefore, as the colon is a same-direction trigger, the agreement was “equal.” A best expresses this meaning.
4. D A good clue for this blank is brevity—the sentence says that the article’s brevity didn’t detract from its importance, so you know that the article was brief. What is another word for brief? Terse!
5. E Here you have a great clue: reduced the population … substantially. So you need a word that means “very deadly.” The choice that most nearly means this is E.
6. D The clue for the first blank is by missteps. Because missteps is another word for “mistakes” you know that the blank must be something like “affected negatively.” A and B do not match this meaning. Eliminate them. The clues for the second blank are the trigger words but andincreasing appreciation. Therefore you know the missteps have not done permanent damage to the author’s reputation. A good word for the second blank is “unimportant.” D best matches this meaning.
7. B Let’s look at the relationship between the blanks. You could be looking for a pair of words like “happy” and “harm,” or you could be looking for a pair like “sad” and “good.” So you’re looking for words that are somewhat opposite. Eliminate A, C, D, and E.
8. C C is the best answer because the clue is rambled for a long time with frequent repetitions about trivial topics. Therefore, words like “rambling” or “boring” would work well in the blank. Because the words in A, B, D, and E do not agree with the clue, they can be eliminated.
9. B B best states the main idea of the passage. A and C are both too extreme; the passage does not argue for or against the procedure. D and E are not supported by the passage; neither deaf culture nor the scientific basis for hearing loss are discussed at length in the passage.
10. B B specifically describes the purpose of all three of the final sentences. A and E are not correct because they refer to only one sentence of the final three. C is incorrect because no alternatives are provided. D is not correct because there is no disputed theory to support.
11. C C is correct because, while several answers were mentioned as possible causes of the riots, the reports mentioned only the composer’s use of unconventional harmonies.
12. D D is the best answer because it can be proven with information from the passage. Because you know that both ballet and sporting events have caused riots, D must be true. A is incorrect because you have no information about the nature of prior riots. B and C are unsupported by the passage. E is a nice thought, but has nothing in the passage to back it up.
13. E Just following lines 11–12, the author says that his family felt a smug sympathy for those poor souls in harsher climates who had to suffer real winters. This means that he was discussing the warmth of the weather he was used to. E is the best paraphrase of this idea.
14. B For a vocab-in-context question, you should cover the word in question, reread line 12, and put your own word into the blank. In this case, you’d probably use a word like “unhappy.” The closest choice is B.
15. C While it takes careful reading, it appears that the mistral is the odd name given to the unusually high winds: It drove people, and animals, crazy. It blew for fifteen days on end.… Thus, C is correct. The remaining answers twist references within the paragraph out of context.
16. D Here you have another vocab-in-context question. If you cover up the word baleful and try to use your own word in its place, you’d probably choose a word like “scary.” Which choice comes closest to this idea? D does.
17. C In the lines preceding line 20, the author discusses how certain people complained about the wind in Provence, and that they would think differently if they had to put up with the gales that come off the English Channel. The author is thereby saying that the gales off the English Channel are worse than anything in Provence. This best supports C.
18. B B is correct because the family was not prepared for the mistral—or winds—that came howling in.
19. A For this question you know from lines 39–41 that Menicucci was concerned that the pipes burst … under the pressure of water that had frozen in them overnight. You also know that Menicucci was a plumber (so he would naturally be working on the pipes). This best supports A.
20. A A is correct because the passage states that winters had been noticeably harder than anyone could remember, as illustrated by the inability of ancient trees to survive. B may be tempting, but the author did not bemoan the loss of the trees, just noted the loss as an example. There is no support for C and D, and E is too strong.
21. C In the first lines of the last paragraph, you find Menicucci clearly expounding on his theory of why the winds were so bitterly cold. He therefore thinks he knows the answer, which allows you to eliminate B, D, and E. Choice A is extreme, so you should avoid it as well. This leaves you with C as the best choice.
22. D Remember that every question will have some support in the passage. Immediately prior to saying mais oui, the passage says that Menicucci allowed himself a brief but dramatic pause. This indicates that he was being somewhat theatrical and pompous. This best supports D.
23. E This is a tough question, so your best bet is to use POE. From the last paragraph you know that Menicucci thinks that the harsher wind was caused by a flattening of the curvature of the earth, which enabled the wind to take a more direct route south from Siberia to Provence. Because the pipes have nothing to do with this question, A should be crossed off. B, C, and D look tempting, but if you reread the paragraph, you’ll see that Menicucci never said any of these things. E sounds just like his theory and is the best answer.
24. C By now it is clear that Menicucci is pompous and has strange theories, so the use of the word unfortunately is sarcastic. Sardonic means sarcastic, making C correct.
1. B B is the best answer, because the clue is she had won the grand prize instead of just any prize. This suggests that her joy would increase, so a good phrase for the blank is “more joy.” None of the other answer choices agrees with the clue; therefore, each can be eliminated.
2. E The clue is increased humidity coupled with oppressively high temperatures, which describes a rather unpleasant situation. A word with a negative connotation would work well in the blank, like “bad.” Because listless in E means lacking energy, it is the best answer.
3. E Our clue here is had … assumed that hunter-gatherers moved combined with the trigger however. So you need a word in the blank that means the opposite of moving—a word that means “staying in one place.” The word that best fits this idea is E.
4. C The clue here is none of the original doors or windows … survived. In that case, the restoration is largely guesswork. C is the best choice.
5. D The clues from the sentence are divided into strong factions, impossible to garner, and support to pass the bill. A good phrase to describe the support that would be needed to pass the bill is “from both sides,” and bipartisan in D means exactly that. Because none of the other answer choices agree with the clues, they are incorrect.
6. E Start with the first blank. If they were expecting to be admonished, then the boys were probably up to “something bad,” or “mischief.” Eliminate the answers that don’t mean something close to “mischief,” so A, B, and C are gone. The second phrase tells us what the parents did, which is “yell at them,” as we know from admonished in the earlier part of the sentence. Eliminate D, leaving E.
7. A In lines 13–15, the first passage says The Industrial Revolution brought even worse air pollution.… Soot, smoke, and sulfur dioxide filled the air. This explains why sulfur dioxide and soot created London smog. This makes A our answer.
8. C According to lines 2–4, some of the causes of pollution included the eruption of volcanoes, dust storms, and marsh gases. In lines 4–12, the passage states that humans were also responsible for pollution. C restates these ideas.
9. C Let’s go back to the passage and read lines 9–12. They mention ancient cities that had pollution problems. This sounds a lot like either B or C. Both of these are plausible, so you should pick the one that is more general and defendable based on what the passage says. Earlier in the passage, the author tells you that people early on began to pollute the air. The passage doesn’t say that the air pollution always existed in cities. Beware of extreme words; they are often wrong. This makes C a better choice than B.
10. A Using the lead words air pollution and Industrial Revolution, and knowing that the answer to the last question was found in the first paragraph, you can find the relevant reference. The second paragraph tells you that The Industrial Revolution brought even worse air pollution and there were large rural areas unaffected by air pollution. In the beginning of the third paragraph, the passage tells you that today rural areas are not unaffected (line 20). A best summarizes this difference. B uses words from the passage but says something the passage didn’t. You don’t know what the factory towns were before they were factory towns. C, D, and E are never mentioned and are therefore incorrect.
11. D If you read these lines in context, you find in lines 27–28 that the astronauts … traced drifting blobs of Los Angeles smog as far east as western Colorado. This means that the smog has spread from a big city to the countryside. This is paraphrased by D. B and C, while tempting, are much too extreme to be correct.
12. E This is an EXCEPT question, so the correct answer choice is not mentioned in the passage. The final paragraph of Passage 1 mentions strained relationships between the United States and Canada, factory closings, and acid rain. This means you can eliminate A, B, and C. The passage also mentions a change in the work habits of traffic police, so D can be eliminated. This leaves E as our best answer.
13. C C is correct because the passages do exactly that; they provide an example. A is quite extreme, so you should avoid it. B is tempting, but the passage never really talks about the long run. Instead, it mentions only a particular historical event.
14. D The lead words here are London smog. You can find London smog described in the first paragraph of Passage 2, where you are told it was a combination of smoke, fog, sulfur dioxide, sulfuric acid, ash, and soot. This is best paraphrased by D.
15. D Lines 64–67 of this paragraph say that air pollution has killed more people than were ever killed in any single tornado. In other words, air pollution is extremely dangerous and deadly. D is a paraphrase of this idea.
16. D D is correct because the author provides several problems associated with the precipitators in lines 74–79. A is, therefore, backwards. The remaining answers are not supported.
17. E Again, let’s look back to the passage. In lines 80–81, you find that the processes to remove sulfur dioxide from air pollution are expensive and in line 88, that they waste a part of the coal’s energy. E says exactly this.
18. D A and B are extreme, so you should avoid them. Neither author discusses eliminating the sources of pollution, so you can also cross off C. Finally, neither author says that the cost of pollution control is much higher than the cost of changing to better energy sources, so you can eliminate E as well. D is a nice SAT-type answer, because it’s fairly general and hard to argue with.
19. E E is correct, because while both passages discuss effects, only Passage 2 examines possible solutions. The remaining answers are wrong about one or both passages.
1. A Take it one phrase at a time. The “sum” means you will add two things. The “squares of x and y” means to square x and square y, or x2 and y2. Add these to get x2 + y2. Cross out any answer that does not have x2 + y2 as the first part of the equation. Only A is left.
2. C If c = 6 and b + c = 8, then you know that b = 2. Because you know that c = 6 and b = 2, you can solve for a: If 3a + 2b + c = 22, then 3a + 4 + 6 = 22, so 3a = 12, and a = 4. Therefore, a + b + c = 4 + 2 + 6, or 12.
Or try stacking:
3. B Because probability = # of outcomes fulfilling the requirements over the total # of outcomes, you need to find the total area of sectors that are labeled 3 and 4 over the total area of the circular spinner. Even though you don’t know the area of the circle, you know that this fraction is the same part of the whole as the total degree measure of central angles that enclose 3 and 4 over the total degree measure of the circular spinner, which is the total area of sectors that are labeled 3 and 4 over the total area of the circular spinner. This gives you , or .
4. C Let’s start by figuring out what the values of x and y could be. You know that 4x – 8 > 0. If you add 8 to each side of the equation, you get 4x > 8, which means that x > 2. So x could be 3, 4, or any integer larger than 2. Likewise, you know that 4y + 8 < 0. If you subtract 8 from each side of this equation, you get 4y < –8, which means that y < –2. So y could be –3, –4, or any integer less than –2. Neither x nor y can be zero, so the product xy cannot be zero. This means you can eliminate E. And because you don’t know whether x and y are odd or even you can also eliminate A and B. You do know, though, that x will always be positive and y will always be negative, so whatever numbers x and y are, you know their product will always be negative.
5. B If a rectangle has length 16 and width 6, then its area will be the length times the width, or 16 × 6, which equals 96. If this is 3 times the area of a triangle, then the triangle will have an area of 32. If a triangle with area 32 has height of 8, you can use the triangle formula for area of a triangle to find the base: × base × height = area. 32 = b × 8, so base × 4 = 32. This means that the base is equal to 8.
6. E Plug in! There are two 30°-60°-90° triangles imbedded in this problem, so that is the best way to tackle this. Plug in for y, and go on from there. If you were to use 18 for y, the height of the cone would be 9. The base of the smaller triangle would be . That is also the radius of the circle, so square that number and get 27, and then multiply by π to get the area of the circle, which is 27π. This is the target. Plug your original value into the answer choices. If y = 18, the only answer that works out to 27π is E. Algebraically, the height is , and the base of the smaller triangle is (using the 30°-60°-90°). Square that and multiply by π, and you get E.
7. D You can set up a proportion, or simply notice that 1,000,000 is 10,000 × 100. So if you multiply 30 by 100 you get 3,000.
8. C Because lines k and l are tangent to the circle, they form right angles with the radii. Angles OAB, AOC, and OCB in quadrilateral OABC are all 90°, and all four angles must add to 360°, so the remaining angle must also be 90°, which makes OABC a rectangle. Because and are radii, they are equal, and you are told that is the same length as the other two sides. Thus, all four sides are equal. So OABC is actually a square. Draw in and you’ll see that it bisects the square, forming two 45°-45°-90° triangles (see the reference information at the beginning of any SAT Math section). So OB = 4 = s. Solving for s gives you 2, which is the length of each side of the square.
9. A This is a great problem for Plugging In. Let’s try using z = 2, n = 5, and b = 15. If $2 will buy 5 pizzas, then how much will 15 pizzas cost? Three times the number of pizzas will have three times the cost, so $6. Now you just need to figure out which choice will give you $6. Try calculating each of the answer choices, and you’ll find that only A equals $6.
10. C Because you have parallel lines, let’s identify the big and small angles. The small angles measure 65°, so the big angles measure 115°. So x + y = z = 115. If you add everything together and substitute x = 55, you get 55 + y + z = 230, so y + z = 175.
11. D Because is a radius of the circle, OP = 8. Because is a radius of the circle, OR = OQ + QR, and OQ = QR, therefore OQ = 4. Using the Pythagorean theorem—or recognizing the ratio of sides in a 30°-60°-90° triangle—will give you the value of PQ: 4. Because area = bh, the area is .
12. B This is a great problem to solve with Plugging In The Answers. Let’s start with C. Could the number of girls on the trip be 40? If there are 14 more boys than girls, then there must be 40 + 14 = 54 boys. But that makes a total of 94 students; that’s too much because there are only 80 students. So you can cross off C, D, and E because they are all too big. Let’s try B. Could there be 33 girls? In this case there will be 33 + 14 = 47 boys, and 33 + 47 equals 80. So B is the answer.
13. B Let’s start by solving for p. You know that p = f(6), which means that it will be equal to (10 – 6)2, or 16. So 4p will be equal to 4(16), or 64. Now you simply have to figure out which choice gives you 64. p(18) will equal (10 – 18)2, which is 64. So, B is the answer.
14. A Be sure to read the question carefully; the key here is must be positive. Let’s try plugging in an easy number for b. If you make b = 2, then let’s see which of the choices is positive. A becomes . B becomes , so you can eliminate it. C becomes . D becomes 0, so you can eliminate it, and E becomes 3. Now let’s try making b = . In this case, A becomes . C becomes –1, so you eliminate it. E becomes 0; eliminate. That leaves you with A.
15. D First find the x- and y-intercepts. The y-intercept is (0, –6). To find the x-intercept, replace y with 0: 0 = x − 6; 6 = x; and x = 9. So, the x-intercept is (9, 0). Now create a triangle and use the Pythagorean theorem: 62 + 92 = 117. The distance between the x- and y-intercepts is .
16. B The second graph moves down 1 and to the left 1. Remember that when a graph moves to the left it is represented by (x + h), which would be the same as x – (–1). So h = –1. Because a negative k represents moving down, k = 1. 1 × (−1) = −1.
1. B Avoid the word being if possible, which eliminates A and D. Also, watch out for verb tense. The non-underlined part of the sentence is in the present tense, so eliminate C and E because they are both in the future tense.
2. A There are no errors in the sentence as it is written. Both D and E use the phrase at least 3 feet wide or wider, which is redundant. B incorrectly uses swung instead of swing, and C is unnecessarily wordy.
3. E The original sentence, A, has the comparative adjective better, which is incorrect when comparing more than two things. B uses can be, which changes the meaning of the sentence. C uses future tense, which doesn’t really make sense. In D, switching the adjective nineteenth-centuryinto a modified noun changes the meaning of the sentence.
4. E E correctly compares American etiquette with the etiquette of other countries. This answer choice includes the phrase that of and thus uses the correct form of comparison. The rest of the choices all have a faulty comparison. A and B are missing the phrase that of and do not correctly establish a comparison. C is closer, but you need to compare American etiquette with the etiquette of other countries (plural). In D, the comparison is not properly drawn. The word what doesn’t do the job.
5. C The problem with the original sentence is that it uses the long-winded and awkward phrase this being that they had to instead of a concise one. B is very concise, but the phrase including read an article is grammatically incorrect. C, on the other hand, is both concise and grammatically correct, so get rid of A, because there is a better alternative. D and E are no less awkward than the original sentence, so eliminate them. C is the remaining choice.
6. C The best choice is C. Only a person can be renowned for her writing, and thus Barbara Kingsolver should follow the comma. However, A follows the comma with Barbara Kingsolver’s poems, while D follows it with the poems of Barbara Kingsolver. B and E incorrectly insert a semicolon in place of the comma, turning the initial modifier into a fragment.
7. A There is no error in the sentence as it is written. Choice B creates a run-on sentence (in particular, a comma splice). Choice C is awkward and wordy because of all the -ing words and states that the experiments have the exacting standards. Choice D is also awkwardly worded because ofbeing. Choice E can be eliminated because of improper verb tense.
8. D A and B both contain comma splices. C tries to rephrase the sentence using the word being, which is seldom desirable, and also suggests that the works that follow are the only two examples in the history of literature. D offers a concise way to introduce examples. E is even more concise, but improperly uses the word like to introduce examples.
9. D The original sentence is awkward, wordy, and incorrectly uses however as a substitute for but or though. B uses along with to join the two halves of the sentence, failing to signal that there is a conflict between the adults and the girls. In C, the word even is unnecessary. E is missing a verb. This leaves D as the best answer.
10. E E is the most concise answer, and because it introduces no grammatical errors, it is correct. A, C, and D all refer to the singular committee as they, while B is unnecessarily wordy and awkward compared to E.
11. A The best choice is A. The sentence is correct as it stands. Eliminate B and C because, with or without the semicolon, a double negative (not hardly) is considered incorrect. The word since in D is unnecessary: It means “because” here and does not make sense in the sentence. The addition of however in E is redundant, because the sentence already uses the word although.
12. B The original sentence contains the word because, so adding the reason is redundant; eliminate A and E. C and D wrongly imply that the ban is on the animals, not on transporting them. This leaves you with B as the best answer.
13. D In D, the present perfect has tripled agrees with the present tense of the past hundred years to indicate a time frame from one point until now, and is the most concise way of stating this idea. A and B are wordy. In C, was tripled is passive—when possible, choose the active voice on the SAT. E has the incorrect verb tense; had tripled is the past perfect while the sentence is discussing something that started in the past, but has not finished.
14. C This sentence’s error is in pronoun agreement: Student is singular, but their is plural in both A and B. D corrects this error but adds always, which changes the meaning. E unnecessarily adds not only … but also. In C, the corrected phrase reads to seek help from teachers, eliminating the pronoun and, thus, the error.