Chapter 25
Drill Answers and Explanations
PART II: ENGLISH
English Drill 1 (Chapter 6)
1. C
This sentence requires a word that will go with the non-underlined object, the many achievements. Choices (A), (B), and (D) do not work with this phrase. Only (C) can work with the non- underlined portions of the sentence, creating the phrase large canvases that celebrate the many achievements.
2. J
Apostrophes should be used only to indicate possession or contractions. Since achievements is not in possession of anything, and achievement is would not work in the context, eliminate all choices with apostrophes: (F), (G), and (H). Only (J), containing no apostrophe, can work in the context.
3. A
Since there is Stop punctuation in the answer choices, use the Vertical Line Test. The first part of the sentence, His portrait of Ice-T, is not a complete idea, so (C) and (D) can be eliminated. Choice (A) is the correct answer because the comma sets off the unnecessary information that follows, the rapper and reality-TV star.
4. H
As written, this sentence is incomplete, so eliminate (F). Choices (G) and (J) do not make the sentence complete, so those can also be eliminated. Only (H) creates a complete idea.
5. A
Pay close attention to the non-underlined part of this sentence. The word them needs to refer back to a specific noun, and only (A) provides the appropriate one: Wiley’s subjects. Choices (B), (C), and (D) do not make the meaning of the sentence clear.
6. G
All four of the answer choices say essentially the same thing. In this case, choose the shortest one that makes the sentence complete, consistent, and clear. Choice (G) is the shortest, and it preserves the meaning of the sentence, so (G) is the correct answer.
7. A
The underlined portion of this sentence is part of a pair of activities: The non-underlined portion says mix the paints, so the underlined portion must match the verb tense of the word mix. Only (A), the original answer, does so.
8. J
As written, this sentence contains an ambiguous pronoun. The word them could refer to assistants, materials, or paints, none of which would work in context, eliminating (F). Choices (G) and (H) are unclear. Only (J) is adequately specific and is therefore the correct answer.
9. C
All four of the answer choices say essentially the same thing. In this case, choose the shortest one that makes the sentence complete, consistent, and clear. Choice (C) is the shortest, and it preserves the meaning of the sentence, so (C) is the correct answer.
10. J
Each sentence in this paragraph contains a description of Wiley’s subjects: various, anonymous men; common people; people from oppressed cultures; and those to whom history pays no attention. Therefore, the first sentence must preview this theme of the “common” or “average” people whom Wiley paints. Choice (J) does so and is therefore the correct answer. Choices (F), (G), and (H) are true statements about Wiley himself, but they do not fit with the focus of this paragraph.
11. D
The underlined portion does not fit where it is now, eliminating (A). The phrase portray of Harlem various, anonymous men does not make sense, eliminating (B). The phrase Wiley of Harlem does not make sense in context because, in addition to being awkwardly phrased, this phrase assumes that Wiley is from Harlem, which is not supported by the passage, eliminating (C). Only (D) can work, as it correctly situates the underlined portion in the phrase the streets of Harlem.
12. F
The recent work is that of Kehinde Wiley, so the only pronoun that can be substituted here is his, as in (F). Choices (G), (H), and (J) do not work in this context.
13. C
Each sentence in this paragraph contains a description of Wiley’s subjects: various, anonymous men; common people; people from oppressed cultures; and those to whom history pays no attention. It would therefore not make sense to include a sentence that lists a museum where Wiley’s paintings have been been shown, eliminating (A) and (B). Choice (D) can also be eliminated because this paragraph is not exclusively about Harlem. Only (C) correctly states that the sentence should not be included and gives the appropriate reason.
14. J
The sentence is not complete as written, which immediately eliminates (F). Choices (G) and (H) also create incomplete sentences, so those too can be eliminated. Only (J) creates a complete idea, so it is the correct answer.
15. B
This sentence states that Wiley’s works can be seen in galleries all over the world, and the underlined portion offers one reason that Wiley’s popularity is so broad. Therefore, there is no reason to delete the information, especially because it does not repeat or undermine earlier parts of the passage. Eliminate (C) and (D). The underlined portion does not contain information about Wiley’s selection of subjects, so (A) can also be eliminated. Only (B) correctly states that the information should be kept and gives an appropriate reason.
English Drill 2 (Chapter 7)
1. C
If you can’t cite a reason to use a comma, don’t use one. This particular comma separates the subject from its verb, so eliminate (A). Choice (B) adds a comma unnecessarily, so it can also be eliminated. Choice (D) uses a single dash, which requires a complete idea before it. After school let out, my best friend and I is not a complete idea, so (D) can be eliminated. Only (C), containing no punctuation, remains.
2. H
Stop punctuation is used in the answer choices, so use the Vertical Line Test. The first part of the sentence, From the little trail beside the school, we’d climb down to the old railway tunnel that had gone dark many years before, is complete. The second part of the sentence, that pitch darkness was terrifying and mysterious, is also complete. These ideas must therefore be separated by Stop punctuation, which eliminates (F) and (G). Choice (J) contains Stop punctuation (comma + FANBOYS), but it introduces a contrast with the word yet that does not make sense in this context. Only (H) works.
3. B
Identify the purpose stated in the question that the correct choice is supposed to fulfill. It asks for a word that indicates that the narrator and his friend held their flashlights nervously. Choices (A) and (C) are neutral and therefore do not contain any hint of this nervousness. Choice (D) does not make sense in this context. Only (B), clutching, fulfills the purpose.
4. H
Pay close attention to the question, which asks for what happened during the summer walks. Only (H) continues the narration in an appropriate way. Choices (F), (G), and (J) break the narrative flow. Also, the word Sometimes in (H) provides the necessary contrast to the word always in the following sentence.
5. C
Since there are colons in the answer choices, use the Vertical Line Test to start. The first part of the sentence (up to the word purpose) is complete, as is the second part of the sentence (from really onward). Therefore, Go punctuation cannot work, eliminating (A) and (B). Choice (D) changes the meaning, so it can also be eliminated. Choice (C) can work because a colon requires only a complete idea before it: The idea after it can be complete or incomplete.
6. F
Choices (F), (G), and (H) sound the same, but make sure you are using the correct pronoun for the context. They’re is a contraction of they are, which cannot work in this context, and their is a possessive pronoun, which also cannot work, eliminating (G) and (H). Choice (J) does not make sense in this context, so only (F) remains as the correct answer.
7. C
The word though in Sentence 6 indicates a contrast with whatever sentence comes before it. Therefore, look for a sentence that contains aimless visits with which this sentence will contrast. Sentence 1 provides these aimless visits, stating that the narrator and his friend didn’t go down into the tunnel with any specific purpose. Therefore, the sentence should go before Sentence 2, as suggested in (C).
8. J
The subject of this sentence is history, so the modifier that comes before it should modify that word. Choices (F), (G), and (H) all create modifiers that describe the narrator or something other than history, so they can be eliminated. Only (J) provides an appropriate modifier for history.
9. D
As written, this sentence suggests that the history teacher gave this bit of information to his students four hundred years earlier, which can’t work, eliminating (A). Four centuries earlier must refer to something about the Dutch settlers, and only (D) provides a placement that will create the appropriate reference.
10. F
There is Stop punctuation in the answers, so use the Vertical Line Test. The first part of the sentence, In fact…region, is complete, but the second part of the sentence, an area…New York, is incomplete. Stop punctuation cannot work, eliminating (H), but there must be some pause, eliminating (G). Choice (J) makes the sentence incomplete, so it too can be eliminated. Only (F) works because a colon can be used only after a complete idea but can be followed by either an incomplete or complete idea.
11. C
This sentence is incomplete as written, so (A) can be eliminated. Choice (D) creates the same problem. Of the remaining two choices, (C) is better because it indicates a contrast between the ruthless behavior of the Dutch and the fact that they held on to many Lenape names.
12. J
All answer choices contain the word the. Choices (F), (G), and (H) put some information before that word, but none of that information is necessary. Therefore, in order to make the sentence as concise as possible, (J) is the correct answer.
13. A
This part of the sentence describes the word influence, and (A) is appropriate because that influence is commemorated by the names. Choices (B), (C), and (D) cannot work in the context, so they can be eliminated.
14. H
This sentence describes corridors of the city that are not well-known, and (F), (G), and (J) provide reasonable synonyms. Choice (H), classified, may be a synonym for secret, but it is not an appropriate synonym in this context. Choice (H) is therefore correct because it would NOT be acceptable.
15. D
A colon must be preceded by a complete idea. Neither we were invited to nor we were invited to give are complete ideas, so (B) and (C) can be eliminated. Eliminate (A) because it inserts a comma where there is not a good reason to insert one. Only (D), containing no punctuation, remains and is the correct answer.
Rhetorical Skills Drill (Chapter 8)
1. B
Cross off LEAST, and use POE. Fame, stardom, and greatness can all work the same way as prominence in the context of the sentence. Projection does not mean the same thing and is the correct answer.
2. J
Try out each answer choice. Live television is the intended meaning.
3. A
Evaluate the reasons given in the answers. The reason given in (A) could be true, but you have to read through the third paragraph to be able to judge. That makes this a good question to do later. In fact, the proposed clause does provide necessary context for the information given in the second and third sentences of the second paragraph.
4. G
Identify the purpose in the question. The correct choice must convey extreme skill. Honing their craft does just that, while all of the other choices contain no specific mention of skill.
5. D
Use POE. Sentences 2 and 3 should go back to back, with sentence 3 providing a list of the young talents mentioned in sentence 2. Eliminate (B) and (C), and compare the difference between (A) and (D). Sentence 1 should precede sentence 4, so (D) is correct.
6. F
Identify the purpose in the question. The correct choice must introduce the paragraph. Finish reading the paragraph, and then return to the question. Since the topic involves problems with the live broadcast, (F) is the correct introduction.
7. C
To crack this type of strategy question, use POE to consider which choice correctly describes the sentence to be deleted. Choice (C) is the correct description.
8. F
Identify the purpose in the question and connect to the correct reason among the answers. Choices (G), (H), and (J) offer reasons that do not support the purpose well, nor describe the content of the essay accurately.
9. D
If you didn’t see the warning at the beginning of the passage, you may have found the flow of the essay jarring. Even if you didn’t, always use POE with order of paragraph questions. Look for topic and concluding sentences to make the flow of ideas consistent. The topic sentence of paragraph 2 makes a good transition after the discussion of accidents in paragraph 4.
PART III: MATH
Fundamentals Drill (Chapter 10)
1. C
You’ll need to find the prime factorization of 54, so use a factor tree. In using this tree, you’ll find the prime factorization of 54 = 6 × 9 = (2 × 3) × (3 × 3) = 2 × 33 . The distinct prime factors of 54, therefore, are 2 and 3. The product of these two numbers is 6, (C). If you chose (E), you may have missed the word distinct! Read carefully!
2. G
Take this problem in bite-size pieces. If x is the least odd prime number, x must be 3. If y is the least positive integer multiple of 10, y must be 10. The difference between these two numbers is therefore 10 − 3 = 7, (G). If you selected (K), be careful, you may have thought that 20 was the first integer multiple of 10, but the first multiple of any number is that number itself!
3. D
Remember MADSPM, and don’t forget Order of Operations, or PEMDAS. Do the parentheses first, and remember, when you raise an exponent to a power, you multiply those exponents: (x−1y−3)−2(x4y7)3 = (x2y6)(x12y21). Now, combine like terms, and remember, when you multiply numbers with exponents, you add those exponents to one another: (x2y6)(x12y21) = x14y27, (D).
4. H
Although this problem involves an imaginary number, you can still use a traditional FOIL method to find the answer. You are asked to square the expression, so do so, and remember to multiply the First, Outer, Inner, and Last terms: (i + 4)(i + 4) = i2 + 8i + 16. None of the answer choices look quite like this, but remember, i2 = −1, so substitute this term: i2 + 8i + 16 = −1 + 8i + 16 = 8i + 15, (H).
5. C
The prime numbers between 10 and 20 are as follows: 11, 13, 17, 19. You want the least sum of three distinct numbers, so the only possible answer is 11 + 13 + 17 = 41, (C). If you chose (B), you may have missed the word distinct.
Algebra Drill (Chapter 11)
1. C
This might look like a traditional plug-and-chug problem, but the problem is asking for a specific value, and the answer choices are all real numbers—a great indication that you can PITA! This time, the problem is asking for the largest, so start with (E). Does the equation work if x = 5? 52 − 4(5) + 3 = 25 − 20 + 3 ≠ 0. Eliminate (E). Try (D): 42 − 4(4) + 3 = 16 − 16 + 3 ≠ 0. Try (C): 32 − 4(3) + 3 = 9 − 12 + 3 = 0. It works, and because you’re using PITA, you can stop once you’ve found a correct answer. If you selected (A), be careful, this is the smallest value of x that solves the equation!
2. G
There are variables in the answer choices, so let’s Plug In. Let’s say x = 2 and plug this in to the equation: 
= 
= −1, which means your target answer is −1. Try x = 2 in the answer choices to see which one gives this target answer. Only (G) works.
3. A
This problem is very confusingly worded, so let’s make sure we use PITA to keep all the work manageable. We’ll start with (C) and work out from there, so our number is 11. “2 less than 3 times 11” is 3(11) − 2 = 31. “4 more than the product of 5 and 3” is 4 + (5 × 3) = 19. The problem tells us these numbers should be the same, and they’re not here, so eliminate (C); you can also eliminate (D) and (E) because we know we need something smaller than 31. Try (B): 10. “2 less than 3 times 10” is 3(10) − 2 = 28—still too big. You can actually stop here, because there’s only one answer choice left, but let’s check it just to be on the safe side. Try (A): 7. “2 less than 3 times 7” is 3(7) − 2 = 19. Bingo! Choice (A) is the correct answer.
4. G
There are no variables in this problem, but it deals with fractions of a “certain number,” which means that this is a Hidden Plug-In. Let’s plug something in for the number of books: It’s usually a good idea to do some common multiple of the denominators, so let’s say there are 30 books. 
of the books are distributed in the morning, which means × 30 = 12 books are distributed in the morning, leaving 18 books. 
of the remaining books are distributed in the afternoon, which means × 18 = 6 books are distributed in the afternoon, leaving 12 books. We’re looking for the fraction of remaining books, so find 
, (G).
5. B
We need to find out what happens as b increases, and there’s no easier way to do that than to try it out. Let’s start with b = 2. If b = 2, a = 
. We want to see what happens when b increases, so let’s try b = 3. If b = 3, a = 
= 1. Therefore, we can see even from these two numbers, that as b increases, a decreases, so we can eliminate (A), (D), and (E). Now, the remaining question is whether a gets closer to 1 or if it continues to get closer to 0. Try b = 4. If b = 4, a = 
. It has continued decreasing past 1, so eliminate (C). Only (B) works.
Geometry Drill (Chapter 12)
1. B
Although this is a geometry problem, it is asking for a specific value and giving a list of numerical answer choices as possibilities. This means you can use PITA. Start with (C). If ∠A = 50, then ∠B = 50, and because it is twice as large as ∠B, ∠C = 100. The sum of the three angles will then be 50 + 50 + 100 = 200, which is too big, so you can eliminate (C), (D), and (E). Try (B). If ∠A = 45, then ∠B = 45, and because it is twice as large as ∠B, ∠C = 90. The sum of the three angles will then be 45 + 45 + 90 = 180, which is exactly what you need, so the answer is (B).
2. F
When two parallel lines are intersected by a third line, it creates two kinds of angles: BIG angles and small angles. All the BIG angles are equal, and all the small angles are equal. Because ∠D is on a separate line, you don’t know anything about it, so it can’t possibly be correct, eliminating (G) and (J). The BIG angles, therefore, are A and C. The small angles are B and E. Only (F) matches like angles, so it is the only possible correct answer.
3. D
Deal with the two right triangles separately. We already have the two legs of ΔABC, so use the Pythagorean theorem (a2 + b2 = c2) to find the hypotenuse. In this case, AB2 + BC2 = AC2, so (20)2 + (15)2 = AC2, and AC = 25. Notice this is a special right triangle: It’s a 3-4-5 with a multiplier of 5! Now that we have AC, we have two sides of the other right triangle and can find the third. This, too, is a special right triangle with sides 7-24-25, and since we have sides 7 and 25, the remaining side must be 24, or (D). If you don’t spot these special right triangles, you can always use the Pythagorean Theorem.
4. G
If you have one piece of information about a circle, you can find everything else you need. The area of circle A is 16π, and because A = πr2, the radius of circle A must be 4. If the radius of circle B is half that of circle A, then the radius of circle B must be 2. Then find the circumference of circle B, with C = 2πr = 2π(2) = 4π, (G).
5. A
Separate the triangles and take this problem in bite-size pieces. You know two sides of the left triangle, so find the third with the Pythagorean theorem: LO2 + MO2 = LM2. Substitute the values you know: (4)2 + MO2 = (6)2, and MO = 2
. Then because we know MO is equal to ON, ON must also be equal to 2. You can either use the Pythagorean theorem to find the third side, or note that this is a 45-45-90 triangle, which means its sides must be in a ratio of x : x : x
, so the third side must be 2 × = 2
, (A).
Word Problems Drill (Chapter 13)
1. C
The question is asking for a specific number and offering a list of numerical answer choices as options. Use PITA! Start with (C). If there are 12 boys in the class, then there must be 27 − 12 = 15 girls. The ratio of boys to girls is therefore 12:15, which, when divided by 3, reduces to 4:5—exactly what you need! Choice (C) is the answer.
2. J
Use an average pie to help Linda fix her mistake. She initially worked with only 5 items to get an average of 88. Multiply this average and this number of items to find the sum total of these five tests: 88 × 5 = 440. Now add the sixth score to the total to find a new total of 522. Divide this number by the correct number of things, 6, to find an average of 87, (J). You’re welcome, Linda.
3. E
Read this problem carefully. Because both percentages are taken “of the original,” add them together to find that 8% of the original amount is lost. Use the percentage translation to find how much is lost: 8% of 490 tons is how much? In math terms, 
× 490 = 39.2 tons lost. The question asks for how much remains, so subtract 490 − 39.2 = 450.8 tons, (E).
4. J
There’s no figure in this problem, so draw one! This problem has variables in the answer choices, which is a dead giveaway that you can Plug In. Let’s say a = 2 and b = 3. To find the surface area, simply find the area of all the surfaces, remember that there will be six in all. The surfaces will have areas of 4, 4, 6, 6, 6, and 6. Add them together to find 4 + 4 + 6 + 6 + 6 + 6 = 32, your target answer. Go to the answer choices to find the one that matches this answer when a = 2 and b = 3. Choice (F) gives 36. Choice (G) gives 12. Choice (H) gives 16. Choice (J) gives 32. Choice (K) gives 26. Only (J) works!
5. C
This problem is asking for arrangements, so start by creating the number of slots you will need:
There is a restriction on the last in that only one letter, W, can go there, so fill this one in first:
Then, fill the rest in as normal, remembering that W is already taken, so there are only four letters left:
Now that you’ve got the slots filled in, go ahead and multiply the numbers to find the number of possible arrangements:
4 × 3 × 2 × 1 × 1 = 24 possible arrangements, (C).
Graphing and Coordinate Geometry Drill (Chapter 14)
1. E
First, use POE to eliminate some answer choices. Since this is only a > sign, we can eliminate (B) and (D) right off the bat. Now, let’s use Plugging In to narrow down the rest. First, let’s try x = −2: −3(−2) − 6 > 9. This equation doesn’t work, because 0 is NOT greater than 9, so eliminate any answer choices that include −2, leaving only (E).
2. G
Use the midpoint formula with the two given points. The midpoint formula is 
, so plug the points into the equation to find 
, resulting in a midpoint of 
, (G).
3. B
In order to find the slope, put this equation into slope-intercept form, or y = mx + b. Combine the x-terms, and subtract 6 from each side to find 12x − 6 = y, in which the m term must be 12, (B).
4. H
Plot your points on a graph, and use them to draw a right triangle. The triangle will rise 4 units and run 3 units, meaning the legs of the triangle will be 3 and 4. You can then use the Pythagorean theorem to find the third side, or if you notice this is a 3-4-5 Pythagorean triple, the third side of the triangle must be 5, (H).
5. C
Use the slope formula, 
or 
with the given points to find that the slope is equivalent to 
, (C). If you selected (E), you may have switched the x- and y-terms!
6. J
The circle formula is (x − h)2 + (y − k)2 = r2, in which (h, k) is the center of the circle, and r is its radius. Since r2 = 9, the radius of the circle must be 3, eliminating (G), (H), and (K). Then look at the first part of the equation, the (x − 3) matches up without any manipulation with the (x − h) part of the equation, so h must equal 3, eliminating (F). Only (J) is left, and we don’t even need to solve for k !
Trigonometry Drill (Chapter 15)
1. D
Use SOHCAHTOA to find that tan θ = 
. Your first impulse here may be to solve for the unknown side, but take a close look at where the θ is. Its adjacent side is 5, meaning the tangent of that angle must have a denominator of 5. Only (D) has it, so it’s the only answer that can work. If you do solve for the unknown side, remember your Pythagorean triples: this is a 5-12-13 triangle, so the unknown side must be 12.
2. H
cot θ is defined as 
. Therefore, because tan θ = 1, substitute to find cot θ = = 
= 1. Only (H) works!
3. C
Remember the special trig identity which states sin2 θ + cos2 θ = 1. Substitute this into the equation, x + sin2 θ + cos2 θ = 4 to find that x + 1 = 4, so x must be equal to 3. Choice (C) is the correct answer.
4. K
Start with POE. If cos θ <0 and sin θ > 0, then θ has to be in Quadrant II, which means that tan θ must be negative. Eliminate (F), (G), and (H). Now use SOHCAHTOA: cos = 
and tan = 
, so the numerator of the cos should be the denominator of the tan. Eliminate (J), and choose (K).
5. C
Start by converting 
into degrees: degrees = 
= 1020°. Unfortunately, this is not an answer, so you need to do a little more work. Angles greater than 360° represent multiple rotations around the unit circle. All the answers are less than 1,020, so keep subtracting 360 until you hit one of the answer choices. 1020 − 360 = 660 − 360 = 300 − 360 = −60. The correct answer is (C).
Advanced Math Drill (Chapter 16)
1. E
Rewrite log3 x = 5 as 35 = x; x = 243.
2. K
The component form of a vector describes the vector in terms of the changes in the x and y values. In other words, if u = <−3, 2>, vector u changes x by −3 and y by 2. First, solve for the vector 4u + (−2v). To do this, multiply u and v by 4 and −2, respectively: 4u + (−2v) = 4<−3, 2> + (−2<7, 5>) = <−12, 8> + <−14, −10>. Next, combine the vectors in component form by adding the x values and adding the y values to get 4u + (−2v) = <−12 +(−14), 8 + (−10)> = <−26, −2>. Substitute this back into the original equation to get <−26, −2> + w = 0. Note that 0 represents a vector with x and y components of 0, so the equation is <−26, −2> + w = <0, 0>. Add <26, 2> to both sides to isolate w and get w = <26, 2>. The correct answer is (K).
3. A
When multiplying a matrix by a constant, you multiply each element by that constant: 3
. Substitute this matrix into the original equation to get 
+ 
= 
. When adding matrices you add the elements in the corresponding locations. This means that 3a + 7 = 13. Subtract 7 from both sides to get 3a = 6; a = 2. The correct answer is (A).
PART IV: READING
Passage I: Prose Fiction (Chapter 18)
1. C
The passage as a whole describes the narrator’s father’s business, the narrator’s own time as head of the business, and his son’s current achievements as head of the business. Choice (C) correctly summarizes this narrative movement. Choice (A) suggests that the narrator does not like the direction in which his son has taken the business, which is untrue. Choice (B) is partially correct, though it is not as complete as (C). Choice (D) is too general for this very personal narrative.
2. F
In the first paragraph, the narrator refers to Singer Stations and Service as the company my father started, eliminating (G). In the second paragraph, the narrator states that my father thought it would put a safer face on the business to change the name to Singer, eliminating (H). In the middle of the third paragraph, the narrator refers back to the name of the station (which he calls alliterative), and he adds, All of the credit for this name has always gone to my father, and I can believe that he was the one behind this smart change, eliminating (J). Only (F) remains, and although the first paragraph cites a sophisticated iPhone app, there is NOT a clear indication that his father was responsible for it.
3. C
The end of the third paragraph says the following: We’ve all had our challenges, regardless of age, so who says one generation has it tougher than the next, and frankly, who cares? Therefore, the narrator does not take a firm stand on whether one generation has it tougher than the next. This agrees with (C). The narrator takes a specific stand about (A) in the final paragraph and (B) and (D) in the second paragraph.
4. F
The middle of the third paragraph says of the narrator’s father, he had that added penchant, almost a poetic sense, for a clever, musical turn of phrase. This poetic sense agrees with (F). The other choices are not specifically supported in the passage.
5. A
The sentence in which the word appears reads as follows: It doesn’t hurt that the kid knows how to make a buck. In this sentence, the word hurt does not have its primary meaning of to cause harm to a person. It is used idiomatically in the phrase It doesn’t hurt, which means something like It helps. Only (A) points toward this secondary, idiomatic meaning.
6. J
The third sentence of the fifth paragraph reads as follows: My father at the very least had a family to come home to, and the saving grace of his religious observance forced him to take at least a day off every week. This sentence establishes a clear link between saving grace and religious observance, meaning that (J) is the correct answer.
7. B
The end of the fifth paragraph reads as follows: In later years, my mother told me secretly that she thought I actually had it worst of all—I had no burning desire to enter this business, but I didn’t really have any other choice. This question asks for the narrator’s mother’s view, which appears only in these lines. Choice (B) gives a clear paraphrase of these lines. Choices (A) and (D) are not mentioned in the text, and although some words from the passage appear in (C), these reflect the narrator’s view of himself, not his mother’s view of him.
8. J
The first line of the sixth paragraph reads, Even so, I was Raman (The Gas Man) Singer’s son. Because the narrator is this man’s son, the man in question must be the narrator’s father, as in (J).
9. B
The middle of the final paragraph states the following: As a result, at the urging of my college-aged daughter Geeta, I decided to try something I always wished that I had done. I enrolled in the business program at the State University, and before long, I realized that Geeta knew me better than I knew myself. I had fun like I never had before. Choice (B) paraphrases these lines. Choices (A), (C), and (D) may be true, but they do not answer the question regarding the narrator’s daughter, nor the lines that the question indirectly references.
10. G
The lines in which the phrase appears read as follows: I had fun like I never had before, and looking back, I came to see that the part of the business that always drew me in was learning. These lines do not have anything to do with coming or going to a place but have more to do with the secondary meaning of come to see, which is a synonym for realize, as in (G).
Reading Drill 1 (Chapter 18)
1. D
While there are hints of (A), (B), and (C) in the passage, none can be called the main point. Each idea is mentioned in the passage, but the author is more interested in presenting many different perspectives. In other words, the author is interested in showing that texting’s social effects are debatable, as (D) suggests.
2. F
As the fifth paragraph states, Fields warns not only that we may have been ‘dumbed down’ by our technologies but also that we may have lost one of the essential elements of the human experience. “The content of our communication with each other…may be ultimately the same,” Fields concedes, “but the real communication lives in the form….” Choice (F) essentially restates these lines, so it is reasonable to infer that Fields would agree with this choice. Google is mentioned in the paragraph on Fields, but she does not offer any ideas on it, eliminating (G). Choices (H) and (J) contradict the lines quoted above.
3. A
In the second paragraph, the author claims, Text messages are already a part of the cultural landscape. She then goes on to offer many examples of places where the text message plays a role, as (A) suggests. Although she mentions two novels that discuss texting, she does not say that these novels are about texting, nor are novels the only examples given in this list, eliminating (B). Though (C) uses words from the first paragraph, it do not describe that paragraph accurately. Choice (D) may be true, but it does not answer the question.
4. J
The fourth paragraph states, we could even say that our very nation was founded in these written communiqués: much of what we know about that era comes from these letters. This idea of providing a historical record is restated in (J), making this the correct answer. Choice (F) does not make sense, and (G) and (H) have no support in the text.
5. B
Of the naysayers, the fourth paragraph states, naysayers have said that everything from the printing press, to the radio, to the movie screen, to Google, has compromised the way we think and understand. In other words, these naysayers speak out against any new technologies as impairing our ability to think. The sports journalists described in (B) provide the closest analogue, in that they warn against changes.
6. J
According to the first paragraph, Hillebrand and Ghillebaert, (J), were early contributors to the creation of the text message to the extent that it has a creator at all. Scorsese is a filmmaker; Wallace and Franzen are novelists; and Fields and Chacon are media theorists.
7. D
Hillebrand states, 160 characters was sufficient to express most messages succinctly. Therefore, he would likely agree with the statement that prefers messages of a sentence or two rather than…two-hour phone conversation[s], thus eliminating (A) and (B). Hillebrand nowhere states that the phone is no longer an effective communicator, eliminating (C). Choice (D) correctly states that Hillebrand would agree and gives a paraphrase of his quotation.
8. F
The last sentence of the second paragraph states, Text messages, in fact, move the whole plot of Martin Scorsese’s 2006 film The Departed, a critical success and eventual Oscar winner for Best Picture. All we know about this film is that text messages play a central role in moving the plot, meaning that text messages must appear in the answer, eliminating (H) and (J). Choice (G) can also be eliminated because there is no support for the idea that the medium exploded in popularity after the film’s release. Only (F) is supported by the passage.
9. C
The second sentence of the third paragraph reads, Speaking on an actual telephone is basically defunct in 2013, not only for the economic reason that “time is money” and a text is quicker than a call but also for a much older desire in all of us for permanence. Only a portion of this sentence relates to “time is money”: the economic reason that “time is money” and a text is quicker than a call. Choice (C) mentions this quickness, so it is the correct answer. Choice (A) is not discussed. Choice (B) is part of this sentence, but it is evidence that works against the idea that “time is money.” Choice (D) is not discussed in this paragraph, and neither the author nor the later theorists argue that text messaging has any positive effects on intimacy.
10. G
In the final paragraph, Chacon observes, Whatever the limitations of this new medium of communication, people are interacting on a day-to-day basis with more people than their ancestors might have met in a lifetime. The words Whatever the limitations suggest that Chacon is about to say something positive about this new medium of communication, the text message. Choices (F), (H), and (J) focus too much on ancestors and lose the main point of the passage and paragraph. Only (G) adequately paraphrases the quote.
Reading Drill 2 (Chapter 19)
1. A
Choice (A) is correct because, although the author discusses having great difficulty and confusion in learning jazz chords, he does not ever identify one that is most confusing. Choices (B), (C), and (D) are incorrect because none of the chords are ever identified as the most confusing chords.
2. F
In the context of the passage as a whole, the author discusses Victor as a source of knowledge about jazz. The author states he did not get straightforward explanations from Victor but that he did learn some things. Choice (F) is correct because, given the context of the passage, it refers to the most likely subject matter the author would be trying to get from Victor. Choice (G) is incorrect because the idea that knowledge about jazz would be forbidden is too strong. There is no evidence that the author was being purposefully excluded from learning about jazz. Choice (H) is incorrect because there is no context to support the idea that the author was asking about literal magic tricks. Choice (J) is incorrect because there is no context to support the idea that the author was trying to learn more about Victor as a person, nor does the passage ever describe Victor as private.
3. D
Upon seeing the author’s invented chord, Victor calmly informs the author of the chord’s proper name. Choice (D) is correct because nonchalance indicates a relaxed, unimpressed manner, which is how Victor responds. Choice (A) is incorrect because Victor would not be amazed by a chord for which he already knows the technical name. Choice (B) is incorrect because Victor would not be jealous that the author could play a chord that was already familiar to Victor. Choice (C) is incorrect because Victor does not show confusion; he shows immediate recognition of what chord the author is playing.
4. G
In the eighth paragraph, the author states that for the next few months, I quietly plucked away at the music found in “The Real Book.” Hence, (G) is correct, and (F), (H), and (J) are incorrect.
5. A
The passage describes the more complex chord types of jazz and describes the effects of using them as introducing subtle hints of chaos and imbalance, adding a worldly imperfection, and becoming more enjoyable as one’s age starts making things like candy taste too sweet and “imperfections” like bitterness make for a more appealing flavor. Choice (A) provides the correct summary for these ideas. Choice (B) is incorrect because the description of jazz’s complexity is not intended to be a critical comment about fundamental flaws in rock and classical music. Just because jazz’s unique chords add detail and depth to the music, that doesn’t mean the author thinks that other styles of music necessarily lack detail and depth. Choice (C) is incorrect because the passage does not specify anything about the confusion and awkwardness of standard jazz chord values; it describes what elements jazz chords add to standard chord values. Choice (D) is incorrect because the context explains that candy starts tasting unpleasantly sweet the older one gets.
6. J
The end of the passage describes the author beginning to develop an ability to play jazz, but his newfound ability is still mentally surprising. Choice (J) summarizes this context best and is therefore correct. Choice (F) is incorrect because the passage does not support the idea that the author was overworked. Choice (G) is incorrect because, although the author is surprised by what his hands can do musically, there is no context to support that the author is actually losing the ability to control his hands. Choice (H) is incorrect because there is no information to support the idea that the author pointing at chords was part of his learning process.
7. D
Choice (D) is correct because the eighth paragraph describes the author’s initial attempts to work through the strange, new combinations he found in “The Real Book.” He mentions F-sharp minor-7 flat-5 while speaking of chords that he had to decode and then understand. Choice (A) is incorrect because the context of this paragraph suggests that the author did indeed have some trouble with these unfamiliar chords. Choice (B) is incorrect because the remark about not knowing the language of a foreign country has no literal relation to this specific chord or the author’s previous travels (about which we know nothing). Choice (C) is incorrect because the passage provides no evidence that the author knew how to play this chord on guitar.
8. H
The fifth paragraph identifies Victor as a member of the author’s rock band as well as a member of a jazz ensemble. This makes (H) correct. Choice (F) is incorrect because the passage states that at age 30, it had been over a decade since the author and Victor had gone their separate ways. Choice (G) is incorrect because the passage states that the author bought his own copy of “The Real Book.” Choice (J) is incorrect because the passage does not say that Victor invented this chord, rather that he told the author the name of the chord the author presumed to have invented.
9. C
The passage begins with the author’s love for jazz. It transitions into his own experiences learning how to play jazz and culminates with his early successes in doing so. Choice (C) is correct because it encompasses the various points of focus throughout the passage. Choice (A) is incorrect because the passage only occasionally refers to a chain of events and never establishes that the author has a jazz career. Choice (B) is incorrect because the author does not try to show that jazz is uncomplicated; he describes the hard work he put into learning its complexity. Choice (D) is incorrect because the central focus of the passage is the author’s learning of jazz. Although the author’s friendship with Victor relates to jazz, it is not the central focus of the author’s discussion.
10. G
In the last few paragraphs, the author describes the process by which he struggled to learn jazz. He begins by seeing jazz as a cryptic message to decode but later describes himself as becoming comfortable and possessing a new melodic understanding. These details make (G) correct. Choice (F) is incorrect because the author never says that the book becomes annoyingly familiar by the end. Choice (H) is incorrect because the author identifies a difference between jazz sheet music and classical sheet music, but this detail does not enter his discussion of his experiences with “The Real Book.” Choice (J) is incorrect because the author has not suggested that he has moved on to other learning tools or more profound study.
PART V: SCIENCE
Basic Approach Drill 1 (Chapter 22)
1. B
As you were reading the question, did you notice that (A) and (B) were the same except that the words “T1” and “T2” were switched? The answer choices are opposites, and one of them will probably be correct. Let’s try (A) and (B) first. At T1, Sample 1 has a greater number of molecules in motion. The introduction clarifies that this corresponds to an increase in kinetic energy. The graph contradicts (A), so the answer appears to be (B). Now let’s check the other two choices. Does an increase in temperature lead to a decrease in kinetic energy? No. The passage states that an increase in temperature leads to an increase in kinetic energy. So we can eliminate (C). Now let’s look at (D). Is it true that water never undergoes a phase change? No; in fact, the text accompanying the graph says just the opposite. So we can eliminate (D). Also, remember to be cautious of extreme language such as “never.” The correct answer is (B).
2. F
The question refers to the second paragraph, which mentions phase changes. What happens during a phase change? Two things happen: (1) Increased kinetic energy weakens the attractive intermolecular forces in the water, and (2) Some molecules escape the liquid as a gas. Now that we have reviewed this information, it’s pretty easy to eliminate (G) and (H). Now let’s look at (J). Did we read anything in the passage that told us about other phase changes? No. This answer is beyond the realm of the passage and can be eliminated. So the correct answer is (F), and again we’ve reached it by using POE.
3. B
The ACT test writers want to see if you can predict what will happen if you raise the temperature of water higher than that of Sample 2. What answer choices should you eliminate? Decide whether the correct answer should begin with a yes or a no. How do we do that? Just check the graph with the results for Samples 1 and 2. When you increase the temperature, will the sample have more or less kinetic energy? It will have more. That means we can rule out (D). We can eliminate (C) because the temperature reading of Sample 2 is lower than the third sample. Now compare (A) with (B) to see which one is correct. Does an increase in temperature lead to greater or fewer numbers of molecules escaping the liquid? Greater. Thus, the correct answer is (B).
4. F
The passage states that when a substance goes from the liquid to the gas phase, it will evaporate. When a substance has reached the temperature at which it undergoes the phase change, it will evaporate. That’s how molecules will escape. Therefore, the answer is (F).
5. C
When you look at the figure, which line goes the highest? Which has the highest kinetic energy at any one point? Well, the curve for T1 goes higher than the curve for T2. T2 has the highest average kinetic energy, but that’s not what this question asks us to find. Therefore, (A) and (B) can be eliminated. Choice (D) is a nonsensical answer choice. Choice (C) is the correct answer.
6. H
Start with POE. Figure 1 shows that the Ea is the same for both of the samples 1 and 2, so temperature does not affect this value. Eliminate (F) and (G). Now, use your answer to Question 3 to help you: a higher temperature leads to more molecules escaping. If no molecules escape at a temperature of A, then A must be less than T1. The correct answer is (H).
Basic Approach Drill 2 (Chapter 22)
1. B
Do we see a solution of thyroxine that is 0.3 µg/ml? No. The ACT test writers want you to “guesstimate” where 0.3 µg/ml would fall on the table. This value would have to lie somewhere between 0.2 µg/ml and 0.5 µg/ml. The question requires that you make a guess within the values given. What do we call this skill? Interpolation! Now if we move across the x-axis to the value of 72 hours, and we move up to the range of values between 0.2 µg/ml and 0.5 µg/ml, we see that the y-values range from about 23 percent to 37 percent. The only one that falls in that range is (B)—30 percent.
2. G
Notice that they want to know what is true for tadpoles in general. Let’s start with (F). This is a ridiculous answer choice. We know that all normal tadpoles undergo metamorphosis. If you’re not sure, take a look at the graph. The control group in the graph represents normal tadpoles. They do have some decrease in tail width, although not a lot, in 120 hours or 5 days. (Notice that you needed to know that 5 days is the same as 120 hours.) Thus, (F) is incorrect. You can also rule out (H) because the figure clearly shows that high concentrations of thyroxine solutions lead to the greatest decrease in tail width. The passage doesn’t mention anything about temperature, thus (J) is out. The correct answer is (G). We see that the control sample shows some reduction in tail size in 120 hours, so it must take longer for the process to be complete.
3. C
You must realize that as the tadpole develops, the tail is reabsorbed—or it shrinks. The graph compares percent decrease in tail width to hours. At 96 hours (4 days), the tadpoles showing the lowest percent decrease in tail width would be the least developed. Therefore, the answer must be (C), the tadpoles in 0.1 µg/ml.
4. G
Thyroxine affects the metamorphosis of the tadpole by influencing the process of cell determination from tadpole cells into mature adult cells. You don’t have to understand this process—just realize that it occurs between tadpole and adult stages. Begin with (F), (G), and (H), because you need a tadpole to start the process. Using POE, the correct answer can be only (G).
5. C
Take a look at the figure provided. When do the lines start to differentiate from one another (showing different rates of tail reabsorption)? We can see that by 24 hours, the tadpoles placed in the various thyroxine solutions have each had a larger percent of their tails reabsorbed than the tadpoles in the control group. Choice (D) can be eliminated. Now look between 0 and 24 hours. At 0 hours and at 12 hours, the percent decrease in tail width is the same for all the tadpoles. Therefore, the change in metamorphosis rate must occur between 12 and 24 hours, so (C) is correct.
6. H
Use POE. The percent decrease in tail width for a 0.15 μg/ml thryroxine solution should be between that of the 0.1 μg/ml and 0.2 μg/ml solutions. The 0.2 μg/ml solution reaches a 22 percent decrease at approximately 72 hours, and 0.1 μg/ml solution reaches this threshold at approximately 96 hours. Therefore, the tadpole in a 0.15 μg/ml solution would reach this threshold somewhere between 72 and 96 hours. Only (H) reflects this.
Basic Approach Drill 3 (Chapter 22)
1. A
Finally, a question about drawing a graph! This question was easy because you only needed to look at the x- and y-axes. The atomic number of the elements was the independent variable, and the atomic radius was the dependent variable. What happens to the atomic radius as you increase the atomic number? It gets smaller. That means we can eliminate (C) and (D). Now we have to decide if it’s a linear relationship or an exponential one. Just check the numbers. Notice that the numbers decrease by a smaller amount each time—so it’s a curve, not a straight line. Thus, the correct answer is (A).
2. J
You should look at relationships between electronegativity and one of the other properties of elements. Let’s start with (G) and (J). Why? They are opposites (the switch again), so they can’t both be true. If an element has a high electronegativity, is it a metal or a non-metal? It’s a non-metal, so eliminate (G). Now we can check the other answer choices. Must an element with a high electronegativity have an even or an odd atomic number? Let’s check. If you look at the two highest electronegative elements, O and F, one is even and one is odd. So (F) is not true. As for (H), we know that elements with high electronegativity pull their outer electrons (the passage defines electronegativity as a measure of that strength). Therefore, we can eliminate (H). The correct answer is (J).
3. B
This question asks you to make a generalization about trends in the chart, with regard to the bigger picture. Let’s take a moment to think about the answer choices. If we want to make generalizations about elements, would an answer that refers to specific elements be the correct one? Probably not. So we can probably eliminate (D). But let’s look at (D) more closely to be sure. Is the atomic radius of F larger than that of N? No. Do all metals have high electronegativity values? No. Now notice that (A) and (B) state opposite trends. Use the chart to determine which is correct. As the atomic radius decreases, electronegativity increases. Thus, the correct answer is (B).
4. G
The first part is easy. Look at the chart to tell you which has a greater electronegativity, Li or F. F, of course! So we can get rid of (J). Now why is the electronegativity of F greater than that of Li? We have to choose between (F) and (G). Can you determine which one of these is correct by using the information in the chart? No. Go back to the introduction and skim for information about electronegativity. The passage says specifically that within a row of the periodic table, the electronegativity tends to increase with increasing atomic number, due to the tighter bonding between protons and electrons. It’s not the number that’s important, but rather how tightly bound they are. F has a higher atomic number than Li and more electrons than Li, therefore, F’s electrons are more tightly bound than Li’s. The correct answer is (G).
5. A
You must take new information given in the question and apply it to the chart given in the passage. Fortunately, this is very easy. Be careful; the question asks for increasing order of ionization energies. Because it follows the same trend as electronegativity, just find the answer that lists elements with increasing electronegativities. The answer can only be (A).
6. G
Based on the introduction, as atomic number increases, the bonds between protons and electrons becomes tighter. The question states that Element X has tighter bonds than Element Y, and Table 1 shows that non-metals have higher atomic numbers than metals, so Element X must be the non-metal. Eliminate (F) and (J) because Li and Be are both metals. Element Y must be the metal; eliminate (H) since B is not a metal. The correct answer is (G).
Fighting Scientists Drill 1 (Chapter 23)
1. A
Scientist 1 argues that natural gas formed where the remains of marine organisms and terrestrial plants piled up on land and on the seafloor over a long period. This indicates that the natural gas reservoir may have formed near the site of a past ocean, where the organic remnants of marine organisms could have been transformed into natural gas over a long period of time. Therefore, (A) is the correct answer. Choice (B) indicates that the natural gas reservoirs would be found near the site of a present day ocean, where none had existed in the past, leaving no time for the conversion process described by Scientist 1 to occur. Choice (C) is not mentioned by Scientist 1. Neither scientist’s argument includes formation of microorganisms from non-living carbon sources, eliminating (D).
2. H
Scientist 1 mentions that natural gas would have formed at depths greater than 10 miles below Earth’s surface. Natural gas formed 20 miles below the surface of Earth is consistent with the mechanism described by Scientist 1. Therefore, (H) is the correct answer.
3. D
Pressure will increase as the depth below Earth’s surface increases. Scientist 2 indicates that natural gas formed at depths of 2 to 10 miles below the surface. Scientist 1 indicates that natural gas formed at depths of more than 10 miles. As a result, Scientist 2, who indicates that natural gas formed at shallower depths, also indicates that natural gas formation occurred at lower pressures. Therefore, (D) is the correct answer.
4. G
According to Scientist 2, natural gas formed at depths from 2 to 10 miles beneath the surface of Earth. This eliminates (F) and (H), which depict natural gas as forming at depths of greater than 10 miles beneath Earth’s surface. The first paragraph of the passage explains that natural gas reservoirs are located between 0 and 0.5 miles beneath Earth’s surface. As this information precedes the discussion of the individual scientists’ specific arguments, this information is not disputed and is acknowledged by both scientists, so Scientist 2’s description should be consistent with this information. Only (G) depicts a natural gas reservoir located between 0 and 0.5 miles beneath Earth’s surface.
5. D
According to Scientist 2, microorganisms convert the carbon compounds and water into the hydrocarbons of natural gas. The reaction of carbon dioxide (CO2), a carbon-containing compound, and water would be an example of such a reaction and would therefore support Scientist 2’s argument that microorganisms convert organic material into natural gas. Thus, (D) is the correct answer.
6. H
Scientist 2 states that carbon-13 is contained in the natural gas brought up to the reservoir, eliminating (F) and (G). In order for the gas to rise upward through the material in which it migrates, it must be less dense than that material, eliminating (J). Therefore, (H) is the correct answer.
7. B
According to Scientist 2, microorganisms convert the carbon compounds and water into the hydrocarbons of natural gas. Carbon dioxide (CO2) (III) is a carbon-containing compound and could be involved in the formation of natural gas as described by Scientist 2. Neither F2 (I) nor KCl(II) are water or carbon compounds, eliminating (A), (C) and (D). Therefore, (B) is the correct answer.
Fighting Scientists Drill 2 (Chapter 23)
1. B
This paragraph is about three students’ explanations for effusion rates. In this passage, since the fighting scientists (in this case, fighting students) didn’t perform the experiment for which they’re offering competing explanations—the professor did—the question references the professor rather than the students. According to the passage, the time required for all 100 mL of the gas to effuse from the syringe into the empty flask was measured. As a result, the volume of gas in the flask continued to increase until all of the gas was emptied from the syringe. Therefore, the correct answer is (B).
2. F
Student 1 proposes that gases with greater molecular masses diffuse more slowly. Therefore, gases with smaller molecular masses diffuse more quickly. Of the choices listed, hydrogen gas (2.016 amu) possesses the smallest molecular mass and will effuse most quickly. Thus, (F) is the correct answer.
3. B
Student 1 proposes that gases with greater molecular masses diffuse more slowly. According to the results of the experiment, Gas A’s total effusion time is 4 seconds, and Gas B’s total effusion time is 16 seconds. The question states that nitrogen gas’ effusion time is 9 seconds—longer than Gas A’s total effusion time but shorter than Gas B’s total effusion time. Consequently, nitrogen gas’ molecular mass must be greater than Gas A’s molecular mass and smaller than Gas B’s molecular mass. Thus, (B) is the correct answer.
4. F
According to Student 2, gases with greater molecular volumes effuse more slowly. Table 1 shows you that xenon’s molecular volume is greater than krypton’s. Based upon this, krypton should effuse more slowly than does xenon and contradicts the claim made in the question. Thus, (F) is the correct answer.
5. A
Student 3 proposes that gases with greater densities effuse more slowly than gases with lesser densities. Table 1 says that xenon is denser than krypton and that krypton is denser than oxygen. Xenon, the densest gas, should therefore have the smallest relative effusion rate, while oxygen, the least dense gas, should have the greatest relative effusion rate. The relative effusion rate of krypton should be between the relative effusion rates of xenon and oxygen. Choice (A) correctly demonstrates this relationship between effusion rates.
6. J
Student 1 proposes that gases with greater molecular masses diffuse more slowly than gases with smaller molecular masses. Student 2 proposes that gases with greater molecular volumes effuse more slowly than gases with smaller molecular volumes. Student 3 proposes that gases with greater densities effuse more slowly than gases with lesser densities. According to Table 1, helium’s molecular mass and density is greater than hydrogen’s, while hydrogen’s molecular volume is greater than helium’s. Students 1 and 3, then, would predict that helium would effuse more slowly; Student 2 will predict that hydrogen will effuse more slowly. The professor’s experiment finds that Gas B effuses more slowly than Gas A. If helium were Gas B and hydrogen were Gas A, then Student 1’s prediction and Student 3’s prediction would be consistent with the professor’s finding, while Student 2’s prediction would not be. Thus, (J) is the correct answer.
7. C
Student 1 proposes that gases with greater molecular masses diffuse more slowly than gases with smaller molecular masses. Student 2 proposes that gases with greater molecular volumes effuse more slowly than gases with smaller molecular volumes. Student 3 proposes that gases with greater densities effuse more slowly than gases with lesser densities. According to the information provided in the table in the question and in Table 1, krypton’s molecular mass and density are greater than carbon dioxide’s, while carbon dioxide’s molecular volume is greater than krypton’s. Student 1 and Student 3 would predict that carbon dioxide effuses more quickly than krypton, yielding shorter effusion times for carbon dioxide. Student 2 would predict the opposite, that krypton would effuse more quickly than carbon dioxide, yielding shorter effusion times for krypton. Therefore, (C) is the correct answer.