GRE Premier 2017 with 6 Practice Tests
Part V. PRACTICE TEST
Chapter 21. Practice Test Answers
Answer Key
VERBAL REASONING 1
1. C
2. B
3. A, D
4. B, D
5. A, E, H
6. A, E
7. C, E
8. A, D
9. B, C
10.D, F
11.A
12.D
13.C
14.D
15.A, B
16.E
17.E
18.A, B
19.C
20.D
Answer Key
QUANTITATIVE REASONING 1
1. C
2. A
3. C
4. D
5. B
6. C
7. A
8. D
9. B
10.30
11.E
12.6
13.C
14.B, D
15.8
16.D
17.D, E
18.C
19.C
20.C, D
Answer Key
VERBAL REASONING 2
1. B
2. B, D, G
3. A, F, H
4. E
5. A, E, I
6. D
7. A, F
8. A, F
9. B, D
10.B, C
11.E
12.C
13.A, B
14.C
15.E
16.D
17.A
18.B
19.C
20.E
Answer Key
QUANTITATIVE REASONING 2
1. D
2. A
3. B
4. D
5. C
6. A
7. A
8. C
9. D
10.D
11.B
12.0.9
13.D
14.B, C, E
15.60
16.E
17.B, D
18.D
19.B
20.E
Answers and Explanations
ANALYTICAL WRITING 1: ANALYZE AN ISSUE
1. SAMPLE ESSAY RESPONSES
Issue Essay Sample Response: Score of 6
Note that your essay need not be perfect to receive a very high score. It just needs to be a very strong rough draft.
At face value, the belief that “one should look upon any information described as ‘factual’ with skepticism since it may well be proven false in the future,” seems ludicrous almost to the point of threatening anarchy. Yet not only does this belief prove well justified, it is also the linchpin around which our complex, highly technical society creates and consolidates its advances.
Science itself provides the best evidence and examples in support of this statement. One need look no further than contemporary medicine to see how far we have come from the days when illness was perceived as a sign of moral weakness or as a punishment from on high. In fact, the most outstanding characteristic of what we call “the scientific method” amounts to endless questioning of received theory in search of a more comprehensive explanation of what we perceive to be true. This iterative style of inquiry (and re-inquiry) perpetuates an ongoing scientific dialogue that catalyzes further breakthroughs in the developed world.
Furthermore, advances made through constant questioning are not limited to the scientific arena: the skeptical attitudes of ancient Greek philosophers, as well as those of Renaissance mariners, 19th century suffragists, and 20th century civil rights activists, have left the world a richer and more hopeful place. By refusing to accept the world as explained by contemporary “fact,” these doubters helped give birth to societies and cultures in which human potential and accomplishment have been enabled to an unprecedented degree.
In contrast, those societies that cultivate adherence to received belief and a traditional non-skeptical approach have advanced very little over the centuries. In Tibet, for instance, the prayer wheels spin endlessly around a belief system as secure and unquestioning as the Himalayas themselves. While there may very well be things worth learning from such a society, Tibet has proven to lack adaptability and expansiveness and prefers to turn inward, away from the modern world. Such introspection has given Tibet neither immunity nor an array of defenses in the face of contemporary medical, social, and political problems. Thus, cultural inflexibility regarding received wisdom and convention comes with a price.
To conclude, it seems clear from the above discussion that a healthy skepticism remains the hallmark of Western epistemology as we face the future. A close look at the statement reveals that it is not advocating the wholesale rejection of orthodox thinking, but rather that we be open to redefining our assumptions. As the basis of our resiliency and creativity, this attitude offers the most positive prognosis for a society that revels in the solution of conundrums that its own constant questioning brings continually into view.
Answers and Explanations
ANALYTICAL WRITING 2: ANALYZE AN ARGUMENT
1. Argument Essay Sample Response: Score of 6
Again, note that an essay need not be perfect (this one contains quite a few typos) in order to achieve a very high score.
In this memo, the owner of the Juniper Café; concludes that cutting hours is the “best strategy for us to save money and remain in business without having to eliminate jobs.” While the café ’s employees are undoubtedly grateful for the intent of the memo, they may see that its logic is flawed. First, the memo does not provide enough supporting evidence to prove that the money saved by cutting hours would exceed the money lost by losing early-morning and weekend clients. Second, the owner does not seem to evaluate other options that would either cut back on overhead or change the café’s operation to bring in more revenue.
First, the owner relies on an unproven assumption about the cause of the overhead. He concludes, without justifying, that being open too many hours is causing too much overhead expense. There may be other causes, however, such as waste in other areas of management. While it is true that reducing café hours would save money spent on utilities, employee wages, and other operating costs, there is no evidence that those savings would outweigh the café’s loss of business. The owner’s message fails to give details of operating costs, wages, and utilities saved if the café is closed for the hours suggested by the memo. Perhaps the highest utility expenses are actually incurred between noon and 3 p.m., when the sun is the hottest and the café’s air conditioning and refrigeration are most in use. The owner needs to do more research, including the habits and demography of the town. For example, since the café is located in the downtown area, perhaps increasing the number of hours the café is open would be a better solution.
Yes, it would cost more in overhead, but doing so might, in fact, make much more money for the café. Say, for instance, the Juniper becomes the only restaurant open on Friday and Saturday date nights, after the football games and movies let out. Second, the owner of the Juniper Café is not considering that the café serves a small American city. Cutting early-morning hours at a café, in a downtown area, where businesspeople and city workers most likely stop for coffee or breakfast on their way to work, seems very short-sighted and ill-informed. Are there one or more other cafés that will gladly steal business from 6 a.m. to 8 a.m. weekdays and that will perhaps win the permanent loyalty of those customers for lunch and dinner?
Furthermore, the owner does not seem to have evaluated other options to save the café. There are other places where overhead costs could potentially be cut. Certainly the owner would benefit from a brainstorming session with all employees, to get other ideas on the table. Maybe a new, lower-rent freezer storage facility is nearby. Maybe employees can suggest cutting waste in the purchasing department or dropping services the café doesn’t need. It stands to reason that there is a plurality of ways to decrease overhead, aside from simply cutting hours.
In conclusion, the memo as it stands now does not logically prove that reduction in those particular hours will result in financial and future success for the café. There are several unstated assumptions upon which the argument turns, principally the assertion that simply being open for a certain number of hours is causing crippling overhead expenses. The owner’s argument would profit enormously from further research, which may affect the hours he chooses to cut. Customer polling could show that few people eat or want coffee in that part of town between 2 p.m. and 5 p.m., and the café could be closed between lunch and dinner, adding flex hours or overlapping shifts for the staff. The memo lacks outlining what other restaurant services are available in the area and how or if they affect the 6 a.m. to 8 a.m. block and weekend hours. Once the marketing research and brainstorming is complete, the owner of the Juniper Café will make a better informed choice for his café’s operating hours.
Answers and Explanations
VERBAL REASONING 1
1. CThis particular sentence has no detour road signs. Here the key phrase is “known for their devotion to their masters,” so you might predict that the missing word means something like “loyalty” or “devotedness.” The correct answer, (C) fidelity, is a close match for this prediction.
2. BThis sentence contains a detour road sign, “nonetheless,” so you can expect the first part of the sentence to contrast with the fact that Larkin “maintained a spirited correspondence with a wide circle of friends.” So you might predict that the missing word means something like “withdrawn” or “shy.” Choice (B) matches this prediction: “By nature reclusive, Philip Larkin nonetheless maintained a spirited correspondence with a wide circle of friends.” That makes perfect sense.
3. A, DThe road sign “because” in the first half of this sentence tells you that the second half will continue the thought of the first. The second half indicates that there was “no way to predict” the decision-making process’s outcome, so a description of the process as “random” makes sense. The prediction matches (A) arbitrary, meaning “determined by chance, whim, or impulse.” Choice (B) regimented, meaning “rigidly organized,” means the opposite of what the sentence requires. Choice (C) unilateral, meaning “relating to only one side,” is also incorrect—the fact that the decision-making process may have been entirely in the hands of one person does not logically lead to there being “no way to predict its outcome.” The sentence compares the decision-making process to throwing dice, so a good prediction would be, “making decisions was similar to throwing dice.” The best match is (D) likened to. Choice (E) belittled by doesn’t make sense in context, and (F) dissimilar to means the opposite of what the sentence requires.
4. B, DLook at blank (ii) first. The tax burden of most of the citizens comes from an “unvarying” tax, so the legislation mentioned earlier in the sentence must have had a minor effect on the middle class. (D) negligible matches perfectly. The road sign “although” indicates contrast, so the bill that produced “negligible” results must have been expected not only to have a significant effect, but a positive one. A prediction is “optimism” or “praise.” (B) acclaim works best. (C) hullabaloo and (A) commotion are tempting choices, but they do not have sufficiently strong positive connotations, particularly as the bill is described as having been “heralded.”
5. A, E, HThe three blanks are related in this sentence: blank (i) causes blank (ii) and prevents blank (iii). In the first blank, only an (A) established viewpoint could potentially (E) skew the reader’s opinion, and an (A) established viewpoint would logically exclude an (H) impartial viewing. With the information given, only established, skew, and impartial logically follow each other.
6. A, EThis is a high-difficulty sentence, but elimination and prediction will help you out a great deal. The first clause and then the road sign “therefore” suggest that the clause with the blanks will provide an alternative to the fact that moving away from fossil fuels is insufficient to stabilize carbon emissions. Blank (ii) has a meaning similar to “store,” so eliminate (F) liberate. (D) incarcerate means to put in prison and refers to people, not substances, so it cannot be correct. (E) capture matches. For blank (i), notice that the technologies must also be for “storing” carbon waste. Choices (B) reduction and (C) diminution can be eliminated. Choice (A) sequestration matches the prediction of “storing” and is correct.
7. C, ETo figure out what fits in the blank, note the detour road sign “although” between the first and second halves of the sentence. This tells you that what came before will be contradicted by what comes after. The first clause tells you that Handy’s nickname is “self-conferred,” so you can speculate that not everyone shares Handy’s self-assessment. You could paraphrase the sentence this way to predict the blank: “Handy feels he’s the father of the blues, but other musicians ‘disagree.’” You’re looking for a synonym for “disagree.” You can eliminate choices (A), (D), and (F), which say that Handy’s moniker was professed, proven, or demonstrated—they mean the opposite of what you want. Choice (B), which states that Handy’s nickname was widely deconstructed, or “examined,” could be right since other musicians came up with a different opinion, so keep it as a possibility. Choice (C), disputed, has exactly the meaning you need, so keep this, too. That leaves choice (E) contested, which produces a sentence with the same meaning as choice (C), so (C) and (E) are the correct answers.
8. A, DIn this sentence, which has no road signs, read for key words and what’s implied (i.e., for logic). When an “expectation of instant gratification” isn’t fulfilled, a feeling of disappointment would ensue. So the answer choices have to mean “disappointment.” You can eliminate choices (B) and (E), endearment and elation, right away since they have the opposite meaning. Choice (F) pacifism, “an opposition to war of any kind,” isn’t right for this sentence—an unreturned message would cause conflict in a relationship, rather than promote peace. Choice (C) recompense means “compensation” and can also be eliminated. That leaves (A) and (D), chagrin and vexation, both of which match the prediction and have the right meaning for the sentence.
9. B, CThis is an intriguing sentence since the answer choices include two arcane words, augmented and meliorated. A good strategy for questions like this is to use the process of elimination on the answer choices. First, look at what the sentence implies, paraphrase it, and predict the answer: “The zookeepers are ‘changing’ the exhibit to handle more visitors.” All the answer choices except (D) and (F), maintained and neglected, express change, so eliminate those two. Of the remaining choices, (A) and (E), abridged and truncated, mean “to make shorter,” which, when applied to the sentence, wouldn’t help the exhibit accommodate more traffic. The final choices are (B) and (C), which are two high-level vocabulary words (meaning “added to” and “improved,” respectively) and the correct answers.
10.D, FWithout structural road signs, you need to see if paraphrasing or key words can help you find synonyms. Scientists have observed odd fish behavior that precedes seismic events—the fish jump out of the water. Your paraphrase and prediction might look something like this: “Scientists ‘theorize’ that fish respond to physical precursors of seismic events.” Both choices (D) and (F), hypothesize and contend, fit this definition, and are therefore the correct answers. Choice (A) repudiate means to reject an idea, not present one. Scientists don’t authorize information, so choice (B) is also incorrect. Choice (C) foresee does imply prediction, but one based on intuition, not on observed behavior. Finally, it wouldn’t make sense for scientists to (E) question their own prediction in this context.
11.AYou’re asked to find the statement or statements that have direct support in the passage. The last sentence in the passage states that most orders are not exclusively beneficial or exclusively parasitic, but include species with both characteristics. That’s choice (A). Choice (B) is too extreme, since the author speaks of minimizing harm to other species, not eliminating it. Choice (C) presents a scenario that’s the opposite of what the passage expresses: facilitating the development of parasitic insects isn’t in line with the goal of controlling pest species.
12.DThe word “extirpation” means “destruction” or “cutting out” or “uprooting.” The phrase “protecting benign native insect species” implies that entomologists are trying to prevent these ecosystem-balancing species from destruction. Obliteration, choice (D), is a good description of what they’re trying to avoid. (A) intrusion might be tempting because ecosystems are sometimes protected from human activity altogether, but it is the species that is being protected from extirpation, not the ecosystem. Choices (B) excision and (E)ablation both refer to the surgical removal of tissue, another meaning of “extirpation” but not in accord with the context here. Choice (E) uprooting means pulling up a plant by the roots. This is yet another meaning of “extirpation” but again does not fit the context.
13.CIn this Function question, you have to characterize the relationship between the two highlighted phrases. The conclusion of this passage is that the Easter Rising was a key turning point in the battle against English rule. Thus, the first phrase, which calls the Easter Rising a “landmark event,” is a paraphrase of the author's main conclusion. The second highlighted phrase, which calls the battle a “failure,” would seem to contradict the conclusion that the battle was a positive turning point. The contrast key word “while,” which precedes the second highlighted phrase, emphasizes the contradictory nature of the Easter Rising. Choice (C) matches both halves of the prediction perfectly. Choice (A) calls the first phrase evidence, which is incorrect. Choice (B) flips the two phrases’ roles. Choice (D) refers to intermediate conclusions, which neither of the phrases is. Finally, choice(E) refers to an “outside position,” which the passage does not have.
14.DThis Global question asks you to sum up the passage’s purpose. The author’s tone is one of explanation rather than argument, so you can rule out (A) arguing that . . . and (E)persuading readers . . . right away. The passage explains how the terms Persian and Iranian intersect and provides two perspectives on why one term might be preferable to the other. That’s choice (D). The author does not mention the fall of the Persian Empire, so choice (B) is incorrect. Although three groups are mentioned, the author doesn’t focus on differentiating among them, so (C) isn’t the best summary of the passage, either.
15.A, BTo select the correct choices, you must identify the groups to whom the term Persian applies according to the passage. Since both Iranian and Afghani people may use the descriptor, the woman in (A) could be described as Persian. The first sentence says that both Iranian immigrants and U.S.-born Iranian Americans identify as Persian, so the man in (B) also fits the criteria. However, it is clear that the term refers to heritage or citizenship or both, so it would not be accurate to describe someone of English descent who is an American citizen, choice (C), as Persian.
16.EThe verb “cites” indicates that this is a Detail question, so look directly in the passage for the answer. The first two lines of the passage state that Iranian Americans call themselves Persian, and “this descriptor is a frequent cause of confusion among non-Persians.” Bingo. Choice (E) is a perfect match. Choice (A) is a misused detail. It’s a reason why some people oppose the use of the term Persian, not a reason why non-Persians are confused by the term. Similarly, choices (B), (C), and (D) all relate to arguments about whether the term Persian should be used; none of them have anything to do with the cause of some non-Persians’ confusion, which is what the question asks for.
17.EThe question asks which choice is most analogous in meaning to the highlighted sentence, “To look feminine, fashionable sixth-century women would achieve the same ideal by bleeding themselves.” All the choices are about animals, not people, but only (E) contains an analogous situation: self-destructive physical harm to (allegedly) produce an image befitting one’s gender. Choice (A) mentions light and dark coloring, which the passage does discuss, but it’s not analogous to the highlighted sentence in meaning. The second choice, (B), concerns camouflage only. While (C) includes self-destructive physical harm, that harm is inflicted for survival purposes, not for the sake of appearing more masculine or feminine. The opening phrase of (D) sounds like the highlighted sentence, but the remainder of this answer choice discusses a naturally occurring trait, not a self-inflicted one.
18.A, BThe author describes several societies in which women lightened their skin as dictated by the fashion of the time, but she also cites a culture in which darker colors were preferred (Persians with henna dye). Hence, choice (A) is correct. The passage states that in 13th-century Italy, the use of makeup was a sign of social status, so choice (B) is correct. The passage begins with the Greco-Roman societies, but it doesn’t say whether the practice of lightening skin originated there, so (C) is incorrect.
19.CFor varied reasons—to flaunt affluence (A), to attract attention (D), and to look feminine (E)—most of the societies described in the passage preferred white color or paleness on women’s faces. These three choices are thus incorrect. The Egyptians preferred a light foundation also, but of a golden hue, so (B) is incorrect. In this passage, only the Persians went for a darker look with henna dye in their hair and on their skin to “summon the majesty” of the earth. Choice (C) is therefore a reason for preferring artificially darker rather than lighter skin, and it is the correct answer.
20.DThe passage discusses a particular “ism” (a theory or concept) called solipsism, which is the view that oneself is the only object of real knowledge or that nothing but the self exists. The best answer to the question, then, is (D), presenting the definition of a concept. Choice (A) is close, except that solipsism is a belief, not a phenomenon, which is an observable fact or event that can be scientifically described. The author doesn’t “refute” anything, so (B) is incorrect. Also, there are no key words, such as “conversely” or “on the other hand,” to indicate “contrasting” schools of thought, so (C) is incorrect. The phrase “a physical object to a person” describes what the author means by “anything else” and is not the basis of any comparison, so (E) is incorrect.
Answers and Explanations
QUANTITATIVE REASONING 1
1. CRight triangles ABD and CDB share a hypotenuse, segment DB. The shared hypotenuse should clue you to use the Pythagorean theorem. See that w and x are lengths of the legs of right triangle ABD; side AD has length w, side AB has length x. Also, y and z are lengths of the legs of right triangle CDB; side CD has length z, side CB has length y. Where a and bare lengths of the legs of a right triangle, and c is the length of the hypotenuse, a^{2} + b^{2} = c^{2}. So here w^{2} + x^{2} = length BD^{2}; y^{2} + z^{2} also equals length BD^{2}. The quantities are equal, and the answer is (C).
2. AYou have x + 4y = 6 and x = 2y, and you want to compare x and y. Let’s start by finding y. Substitute 2y for x in the first equation and get 2y + 4y = 6 or 6y = 6. Divide both sides by 6 and get y = 1. If y = 1 and x = 2y, as the second equation states, x must equal 2. Because 2 is greater than 1, Quantity A is greater.
3. CThe problem doesn’t say how many employees work at the firm, so let’s pick a number. Since the problem involves percents, let’s pick 100 as the total number of employees.
If there are 100 employees working at the firm, then one quarter of them, or 25, are managers. That leaves 75 employees, one-third of which, or 25, are assistants. Consequently, 100 − 25 − 25 = 50 employees are left to be technicians. Now check the quantities. Quantity A, the number of managers, is 25. Quantity B, half the number of technicians, is half of 50, which is also 25. Pick (C) the two quantities are equal.
4. D
To make the quantities look as much alike as you can, use FOIL to multiply out Quantity A. You’ll multiply a × b, 1 × b, 1 × a, and 1 × 1 and get ab + a + b + 1. Quantity B also has ab + 1. Quantity A has the additional terms a and b. There is no information given about possible values for a or b. Because a + b could be positive, negative, or zero, a relationship cannot be determined, and the answer is (D).
You can also use Picking Numbers; let a = 1 and b = 2. Then Quantity A is (1 + 1)(2 + 1) = 6 and Quantity B is (1 × 2) + 1 = 3. In this case, Quantity A is greater. But if you let a= −1 and b = −2, you have Quantity A = (−1 + 1)(−2 + 1) = 0 and Quantity B = (−1 × −2) + 1 = 3. In this case, Quantity B is greater. You have demonstrated that a definite relationship cannot be determined, leading to answer choice (D).
5. BIn the two-digit number jk, the value of digit j is twice the value of digit k. You have to compare the value of k in Quantity A with 6 in Quantity B. If you plug in 6 for k, it is not possible to enter “twice the value of the digit k” for the digit j. That is because j can only be a single digit; it cannot be 12. In other words, k has to be something less than 6, so the answer must be (B). The value in Quantity B is greater.
6. CHenry purchased x apples, and Jack purchased 10 apples less than one-third the number of apples Henry purchased. One-third of means the same as one-third times, and the number of apples Henry purchased is x. Thus, this boils down to You can plug this in for Quantity A. We have in Quantity A and in Quantity B. Now you can clear the fraction in Quantity B. Let’s split Quantity B into two fractions: Leave the alone and cancel the factor of 3 from the numerator and denominator of and you’re left with What’s It’s one-third of x. So Quantity A equals while Quantity B also equals and the answer is (C).
7. AThe figure shows a circle with diameter 8. The circumference of the circle is therefore 8π. Since the 90° central angle cuts a quarter of the circle, the length of arc QRS must likewise be a quarter of the circumference. Quantity A is therefore one-quarter of 8π, or 2π. Because π is a positive number, 2π must be greater than 2. Pick (A) Quantity A is greater.
8. DYou can suspect (D) because there is a range of possible values for the variables. In Quantity A, you have the volume of a rectangular solid with length 5 feet, width 4 feet, and height x feet. The formula is length times width times height, so the volume is 5 times 4 times x, or 20x. The volume of Quantity B is therefore 10 times 8 times y, or 80y. If 4 < x< 6, then the range of values for Quantity A is 80 < V < 120. If 1 < y < 2, then the range of values for Quantity B is 80 < V < 160. Since the two ranges overlap, it’s possible that the two quantities are equal or that one is greater than the other. So, the correct answer is (D).
9. B
The goal is to find x, the measure of one of the angles formed by the intersection of ST and PT. Now angle QRS is labeled 80°. You also know PQ and ST have the same length and QR and RS have the same length. If you add PQ and QR, you get PR. If you add ST and RS, you get RT. If you add equals to equals, you get equals, so PQ + QR must be the same as ST + RS, which means that PR and RT are the same. Thus, you have isosceles triangle PRT, and you’re given one angle that has measure 80 and a second angle that has measure x. The angle measuring x is opposite equal side PR. That means the other angle must have the same measure. The sum of the interior angles in a triangle always equals 180°. Thus, x + x + 80 must equal 180, 2x = 100, and x = 50. The answer is (B).
10.30This is a permutation problem because the order in which the duo is chosen matters. The producer has two slots to fill. For the lead role, there are 6 people to choose from. For the supporting role, there will be 5 people to choose from. So the number of possible duos is 6 × 5 = 30.
11.E
The question asks for the number of different dinners Jane could make. Since the order of the selections in the dinner doesn’t matter, this is a combination problem. But it involves three possible combination types: Veg, Meat, Meat; Veg, Veg, Meat; or Veg, Veg, Veg. We must calculate the possibilities for each type of combination and then add the results to find the total number of different combinations possible.
Let V represent vegetarian and M represent meat.
Then with V, M, M, she has 5 choices for the vegetarian (she must choose 1) × 4 choices for meat (she must choose 2).
For V, V, M, she will choose 2 from among 5 for the vegetarian and 1 among 4 for the meat.
If she goes with V, V, V, the all-vegetarian menu, she will choose a subgroup of 3 from among 5 vegetarian choices.
If n and k are positive integers where n = k, then the number of different subgroups consisting of k objects that can be selected from a group consisting of n different objects, denoted by nCk, is given by the formula
Here the total number of different possible servings for a plate is (_{5}C_{1})(_{4}C_{2}) + (_{5}C_{2})(_{4}C_{1}) + (_{5}C_{3}).
Now _{5}C_{1} represents choosing 1 type of vegetable selection from 5 different types, so _{5}C_{1} = 5. (The formula also gives this result.) Now we use the formula to find the next two combinations:
Here _{4}C_{1} corresponds to choosing 1 type of meat selection from 4 different types, so _{4}C_{1} = 4. Then we use the formula again:
So the number of different possible dinners of these three items is 5 × 6 + 10 × 4 + 10 = 80, choice (E).
12.6You could find the number of tasks per hour from one computer, but that would add extra steps, because you want to find out how many computers you need to do a certain number of tasks in three hours. Well, if the computer can do 30 tasks in six hours, it can do 15 tasks in three hours. So, two computers could complete 30 tasks in that time. Three computers could do 45; four could do 60; five could do 75; six could do 90. You can’t get by with five computers because you have to get 80 tasks done, so you’ll need 6computers.
13.C
Picking Numbers is the best strategy, since there are variables in the question and the answer choices. If c = 3, then 2c = 6. There are two integers between 3 and 6, so plug c = 3into the answer choices to see which one is equal to 2.
1.
2. 3 ≠ 2
3. 3 − 1 = 2
4. 3 − 2 ≠ 2
5. 3 + 1 ≠ 2
The only answer choice that equals 2 when c = 3 is (C), so (C) is correct.
14.B, DYou’re asked to find what could be; that tells you there may be more than one possible value for You’re told the ratio of 2a to b is 8 times the ratio of b to a. That’s awkward to keep track of in English—it’s a little easier to write fractions. The ratio of 2a:b equals So, or Cross multiply to get 2a^{2} = 8b^{2}, or a^{2} = 4b^{2}. Multiply each side of the equation by This is the same as Take the square root of both sides of the equation: The ratio of b to a is or So, (B) and (D) are the answers. This problem is also a great candidate for Backsolving, although since this question could have more than one correct answer, you would need to test all answer choices to see which ones work out.
15.8
It is given that the area of triangle ABC is 35, and in the diagram, you’re given a height for triangle ABC. If you use BC as the base of the triangle, the triangle’s height is 7, so you can find the length of BC. The length BC, which is the base of triangle ABC, is also the hypotenuse of right triangle BDC. Given the hypotenuse and the length of leg BD, which is given in the diagram as 6, you’ll be able to find the third leg of the triangle, side DC, which is what you’re looking for.
Going back to triangle ABC, the area is 35 and the height is 7. The area of a triangle is so is 35. Therefore, BC is 35. That means 7 × length BC is 70, so BC must have length 10. Now look at right triangle BDC. Here is a right triangle with one leg of length 6, the hypotenuse of length 10, and the third side unknown. That’s one of the famous Pythagorean ratios—it’s a 3:4:5 triangle. So DC must have length 2 × 4, or 8.
16.DFirst, find the value of m. You are told that 3m is 81. Well, 81 is 9 × 9 and 9 is 3^{2}. So you have 3^{2} × 3^{2} = 81 or 3 × 3 × 3 × 3 = 81. There are four factors of 3 in 81, so m has the value 4. Now 4^{3} is 4 × 4 × 4 is 64. So (D) is correct. Note that (A) is a trap—that’s the value of m, not m^{3}.
17.D, E
The problem states that x is between 0 and 1, so x must be a positive fraction (or decimal) less than 1. We can pick a number to get to the correct answer(s) here because both the question and the answer choices have variables. The decimal 0.5 is in the middle of the given range, so it’s a good starting point.
(A) Incorrect. Doubling any positive value always produces a greater value, not a lesser value.
(B) Incorrect. 2 × 0.5 = 1; a smaller fraction could make this statement true, but our correct answer(s) must always be true.
(C) Incorrect. 2 × 0.5 = 1; a larger fraction could make this statement true, but our correct answer(s) must always be true.
(D) Correct. 0.5^{2} = 0.25; the square of any number between 0 and 1 (exclusive) will be less than the original number. This example illustrates that property.
(E) Correct. 0.25 < 1; the square of any number between 0 and 1 (exclusive) will be less than 1. This is an example of that property. So, the correct answers are (D) and (E).
18.CTo find how many categories had energy use greater than 150 million kilowatt-hours, you have to find out how many total kilowatt-hours were used in that year using the line graph. You see that 600 million kilowatt-hours were used in 1995. What is the relationship of 150 million kilowatt-hours to 600 million kilowatt-hours? It’s 25% of 600 million kilowatt-hours, so you’re looking for categories with more than 25% of the energy use for 1995. How many categories exceeded 25%? Just two, government and industrial. So your answer is (C).
19.CTo find the per capita, or per person, personal energy use in Country Y in 2005, divide the personal energy use by the number of people. Since the question gives you the population—500 million people—you only need to find the personal energy use.
According to the top graph, total energy use in 2005 was about 675 million kilowatt-hours. According to the bottom graph, personal energy use was about 20% of the total, or 675 × 0.20 = 135 million kilowatt-hours. Divide this number by the population of Country Y in 2005: 135 million kilowatt-hours divided by 500 million people = 0.27 kilowatt-hours per person, or choice (C).
20.C, D
Since this is an all-that-apply question, check each choice systematically.
Choice (A): According to the bottom graph, energy for farm use decreased from 30% to 20% of the total between 1990 and 1995. Since 30 is 50% greater than 20, total energy use would have had to increase by at least 50% to compensate. The top graph shows that it did not, so choice (A) is incorrect.
Choice (B): According to the bottom graph, energy for farm use decreased from 20% to a little more than 10% of the total between 1995 and 2000. Since 20 is double 10, total energy use would have had to nearly double in order to compensate—that definitely did not happen! Choice (B) is out.
The bottom graph shows that energy for farm use, as a percentage of the total, increased from 2000 onward. Since total energy use increased every year, total farm energy use must have increased also. Thus, without any calculation, you know that choices (C) and (D) must be correct.
Answers and Explanations
VERBAL REASONING 2
1. B“Instead” is a detour road sign that tells you that the second half of the sentence will say the opposite of the first half. That means diversification shouldn’t “divert” the organization, so you’re looking for a word that means the opposite of “divert”. The answer is (B) furthering, which means “advancing or promoting.” (A) undermining, (C) retracting, and (E)deterring are all the opposite of what you need—they say that diversification will negatively affect the historical purpose. Choice (D) classifying doesn’t make sense in context.
2. B, D, G
The best way to approach the first blank is to consider the logic of this sentence and predict an answer. A “keen” sense of smell is a positive attribute. What should a bee with a keen sense of smell be able to do with regard to kin and foe? To (A) promulgate is to make known, in the sense of “to announce.” (B) discern means “to perceive or recognize.” And (C) arbitrate means “to decide between disputants.” A bee would want to “recognize” friend from foe, whether or not it did either of the other two things, so (B) discern is the correct choice.
The road sign “by contrast” tells you that some other ability is not as good. Indeed, the bees have a “deficiency” of some kind, specifically one that makes them unable to protect themselves from disease. Which phrase most closely describes the desired response? Any of the three answer choices could work, but, as we said in the strategies section, the question gives you clues. Read the third sentence to see if the answer becomes clear. When you do, you’ll note the key words “various diseases” matches one of the second blank’s answer choices, pathogens. Let’s hold on to (D) for now.
The third sentence is a bit convoluted, and some of the answer choices are uncommon words, so paraphrase it to put it into simpler terms and predict the answer: “Bees ‘protect’ their colony through grooming behavior.” Only one of the answer choices, (G) minimizes incursions by, fits our prediction. If you substitute the other terms into the blank and reread the sentence, you can confirm (G) as the correct choice; neither (H) implicates replication of or (I) simulates action by makes sense in context.
Now that we have two of the blanks filled, we can return to blank (ii). When we read (D) pathogens into the sentence, the three sentences make sense together, and (D) is correct.
3. A, F, H
The key word in this sentence is “crisis.” You need adjectives and verbs that play well off of it. If you don’t know the meaning of exigent, you can use the process of elimination to identify the right answer. (B) cretaceous means “chalky,” and one wouldn’t describe a need as chalky.
You can eliminate (C) specious—it means “false” and is the opposite of what you’re looking for. That leaves (A) exigent, which means “immediate.” It is the correct answer.
Which of the actions would be required in a situation of “critical necessity”? Recall that there is a water crisis, so the resource involved is water. The word ineffable means “unable to be expressed,” so it makes no sense in this context. However, if you didn’t know that word, you could use the process of elimination to narrow your choices. If there were a water crisis, water would not be abundant, so you can eliminate (E). That leaves (F) mobilize limited resources. “Limited” makes sense in the context of a crisis, so it is the correct choice and a solid guess if you weren’t certain of the meaning of choice (D).
If you’re galvanizing political efforts to stave off a crisis, it’s likely you would want to (H) focus, or concentrate, international attention on water use. (G) foment, “to incite,” and (I)ferment, “to brew,” both have connotations about creating; neither makes sense in context, so both are incorrect.
4. EThe detour road sign “although” contrasts the honor Pétain received for World War I with what he “incurred” during World War II. The sentence’s structure implies that the word in the blank will have a negative charge, so you can rule out the positive answer choices (A) status (“relative rank in a hierarchy”) and (C) kudos (“congratulations”). Choice (B)reputation doesn’t make sense—one earns a reputation; it is not “incurred”. Choice (D) recompense doesn’t make sense either, since the French wouldn’t compensate someone for a dishonorable action. That leaves you with the correct answer, (E) obloquy, “disgrace or public censure.” One would heap obloquy on a person who’s done something hateful, like collaborating with the enemy.
5. A, E, I
This is a long set of sentences, so you should paraphrase them to make the topic easier to get a handle on: “Although people don’t think of cellophane as paper, this material is made from the same stuff as paper bags. It was invented to prevent stains, but its usefulness became and resulted in a product.”
For the first blank, you’re looking for a term that describes cellophane. Even if you don’t know what cellophane is, the key words “transparent, plasticky film” provide a great prediction for the blank. The correct answer is (A) diaphanous, which means “see-through.” Choice (B) standardized has nothing to do with transparency. Choice (C) opaquemeans the opposite of what you need.
After Jacques saw how useful cellophane was, he decided to patent it. For the second blank, therefore, predict a word like “visible” or “evident.” Choice (E) apparent is a great match. Choices (D) marketable and (F) fashionable may be true of cellophane, but the second blank describes the utility of cellophane, not cellophane itself. It wouldn’t make sense to say that cellophane’s utility became “marketable to” or “fashionable to” the very person who invented it.
Having filled in the first and second blanks, you quickly test the third. Nothing in the sentences describes cellophane as (G) amorphous, “shapeless,” so eliminate it. Choice (H) is a trap—don’t confuse ingenuous, or “innocent,” with “ingenious,” or “brilliant.” You would expect a product with “overwhelming usefulness” to be (I) ubiquitous, “available everywhere,” and that’s the correct answer.
6. DFrom the detour road sign “unlike,” you can tell that Hume isn’t trying to determine whether an objective reality exists. Why wouldn’t he do so? Following this logic reveals the right word for the sentence. Hume disregarded objective reality not because he thought the issue was (A) pragmatic, “practical,” or (B) challenging. That would have made him want to investigate it. He probably didn’t try because he felt that the issue was either unverifiable or uninteresting. Choice (D) insoluble, “not capable of being solved,” fits the blank best. It’s unclear that Hume would be “unlike most other philosophers” if he thought the issue was (C) theoretical or (E) esoteric (“understood only by a select few”), so both are incorrect.
7. A, F
This is a long sentence and the blank occurs in the middle, so paraphrase it. As you do so note that the phrase “even though” is a detour road sign that indicates a contrast. A good paraphrase is, “People smoke, even though nicotine has a effect on their health.” You are looking for a pair of synonyms that have a negative tone and mean something like “bad” or “harmful.” Choices (A) deleterious and (F) pernicious both mean “harmful,” so that’s the correct pair. Choice (B) addictive is a property of nicotine, but the sentence deals with nicotine’s harmfulness, not its addictiveness. Choices (C) anemic, meaning “weak,” and (E) benign, meaning “harmless,” are contrary to the prediction. Finally, choice (D) antagonistic, meaning “hostile,” is a tempting trap. While “hostile” is a negatively charged word, being hostile is not the same as causing harm.
8. A, F
The phrase “to the public’s great shock” is a key phrase—it tells you there’s a contrast between what was expected (“peaceable reform”) and what really happened. The correct answers must mean something like “violent rebellion.” Contumacious is a difficult vocabulary word, so we’ll use the process of elimination to go through all the answer choices. Choice (B) endemic means “inherent,” which doesn’t fit the context of the sentence. Choices (C) and (E), erratic and irresolute, both mean “unpredictable” or “uncertain.” If you weren’t sure of irresolute, consider its root, resolute, and think of a similar word, resolution in this case. A resolution is something you commit to doing, and irresolute is its opposite, “unsure” or “unable to make a decision.” These two words are plausible choices because they imply that the group didn’t fulfill its promises, but they don’t work in context. You need a contrast with “peaceable reform,” something that would result in people’s shock—unpredictability and uncertainty aren’t shocking.
Choice (D) estimable, “worthy,” means the opposite of what you want. If you didn’t know the meaning of this word, you could consider its root, esti. Think of words with a similar root that you can define, such as esteem. Knowing that esteem has a positive tone, you could deduce that estimable does as well, making it incorrect. That leaves you with choices (A) and (F)—contumacious and seditious—both of which mean “rebellious” and are the correct choices.
9. B, D
Some of the answer choices are fairly difficult words, but you can tell from the key word “concealed” that you want a word negative in tone. Based on that, two words pop out from the answer choices, (B) artifice and (D) chicanery, both of which are negative and both of which mean “deception.” But you should go through the answer choices one at a time to confirm your selections.
Choice (A) cabal means “a secret group,” and it doesn’t work in context.
Choice (B) artifice sounds a lot like a word you’re probably familiar with—“artificial,” which means looking like one thing while actually being another. Artifice means “trickery.” “Photo retouching and inflated claims” are forms of trickery, so this is one of the correct answers.
If you don’t know the meaning of the word hegemony (C), put it aside until you go through the other answer choices. Choice (E) dominance means “supremacy” or “domination,” and it doesn’t make sense in context. Eliminate it. Choice (D) chicanery also means “deception and trickery,” so it’s also correct. To determine the meaning of imprecation, choice (F), think of a word with a similar root. One is “precarious,” which means “dangerous.” Are advertising ploys dangerous? No. This word is too extreme to work in context. That leaves you with only hegemony outstanding. Even if its meaning is unclear, you have, through the process of elimination, two synonymous answer choices that fit well in context, and you should go with them. Hegemony means “influence” or “dominance.” If you knew this definition, you’d know that hegemony is a synonym for another answer choice, dominance, and this is another example of a question with two sets of synonyms in the answer choices.
10.B, CWhile this sentence includes a classic detour road sign, “however,” its structure is such that you can’t identify what “however” is contradicting. As you’ve learned from Kaplan’s strategies, key words can help you figure out the missing word in a sentence. The key words in this sentence are “conservative” and “unreceptive.” You need to predict the kind of joke a conservative audience at a charity event would receive poorly. Choice (A) plucky means “brave,” so eliminate it. Choices (B) and (C)—ribald and coarse—both mean “vulgar.” These are likely correct, but continue to test the other choices before answering definitively. Choices (D) and (F)—traitorous and treacherous—are synonyms that mean “disloyal.” Although the performers betrayed the spirit of the event, this is not the meaning of the words needed to describe the jokes. Choice (E) politic means “diplomatic.” This has the opposite meaning of the word you’re looking for, so eliminate it. The correct answers are ribald and coarse.
11.EThe first highlighted sentence expresses the passage’s main idea (sharks are different from other fish), and the second highlighted sentence explains one of the ways in which this is true (they have livers, not swim bladders). That’s choice (E). Since no opposing perspective is included, you can rule out (A). Choice (B) reverses the roles of the two sentences; the second sentence supports the first, not vice versa. No opposing argument is addressed, and the author forms no intermediate conclusion, so (C) and (D) are incorrect.
12.CThis Inference question asks you to consider the information in the passage and speculate about the events that may have preceded those described. The phrase “for themselves” implies the patrons’ ability to locate their own books, so it follows that they would previously have needed assistance from librarians, choice (C). The passage says that Dewey was the first standardized method, but you have no basis to assume that no classification method existed before, (A). Similarly, nothing suggests that libraries kept their methods confidential, (B). Although Dewey helped patrons find materials themselves, no information in the passage implies that this change affected librarians’ jobs directly, so you can eliminate (D). As for choice (E), the passage implies that patrons may have had difficulty locating items, but to say that they were never able to understand any given library’s system is too extreme.
13.A, BA lower risk of fatal disease meant that vaccination was safer than inoculation, so (A) is correct. Since the passage mentions “enormous variations” between batches of inoculum, the “standard dose” used in vaccines would be more likely to be consistent, so (B) is also correct. Choice (C) is incorrect because it deals with tuberculosis inoculations, which are beyond the scope of the passage.
14.CThis question refers to the second half of the second sentence, which begins, “Modern epidemiologists believe . . .” This sentence uses both the word “contract” and “contracted,” and the meaning in context is the same for both. The passage discusses the process of inoculation: patients are given a mild case of the illness against which they wish to develop immunity. The sentence referred to by the question describes the effectiveness of the procedure in further detail: because the patients got the disease through their skin instead of through inhalation, it was less likely to be fatal. To form a prediction for the answer, you could read the sentence, substituting the simple words “got,” “received,” or “caught” for the word “contracted.” The answer choices all represent possible meanings of the word “contracted,” but only choice (C) acquired matches your prediction for a word that could substitute logically into the sentence as written.
15.EThe passage as a whole is concerned with how to come up with a good definition of tragedy. The author leads into Scylla and Charybdis by mentioning “overly broad definitions” and “overly narrow ones,” respectively. Just afterward, she calls this situation a “definitional dilemma.” From these clues, you’re thus led to infer that Scylla and Charybdis are names for the dangers that may befall anyone who tries to come up with a good definition of tragedy. (E) is in line with this inference and is correct. (A) cannot be correct because Terry Eagleton begs off providing a good definition in the first place. He seems to think that the task is simply impossible. So broad and narrow definitions, represented by Scylla and Charybdis, respectively, are not signs of Eagleton’s principal faults. (B) is outside the scope of the passage. The author is making no larger claim about the significance of myth. Similarly, (C) is outside the scope. While Scylla and Charybdis are drawn from myth, they in no way establish that Eagleton’s dilemma has its origins in myth. Like (B) and (C), (D)is also outside the scope. Because the author makes no reference to other intellectual inquiries, you have no reason for believing that they are applicable to the case at hand.
16.DWhat is the main point of the passage? It is to criticize two authors’ views of tragedy (paragraphs 1–2) and to generate a new necessary condition for tragedy (paragraph 3). The choice that most closely matches this understanding is (D). Consider that (A) is too narrow: Mandel isn’t even mentioned by this choice, despite the fact that he is the “main character” in the passage. The problem with (B) is that it includes Eagleton in the author’s criticism of Mandel. In other words, the author does criticize Mandel for not providing all the necessary conditions for tragedy. But she does not have anything explicit to say about whether Eagleton falls prey to the same problem. Consequently, (B) is a distortion. Moreover, it is incomplete as it leaves out the author’s own criterion, set forth in the final paragraph, for what constitutes tragedy. Choice (C) is the opposite of what the author says. The author implies throughout the passage that tragedy is definable. Though she pokes holes in both theorists’ accounts, the author seems, if anything, more sympathetic to Mandel, who thinks that tragedy is definable, than she is to Eagleton, who does not. (E), finally, is a distortion: the author takes issue with Mandel’s view that tragedy requires the “inevitability requirement.” She does not find fault with his view that tragedy requires great suffering.
17.AThis question tests your ability to identify GRE vocabulary words within the Reading Comprehension portion of the exam. At the very least, you should be thinking that the author liked, esteemed, and pitied these characters. She says as much when she describes them as being “well-educated, tireless, but spiritually drained” (lines 44–45). The only answer that comes close is (A) laudatory, meaning “worthy of praise.” Choice (B), conciliatory, means “intending to placate,” so this does not work. Choice (C), despondent, means “very sad.” You could infer that the characters themselves are despondent, but “the author’s attitude” is surely not despondent. Therefore, (C) is incorrect. Choice (D) myopic means “shortsighted,” and that has nothing to do with the passage before you, let alone the author’s attitude toward the protagonists in this work, so it can be eliminated. And (E) diffident means “modest” or “timid,” and that’s not on target. In sum, none but (A) rings true.
18.BThis Inference question is essentially asking you to consider not only what Eagleton and Mandel have in common, but also what they do not. What do they have in common? According to the author, they don’t give us an adequate conception of tragedy. And now what are the main differences between them? They take different approaches to the task, with Eagleton throwing his hands up and saying, in effect, that tragedy can’t be defined and Mandel digging his heels in and saying that it can. (B) captures what they share (that is, failure) and what they differ on (that is, the reasons for their respective failures). Regarding (A), the author does not think that their ideas should be dismissed. Why would she have bothered methodically working through their ideas in the first place if this was her attitude toward their ideas? No, clearly she thinks that much can be learned from them. Thus, (A) is the opposite of what the passage says. As for choice (C), the author’s ultimate assessment is that neither Eagleton’s nor Mandel’s view will do. What’s more, the passage never states whether the first thing about sadness should be weighed as heavily as the second thing about inevitability. For both of these reasons, (C) can’t be inferred. (D) is incorrect because you can’t validly infer from the fact that a work is very sad that the heroes have necessarily suffered greatly. In Eagleton’s view, the fact of great suffering is, at best, probable and not certain. The key word in (E) is combines. The author does examine different thinkers’ ideas, but her strategy is not to combine those ideas; her strategy is to criticize these ideas. Consequently, (E) can’t be inferred.
19.C
In this question, you should only look at paragraph 3. Make sure that “present conception of tragedy” refers to Mandel’s view. Think about what the opening sentence is doing: it’s making clear to you the author’s chief complaint with Mandel. And then consider that the rest of the paragraph is trying to provide evidence for the complaint already mentioned.
Thus, (C) is correct. No such luck with (A). Don’t be fooled: all talk of genre and influence goes beyond the bounds of the passage. You run into a similar problem with (B). The author has nothing to say about aesthetic value, supreme or otherwise. In sum, (A) and (B) are outside the scope. On the face of it, (D) looks pretty good. True, the author is worrying about something in Mandel’s definition. However, she is not taking issue with all three criteria—only with one criterion (the inevitability requirement). Consequently, (D) is incorrect. Turning to (E), we don’t see much to recommend it. For one thing, the author is not defending conclusions (she is, as the question tells you, simply voicing dissatisfaction). For another, she is not pointing out a trap that Mandel is falling into.
20.E
To begin with, understand the scope of the question squarely before you. The question has to do with the whole passage, not with one of its parts. Now think about the first two requirements. The first is that the protagonist is worthy of esteem; the second that he or she suffers greatly. Ask yourself: What do you think the author’s opinion about these two requirements is? Does she like them? Dislike them? It’s the first: she most likely thinks that they are good things. Evidence for the first part of this conclusion can be found in paragraph 3 where the author seems to look favorably on the characters in the modern tragedy Three Sisters. (E) puts this point even more delicately by making us see that both requirements are OK so long as they don’t contradict the condition of powerlessness. Therefore, (E) is the correct answer.
(A) is the opposite of the correct answer. The author provides no reason to believe that these requirements would not fit with the condition of powerlessness. With respect to (B), the first condition isn’t at all at odds with the condition of powerlessness. The author implies as much in paragraph 3 when she shows that good characters in works of tragedy necessarily feel powerless. (C) is also incorrect. From all that you read in paragraph 3, you can reasonably conclude that the sisters do suffer a good deal. That leaves you with (D)to consider. (D) is without question quite tempting. Yet it goes outside the scope of the passage to say that both requirements should not figure prominently. You have reason to believe that they should figure in some way, but we can’t know for sure how prominently they should figure. The answer is (E).
Answers and Explanations
QUANTITATIVE REASONING 2
1. DThe perimeter of ABC is 40 and the length of BC is 12, and you want to compare the length of AB with 14. In an isosceles triangle, there are two sides with equal length, but you don’t know whether side BC is one of those sides or not. If side BC is the unequal side, there are two unknown sides plus 12, and they have a sum of 40, the perimeter. The two remaining sides have a sum of 28, so each is 14. That would mean that AB and AC would have length 14. Then the answer would be (C). If BC is one of the equal sides, however, there are two sides with length 12 and a third unknown side, and the sum is 40. Because 12 + 12 is 24, the third side has length 16. AB could be one of the sides of length 12 or the side of length 16. There are three possible lengths for side AB—16, 14, and 12—so the answer is (D).
2. APlug 0.5 in for x and solve. f(0.5) = (0.5+3)^{2} = 3.5^{2} = 12.25. This is greater than 9, so the answer is (A).
3. B
In both quantities, use the basic formula: rate × time = distance. In Quantity A, 40 mph × 4 hours traveled gives you 160 miles. In Quantity B,
As 175 is greater than 160, the answer is (B).
4. DQuantity A cannot be precisely defined, but Quantity B can. The grape bag weighs 50 grams, and each grape weighs exactly 1 gram, so there must be 50 grapes in the bag. Quantity B is 50.
Now consider Quantity A. If every cookie in the bag is on the lighter end, weighing only 5 grams, then the number of cookies in the bag is 300 divided by 5, or 60. If, contrarily, the bag is full of the heaviest cookies in town, each weighing 15 grams, then there are 300 divided by 15, or 20, cookies in the bag. Thus, Quantity A is somewhere between 20 and 60, which means it could be less than, equal to, or greater than Quantity B. You have no idea which is the case, so pick (D).
5. C
Here you have triangle ABC—base BC has been extended on one side and there is an exterior angle drawn in and labeled 120°. You want to compare side lengths AB and BC. In any triangle, the largest side will be opposite the largest angle, so you want to see which of these sides is opposite a larger angle. Angle A is labeled 60°, but is angle C less than, equal to, or greater than 60? Notice that the adjacent angle is 120°—the two together form a straight line, so their sum is 180°. And 180 − 120 = 60, so angle C is a 60° angle. Since the angles are equal, the sides are equal, and the answer is (C).
6. ANotice the way the diagram is set up: a + b is the same as PQ. The equation is 8a + 8b = 24. Divide both sides by 8. You end up with a + b = 3. PQ is 3 and because 3 is greater than 2, the answer is (A). Note that you did not have to solve for a or b individually.
7. AAll you know is that x is less than y, but even though you don’t know their values, you know enough to determine a relationship. In Quantity A, you have y − x, the larger number minus the smaller number, so you must get a positive difference, even if both numbers are negative. In Quantity B, you have the smaller number minus the larger number—this time the difference is negative. So you can determine a relationship—you know the answer is (A), Quantity A is always greater than Quantity B.
8. CThe area of a triangle equals . Triangles ACE and ABD have the same height, because they have the same apex point A. The problem states that their areas are equal, so they must have the same base, too. Thus, EC = DB and ED = CB. Since triangle ABE is equilateral, you also know that AE = AB. This means that sides AD and AC are equal as well. If they weren’t, one of ED or CB would have to be longer than the other, and you already know they’re equal. The answer is (C).
9. DIf the radius of each circle is 3, then the diameter of each circle is 6. Then PS and QR each equal 6, and PQ and SR each equal 12. The perimeter of rectangle PQRS = 6 + 12 + 6 + 12 = 36. The answer is (D).
10.DIn this question, you have a fraction as a base and must consider various values for x, the exponent. Consider what happens when x = −1. We know that Putting that into the full equation, we get This is not greater than zero, and if x = −2, the result will be even lower, so choices (A) and (B) are out. Next, consider what happens when x = 0. Any base to the zero power equals 1; then You want the value of x that makes the expression greater than 0, so try x = 1: . The answer is (D).
11.B
Begin with cross multiplication and use algebra to isolate
7(p − q) = 2p |
Cross multiply. |
7p − 7q = 2p |
Remove parentheses. |
5p = 7q |
Add 7q; subtract 2p on both sides. |
Divide both sides by 7p. |
Choice (B) is correct.
12.0.9
The shaded region is a right triangle. So, use the numbers on the grid to calculate the base and height of the triangle. The length horizontally is (−2.0) − (−0.5) = −2.0 + 0.5 = −1.5. Distances are always positive, so use 1.5 as the base of the triangle. The height of the triangle is 1.6 − 0.4 = 1.2. Use the equation for the area of a triangle:
The area is 0.9.
13.D
The question asks for the number that is 850% greater than 8 × 10^{3}. First, determine the value of 8 × 10^{3}. That number is 8,000. To 8,000, you need to add 850% of 8,000. Here’s what the math looks like:
8,000 + (850% × 8,000) = 8,000 + (8.5 × 8,000) = 8,000 + 68,000 = 76,000
In scientific notation, this is 7.6 × 10^{4}, choice (D).
14.B, C, E
List the factors for each number to check for all correct choices.
Number |
Factors |
Number of Factors |
4 |
1, 2, 4 |
3 |
6 |
1, 2, 3, 6 |
4 |
8 |
1, 2, 4, 8 |
4 |
12 |
1, 2, 3, 4, 6, 12 |
6 |
14 |
1, 2, 7, 14 |
4 |
So the correct choices are (B), (C), and (E).
15.60
You’re trying to find the shortest distance in meters a person would walk to go from point A to a point on side BC of the triangular field represented in the diagram. To get the shortest distance from point A to side BC, draw a perpendicular line from point A to side BC. Call the new vertex point D. Now two smaller right triangles, ADC and ADB have been created.
From the diagram, length BC is 160 meters, AB is 100 meters, and AC is 100 meters. Each of the two right triangles formed has 100 meters as the length of its hypotenuse. What does that tell you about triangle ABC? AB and AC have the same length, so this is an isosceles triangle. That means that when you drew in the perpendicular distance from A down to D, you split the isosceles triangle ABC into two identical right triangles. Length BD is the same as length CD. So each of them is half of 160 meters, or 80 meters. Each right triangle has an hypotenuse of 100 meters and one leg of 80 meters. This is a 3:4:5 right triangle, with each member of the ratio multiplied by 20. So AD must have length 60, and the minimum distance is 60 meters.
16.EThe average is Here you have y − z and the other number, which you can call x. The average of x and y − z is 3y, so Multiplying both sides by 2 gives 6y = x + y − z. Subtracting y − z from both sides gives 5y + z = x. So the other number, x, is 5y + z, answer choice (E).
17.B, D
Test each point. Substitute a value for x and compare the result to the given value for y in the ordered pair.
Let x = −3.
Let x = −2.
Let x = −1.
Let x = 1.
Let x = 3.
So, the correct answers are (B) and (D).
18.DYou’re looking for the lowest ratio of males to females. In the double bar graph, the males outnumber females in each double bar, so you want the specialty in which the numbers of males and females are closest. Skimming the bar graphs, you can see that in pediatrics, the female graph and the male graph are closer than any of the others. (D) pediatrics is the correct answer.
19.B
How many male general surgery physicians were under 35 years old? The pie chart breaks down general surgery physicians by age, so work with that. And because you’re looking for a number of general surgery physicians, you know that you’re going to have to find the total number of general surgery physicians and then break it down according to the percentages on the pie chart.
The number of female general surgery physicians in the under-35 category represented 3.5% of all the general surgery physicians. What this does is break that slice of the pie for under-35 into two smaller slices, one for men under 35 and one for women under 35. Now the whole slice for under-35-year-olds is 30% of the total, and the question states that the number of females under 35 is 3.5% of the total. So the difference between 30% and 3.5% (26.5%) must be the men in the under-35 category.
From the top graph, estimate the total number of general surgery physicians as 37,000 (35,000 male plus 2,000 female). Multiply 37,000 by 26.5%: 0.265 × 37,000 = 9,805, which is very close to (B), the correct answer.
20.EThe bar graph doesn’t give the total number of general practice physicians, but if you add the number of males to the number of females, you get the total number of GP physicians. To find the percent who are male, take the number of males and put it over the total number. There are about 2,000 women and about 23,000 men, making the total about 25,000. Well, if there are around 25,000 GP physicians altogether and 2,000 of them are female, that’s around 8%. About 92% are male, which is closest to 90%, (E).
Diagnostic Tool
Tally up your score and write the results below.
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Total
Total Correct: out of 80
By Section
· Verbal Reasoning out of 40
· Quantitative Reasoning out of 40
Analytical Writing Scoring Rubric
1. 6:
“Outstanding” Essay
· Insightfully presents and convincingly supports an opinion on the issue or a critique of the argument
· Communicates ideas clearly and is generally well organized; connections are logical
· Demonstrates superior control of language: grammar, stylistic variety, and accepted conventions of writing; minor flaws may occur
2. 5:
“Strong” Essay
· Presents well-chosen examples and strongly supports an opinion on the issue or a critique of the argument
· Communicates ideas clearly and is generally well organized; connections are logical
· Demonstrates solid control of language: grammar, stylistic variety, and accepted conventions of writing; minor flaws may occur
3. 4:
“Adequate” Essay
· Presents and adequately supports an opinion on the issue or a critique of the argument
· Communicates ideas fairly clearly and is adequately organized; logical connections are satisfactory
· Demonstrates satisfactory control of language: grammar, stylistic variety, and accepted conventions of writing; some flaws may occur
4. 3:
“Limited” Essay
· Succeeds only partially in presenting and supporting an opinion on the issue or a critique of the argument
· Communicates ideas unclearly and is poorly organized
· Demonstrates less than satisfactory control of language: contains significant mistakes in grammar, usage, and sentence structure
5. 2:
“Weak” Essay
· Shows little success in presenting and supporting an opinion on the issue or a critique of the argument
· Struggles to communicate ideas; essay shows a lack of clarity and organization
· Meaning is impeded by many serious mistakes in grammar, usage, and sentence structure
6. 1:
“Fundamentally Deficient” Essay
· Fails to present a coherent opinion and/or evidence on the issue or a critique of the argument
· Fails to communicate ideas; essay is seriously unclear and disorganized
· Lacks meaning due to widespread and severe mistakes in grammar, usage, and sentence structure
7. 0:
“Unscorable” Essay
· Completely ignores topic
· Attempts to copy the assignments
· Written in a foreign language or contains undecipherable text