8. The correct answer is (D). To answer the question, there’s no way around doing some pencil-work. You need to solve for x in each equation, then square it. Let’s start with statement (2), which is a bit easier to work with: 2x 1 5 5 1 2x 524 x 522 x 2 5 4 Now let’s tackle statement (1), which presents a more complex equation: ~x 2 3! 2 5~x 1 7! 2 ~x 2 3!~x 23!5~x 1 7!~x 1 7! x 2 2 6x 1 9 5 x 2 1 14x 1 49 20x 5240 x 522 x 2 5 4 As you can see, both statements provide essentially the same information about x. With either statement, you can answer the question. Hence the correct answer is choice (D). 9. The correct answer is (E). Referring to the ice cream flavors as A, B, C, and D, there are 10 possible two-scoop combinations: A 1 either A, B, C, or D B 1 either B, C, or D C 1 either C or D D 1 D For each of these 10 combinations, either of two toppings can be used. Thus, the total number of different types of sundaes is 20. 10. The correct answer is (B). You’re looking for the point at which the dotted line (ABC’s stock price) is furthest above the solid line (XYZ’s stock price). The dotted line lies above the solid line only during the second half of the 2nd quarter and the first half of the 3rd quarter; the end of the 2nd quarter marks the greatest difference between prices during that period. At that time, ABC stock was priced at approximately $7.60, while XYZ stock was priced at approximately $5.00 per share. The difference between those two prices is $2.60. answers practice test 4 Practice Test 4 543 www.petersons.com 11. The correct answer is (A). For each investment, calculate the dollar increase in value (approximating percent gains in share price will suffice): (A) The investment amount was $1500 (500 shares at $3 per share). The share price increased by about 50%, for about a $750 gain. (B) The investment amount was $500. The share price increased by about 100%, for about a $500 gain. (C) The investment amount was $1000. The share price decreased (by about 35%). (D) The investment amount was $1100 (200 shares at $5.50 per share). The share price increased by almost 50%, for nearly a $550 gain. (E) The investment amount was $150. The share price increased by just under 400%, for nearly a $600 gain. 12. The correct answer is (E). The two statements provide identical information—that the point defined by the xy pair (0,2) lies on line L. Knowing only one point on a line is insufficient to define the line. 13. The correct answer is (C). Statement (1) alone does not suffice to answer the question; x and y could each be either positive or negative. Nor does statement (2) alone suffice, since no information about the value of y is provided. Statements (1) and (2) together establish that 21 , y , 1, and hence that x . y. 14. The correct answer is (B). By definition, 5(x 1 y) is divisible by 5, but you also need to know whether z is divisible by 5. Statement (1) provides no additional information. However, statement (2) alone is sufficient to answer the question. A quantity that is divisible by 5 added to another quantity, z, divisible by 5 results in a sum that is divisible by 5. (If x and y both equal 0, then 5(x 1 y) 1 z 5 z.) 15. The correct answer is (B). The width of the door is 60 inches (5 feet), and its length is 80 inches (6 feet, 8 inches). This is a 6:8:10 triangle (conforming to the 3:4:5 Pythagorean triplet), with a diagonal of 100 inches, or 8 feet 4 inches. 16. The correct answer is (A). Since the base numbers 9 and 11 appear in both the numerator and denominator, you can cancel 9 9 and 11 9 : 9 11 3 11 9 11 11 3 9 9 5 9 2 11 2 5 81 121 17. The correct answer is (D). Since 3a 5 90, a 5 30. Since 5b 5 90, b 5 18. Thus, ab 5 (30)(18) 5 540. 18. The correct answer is (C). You can determine the average of a, b, and c if you know their sum. Statement (1) alone tells you that the sum of a and b is 10, but it provides no information to help you determine the value of c. Statement (2) alone tells you nothing about the value of either a or b, but it provides the value of c. Together, the two statements allow you to determine the sum of the three terms (10 1 9) and in turn their mean: 10 1 9 3 5 19 3 . 544 PART VI: Five Practice Tests www.petersons.com 19. The correct answer is (B). Although statement (1) tells us the sum of b and f,ittells us nothing about their individual values or the size of the other angles. Now consider statement (2) alone. In any triangle, the sum of the measures of the three angles is 180°. Thus, the bottom angle of the top triangle must measure 70°. Notice that ∠ABC is vertical to that 70° angle, which means that ∠ABC also measures 70°. Now you have the information you need to answer the question. Referring to DABC, we know that c 1 d 1 70 5 180. Accordingly, the sum of c and d must be 110. 20. The correct answer is (A). Multiply both sides of the equation by –1, and reverse the inequality. Then, solve for x: 2x , 5 x , 5 2 21. The correct answer is (C). The area of a circle is pr 2 . The area of a circle with a radius of x is px 2 , which is given as 4. The area of a circle with radius 3x is p(3x) 2 5 9px 2 . Therefore, the area of the larger circle is 9 times the area of the smaller circle, or 36. 22. The correct answer is (B). Assign a “weight” to each of the three salary figures (to save time, express all numbers in thousands): 5(150) 5 750 3(170) 5 510 1(180) 5 180 Then determine the weighted average of the nine salaries (again, express all numbers in thousands): 750 1 510 1 180 5 1440 1440 9 5 160 23. The correct answer is (A). First, combine the two terms inside the radical. Then, remove perfect squares from inside the radical: Î x 2 36 1 x 2 25 5 Î 25x 2 1 36x 2 ~36!~25! 5 Î 61x 2 ~36!~25! 5 |x| ~6!~5! Î 61 1 5 x 30 = 61 24. The correct answer is (C). Statement (1) alone provides no information about the number of painters in relation to the number of sculptors. Statement (2) alone provides no information about the total number of painters and sculptors. However, both statements together tell you the number of painters at the fair. Why? The 14 sculptors who are also painters along with the 7 that are not adds up to 21. Thus, there must be 37 painters at the fair (23 of whom are not sculptors). answers practice test 4 Practice Test 4 545 www.petersons.com 25. The correct answer is (B). You can solve this problem algebraically. But it’s quicker and easier to work backward from the answer choices. First, test choice (A): $3000 at a 5% rate earns $150 interest. The remainder of the $10,000 is $7000. At a 6% rate, that amount will earn $420. The total interest earned would be $570, which does not match the $560 figure given in the question. Next, try choice (B): $4000 3 0.05 5 $200, and $6000 30.06 5 $360. Total earned interest 5 $200 1 $360 5 $560, which matches the figure given in the question. 26. The correct answer is (C). Statement (1) alone is insufficient to answer the question. A quadrilateral with a longer perimeter than another might have a greater area than the other. But a longer perimeter does not necessarily create a larger area. For example, visualize a rectangle with width approaching zero (0) and length approaching infinity. The rectangle’s perimeter is great, while its area approaches zero (0). Statement (2) alone provides no information for comparing the size of the two quadrilaterals, and thus is obviously insufficient to answer the question. Considered together, however, the two statements do suffice to answer the question. The larger a square’s perimeter, the larger its area. 27. The correct answer is (C). First apply the defined operation N to each parenthesized pair: (21 N 22) 521(21 2 [22]) 521(1) 521 (1 N 2) 5 1(1 2 2) 5 1(21) 521 Then apply the defined operation again, substituting 21 for both x and y: (21 N 21) 521(21 2 [21]) 521(0) 5 0 28. The correct answer is (D). The degree measure of minor arc AB is the same as the degree measure of the central angle that forms it (∠AOB ). The key to this problem is that OA ≅ OB. (Each of these two line segments is the circle’s radius.) Given statement (1) alone, DOAB must be equilateral, and all angle measures are 60°. Now, consider statement (2) alone. Since OA ≅ OB, the angles opposite those sides are also congruent—that is, m∠OAB 5 m∠OBA. Based on statement (2), both angles measure 60° and, accordingly, so does ∠AOB—the central angle that defines minor arc AB. 29. The correct answer is (E). To determine the maximum value of h, answer the question: “9 is 15% of what number?” To find the answer, divide 9 by .15 (or 900 by 15). The quotient is 60. (This is the maximum number of horses that competed.) Similarly, to determine the minimum value of h, answer the question: “9 is 30% of what number?” To find the answer, divide 9 by 0.3. The quotient is 30. (This is the minimum number of horses that competed.) Including the greatest and least possible values of h (60 and 30), there are 31 possible values of h. 30. The correct answer is (E). First, order the numbers you know from least to greatest: {7, 10, 10, 12, 15}. Since distribution Q contains an even number of terms (including x), the median is the arithmetic mean (simple average) of the two middle terms. Thus, if x 5 12, the median would be 11 (the average of 10 and 12). The same would be true for any value of x greater than 12. However, if x , 12, then the median of Q must be less than 11 (the average of 10 and some number less than 12). 546 PART VI: Five Practice Tests www.petersons.com 31. The correct answer is (D). The key to handling this question is to convert ratios to fractional parts that add up to 1. The ratio of X’s rate to Y’s rate is 3 to 1, and the ratio of Y’s rate to Z’s rate is 1 to 2. You can express the ratio among all three as 3:1:2 (X:Y:Z). Accordingly, Y’s production accounts for 1 6 of the total widgets that all three machines can produce per day. Given that Y can produce 35 widgets per day, all three machines can produce (35)(6) 5 210 widgets per day. 32. The correct answer is (D). Points (21,21) and (2,21) connect to form a horizontal line segment of length 3. Similarly, points (2,3) and (25,3) connect to form a horizontal line segment of length 7. Since the two segments are parallel, the resulting quadrilateral is a trapezoid. The vertical distance between the two parallel segments is 4. Apply the formula for a trapezoid’s area (AB and CD represent the two parallel segments, and h is the quadrilateral’s height): A 5 AB 1 CD 2 3 h A 5 3 1 7 2 3 4 A 5 20 You can also plot the quadrilateral on the grid, divide it into a right isosceles triangle and one rectangle, then calculate the area of each one. (The rectangle’s area is 12, and the triangle’s area is 8.) 33. The correct answer is (A). Solve this problem using the basic probability formula: winner card total cards 5 1 6 In this case, total cards (the fraction’s denominator) equal 25 1 160, less the number of “Try Again” cards to be removed (let x this number): winner card total cards 5 25 25 1~160 2 x! 5 1 6 Solve for x (use the cross-product method to clear fractions): 25 25 1~160 2 x! 5 1 6 25 1 160 2 x 5 150 2 x 5235 x 5 35 34. The correct answer is (B). Statement (1) alone establishes no clear pattern for the series. For example, each successive number might exceed the previous number by 300, or it might be a multiple of the previous number. Statement (2) alone establishes the pattern—a constant multiple of three from one number to the next in the series. (The ninth number must be 150, the eighth number must be 50, and so on.) answers practice test 4 Practice Test 4 547 www.petersons.com 35. The correct answer is (A). Apply the cross-product method to eliminate fractions. Rewrite the equation in unfactored form. (If you recognize the difference of two squares, you’ll rewrite more quickly.) Simplify, and then solve for x: x~x 1 y!5~x 2 y!~x 1 y! x 2 1 xy 5 x 2 2 y 2 xy 52y 2 x 52y 36. The correct answer is (E). Each of the four outer surfaces of the cube is 9 square inches with the other two being 8 (subtract one for the hole), and so the cube contains a total of 52 square inches of outer surface area. Each of the four inner surfaces (inside the hole) accounts for an additional 3 square inches—for a total of 12 square inches of inner surface area. The solid’s total surface area 5 52 1 12 5 64 square inches. 37. The correct answer is (C). Statement (1) alone provides no information about actual price. Statement (2) alone provides no information about the change in price. Together, however, the two statements establish that the price was $2.10 on January 1, and, with this information, you can determine the percent decrease. (The answer to the question is the percent equivalent of the fraction 20 210 .) Verbal Section 1. D 2. B 3. B 4. C 5. B 6. D 7. E 8. D 9. C 10. C 11. A 12. D 13. A 14. E 15. A 16. C 17. C 18. D 19. C 20. C 21. B 22. D 23. C 24. A 25. E 26. A 27. D 28. C 29. B 30. E 31. E 32. C 33. D 34. A 35. B 36. E 37. A 38. B 39. D 40. E 41. A 1. The correct answer is (D). The original version contains a subject-verb agreement error: the singular noun need should take the singular verb is rather than the plural form are. Also, the grammatical element need for should not be split. Choice (D) corrects both problems by replacing are with is and by reconstructing the underlined part. 2. The correct answer is (B). In the underlined part, the three listed items are not grammatically parallel. Choice (B) solves the problem by omitting the word its. Choices (D) and (E) also fix the faulty parallelism. However, choice (D) omits the word other, thereby implying that museums and libraries are not cultural institutions—which they are, of course, as the original sentence points out—while choice (E) is unnecessarily wordy. 548 PART VI: Five Practice Tests www.petersons.com 3. The correct answer is (B). The passage’s first two sentences, considered together, suggest that the manufacturers probably knew about the risk to public health but, to save money, decided to emit the harmful chemicals anyway. In all likelihood, then, it’s more important to them that they save money than help ensure that their chemicals do not harm the neighboring public. 4. The correct answer is (C). Although the original version is grammatically correct, the fact is superfluous and can simply be omitted. Choice (C) provides an even more concise alternative. 5. The correct answer is (B). The argument relies on the assumption that job applicants know which employers regularly investigate employee medical histories and which ones don’t—but disregard this distinction in deciding to which companies they’ll apply. Choice (B) directly refutes this assumption. 6. The correct answer is (D). One of the judging criteria is flavor. If the judges prefer the flavor of cherry pie over other flavors, this fact would increase the likelihood that a cherry pie will win the contest. Admittedly, flavor is only one judging criterion. Nevertheless, choice (D) is the best of the five answer choices. 7. The correct answer is (E). The author cites “Migrant Mother” as an example of “[h]er finest images” (line 16)—i.e., as an example of one of her best photographs. 8. The correct answer is (D). The passage provides absolutely no information about Lange’s motives or reasons for accepting her FSA commission. 9. The correct answer is (C). Admittedly, choice (C) is not an ideal characterization of the passage, which seems more concerned with Lange’s work than with making a broader argument about the power of pictures. Nevertheless, the author does allude to Lange’s ability to convey a need for social change through her photographs. Accordingly, the passage can be characterized as presenting one example (Lange) to support the broader point suggested by choice (C). 10. The correct answer is (C). The original version incorrectly uses their instead of they’re (they are). Choice (C) rephrases the idea in a clear manner. Choice (B) alters the meaning of the original sentence. In choice (D), explain why the difference is not idiomatic (why should be omitted). Choice (E) commits the same usage error as the original version. 11. The correct answer is (A). The original sentence is perfectly fine. The singular pronoun it refers properly to the singular course. And a great deal is idiomatic. 12. The correct answer is (D). In the original sentence, two main clauses are incorrectly separated only by a comma, without an appropriate connecting word after the comma. Choice (D) inserts the word and, which makes sense in context—providing an appropriate rhetorical balance between the ideas in the two clauses. Although their levels of radiation is a bit wordier than radiation levels, the phrase is clear and grammatically correct. answers practice test 4 Practice Test 4 549 www.petersons.com 13. The correct answer is (A). Choice (A) is irrelevant to the argument, without certain additional assumptions. Even if the same writers who write for television also write for movies, the passage provides no information about whether these writers would also strike against movie studios. Even if they would, we are not informed how the impending strike might affect the quality of new movie screenplays, if at all, and how this outcome might in turn affect movie-theater attendance and profits, if at all. (All of the other answer choices are necessary assumptions.) 14. The correct answer is (E). A typical weekend horse show generates more revenue than a typical weekend market. Hence, increasing the number of weekend horse shows is the surest way, among the five choices, for Alpha to maximize revenue—especially if the number of days per year that the grounds are used as a market would at least remain the same, as choice (E) suggests. 15. The correct answer is (A). In the first paragraph, the author points out how a land-based perspective can lead to the wrong conclusion about corals—stated more generally, how people’s perceptions of other habitats (the ocean) are influenced by their own environment (the land). Choice (A) expresses this broad point of the paragraph. 16. The correct answer is (C). In the second paragraph, the author tells us that there’s a functional relationship between lichen and its photosynthesizing organism (which the author does not identify or discuss) that is similar to the functional relationship between corals and zooxanthellae. 17. The correct answer is (C). The passage’s second paragraph indicates that corals provide zooxanthellae “certain by-products of the coral’s metabolism . . . which zooxanthellae require to grow and reproduce.” 18. The correct answer is (D). Choice (D) is the best answer because it substantiates an assumption that is necessary for the argument. Unless it is possible to build more new homes in Ocean View to begin with, the argument’s proposal—to build new homes that are affordable—would be impossible to implement. Choice (C) tends to show that Ocean View workers, as a group, prefer home ownership over renting. To this extent, choice (C) strengthens the argument that if Ocean View homes were more affordable, then Bayview workers would buy them. But the argument does not depend on an oversupply of rental housing; hence, choice (D) is a better answer. 550 PART VI: Five Practice Tests www.petersons.com 19. The correct answer is (C). According to the argument, any person eligible for the internship program is likely to gain admission to the local law school if he or she applies, and some people eligible for the program are among this year’s Faimount College graduates. It follows logically that some of this year’s Faimount College graduates are likely to gain admission to law school if they apply. To follow these logical steps, it helps to express the premises and conclusion symbolically, as follows (E 5 eligible for the program), A 5 likely to gain admission to law school, F 5 Faimount College graduate this year): Premise: All E are A. Premise: Some E are F. Conclusion: Some F are A. Choice (C) provides the above conclusion. None of the other choices provides a valid conclusion. 20. The correct answer is (C). The first clause in the original version is a dangling modifier; what is considered the most unforgiving course is never mentioned in the sentence. The sentence should be reconstructed to eliminate this problem. Only choice (C) corrects this problem without creating another one. 21. The correct answer is (B). There are two problems with the original version. First, is proved is an improper verb form (is proven is the correct present-perfect form). Also, be a cause of is wordy. Choice (B) corrects both problems. So does choice (D); however, the resulting sentence is nonsensical, suggesting that drugs (rather than researchers) do the proving. 22. The correct answer is (D). Choice (D) actually strengthens the argument, insofar as by prolonging life the new drugs would make it possible for the elderly to develop even more new ailments. (The argument does not equate health with prolonged life.) 23. The correct answer is (C). The argument relies on the unstated assumption that the funds used to maintain the roads would be available for the education program should the ordinance be repealed. Choice (C) provides evidence that this assumption is a reasonable one; if the roads are of no other practical use, then there would be no need to continue to spend county funds to maintain them. Choice (D) does admittedly lend some measure of support to the argument. Common sense tells us that the education program would be effective only if the group of individuals whom it is designed to benefit actually benefit from it. However, we are not informed whether the entire population is in fact susceptible to Smith’s Disease. Without this additional information, it is impossible to assess the degree to which choice (D) strengthens the argument. 24. The correct answer is (A). Although the original version uses the passive voice, the sentence contains no grammatical or diction errors. Choices (B) and (C) both create dangling modifiers. In choice (B), who is it that devises? In choice (C), who are they? Choice (C) is also wordy. In choice (D), access becomes devised is very awkward. Choice (E) replaces the plural verb are with the singular form is. However, the noun means is plural in context and therefore should take the plural form are. answers practice test 4 Practice Test 4 551 www.petersons.com 25. The correct answer is (E). The sentence begins with the modifying phrase Contrary to earlier physicists The main clause should begin by indicating who it is that is “contrary.” Choices (B) and (E) both reconstruct the underlined part to clarify the reference. However, choice (E) is more graceful and concise. 26. The correct answer is (A). The passage explains how and why the various groups named in choices (B) through (E) have a stake in the current forms of aid. Environmentalists are not among them. In fact, in the first paragraph, the passage indicates that bankers, governments, and others should adopt the environmentalist philosophy of “small is better” in order to combat poverty more effectively. The implication here, if any, is that environmental groups would be philosophically opposed to the current forms of aid. 27. The correct answer is (D). In the second paragraph, the author strongly recommends programs that provide “simple agricultural technology” including “implements”—which means agricultural tools. The other answers are examples of the massive development projects the author rejects as ineffective. 28. The correct answer is (C). Throughout the passage, the author describes the current ineffective programs and explains how, in his opinion, they ought to be changed in order to have a greater impact on the hunger problem. Choice (C) essentially provides this recap of the passage. 29. The correct answer is (B). In stating, “Ultimately, however, means must be found to make it contrary to anyone’s interest to keep others poor,” the author strongly implies that developed countries are unlikely to implement the various reforms suggested in the preceding paragraphs unless and until those reforms are in their own economic self-interest—rather than in the interest of alleviating hunger. In other words, developed countries are unwilling to make “true sacrifices.” 30. The correct answer is (E). Any information that helps determine the actual cause of the immediate performance boost will help evaluate the researcher’s hypothesis. Of the five avenues of investigation listed, only choice (E) will yield this type of information. If it turns out that a new chain reduces gear friction, thereby allowing the cyclist to ride just as fast but with less effort, then this fact would help disprove the researcher’s hypothesis—especially if friction increases materially during the first three weeks of use. 31. The correct answer is (E). This argument relies on the general assumption that all other factors in the incidence of lung cancer will remain unchanged in the near future. Choice (E) provides information that, if true, directly refutes this assumption. 32. The correct answer is (C). There’s no need to refer to the jury’s award just before mentioning the award. Choice (C) is less repetitive but still makes the sentence’s meaning clear. So does choice (E); however, choice (C) is more concise. 33. The correct answer is (D). The original version incorrectly uses itself (instead of themselves) to refer to the plural antecedent stories. Also, although outside itself is acceptable, else is also appropriate and is more concise. Choice (D) fixes both problems. 552 PART VI: Five Practice Tests www.petersons.com . number less than 12). 546 PART VI: Five Practice Tests www.petersons.com 31. The correct answer is (D). The key to handling this question is to convert ratios to fractional parts that add up to. problems by replacing are with is and by reconstructing the underlined part. 2. The correct answer is (B). In the underlined part, the three listed items are not grammatically parallel. Choice (B). to determine the sum of the three terms (10 1 9) and in turn their mean: 10 1 9 3 5 19 3 . 544 PART VI: Five Practice Tests www.petersons.com 19. The correct answer is (B). Although statement