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127 Answer Explanations SAT Practice Test #4 Section 1: Reading Test QUESTION 1. Choice C is the best answer. The narrator initially expresses uncertainty, or uneasiness, over his decision to set out for the North Pole: “my motives in this undertaking are not entirely clear” (lines 9-10). At the end of the pas- sage, the narrator recognizes that because of this journey he is “on the brink of knowing . . . not an ethereal mathematical spot,” the North Pole, but him- self (lines 56-57). Choices A, B, and D are incorrect because the narrator does not suggest that he fears going on the expedition, doubts his own abilities, or feels disdain for the North Pole. QUESTION 2. Choice D is the best answer. Lines 56-57 provide evidence that the narra- tor eventually recognizes his motives for traveling to the North Pole: “What I am on the brink of knowing, I now see, is not an ephemeral mathematical spot but myself.” The narrator initially was unsure of why he was traveling to the North Pole, but realizes that he has embarked on a journey to find himself. Choices A, B, and C are incorrect because they do not provide the best evi- dence that the narrator eventually recognizes his motives for traveling to the North Pole. Rather, choices A, B, and C all focus on the narrator’s prepara- tions and expectations for the journey. QUESTION 3. Choice D is the best answer. In lines 1-6, the narrator says that he feels a “vast yearning” and that his emotions are “complicated.” He explains that he does “not understand quite what it is that the yearning desires.” In this con- text, his emotions are “not readily verifiable,” or not completely understood.

165 QUESTION 34. The correct answer is 150. In the study, 240 male and 160 plus another 100 female bats have been tagged, so that 500 bats have been tagged alto- gether. If x more male bats must be tagged for 3 _ 5 of the total number of bats to be male, the proportion male bats _ total bats = 240 + x _ 500 + x = 3 _ 5 must be true. Multiplying each side of 240 + x _ 500 + x = 3 _ 5 by 5(500 + x ) gives 5(240 + x ) = 3(500 + x), which simplifies to 1200 + 5x = 1500 + 3x. Therefore, x = 150, and 150 more male bats must be tagged; this will bring the total to 390 male bats out of 650 bats, which is equal to 3 _ 5 . QUESTION 35. The correct answer is 2.25 or 9 _ 4 . Let q s be the dynamic pressure of the slower fluid moving with velocity v s, and let q f be the dynamic pressure of the faster fluid moving with velocity v f . Then v f = 1.5v s . Given the equation q = 1 __ 2 nv 2, substituting the dynamic pressure and velocity of the faster fluid gives q f = 1 __ 2 nv f 2. Since v f = 1.5v s, the expression 1.5v s can be substituted for v f in this equation, giving q f = 1 _ 2 n (1.5v s)2. This can be rewrit - ten as q f = (2.25) 1 _ 2 nv s 2 = (2.25)q s. Therefore, the ratio of the dynamic pres- sure of the faster fluid is q f _ qs = 2.25q s _ qs = 2.25. Either 2.25 or the equivalent improper fraction 9 _ 4 may be gridded as the correct answer. QUESTION 36. The correct answer is 29, 30, 31, 32, 33, or 34. Since the radius of the cir - cle is 10, its circumference is 20π . The full circumference of a circle is 360°. Thus, an arc of length s on the circle corresponds to a central angle of x °, where x _ 360 = 2 _ 20π , or x = 360 _ 20π s . Since 5 < s < 6, it follows that 360 _ 20π (5) < x < 360 _ 20π (6), which becomes, to the nearest tenth, 28.6 < x < 34.4. Therefore, the possible integer values of x are 29, 30, 31, 32, 33, and 34. Any one of these numbers may be gridded as the correct answer.

166 QUESTION 37. The correct answer is .72. According to the analyst’s estimate, the value V, in dollars, of the stock will decrease by 28% each week for t weeks, where t = 1, 2, or 3, with its value being given by the formula V = 360(r) t. This equation is an example of exponential decay. A stock losing 28% of its value each week is the same as the stock’s value decreasing to 72% of its value from the previous week, since V − (.28)V = (.72)V . Using this information, after 1 week the value, in dollars, of the stock will be V = 360(.72); after 2 weeks the value of the stock will be V = 360(.72)(.72) = 360(.72) 2; and after 3 weeks the value of the stock will be V = 360(.72)(.72)(.72) = 360(.72) 3. For all of the values of t in question, namely t = 1, 2, and 3, the equation V = 360(.72) t is true. Therefore, the analyst should use .72 as the value of r . QUESTION 38. The correct answer is 134. The analyst’s prediction is that the stock will lose 28 percent of its value for each of the next three weeks. Thus, the predicted value of the stock after 1 week is $360 − (0.28)$360 = $259.20; after 2 weeks, $259.20 − (0.28)$259.20 ≈ $186.62; and after 3 weeks, $186.62 − (0.28)$186.62 ≈ $134.37. Therefore, to the nearest dollar, the stock analyst believes the stock will be worth 134 dollars after three weeks.