segments remain ahead. Since the boat’s average speed is the same before and after buoy 10, it takes the boat 5 3 5 = 25 minutes to travel from buoy 10 to buoy 15. 10. The correct answer is (A). Given n = 2, the 25th term of SetR=25n + 25 = 25(2) + 25 = 75. Given n = 2, the 24th term of Set S = n +23=2+23 = 25, and two times that 24th term is 50. 11. The correct answer is (C). There’s no need to calculate either quantity, and you can cancel the product st from both columns. To make the comparison, observe the place-value shifts from the decimal number 9.3. In Column A, the decimal point shifts 3 places left (9,300) and 3 places right (.0093), so the quantity is equivalent to (9.3)(9.3). You can now see that Quantity B, which is (9.3)(9.3), is the same as Quantity A. 12. The correct answer is (B). There’s no need to calculate either quantity. Given an area of 12,000 square feet, the shortest possible rectangular perimeter is achieved with a square, in which all sides are the same length. Column B describes a corral with a width of 300 feet and a length of 400 feet. This corral would require more fence posts than a square corral. 13. The correct answer is 51.25. Think of Cynthia’s average rate as the average of eight equally weighted one-hour trips. Seven of those trips receive a weight of 50, and one of the trips receives a weight of 60. You can express this algebra- ically as follows: 750 60 8 350 60 8 410 8 51 25 () . + = + == Cynthia’s average rate during the entire trip was 51.25 mph. (There’s no need to round either up or down to the nearest hundredth.) 14. The correct answer is (D). Sep- tember and October each saw pre- cipitous declines in the price of BioFirm stock and CompuWin stock, but only a modest increase in the price of Ardent stock. During each of these two months, the aggregate change was clearly negative. In July, however, a substantial price increase in CompuWin stock more than offset the combined decrease in the price of the other two stocks. 15. The correct answer is (E). The investor paid about $800 for 40 shares of Ardent stock (priced at about $20 per share), and then sold those 40 shares for about $2,200 (priced at about $55 per share). Accordingly, the investor’s profit amounted to approximately $1,400. 16. The correct answer is (B). The area of any triangle = 1 2 3 base 3 height. Using 7 kilometers as the base of the triangle in this problem, the triangle’s height is the north- south (vertical) distance from A to an imaginary line extending west from B. Given that farmhouse A is located a total of 10 kilometers farther west than farmhouse C, the extension is 3 kilometers long. The triangle’s height is 4 kilometers (3 2 +4 2 =5 2 , by the Pythagorean theorem). Accordingly, the area of triangle ABC = 1 2 3 7 3 4=14km 2 . answers practicetest2 Practice Test 2 433 . www.petersons.com 17. The correct answer is (B). You can make the comparison quickly by rec- ognizing that Quantity A is the “dif- ference of two squares” (x 2 2 y 2 )in the factored form (x+y)(x 2 y), where y = 2. Or, you can multiply the two binomials in Column A, and then simplify: (x +2)(x 2 2) = x 2 +2x 2 2x 2 4=x 2 2 4. Since x 2 2 4 , x 2 2 2, Quantity A , Quantity B. 18. The correct answer is (A). K percent is based on $100. Therefore, K percent = K dollars, and Quantity B will always be $1 less than Quantity A. 19. The correct answer is (A). Apply the formula for determining arith- metic mean (called AM below), or simple average. Letting x equal the other number, solve for x: AM Q PQ Q PQ Q PQ Q = + = + =+ −= x x x x 2 2 2 2 20. The correct answer is (D). Letting x equal the number of ounces of soy sauce added to the mixture, 18 + x equals the total amount of the mixture after the soy sauce is added. The amount of peanut sauce (5.76 ounces) must equal 12% of the new total amount of the mixture, which is 18 + x. You can express this as an algebraic equation and solve for x: 5.76 5 0.12~x +18! 576 5 12~x +18! 576 5 12x + 216 360 5 12x 30 5 x 30 ounces of soy sauce must be added to achieve a mixture that includes 12% peanut sauce. 21. The correct answer is (C). x + y + the measure of the third interior angle (let’s call it w) = 180. Also, w + z = 180 (because their angles combine to form a straight line). So, you have two equations: x + y + w = 180 or x + y = 180 2 w w + z = 180 or z = 180 2 w Therefore, x + y = z (Quantity A = Quantity B). 22. The correct answer is (D). The centered information establishes that Quantity B, pq, must be negative, because the product of a positive number and a negative number is always negative. As for Quantity A, try substituting some simple numbers for p and q.Ifp =1 and q = 21, then p + q = 0 while pq = 21, and therefore p + q . pq. But if p = 1 4 and q = 2 1 2 , p + q = 2 1 4 while pq = 1 8 , and therefore p + q , pq. Thus, which quantity is greater depends on the values of p and q. 23. The correct answer is (B). The range of D = 10 2 3 = 7. The median of D = the arithmetic mean of 6 and 9 (the two middle terms) = 7.5. PART VI: Five Practice Tests434 . www.petersons.com 24. The correct answer is (B). Let {A, B, C, D, E} represent the set of ice cream flavors. 10 triple-scoop combi- nations are available: {ABC}{ABD}{ABE}{ACD}{ACE}{ADE} {BCD}{BCE}{BDE}{CDE} Each of these combinations is available on either of the two cone types. Thus, the total number of dis- tinct triple-scoop cones having three different ice cream flavors is 20. 25. The correct answer is (C). The question asks you to select the choice that does NOT describe sales totaling at least 10,000. Choice (C) describes 1.7K + 4.9K + 2.2K = 8.8K sales, which is less than $10,000. Choice (A) describes 8.5K + 1.9K = 10.4K sales. Choice (B) describes 7.5K + 1.0K + 2.0 + 0.8 = 11.3K sales. Choice (D) describes 4.9K + 5.1K = 10.0K sales. Choice (E) describes 8.5K + 4.9K = 13.4K sales. 26. The correct answer is (A). The number of basic models was 13,800 (the sum of all numbers in the “Basic” column). The number of standard models sold was 29,900 (the sum of all numbers in the “Standard” column). The difference is 16,100. To find the average premium paid for a standard model, divide $41,000,000 by $16,100. Rounding these figures to $40 million and $16,000, the quotient is $2,500. 27. The correct answer is (D). Without the square hole, each of the cube’s six outer surfaces contains 9 square inches, for a total of 54 square inches of outer surface area. The square hole reduces that total outer surface area by 2 square inches, to 52. 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 areas. The solid’s total surface area is 52 + 12 = 64 square inches. 28. The correct answer is (B). Since x is a negative number (less than 21), x 3 is negative and x 2 is positive. Hence, Quantity A is a negative number less than x 3 . Quantity B, on the other hand, is a positive number greater than x 2 . answers practicetest2 Practice Test 2 435 . www.petersons.com ANSWER SHEET PRACTICE TEST 3 Analytical Writing—Issue Task -------------------------------------------------------------------------------------------------------------------------------------------- ✃ answer sheet Practice Test 3 437 . www.petersons.com PART VI: Five Practice Tests438 -------------------------------------------------------------------------------------------------------------------------------------------- ✃ . www.petersons.com Analytical Writing—Argument Task -------------------------------------------------------------------------------------------------------------------------------------------- ✃ answer sheet Practice Test 3 439 . www.petersons.com PART VI: Five Practice Tests440 -------------------------------------------------------------------------------------------------------------------------------------------- ✃ . www.petersons.com Quantitative Reasoning 1. j A j B j C j D j E 2. j A j B j C j D 3. j A j B j C j D 4. j A j B j C j D j E 5. j A j B j C j D j E 6. j A j B j C j D 7. j A j B j C j D 8. j A j B j C j D j E 9. j A j B j C j D j E 10. j A j B j C j D j E 11. j A j B j C j D 12. j A j B j C j D 13. j A j B j C j D 14. j A j B j C j D 15. j A j B j C j D 16. j A j B j C j D j E 17. j A j B j C j D 18. j A j B j C j D 19. j A j B j C j D 20. j A j B j C j D j E 21. j A j B j C j D j E 22. j A j B j C j D j E 23. j A j B j C j D 24. 25. j A j B j C j D 26. j A j B j C j D j E 27. j A j B j C j D j E 28. j A j B j C j D j E Verbal Reasoning 1. j A j B j C j D j E 2. j A j B j C j D j E 3. j A j B j C j D j E 4. j A j B j C j D j E 5. j A j B j C j D j E 6. j A j B j C j D j E 7. j A j B j C j D j E 8. j A j B j C j D j E 9. j A j B j C j D j E 10. j A j B j C j D j E 11. j A j B j C j D j E 12. j A j B j C j D j E 13. j A j B j C j D j E 14. j A j B j C j D j E 15. j A j B j C j D j E 16. j A j B j C j D j E 17. j A j B j C j D j E 18. j A j B j C j D j E 19. j A j B j C j D j E 20. j A j B j C j D j E 21. j A j B j C j D j E 22. j A j B j C j D j E 23. j A j B j C j D j E 24. j A j B j C j D j E 25. j A j B j C j D j E 26. j A j B j C j D j E 27. j A j B j C j D j E 28. j A j B j C j D j E 29. (i) ______ (ii) ______ (iii) ______ 30. j A j B j C j D j E -------------------------------------------------------------------------------------------------------------------------------------------- ✃ answersheet Practice Test 3 441 . www.petersons.com . Writing—Issue Task -- -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - ✃ answer. Writing—Argument Task -- -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - -- - ✃ answer