Reading Practice Test 6 Answers Part 3

Section 4: Math (Calculator) 1. A Whenever the question asks for a specific value and the answer choices are numbers, think Plugging In the Answers. In (A), a = –0.75. Plug –0.75 in for a in the equation to get 16(–0.75)2 + 4(–0.75) – 6 = 0. Solve the left side of the equation to get 16(0.5625) + (–3) – 6 = 0, or 9 – 3 – 6 = 0. Since, this statement is true, the correct answer is (A). 2. B So far the zoo has sold 4 × 48 = 192 tickets. To make a profit, the zoo will need to sell at least 350 – 192 = 158 additional tickets. Therefore, z needs to be at least 158. Calculate z in each of the answers to see which gives you a value of z ≥ 158. In (A), z ≤ 350 – 4(48), so z ≤ 158. Eliminate (A). Choice (B) gives you z ≥ 158. Keep (B). Choice (C) gives you z ≥ –158. Eliminate (C). Choice (D) gives you z ≤ –158. Eliminate (D). Choice (B) is the correct answer. 3. D Line 1 shows exponential growth, because the line curves upward. Because birth rate and death rate are per 1,000 people, a birth rate higher than a death rate will result in exponential growth (because births – deaths will increase as the population increases). Immigration and emigration numbers are per year and therefore have a linear effect on the graph (as the absolute change in the population due to immigration—emigration is constant). South Zealand has more births per 1,000 than deaths per 1,000, so (D) accurately reflects Line 1. 4. A Start with Process of Elimination. Since the number of people in the theater decreases over time, eliminate (D). Choices (A) and (B) are exponential functions, while (C) is linear. The number of people that leave the theater every 15 minutes is not constant, since it is proportional to the number of people currently in the theater; therefore, this function is not linear, and you can eliminate (C). Choice (A) must be correct because the function decreases quickly and then the number leaving every successive 15 minutes is less than the time before (10% of 250 is more than 10% of 225). 5. B Cross-multiply to get 2y2 = 72. Solve for y to get y2 = 36, so y ± 6. Another way to solve would be to Plug In the Answers, because the question asks for a specific value and there are numbers 6 −6 = , in the answer choices. In (A), y = –6. Plug –6 into the equation and see if it works: 2( −6) 12 −6 6 = . Because this statement is true, one of the possible solutions for the equation is or − 12 12 y = –6. Eliminate (C) and (D) because neither of these answers includes –6. According to (B), an6 6 6 6 = . other possible value for y is 6. Plug 6 into the equation to see if it works: = , or 2(6) 12 12 12 Since this statement is also true, the correct answer is (B). 6. C The 36-year-old runner ran under 3:00:00 when almost 3:30:00 is expected. The 39-year-old runner ran slightly above 3:00:00 when 3:30:00 is expected. The 41-year-old runner ran slightly above 3:00:00 when about 3:45:00 was expected. Therefore, three runners ran at least 15 minutes faster than predicted, which matches (C). If you chose (B), you may have based your choice on the number of runners who ran more than 15 minutes slower than their predicted time. 7. C According to the table, the relative investment in wind resources in 2007 was 0.40 of the total 1.00. Probability is defined by the number of things that fit the requirements divided by the total 0.40 number of things. In this case, that would be . You don’t need to worry about the actual dol1.00 lar values, because both of these numbers relate to the same total of $75 million. You do, however, 10 4 2 need to simplify this fraction. You can multiply it by to get , which then reduces to . 10 10 5 You could also divide it on your calculator to get 0.4, and then divide each fraction in the answer choices to see which one is also equal to 0.4. Either way, the correct answer is (C). 8. B Examine each answer choice and use Process of Elimination. For (A), the 2007 investment in biofuels was 0.31 out of 1.00, or about one-third of the total, according to the chart. The total that year was $75 million, so the Ballpark value would be about $25 million. The $50 million value in (A) is too high, so eliminate it. Choice (B) refers to percents, but the chart is in “relative” investment. If the 2007 relative investment in wind is 0.40 out of 1.00, it is equivalent to 40% of the total. The wind investment in 2017 is projected to be .32, or 32% of the total, which is a decrease of 8%. Check out (C) and (D) just to be certain. For fuel cells, the percent of the total is projected to double, but the total in 2017 is projected to be much higher. Therefore, the total dollar amount invested in wind in 2017 will be much more than double the 2007 investment. For (D), the top three energy types—biofuels, wind, and solar—are projected to be more equally invested in for 2017 than they were in 2007, so (D) is the opposite of what the chart shows. Eliminate (C) and (D), and choose (B). 9. C Whenever there are variables in the question and in the answers, think Plugging In. If m = 10, then Monster Truck Inc., receives a down payment of $3,200 plus 10 months’ worth of monthly payments. This can be calculated as 3,200 + 10(380) = 3,200 + 3,800 = $7,000. Plug in 10 for m in the answers to see which function equals 7,000. Choice (A) becomes f(m) = 380 + 3,200(10) = 380 + 32,000 = 32,380. Eliminate (A). Choice (B) becomes f(m) = 3,200 + 36(10) = 3,200 + 360 = 3,560. Eliminate (B). Choice (C) becomes f(m) = 3,200 + 380(10) = 3,200 + 3,800 = 7,000. Keep (C), but check (D) just in case it also works. Choice (D) becomes f(m) = 10,480 – 380(10) = 10,480 – 3,800 = 6,680. Eliminate (D). The correct answer is (C). 10. A Plugging In the point (6, –5) in the answer choices could work, but it will likely make more than one equation true. The x-intercept is where the line crosses the x-axis, at the point where y = 0. Therefore, one point on the line is (3, 0). The choices are all in the slope-intercept form, y = mx + b, where m is the slope. To find the correct answer, calculate the slope of the line with the two points y2 − y1 known to be on the line. The slope of a line is determined by the equation . Therefore, the x2 − x1 −5 − 0 −5 −5 slope of the line shown can be calculated as follows: = . Only (A) has a slope of , so 6 −3 3 3 that is the correct answer. 11. D There are 12 inches in one foot, so a reel is 12 ´ 1,000 = 12,000 inches long. Set up a prox frames 1 frame = . Cross-multiply to get portion to determine how many frames per reel:3 , 000 inches 12 inch 4 3 3 x = 12,000. Divide both sides by to get x = 16,000 frames per reel. Next, find the number 4 4 of frames the film requires. Convert the time to seconds. There are 60 minutes in an hour, so 2 hours and 47 minutes is equal to (2 ´ 60) + 47 = 167 minutes. There are 60 seconds in a minute, so there are 60 ´ 10,020 seconds in this film. If each second consists of 24 frames, then there are 24 ´ 10,020 = 240,480 frames in this film. To determine the number of reels, divide by the number of frames per reel: , 480 240 = 15.03 reels. Because 15 reels does not hold quite enough frames, 16 ,000 the film requires 16 reels, which is (D). 12. C So far, Hua has received 1,350 + 900 = 2,250 surveys. Hua needs 3,800 – 2,250 = 1,550 additional surveys. Given that Hua receives 1 completed survey for every 5 she sends out, she will need to send out at least 5 ´ 1,550 = 7,750 surveys. Therefore, the correct answer is (C). 13. B Since line AE is perpendicular to the line containing segment AB and the line containing segment DE, these two lines must be parallel. Therefore, ÐABC is equal to ÐCDE because they are both small angles created by a line crossing two parallel lines. Since ÐDCE and ÐACB are opposite each other, they must be equal as well, so these are two similar right triangles. The question also tells you that C is the midpoint of BD, which means that BC and CD are equal. When you have two sides and the included angle of one triangle congruent to two sides and the included angle of a second triangle, you know that the triangles are congruent. This means that AB = DE and AC = CE. Lastly, the question states that AC = DE , which means that AB = AC, and these must be isosceles right triangles. Angle ABC is therefore 45°, and n, which is opposite ÐABC , must be 45° as well. The correct answer is (B). 14. D Start with the easier equation and use Process of Elimination. The easier equation is related to the total number of turkey and bread slides, t + b, on the 4 platters. According to the question, each platter contains 100 slices, so the 4 platters contain 100 ´ 4 = 400 slices. Therefore, one of the equations in the correct answer must be t + b = 400. Eliminate (A) and (B) because neither of these answers contains that equation. The second equation deals with the weight of the slices. According to the problem, the slices on each platter weigh 160 ounces. Therefore, the total weight of the slices on all 4 platters is 160 ´ 4 = 640. Eliminate (C) because the total is wrong in the weight equation. The correct answer is (D). 15. D Whenever there are two equations with the same two variables, they can be solved simultaneously by adding or subtracting them. The key is to get one variable to disappear. Multiply the second equation by –2, to get 6a – 2 z = 20. Stack the two equations and add them. 4a + 2z = 10 6a – 2z = 20 10a = 30 Therefore, the correct answer is (D). Be careful of (C)—the question did NOT ask for the value of a. 16. B We know that Isabella starts with $1,000 in her account, so this eliminates (D). She is earning money from the interest, so the line must have a positive slope, eliminating (C), which has a constant slope. The two best choices are (A) and (B), but in (A) Isabella’s money doesn’t begin to increase until the 5-year mark, which doesn’t make sense—thus (B) is the correct answer. 17. A Find a point on the graph and plug that point into each of the answers to see which equation works. The graph goes through the point (0, –6). Using that point, (A) becomes –6 = 02 – 0 – 6. Solve the right side of the equation to get –6 = –6. Keep (A), but check the remaining answer choices just in case. Choice (B) becomes –6 = 02 + 0 –12. Solve the right side of the equation to get –6 = –12. This is not true, so eliminate (B). Choice (C) becomes –6 = 02 + 6(0) + 9. Solve the right side of the equation to get –6 = 9. Eliminate (C). Choice (D) becomes –6 = 02 + 5(0) + 6. Solve the right side of the equation to get –6 = 6. Eliminate (D). The correct answer is (A). 18. A The key to this problem is understanding that the three friends plan to climb an equal number of stairs. Start with the building for which we know the number of stairs. Each of the friends is planning to climb 3,639 ¸ 3 = 1,213 stairs. Since 1,213 must be a part of the correct answer, eliminate (B) and (D). Given that Dalia will complete only 75% of her goal, Dalia’s total must be multiplied by 75%, or 0.75. This eliminates (C). The correct answer is (A). 19. C Let’s break this question into Bite-Sized Pieces. First, to find the number of U.S. residents who visit European countries every year, we will need to determine how many residents hold passports: 36% of 315 million = 0.36 ´ 315 = 113.4 million. Next, we can calculate how many of those passportholders travel internationally each year: 8% of 113.4 million = 0.08 ´ 113.4 = 9.072 million. Finally, we can calculate how many of those international travelers visit Europe each year: 10% of 9.072 million = 0.1 ´ 9.072 = 0.9072 million. 0.9072 million is equivalent to 907,200, which is (C). The percentage calculations can also be done in one step: 0.1 ´ 0.08 ´ 0.36 ´ 315 = 0.9072 million. 20. A Given that all of the answer choices are possible values for y, Plug In the Answers. In (A), y = x – 6. Plug this value into (x + 2)y2 to get (x + 2)(x – 6)(x – 6). Multiply the last two factors together to get (x + 2)(x 2 – 12x + 36). Multiply the two resulting factors together to get x3 – 12x 2 + 36x + 2 x 2 – 24x + 72. Combine like terms to get x3 – 10x 2 + 12x + 72. This is the same as the third degree polynomial in the question. Therefore, the correct answer is (A). 21. C In 2010, as counted, there were 354 + 225 + 757 = 1,336 elephants in Wakanda. If the margin of error was 17.4, the lowest population of elephants that could fit within the margin of error would be 1,336 – 17.4 = 1,318.6 elephants. Because there cannot be fractional elephants, 1,319 is the smallest value that would be within the margin of error. The correct answer is (C). 22. C Start by using Process of Elimination to eliminate (D) because the entire question is about finding the height, and (D) has nothing to do with height. The difference between the left and middle stacks is 2 stacked sawhorses. The height added to the stack of sawhorses by adding two to the stack can therefore be calculated as 92 – 60 = 32. Therefore, the added height of one stacked sawhorse is 32 ¸ 2 = 16. From this information, keep subtracting the 16 inches added to the top of a stack by each additional sawhorse until you get down to one sawhorse in the stack. If three sawhorses are 60 inches tall, two will be 60 – 16 = 44 inches tall and one sawhorse will be 44 – 16 = 28 inches tall. Choice (A), the height of one sawhorse, can now be eliminated. Another way to think about the height added to the stack of sawhorses by each additional sawhorse is to think of it as the distance between the top of one sawhorse and the top of the next. Since all the sawhorses are the same height, this distance is also the distance from the bottom of one sawhorse to the bottom of the next. Since this distance is 16, eliminate (B). Therefore, the answer is (C). The height of one sawhorse is 28, which is b + c, so the overlap, c, is 28 – 16 = 12. 23. B Remember that sin a = cos b means that a and b are complementary angles. Therefore, the two triangles are similar and cos a = sin b as well. You can set up the following equation: 5 7 = . Now that you have solved for EF (11.2), you can use the Pythagorean Theorem 8 EF (a2 + b2 = c 2) to solve for DF. 11.22 = 72 + DF2 . The correct answer is (B). Alternatively, you could have used the Pythagorean Theorem to solve for BC and then set up a proportion between the similar triangles. Just make sure that you recognize that AC corresponds to DE rather than DF. 24. B First, solve for Rick’s hourly rate and Shane’s hourly rate. Since Work = Rate ´ Time, Rick produces 8 widgets per hour (28 widgets ¸ 3.5 hours without breaks) and Shane produces 27 ¸ 4.5 = 6 widgets per hour. Now Plug In. Since you know they have a combined rate of 14 widgets per hour, choose a total amount that is divisible by 14. Let’s say they were each assigned 14. This means that the total produced is 28, and at a total rate of 14 per hour. Therefore, it takes them 2 hours to finish. During this time, Rick would produce 16 widgets and Shane would produce 12 widgets. Therefore, Rick must have done 2 of Shane’s originally assigned 14 widgets, which is 14.3% of 14. Choice (B) is the correct answer. 25. D difference × 100 . original For choice (A), plug in a difference of about 200,000 and an original of about 1,000,000: To answer this question, you need the formula for percent change: 200,000 × 100. This simplifies to 20%. For (B), plug in a difference of about 200,000 and an 1,000,000 200,000 ×100. This simplifies to about 22%, so you can eliminate original of about 900,000: 900,000 (A). Choice (C) is incorrect because the Sylvilagus brasiliensis population increased during that time. (If you chose (C), you may have calculated the percent change of the Chrysocyon brachyurus population.) For (D), plug in a difference of about 200,000 and an original of about 800,000: 200,000 × 100 . This simplifies to approximately 31%. This is the greatest percent decrease; there800,000 fore, (D) is correct. 26. C Start by setting the two equations equal to each other to get x 2 – 2 x = 2x – 1. Manipulate the equation into the ax2 + bx + c = 0 form, which is x 2 – 4 x + 1 = 0. Use the quadratic equation, which states that x= x= 4 ± 16 − 4 2 − b± b2− 4 ac 2a , then x = to get x = −(−4) ± ( −4)2 − 4(1)(1) 2 (1 ) . Solve for x to get 4 ± 12 4 ±2 3 or x = , so x =2 ± 3 . The greater of the two pos2 2 sible values for x is x 2= + 3 . Therefore, the correct answer is (C). 27. B 1 hypotenuse . Make a right triangle and plug in for the side lengths. Beor opposite sine hypotenuse , make the hypotenuse 1.66 and the side opposite the angle measure cause opposite Cosecant is θ equal to 1. Use the Pythagorean Theorem to solve for the missing side: 12 + x 2 = 1.662; θ, use 1 + x 2 = 2.7556; x 2 = 1.7556; x ≈1.32. Make this the other leg of the triangle. To find tan opposite 1 : , which is (B). adjacent 1 .32 28. D If two patients are added to the trial, there will be 12 total patients. If the mean height of 12 patients is 169 cm, then the 12 patients have a total height of 12 ´ 169 = 2,028 cm. The total height of the first 10 patients is 184 + 176 + 181 + 157 + 168 + 154 + 148 + 165 + 190 + 162 = 1,685 cm, so the two new patients must have a total height of 2,028 – 1,685 = 343 cm. Add up the heights and eliminate any choice that does not equal 343. Only (D) works. 29. D Plugging in the given point to see which equation is true is not easy on this one, since both values have weird decimals. The answer choices are also likely written so that more than one is true for that point, so try to find another point on the line. The x-intercept of a line is where the line crosses the x-axis. At that point, the value of y is 0. Therefore, (2, 0) is also a point on the line. Plug this point into the answers, as it is easier to calculate. If it works in more than one equation, plugging in the ugly point will determine the correct answer, which must work with both points. Plug point (2, 0) into (A) to get 0 + 5.9 = 2.5(2). Solve both sides of the equation to get 5.9 = 5. Eliminate (A). Plug (2, 0) into (B) to get 4(0) + 12(2) = 29.1. Solve both sides of the equation to get 4 + 24 = 29.1, or 28 = 29.1. Eliminate (B). Plug (2, 0) into (C) to get 6(0) + 27.15 = 12(2). Solve both sides of the equation to get 0 + 27.15 = 24. Since this is clearly not a true statement, eliminate (C). Plug (2, 0) into (D) to get 10(0) – 13(2) = –26. Solve both sides of the equation to get –26 = –26. Since (D) is the only answer for which the point (2, 0) works, the correct answer is (D). 30. B Whenever there are variables in the question and in the answers, think Plugging In. If P0 = 4, k = 2, and t = 3, then P = (4)(10)6 = 4,000,000. Plug these values into the answer choices to see which answer works. Choice (A) becomes =3 4 log 4 ,000 ,000 2    . Simplify the right side of the 1  log  1, 000, 000   −6 equation to get 3 = , then 3 = , and finally 3 = –3. This isn’t true, so elimi2 2 4, 000, 000  log    4 nate (A). Choice (B) becomes 3= . Simplify the right side of the equation to 2 get 3 = log(1, 000, 000) 6 , then 3 = , and finally 3 = 3. Keep (B), but check the remaining an2 2 swer choices just in case. Choice (C) becomes =3 of the equation to get 3 = log ( , 4 000 , 000 × 2 ) 4. Simplify the right side log (16, 000, 000) , or 3 ≈ 3.6. Eliminate (C). Choice (D) becomes 2   4 1 3 = 2 log  2  , then . Simplify the right side of the equation to get 3= log 4,000,000 1,000,000   3 = 2(–6), and finally 3 = –12. Eliminate (D). The correct answer is (B). 31. 48 Set up a proportion: 1 euro 40 euros = . Cross-multiply and get x = 1.2 ´ 40 = 48. 1 .2 dollars x dollars 32. 558 During the summer the ice cream vendor sells an average of 2(50) – 7 = 93 popsicles per day. Over 6 summer days, 93 ´ 6 = 558 popsicles are sold. The correct answer is 558. 7 or 3.5 2 33. First, get rid of the decimals in the first equation by multiplying the first equation through by 10 to get 13g + 17h = 50. In the second equation, move all the variables to the left of the equal sign to get –13g + 3h = 20. Whenever there are two equations with the same two variables, they can be solved simultaneously by adding or subtracting them. The key is to get one variable to disappear. Stack the equations on top of each other and add them. 13g + 17h = 50 –13g + 3h = 20 20h = 70 70 7 Therefore, h = . Because this number is too large to grid in, either reduce the fraction to , or 2 20 convert the fraction to the decimal 3.5. 34. 16 To find the percent of registered Democrats planning to vote for Candidate A, divide the number of Democrats planning to vote for Candidate A by the total number of registered Democrats: 35. 30 24 = 0 .16= 16 % , which makes 16 the correct answer. 150 Start by drawing the picture, as this question doesn’t provide one. To do so, change each of the equations into the slope-intercept form of an equation y = mx + b, where m is the slope and b is the y2 intercept. The second equation becomes 3y ≥ 2x – 12, or y ≥ x – 4. The third equation 3 2 becomes 5y ≤ –2x + 20, or y ≤ – x + 4. The ≥ sign in the second equation means that 5 everything above the line should be shaded, and the ≤ sign in the third equation means that everything below that line should be shaded. To graph the first equation x ≥ 0, shade everything to the right of the y-axis. The resulting picture should look like this: y y ≤ –25 x + 4 y ≥ –2 x – 4 3 x x>0 1 The formula for the area of a triangle is A = b ´ h. It is easiest to think of the side that is along 2 the y-axis as the base. That side goes from a y-coordinate of 4 to –4, for a length of 8. The height of the triangle is the x-coordinate of the point where the two slanted lines meet; set the two equations 2 2 equal to find it. Start with x – 4 = – x + 4 and multiply everything by 15 to get 10x – 60 = –6x 3 5 + 60. Then add 6x and 60 to both sides to get 16 x = 120, so x = 7.5, and the height is 7.5. The resulting figure should look like this: y y ≤ – 25 x + 4 y ≥ –2 x – 4 3 7.5 8 x>0 0 x 1 Plug the measurements for the base and the height into the area formula to get A = (8)(7.5) = 30. 2 The correct answer is 30. 36. 0 Start by multiplying the terms together. To multiply (x 2 + 2x – 3)(2x + 5), multiply each term in the left parenthesis by each term in the right parenthesis to get 2 x3 + 5x 2 + 4 x 2 + 10x – 6 x – 15. Combine like terms to get 2x3 + 9x 2 + 4 x – 15. To multiply (x + 1)(x – 1)(x + 3), do one set of parentheses first; then multiply that product by the remaining parenthesis. You may notice that (x + 1)(x – 1) is a common quadratic, which equals x 2 – 1. Then you need to multiply x 2 – 1 by (x + 3). As you did before, multiply each term in the first parenthesis by each term in the second to get x3 + 3x 2 – x – 3. Now you can do (2x3 + 9x 2 + 4 x – 15) – (x3 + 3x 2 – x – 3). It is easiest to distribute the negative sign into the second parenthesis: (2x3 + 9x 2 + 4 x – 15) + (–x3 – 3x 2 + x + 3). Now you can combine like terms to get x3 + 6x 2 + 5x – 12. This is in the form ax 3 + bx 2 + cx + d, so a = 1, b = 6, c = 5, and d = –12. This means a + b + c + d = 1 + 6 + 5 + (–12) = 0. 37. 195 Use the definition of inverse proportion: x1 y1 = x 2 y2. Plug in 1.5 for x1, 260 for y1, 2 for x 2, and solve for y2: (1.5)(260) = (2)(y2); 390 = 2y2. Divide both sides by 2, and you find y2 = 195. 38. 15 Start by converting the qualifying distance of 68.58 meters into yards. Set up a proportion: 1 yard x yards = . Cross-multiply to get 0.9144x = 68.58. Divide both sides by 0 .9144 meters 68 .58 meters 0.9144 to find that the qualifying distance is 75 yards. If his current best is 60 yards, he needs to throw 75 – 60 = 15 more yards.