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QUESTION EXPLANATIONS

For NEW SAT PRACTICE TEST 4 (Calculator Math Test)

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31 32 33 34 35 36 37 38

 
1. (C) — The substance increases by 48 grams/30 minutes. Therefore, after an hour, the substance will have increased by 96 grams. 111 – 96 = 15.
 
2. (B) — If Bartleby works every day and edits 33 manuscripts, we can write 33 = x + 2.5x + 3.5x + 4x = 11x, so x = 3.
 
3. (C) — Skye spends $1.75 per day for 31 + 31 + 30 = 92 days. $1.75 x 92 = $161.
 
4. (C) — We can multiply both sides of the first equation by 6 to find to find 6x/y = 24.
 
5. (A) — Expression II is equal to 5x2 – 7x – 6. Expression III is equal to 5x2 + 5x – 30. Therefore, only Expression I equals the original expression.
 
6. (C) — Of the 77 people between 18 and 34 represented in the survey, 53 or “68.8%” oppose the regulation; of those between 55 and 74, 32 or “31.1%” oppose the regulation.
 
7. (D) — We can set the equations equal to each other: 6x + 2 = + 5x – 4, and rearrange to get 0 = – x – 6. Factoring this gives us (x – 3)(x + 2), so x can be 3 or -2. Plugging these values back into either equation gives y = 20 when x = 3 and y = -10 when x = -2, so the product xy can be either 60 or 20. Only 60 is given as an option.
 
8. (C) — We can write the equation in standard form as 6y = mx – 24, or y = mx/6 – 4. Plugging in (3, 6) for x and y gives 6 = m 3/6 – 4, or ½m = 10, so m = 20.
 
9. (A) — The equation simplifies to 3x + 15 + 7 = 22, or 3x + 22 = 22, so x = 0.
 
10. (A) — This inequality is the same as –6 ≤ x – 4 ≤ 6, so adding 4 to all terms gives –2 ≤ x ≤ 10.
 
11. (A) — Answers B) and C) do not work when x = 0. Answer D) does not work when x = 3.
 
12. (C) — The equation describes quadratic growth. The scenario in answer A) is exhibiting exponential growth; answer B) decreases rather than grows with time; answer D) also describes exponential growth.
 
13. (B) — There are 1782 employed workers; of these, 198 + 510 = 708 have not attended college. 708/1782 = 39.7%.
 
14. (A) — We can examine the line of best fit to find that when T = 200, S is about 40, and when T = 400, S is about 80. Since 40/200 or 80/400 = 0.2, this yields an equation of S = 0.2T.
 
15. (A) — We can split the first equation into parts and multiply the second equation by each part in turn:
 
16. (B) — In one week, an armadillo will eat 7 x 3 lbs = 21 lbs of food; three armadillos will eat 63 lbs. Since only 10% of that consists of plant matter, three armadillos will eat 6.3 lbs of plant matter in a week.
 
17. (B) — If 17 females had litters of 4, there were 17 x 4 = 68 armadillos born. Including the 20 armadillos counted in 2012, there should be 88 armadillos in 2014 if they all survived. Since we see only 54 armadillos in 2014, we can conclude that 88 – 54 = 34 armadillos did not survive.
 
18. (A) — We can see that the slope of the line is ½, since a rise (change in y) of 1 corresponds to a run (change in x) of 2. Only answer A) has a slope of ½.
 
19. (C) — The mean of Data Set A is 3; the mean of Data Set B is also 3, so answers A) and B) are incorrect. The standard deviation of Data Set A is 2; the standard deviation of Data Set B is , so D) is also incorrect.
 
20. (C) — The volume of package 1 is 10 in x 6 in x 2 in = 120 ; the volume of package 2 is 6 in x 6 in x 4 in = 144 . The efficiency of package 1 is 120/184 = 0.65; the efficiency of package 2 is 144/168 = 0.86. So package 2 is more efficient than package 1 by approximately 0.20.
 
21. (C) — Car 1 has a pre-sale price of $4,500. 5% off brings the price to $4,275, and 8% of the pre-sale price (for 80,000 miles) is $360, so the final price of Car 1 is $4,275 – $360 = 3915. Car 2 has a pre-sale price of $5,200; 5% off gives $4,940, and 2% of the pre-sale price (for 20,000 miles) is $104, leaving $4,940 – $104 = $4,836. $4836 – $3915 = $921.
 
22. (B) — First, we simplify the first equation by dividing both sides by 2 to get y = x/10 – ½. Setting the equations equal to each other gives x/10 – ½ = (2x + 8)/3. Multiplying both sides by 30 to cancel the denominators gives 3x – 15 = 20x + 80, which we can rewrite as 17x = –95, so x = –95/17. Plugging this in to either equation gives us y = –18/17. For example, plugging into the first equation gives 2y = (–95/17)/5 – 1, or 2y = –19/17 – 17/17. So 2y = –36/17, and y = –18/17.
 
23. (A) — If 8% of the population if 56 students, there are 700 students total (multiply by 12.5 to get 100% = 700). 7% of the students are affected indirectly, as shown in the graph, and 7% of 700 = 49 students.
 
24. (D) — f(3) = 5(3)2 + 8(3) – 4 = 45 + 24 – 4 = 65. g(3) = 3 + 2 = 5. 65/5 = 13.
 
25. (B) — Pre-experiment levels were the same for all groups, so A) is incorrect, since sharing goals showed a greater increase in physical activity. Although the control group showed a small decline, without error bars we cannot conclude whether it is statistically significant, and so C) is not supported by the data. Answer D) may be true, but this conclusion is not related to the data presented.
 
26. (B) — Although there were fewer establishments in 2007 than in 2002, the value of shipments increased, so A) is incorrect. Similarly, employment and payroll per employee also increased during that period, so C) and D) are incorrect.
 
27. (A) — The ratio of value of annual shipments to annual payroll in 1997 was 173,985/20,798 = 8.365. The ratio in 2007 was 413,525/40,687 = 10.164. Percentage growth from 1997 to 2007 is the value in 2007 divided by the value in 1997, minus 100% (since growth is the value above 100%): 10.164/8.365 = 121.5% – 100% = 21.5%.
 
28. (B) — 480 minutes is equal to 8 hours, or five 1.6-hour periods. This means that the salbutamol loses half of its therapeutic activity five times. After one 1.6-hour period, its activity is 240; after two periods, its activity is 120, and so on. After five 1.6-hour periods, its activity is 15.
 
29. (D) — Answer A) is incorrect; the chart does not incorporate other modes of transportation (subways, for example). Answer B) is also incorrect: although the percent of commuters decreased, the actual number may have stayed the same or even increased. Finally, answer C) is incorrect because by looking at the slope of each line segment, we can see that the percentage of commuters who walked to work actually decreased more slowly between 1990 and 2000 than between 1980 and 1990.
 
30. (C) — The length of an arc is equal to twice the inscribed angle (converted to radians) times the radius. Since 50 degrees x 2 radians/360 degrees = 5/18, the length of the arc is 2 x 5/18 x 10 = 50/9.
 
31. (4) — When y = 6, we can write 6 = 0.25x + 5, or 1 = 0.25x. Multiplying both sides by 4 gives x = 4.
 
32. (70) — The missing angle on the leftmost triangle is 180° – 90° – 15° = 75°. Since the bases of the triangles lie in a line (180°), we can find the bottom-left angle of the rightmost triangle by finding 180° – 75° – 50° = 55°. Since this is an isosceles triangle (as indicated by the marks on the sides), the bottom-right angle is also 55°, so 180° – 55° – 55° = 70° = x.
 
33. (1.2) — 16 crates of 5 pounds each means 80 pounds of oranges on the truck. $96/80 pounds = $1.20/pound.
 
34. (19) — f(3) = 6(3) + 1 = 19. f(0) = 6(0) + 1 = 1, and g(1) = 2(1) – 1 = 1. 19/1 = 19.
 
35. (487) — The time it takes to orbit the sun is 24 x 365 = 8760 minutes. If a day is only 18 hours, there are 8760/18 = 486.7 or about 487 days in a year.
 
36. (18) — We can rewrite this equation as 3 = ). Squaring both sides gives 9m = 162, and dividing by 9 gives m = 18.
 
37. (117) — If we plug in 78 kilopascals for pressure and 30 cm2 for volume, we get 78 x 30 = k, so k = 2340. Since k is constant, we can find the new pressure by writing 2340 = P(20). Solving for P gives 117.
 
38. (26) — The value of k for this gas is 15.6 x 50 = 780. Decreasing the volume of the container by 40% can be written as 50 x 0.6 = 30, so the new pressure is 780 = P(30). Solving for P gives 26.


The substance increases by 48 grams/30 minutes. Therefore, after an hour, the substance will have increased by 96 grams. 111 – 96 = 15.
If Bartleby works every day and edits 33 manuscripts, we can write 33 = x + 2.5x + 3.5x + 4x = 11x, so x = 3.
Skye spends $1.75 per day for 31 + 31 + 30 = 92 days. $1.75 x 92 = $161.
We can multiply both sides of the first equation by 6 to find to find 6x/y = 24.
Expression II is equal to 5x2 – 7x – 6. Expression III is equal to 5x2 + 5x – 30. Therefore, only Expression I equals the original expression.
Of the 77 people between 18 and 34 represented in the survey, 53 or “68.8%” oppose the regulation; of those between 55 and 74, 32 or “31.1%” oppose the regulation.
We can set the equations equal to each other: 6x + 2 = + 5x – 4, and rearrange to get 0 = – x – 6. Factoring this gives us (x – 3)(x + 2), so x can be 3 or -2. Plugging these values back into either equation gives y = 20 when x = 3 and y = -10 when x = -2, so the product xy can be either 60 or 20. Only 60 is given as an option.
We can write the equation in standard form as 6y = mx – 24, or y = mx/6 – 4. Plugging in (3, 6) for x and y gives 6 = m 3/6 – 4, or ½m = 10, so m = 20.
The equation simplifies to 3x + 15 + 7 = 22, or 3x + 22 = 22, so x = 0.
This inequality is the same as –6 ≤ x – 4 ≤ 6, so adding 4 to all terms gives –2 ≤ x ≤ 10.
Answers B) and C) do not work when x = 0. Answer D) does not work when x = 3.
The equation describes quadratic growth. The scenario in answer A) is exhibiting exponential growth; answer B) decreases rather than grows with time; answer D) also describes exponential growth.
There are 1782 employed workers; of these, 198 + 510 = 708 have not attended college. 708/1782 = 39.7%.
We can examine the line of best fit to find that when T = 200, S is about 40, and when T = 400, S is about 80. Since 40/200 or 80/400 = 0.2, this yields an equation of S = 0.2T.
We can split the first equation into parts and multiply the second equation by each part in turn:
In one week, an armadillo will eat 7 x 3 lbs = 21 lbs of food; three armadillos will eat 63 lbs. Since only 10% of that consists of plant matter, three armadillos will eat 6.3 lbs of plant matter in a week.
If 17 females had litters of 4, there were 17 x 4 = 68 armadillos born. Including the 20 armadillos counted in 2012, there should be 88 armadillos in 2014 if they all survived. Since we see only 54 armadillos in 2014, we can conclude that 88 – 54 = 34 armadillos did not survive.
We can see that the slope of the line is ½, since a rise (change in y) of 1 corresponds to a run (change in x) of 2. Only answer A) has a slope of ½.
The mean of Data Set A is 3; the mean of Data Set B is also 3, so answers A) and B) are incorrect. The standard deviation of Data Set A is 2; the standard deviation of Data Set B is , so D) is also incorrect.
The volume of package 1 is 10 in x 6 in x 2 in = 120 ; the volume of package 2 is 6 in x 6 in x 4 in = 144 . The efficiency of package 1 is 120/184 = 0.65; the efficiency of package 2 is 144/168 = 0.86. So package 2 is more efficient than package 1 by approximately 0.20.
Car 1 has a pre-sale price of $4,500. 5% off brings the price to $4,275, and 8% of the pre-sale price (for 80,000 miles) is $360, so the final price of Car 1 is $4,275 – $360 = 3915. Car 2 has a pre-sale price of $5,200; 5% off gives $4,940, and 2% of the pre-sale price (for 20,000 miles) is $104, leaving $4,940 – $104 = $4,836. $4836 – $3915 = $921.
First, we simplify the first equation by dividing both sides by 2 to get y = x/10 – ½. Setting the equations equal to each other gives x/10 – ½ = (2x + 8)/3. Multiplying both sides by 30 to cancel the denominators gives 3x – 15 = 20x + 80, which we can rewrite as 17x = –95, so x = –95/17. Plugging this in to either equation gives us y = –18/17. For example, plugging into the first equation gives 2y = (–95/17)/5 – 1, or 2y = –19/17 – 17/17. So 2y = –36/17, and y = –18/17.
If 8% of the population if 56 students, there are 700 students total (multiply by 12.5 to get 100% = 700). 7% of the students are affected indirectly, as shown in the graph, and 7% of 700 = 49 students.
f(3) = 5(3)2 + 8(3) – 4 = 45 + 24 – 4 = 65. g(3) = 3 + 2 = 5. 65/5 = 13.
Pre-experiment levels were the same for all groups, so A) is incorrect, since sharing goals showed a greater increase in physical activity. Although the control group showed a small decline, without error bars we cannot conclude whether it is statistically significant, and so C) is not supported by the data. Answer D) may be true, but this conclusion is not related to the data presented.
Although there were fewer establishments in 2007 than in 2002, the value of shipments increased, so A) is incorrect. Similarly, employment and payroll per employee also increased during that period, so C) and D) are incorrect.
The ratio of value of annual shipments to annual payroll in 1997 was 173,985/20,798 = 8.365. The ratio in 2007 was 413,525/40,687 = 10.164. Percentage growth from 1997 to 2007 is the value in 2007 divided by the value in 1997, minus 100% (since growth is the value above 100%): 10.164/8.365 = 121.5% – 100% = 21.5%.
480 minutes is equal to 8 hours, or five 1.6-hour periods. This means that the salbutamol loses half of its therapeutic activity five times. After one 1.6-hour period, its activity is 240; after two periods, its activity is 120, and so on. After five 1.6-hour periods, its activity is 15.
Answer A) is incorrect; the chart does not incorporate other modes of transportation (subways, for example). Answer B) is also incorrect: although the percent of commuters decreased, the actual number may have stayed the same or even increased. Finally, answer C) is incorrect because by looking at the slope of each line segment, we can see that the percentage of commuters who walked to work actually decreased more slowly between 1990 and 2000 than between 1980 and 1990.
The length of an arc is equal to twice the inscribed angle (converted to radians) times the radius. Since 50 degrees x 2 radians/360 degrees = 5/18, the length of the arc is 2 x 5/18 x 10 = 50/9.
When y = 6, we can write 6 = 0.25x + 5, or 1 = 0.25x. Multiplying both sides by 4 gives x = 4.
The missing angle on the leftmost triangle is 180° – 90° – 15° = 75°. Since the bases of the triangles lie in a line (180°), we can find the bottom-left angle of the rightmost triangle by finding 180° – 75° – 50° = 55°. Since this is an isosceles triangle (as indicated by the marks on the sides), the bottom-right angle is also 55°, so 180° – 55° – 55° = 70° = x.
16 crates of 5 pounds each means 80 pounds of oranges on the truck. $96/80 pounds = $1.20/pound.
f(3) = 6(3) + 1 = 19. f(0) = 6(0) + 1 = 1, and g(1) = 2(1) – 1 = 1. 19/1 = 19.
The time it takes to orbit the sun is 24 x 365 = 8760 minutes. If a day is only 18 hours, there are 8760/18 = 486.7 or about 487 days in a year.
We can rewrite this equation as 3 = ). Squaring both sides gives 9m = 162, and dividing by 9 gives m = 18.
If we plug in 78 kilopascals for pressure and 30 cm2 for volume, we get 78 x 30 = k, so k = 2340. Since k is constant, we can find the new pressure by writing 2340 = P(20). Solving for P gives 117.
The value of k for this gas is 15.6 x 50 = 780. Decreasing the volume of the container by 40% can be written as 50 x 0.6 = 30, so the new pressure is 780 = P(30). Solving for P gives 26.