import { type PracticeQuestion } from "../../types/lesson";

export const PERCENTAGES_EASY: PracticeQuestion[] = [
  {
    id: "048811bd",
    type: "mcq",
    questionHtml: "What is <strong>10 % sign</strong> of <strong>370</strong>?",
    choices: [
      { label: "A", text: "<strong>27</strong>" },
      { label: "B", text: "<strong>37</strong>" },
      { label: "C", text: "<strong>333</strong>" },
      { label: "D", text: "<strong>360</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. <strong>10 % sign</strong> of a quantity means <strong>(10) / (100)</strong> times the quantity. Therefore, <strong>10 % sign</strong> of <strong>370</strong> can be represented as <strong>(10) / (100) (370)</strong>, which is equivalent to <strong>0.10 (370)</strong>, or <strong>37</strong>. Therefore, <strong>10 % sign</strong> of <strong>370</strong> is <strong>37</strong>.<br>Choice A is incorrect. This is <strong>10 % sign</strong> of <strong>270</strong>, not <strong>10 % sign</strong> of <strong>370</strong>.<br>Choice C is incorrect. This is <strong>90 % sign</strong> of <strong>370</strong>, not <strong>10 % sign</strong> of <strong>370</strong>.<br>Choice D is incorrect. This is <strong>370 − 10</strong>, not <strong>10 % sign</strong> of <strong>370</strong>.",
    hasFigure: false,
  },
  {
    id: "191d167b",
    type: "mcq",
    questionHtml:
      "Last year, <strong>200</strong> students enrolled in an interior design program. This year, the number of students enrolled is <strong>147 % sign</strong> of last year’s number. How many students are enrolled in the interior design program this year?",
    choices: [
      { label: "A", text: "<strong>247</strong>" },
      { label: "B", text: "<strong>294</strong>" },
      { label: "C", text: "<strong>347</strong>" },
      { label: "D", text: "<strong>394</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. It's given that the number of students enrolled in an interior design program this year is <strong>147 % sign</strong> of last year's number, which is <strong>200</strong>. <strong>147 % sign</strong> of <strong>200</strong> can be expressed as <strong>((147) / (100)) (200)</strong>, or <strong>(1.47) (200)</strong>, which is equivalent to <strong>294</strong>. Therefore, <strong>294</strong> students are enrolled in the interior design program this year.<br>Choice A is incorrect and may result from conceptual or calculation errors.<br>Choice C is incorrect and may result from conceptual or calculation errors.<br>Choice D is incorrect and may result from conceptual or calculation errors.",
    hasFigure: false,
  },
  {
    id: "194ae3b1",
    type: "mcq",
    questionHtml:
      "There were approximately 113,000 occupational therapy jobs in the United States in 2012. The Bureau of Labor Statistics has projected that this number will increase by 29% from 2012 to 2022. Of the following, which is closest to the number of occupational therapy jobs the bureau has projected for the United States in 2022?",
    choices: [
      { label: "A", text: "115,900" },
      { label: "B", text: "116,300" },
      { label: "C", text: "142,000" },
      { label: "D", text: "145,800" },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. The decimal equivalent of 29% is 0.29. It’s given that the 113,000 occupational therapy jobs in the United States in 2012 are projected to increase by 29% by 2022. Increasing 113,000 by 29% can be expressed as <strong>113, 000 · (1 + 0 . 2 9, )</strong>, or <strong>113, 000 · 1 . 2 9</strong>. Evaluating this expression yields 145,770. The closest number is 145,800 in choice D.Choice A is incorrect and may result from increasing 113,000 by 2,900 instead of by 29%. Choice B is incorrect and may result from increasing 113,000 by 2.9% instead of by 29%. Choice C is incorrect and may result from increasing 113,000 by 29,000 instead of by 29%.",
    hasFigure: false,
  },
  {
    id: "1c2f50a6",
    type: "mcq",
    questionHtml:
      "During a sale, the original prices of all the items in a clothing store have been reduced by 20%. What is the sale price of a jacket with an original price of $50 ?",
    choices: [
      { label: "A", text: "$12" },
      { label: "B", text: "$30" },
      { label: "C", text: "$36" },
      { label: "D", text: "$40" },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. It’s given that the original price of the jacket has been reduced by 20%. Multiplying the original price, $50, by 20% gives the amount, in dollars, that the price of the jacket is reduced by: <strong>50 · . 2 0 = 10</strong>. Subtracting this value from the original price results in the sale price of the jacket: <strong>50 dollars − 10 dollars</strong>, or $40.Choices A, B, and C are incorrect and may result from a conceptual or calculation error.",
    hasFigure: false,
  },
  {
    id: "273b7f37",
    type: "mcq",
    questionHtml:
      "Isabel grows potatoes in her garden. This year, she harvested <strong>760</strong> potatoes and saved <strong>10 % sign</strong> of them to plant next year. How many of the harvested potatoes did Isabel save to plant next year?",
    choices: [
      { label: "A", text: "<strong>66</strong>" },
      { label: "B", text: "<strong>76</strong>" },
      { label: "C", text: "<strong>84</strong>" },
      { label: "D", text: "<strong>86</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. The number of harvested potatoes Isabel saved to plant next year can be calculated by multiplying the total number of potatoes Isabel harvested, <strong>760</strong>, by the proportion of potatoes she saved. Since she saved <strong>10 % sign</strong> of the potatoes she harvested, the proportion of potatoes she saved is <strong>(10) / (100)</strong>, or <strong>0.1</strong>. Multiplying <strong>760</strong> by this proportion gives <strong>760 (0.1)</strong>, or <strong>76</strong>, potatoes that she saved to plant next year.<br>Choice A is incorrect and may result from conceptual or calculation errors.<br>Choice C is incorrect and may result from conceptual or calculation errors.<br>Choice D is incorrect and may result from conceptual or calculation errors.",
    hasFigure: false,
  },
  {
    id: "28c6bd8c",
    type: "mcq",
    questionHtml:
      "The table above shows a summary of 1,200 responses to a survey question. Based on the table, how many of those surveyed get most of their medical information from either a doctor or the Internet?",
    choices: [
      { label: "A", text: "865" },
      { label: "B", text: "887" },
      { label: "C", text: "912" },
      { label: "D", text: "926" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. According to the table, 63% of survey respondents get most of their medical information from a doctor and 13% get most of their medical information from the Internet. Therefore, 76% of the 1,200 survey respondents get their information from either a doctor or the Internet, and 76% of 1,200 is 912.Choices A, B, and D are incorrect. According to the table, 76% of survey respondents get their information from either a doctor or the Internet. Choice A is incorrect because 865 is about 72% (the percent of survey respondents who get most of their medical information from a doctor or from magazines/brochures), not 76%, of 1,200. Choice B is incorrect because 887 is about 74%, not 76%, of 1,200. Choice D is incorrect because 926 is about 77%, not 76%, of 1,200.",
    hasFigure: true,
    figureUrl: "/practice-images/28c6bd8c_img1.png",
  },
  {
    id: "29c177e6",
    type: "mcq",
    questionHtml: "What is <strong>10 % sign</strong> of <strong>470</strong>?",
    choices: [
      { label: "A", text: "<strong>37</strong>" },
      { label: "B", text: "<strong>47</strong>" },
      { label: "C", text: "<strong>423</strong>" },
      { label: "D", text: "<strong>460</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. <strong>10 % sign</strong> of a quantity means <strong>(10) / (100)</strong> times the quantity. Therefore, <strong>10 % sign</strong> of <strong>470</strong> can be represented as <strong>(10) / (100) (470)</strong>, which is equivalent to <strong>0.10 (470)</strong>, or <strong>47</strong>. Therefore, <strong>10 % sign</strong> of <strong>470</strong> is <strong>47</strong>.<br>Choice A is incorrect. This is <strong>10 % sign</strong> of <strong>370</strong>, not <strong>10 % sign</strong> of <strong>470</strong>.<br>Choice C is incorrect. This is <strong>90 % sign</strong> of <strong>470</strong>, not <strong>10 % sign</strong> of <strong>470</strong>.<br>Choice D is incorrect. This is <strong>470 − 10</strong>, not <strong>10 % sign</strong> of <strong>470</strong>.",
    hasFigure: false,
  },
  {
    id: "2d31caae",
    type: "mcq",
    questionHtml:
      "Call Ratings<br> <br> 1 Star<br> 2 Stars<br> 3 Stars<br> 4 Stars<br> Total<br> Employee A <br> 16<br> 49<br> 72<br> 8<br> 145<br> Employee B<br> <br> 4<br><br> <br> 10<br> 22<br> 34<br> 70<br> Employee C<br> 8<br> 56<br> 45<br> 16<br> 125<br> Employee D<br> 22<br> 42<br> 84<br> 12<br> 160<br> Total<br> 50<br> 157<br> 223<br> 70<br> 500<br> <br>A supervisor at a call center reviewed 500 calls taken by four employees and rated the employees’ performance on each call on a scale from 1 star to 4 stars. The ratings for each employee are shown in the table above. According to the table, to the nearest whole percent, what percent of Employee A’s calls received a rating of 1 star?",
    choices: [
      { label: "A", text: "3%" },
      { label: "B", text: "11%" },
      { label: "C", text: "16%" },
      { label: "D", text: "32%" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. The percent of Employee A’s calls that received a rating of 1 star is the number of Employee A’s 1-star calls divided by the total number of Employee A’s calls. This quotient, <strong>16 over 145</strong>, is approximately equal to <strong>0 . 1 1 0 3</strong>, or <strong>11 . 0 3 %</strong>. To the nearest whole percent, this is 11%.<br><br>Choice A is incorrect. This is the percent of all calls taken by Employee A that received a rating of 1 star. Choice C is incorrect and may result from a conceptual error. For example, 16 is the number, not the percent, of calls taken by Employee A that received a rating of 1 star. Choice D is incorrect. This is the percent of all calls that received a rating of 1 star that were taken by Employee A.",
    hasFigure: false,
  },
  {
    id: "3a6ed720",
    type: "mcq",
    questionHtml:
      "Of <strong>900, 000</strong> beads, <strong>828, 000</strong> are silver. What percentage of the beads are silver?",
    choices: [
      { label: "A", text: "<strong>8 % sign</strong>" },
      { label: "B", text: "<strong>36 % sign</strong>" },
      { label: "C", text: "<strong>72 % sign</strong>" },
      { label: "D", text: "<strong>92 % sign</strong>" },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. The proportion of the beads that are silver can be written as <strong>(828, 000) / (900, 000)</strong>, or <strong>0.92</strong>. Therefore, the percentage of the beads that are silver is <strong>0.92 (100)</strong>, or <strong>92 % sign</strong>.<br>Choice A is incorrect. This is the percentage of the beads that are not silver.<br>Choice B is incorrect and may result from conceptual or calculation errors.<br>Choice C is incorrect and may result from conceptual or calculation errors.",
    hasFigure: false,
  },
  {
    id: "41b71b4e",
    type: "mcq",
    questionHtml: "What number is 20% greater than 60 ?",
    choices: [
      { label: "A", text: "50" },
      { label: "B", text: "72" },
      { label: "C", text: "75" },
      { label: "D", text: "132" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. The decimal equivalent of 20% is 0.2. The number that is 20% greater than 60 is also 120% of 60. The decimal equivalent of 120% is 1.2, and <strong>1 . 2 · 60 = 72</strong>.Alternate approach: 10% of 60 is 6, and 20% of 60 is double that amount, or 12. It follows that the number that is 20% greater than 60 is 12 more than 60, or <strong>60 + 12 = 72</strong>.<br>Choice A is incorrect and may result from dividing, instead of multiplying, 60 by 1.2. Choice C is incorrect because it’s 25% greater than 60, rather than 20% greater than 60. Choice D is incorrect and may result from multiplying 60 by 2.2 instead of 1.2.",
    hasFigure: false,
  },
  {
    id: "6e4a60dd",
    type: "mcq",
    questionHtml:
      "Rita’s total bill at a restaurant was $25.00, including tax. If she left a tip of 20% of the total bill, what was the amount of the tip?",
    choices: [
      { label: "A", text: "$3.50" },
      { label: "B", text: "$4.00" },
      { label: "C", text: "$4.50" },
      { label: "D", text: "$5.00" },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. The total bill was $25.00. The percentage 20% is equivalent to the decimal 0.2. The tip is the product of the percentage and the total bill; therefore, <strong>0 . 2 · 25 = 5</strong>, so the tip was $5.00.Choices A, B, and C are incorrect and may be the result of incorrectly converting the given percentage or a calculation error.",
    hasFigure: false,
  },
  {
    id: "77cf4fa6",
    type: "spr",
    questionHtml:
      "There are <strong>170</strong> blocks in a container. Of these blocks, <strong>10 % sign</strong> are green. How many blocks in the container are green?",
    choices: [],
    correctAnswer: "17",
    explanation:
      "The correct answer is <strong>17</strong>. It's given that there are <strong>170</strong> blocks in a container, and of these blocks, <strong>10 % sign</strong> are green. Since <strong>10 % sign</strong> can be rewritten as <strong>(10) / (100)</strong>, or <strong>0.1</strong>, the number of green blocks in the container is <strong>0.1 (170)</strong>, or <strong>17</strong>.",
    hasFigure: false,
  },
  {
    id: "7ed0d098",
    type: "mcq",
    questionHtml:
      "Lani spent 15% of her 8-hour workday in meetings. How many minutes of her workday did she spend in meetings?",
    choices: [
      { label: "A", text: "1.2" },
      { label: "B", text: "15" },
      { label: "C", text: "48" },
      { label: "D", text: "72" },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. There are 60 minutes in one hour, so an 8-hour workday has <strong>60 · 8 = 480</strong> minutes. To calculate 15% of 480, multiply 0.15 by 480: <strong>0 . 1 5 · 480 = 72</strong>. Therefore, Lani spent 72 minutes of her workday in meetings.Choice A is incorrect because 1.2 is 15% of 8, which gives the time Lani spent of her workday in meetings in hours, not minutes. Choices B and C are incorrect and may be the result of computation errors.",
    hasFigure: false,
  },
  {
    id: "8705ecba",
    type: "mcq",
    questionHtml:
      "The cost of a certain shirt is $20 before a 5% sales tax is added. What is the total cost, including sales tax, to purchase the shirt?",
    choices: [
      { label: "A", text: "$20.05" },
      { label: "B", text: "$20.50" },
      { label: "C", text: "$21.00" },
      { label: "D", text: "$25.00" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. The total cost to purchase the shirt is the $20 cost of the shirt plus the 5% sales tax. The value of the 5% sales tax on the $20 shirt is equivalent to<strong>0 . 0 5 · 20 dollars</strong>, or $1. Therefore, the total cost to purchase the shirt is <strong>20 dollars + 1 dollar</strong>, or $21.Choice A is incorrect and may result from neglecting to multiply by $20 when finding the value of the sales tax. Choice B is incorrect and may result from dividing by 10, instead of by 100, and then neglecting to multiply by $20 when finding the sales tax. Choice D is incorrect and may result from interpreting the sales tax of 5% as $5.",
    hasFigure: false,
  },
  {
    id: "949cd96b",
    type: "mcq",
    questionHtml:
      "The length of the base of a certain parallelogram is <strong>89 % sign</strong> of the height of the parallelogram. Which expression represents the length of the base of the parallelogram, where <strong>h</strong> is the height of the parallelogram?",
    choices: [
      { label: "A", text: "<strong>89 h</strong>" },
      { label: "B", text: "<strong>0.089 h</strong>" },
      { label: "C", text: "<strong>8.9 h</strong>" },
      { label: "D", text: "<strong>0.89 h</strong>" },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. It's given that the length of the base of the parallelogram is <strong>89 % sign</strong> of the height of the parallelogram. Since <strong>h</strong> is the height of the parallelogram, it follows that the length of the base of the parallelogram can be represented by the expression <strong>(89) / (100) h</strong>, or <strong>0.89 h</strong>.<br>Choice A is incorrect. This expression represents <strong>8, 900 % sign</strong>, not <strong>89 % sign</strong>, of the height of the parallelogram.<br>Choice B is incorrect. This expression represents <strong>8.9 % sign</strong>, not <strong>89 % sign</strong>, of the height of the parallelogram.<br>Choice C is incorrect. This expression represents <strong>890 % sign</strong>, not <strong>89 % sign</strong>, of the height of the parallelogram.",
    hasFigure: false,
  },
  {
    id: "9c44f828",
    type: "mcq",
    questionHtml:
      "There are a total of <strong>840</strong> seats in a school auditorium. During an assembly, students occupied <strong>50 % sign</strong> of the seats in the auditorium. How many seats did the students occupy during this assembly?",
    choices: [
      { label: "A", text: "<strong>25</strong>" },
      { label: "B", text: "<strong>50</strong>" },
      { label: "C", text: "<strong>420</strong>" },
      { label: "D", text: "<strong>790</strong>" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. It's given that during an assembly, students occupied <strong>50 % sign</strong> of the <strong>840</strong> seats in the school auditorium. Therefore, the number of seats that the students occupied during this assembly can be calculated by multiplying the number of seats in the school auditorium by <strong>(50) / (100)</strong>. Thus, the students occupied <strong>840 ((50) / (100))</strong>, or <strong>420</strong>, seats during this assembly.<br>Choice A is incorrect. This is approximately <strong>3 % sign</strong>, not <strong>50 % sign</strong>, of <strong>840</strong>.<br>Choice B is incorrect. This is approximately <strong>6 % sign</strong>, not <strong>50 % sign</strong>, of <strong>840</strong>.<br>Choice D is incorrect. This is approximately <strong>94 % sign</strong>, not <strong>50 % sign</strong>, of <strong>840</strong>.",
    hasFigure: false,
  },
  {
    id: "a8fabad0",
    type: "mcq",
    questionHtml:
      "A waiter receives tips from each customer. On average, the tip is 15% of the customer’s bill. At this rate, which of the following is closest to the tip the waiter can expect when a customer has a bill that is $78.20?",
    choices: [
      { label: "A", text: "$8.00" },
      { label: "B", text: "$10.00" },
      { label: "C", text: "$12.00" },
      { label: "D", text: "$14.00" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. If the bill is $78.20, 15% of the bill can be found by multiplying 78.20 by the decimal conversion of 15%, 78.20 × 0.15 = $11.73. The exact amount $11.73 is closest in value to $12.00.Choices A, B, and D are incorrect and may be the result of errors when calculating 15% of the total $78.20.",
    hasFigure: false,
  },
  {
    id: "bb7c8186",
    type: "mcq",
    questionHtml: "What is <strong>23 % sign</strong> of <strong>100</strong>?",
    choices: [
      { label: "A", text: "<strong>23</strong>" },
      { label: "B", text: "<strong>46</strong>" },
      { label: "C", text: "<strong>77</strong>" },
      { label: "D", text: "<strong>123</strong>" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. <strong>23 % sign</strong> of <strong>100</strong> can be calculated by multiplying <strong>(23) / (100)</strong> by <strong>100</strong>, which yields <strong>((23) / (100)) 100</strong>, or <strong>23</strong>.<br>Choice B is incorrect. This is <strong>46 % sign</strong>, not <strong>23 % sign</strong>, of <strong>100</strong>.<br>Choice C is incorrect. This is <strong>23 % sign</strong> less than <strong>100</strong>, not <strong>23 % sign</strong> of <strong>100</strong>.<br>Choice D is incorrect. This is <strong>23 % sign</strong> greater than <strong>100</strong>, not <strong>23 % sign</strong> of <strong>100</strong>.",
    hasFigure: false,
  },
  {
    id: "bd90f87e",
    type: "mcq",
    questionHtml:
      "What was the percent increase of the minimum wage from 1960 to 1970?",
    choices: [
      { label: "A", text: "30%" },
      { label: "B", text: "60%" },
      { label: "C", text: "62.5%" },
      { label: "D", text: "120%" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. According to the table, the minimum wage in 1960 was $1.00 per hour, and in 1970 it was $1.60 per hour. The percentage change is therefore <strong>100 · (the fraction with numerator 1 . 6 0 − 1 . 0 0, and denominator 1 . 0 0, ) = 60 %</strong>.Choice A is incorrect and may result from averaging the two wages before calculating the percentage change. Choice C is incorrect. This is the 1960 wage expressed as a percentage of the 1970 wage, not the percentage change between the two. Choice D is incorrect and may result from a calculation error.",
    hasFigure: false,
  },
  {
    id: "e9fb7774",
    type: "mcq",
    questionHtml:
      "What percentage of <strong>300</strong> is <strong>75</strong>?",
    choices: [
      { label: "A", text: "<strong>25 % sign</strong>" },
      { label: "B", text: "<strong>50 % sign</strong>" },
      { label: "C", text: "<strong>75 % sign</strong>" },
      { label: "D", text: "<strong>225 % sign</strong>" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. Let <strong>x</strong> represent the percentage of <strong>300</strong> that is <strong>75</strong>. This can be written as <strong>(x) / (100) (300) = 75</strong>, or <strong>3 x = 75</strong>. Dividing both sides of this equation by <strong>3</strong> yields <strong>x = 25</strong>. Therefore, <strong>25 % sign</strong> of <strong>300</strong> is <strong>75</strong>.<br>Choice B is incorrect. <strong>50 % sign</strong> of <strong>300</strong> is <strong>150</strong>, not <strong>75</strong>.<br>Choice C is incorrect. <strong>75 % sign</strong> of <strong>300</strong> is <strong>225</strong>, not <strong>75</strong>.<br>Choice D is incorrect. <strong>225 % sign</strong> of <strong>300</strong> is <strong>675</strong>, not <strong>75</strong>.",
    hasFigure: false,
  },
  {
    id: "eaab8bc1",
    type: "spr",
    questionHtml:
      "Out of <strong>300</strong> seeds that were planted, <strong>80 % sign</strong> sprouted. How many of these seeds sprouted?",
    choices: [],
    correctAnswer: "240",
    explanation:
      "The correct answer is <strong>240</strong>. It’s given that <strong>80 % sign</strong> of the <strong>300</strong> seeds sprouted. Therefore, the number of seeds that sprouted can be calculated by multiplying the number of seeds that were planted by <strong>(80) / (100)</strong>, which gives <strong>300 ((80) / (100))</strong>, or <strong>240</strong>.",
    hasFigure: false,
  },
];

export const PERCENTAGES_MEDIUM: PracticeQuestion[] = [
  {
    id: "121dc44f",
    type: "mcq",
    questionHtml:
      "The population of City A increased by <strong>7 % sign</strong> from <strong>2015</strong> to <strong>2016</strong>. If the <strong>2016</strong> population is <strong>k</strong> times the <strong>2015</strong> population, what is the value of <strong>k</strong>?",
    choices: [
      { label: "A", text: "<strong>0.07</strong>" },
      { label: "B", text: "<strong>0.7</strong>" },
      { label: "C", text: "<strong>1.07</strong>" },
      { label: "D", text: "<strong>1.7</strong>" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. It's given that the population of City A increased by <strong>7 % sign</strong> from <strong>20 15</strong> to <strong>20 16</strong>. Therefore, the population of City A in <strong>20 16</strong> includes <strong>100 % sign</strong> of the population of City A in <strong>20 15</strong> plus an additional <strong>7 % sign</strong> of the population of City A in <strong>20 15</strong>. This means that the population of City A in <strong>20 16</strong> is <strong>107 % sign</strong> of the population in <strong>20 15</strong>. Thus, the population of City A in <strong>20 16</strong> is <strong>(107) / (100)</strong>, or <strong>1.07</strong>, times the <strong>20 15</strong> population. Therefore, the value of <strong>k</strong> is <strong>1.07</strong>.<br>Choice A is incorrect. This would be the value of <strong>k</strong> if the population in <strong>20 16</strong> was <strong>7 % sign</strong> of the population in <strong>20 15</strong>.<br>Choice B is incorrect. This would be the value of <strong>k</strong> if the population in <strong>20 16</strong> was <strong>70 % sign</strong> of the population in <strong>20 15</strong>.<br>Choice D is incorrect. This would be the value of <strong>k</strong> if the population increased by <strong>70 % sign</strong>, not <strong>7 % sign</strong>, from <strong>20 15</strong> to <strong>20 16</strong>.",
    hasFigure: false,
  },
  {
    id: "566759ef",
    type: "mcq",
    questionHtml:
      "Thomas installed a new stove in his restaurant. At the time of installation, the stove had a value of $800. Thomas estimates that each year the value of the stove will depreciate by 20% of the previous year’s estimated value. What is the estimated value of the stove exactly 2 years after Thomas installed it?",
    choices: [
      { label: "A", text: "$480" },
      { label: "B", text: "$512" },
      { label: "C", text: "$556" },
      { label: "D", text: "$640" },
    ],
    correctAnswer: "",
    explanation:
      "Choice B is correct. If the stove’s value depreciates by 20% of the previous year’s estimated value, then each year it retains 100% – 20% = 80%, or 0.80, of the previous year’s estimated value. Since the stove’s value was $800 when Thomas installed it, the estimated value after two years would be (0.80)(0.80)($800) = $512.Choice A is incorrect. This is the value of the stove if each year it had depreciated by 20% of the original value rather than by 20% of the previous year’s estimated value. Choice C is incorrect and may be the result of a computational error. Choice D is incorrect. This is the estimated value of the stove 1 year after Thomas installed it, not 2 years.",
    hasFigure: false,
  },
  {
    id: "63573fea",
    type: "mcq",
    questionHtml:
      "During the first month of sales, a company sold 1,300,000 units of a certain type of smartphone. During the same month, 15% of the units sold were returned. If sales and the return rate remain the same for each of the next 5 months, about how many units of this smartphone will be returned to the company during this 6-month period?",
    choices: [
      { label: "A", text: "195,000" },
      { label: "B", text: "975,000" },
      { label: "C", text: "1,170,000" },
      { label: "D", text: "6,630,000" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. Of the 1,300,000 units sold during the first month, 15% were returned, so <strong>1, 300, 000 · 0 . 1 5 = 195, 000</strong> units were returned during the first month. If the units were sold and returned at the same rate for the next 5 months, then a total of <strong>195, 000 · 6 = 1, 170, 000</strong> smartphone units were returned during the 6-month period.Choice A is incorrect. This is the number of units that were returned in 1 month. Choice B is incorrect. This is the number of units that were returned in 5 months. Choice D is incorrect. This is the number of units sold and not returned during the first 6 months.",
    hasFigure: false,
  },
  {
    id: "707db2d3",
    type: "mcq",
    questionHtml:
      "For the finale of a TV show, viewers could use either social media or a text message to vote for their favorite of two contestants. The contestant receiving more than 50% of the vote won. An estimated 10% of the viewers voted, and 30% of the votes were cast on social media. Contestant 2 earned 70% of the votes cast using social media and 40% of the votes cast using a text message. Based on this information, which of the following is an accurate conclusion?",
    choices: [
      {
        label: "A",
        text: "If all viewers had voted, Contestant 2 would have won.",
      },
      {
        label: "B",
        text: "Viewers voting by social media were likely to be younger than viewers voting by text message.",
      },
      {
        label: "C",
        text: "If all viewers who voted had voted by social media instead of by text message, Contestant 2 would have won.",
      },
      {
        label: "D",
        text: "Viewers voting by social media were more likely to prefer Contestant 2 than were viewers voting by text message.",
      },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. It is given that Contestant 2 earned 70% of the votes cast using social media and 40% of the votes cast using a text message. Based on this information, viewers voting by social media were more likely to prefer Contestant 2 than were viewers voting by text message.Choices A, B, and C are incorrect. There is not enough information about the viewers to reach these conclusions.",
    hasFigure: false,
  },
  {
    id: "709e04de",
    type: "mcq",
    questionHtml:
      "The value of <strong>z</strong> is <strong>1.13</strong> times <strong>100</strong>. The value of <strong>z</strong> is what percent greater than <strong>100</strong>?",
    choices: [
      { label: "A", text: "<strong>11.3</strong>" },
      { label: "B", text: "<strong>13</strong>" },
      { label: "C", text: "<strong>130</strong>" },
      { label: "D", text: "<strong>213</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. It’s given that the value of <strong>z</strong> is <strong>1.13</strong> times <strong>100</strong>. This can be written as <strong>z = (1.13) (100)</strong>, which is equivalent to <strong>z = (1 + 0.13) (100)</strong>, or <strong>z = (1 + (13) / (100)) (100)</strong>. It follows that the value of <strong>z</strong> is <strong>100 % sign</strong> of <strong>100</strong> plus <strong>13 % sign</strong> of <strong>100</strong>. Therefore, the value of <strong>z</strong> is <strong>13 % sign</strong> greater than <strong>100</strong>.<br>Choice A is incorrect. This gives a value of <strong>z</strong> that is <strong>1.113</strong>, not <strong>1.13</strong>, times <strong>100</strong>.<br>Choice C is incorrect. This gives a value of <strong>z</strong> that is <strong>2.30</strong>, not <strong>1.13</strong>, times <strong>100</strong>.<br>Choice D is incorrect. This gives a value of <strong>z</strong> that is <strong>3.13</strong>, not <strong>1.13</strong>, times <strong>100</strong>.",
    hasFigure: false,
  },
  {
    id: "7b731fc3",
    type: "spr",
    questionHtml:
      "What number is <strong>40 % sign</strong> greater than <strong>115</strong>?",
    choices: [],
    correctAnswer: "161",
    explanation:
      "The correct answer is <strong>161</strong>. For a number to be <strong>40 % sign</strong> greater than <strong>115</strong>, it follows that the number is <strong>(100 % sign of 115) + (40 % sign of 115)</strong>, which can be written as <strong>(100) / (100) (115) + (40) / (100) (115)</strong>. This expression is equivalent to <strong>1 (115) + 0.4 (115)</strong>, or <strong>1.4 (115)</strong>, which is equal to <strong>161</strong>. Therefore, <strong>161</strong> is <strong>40 % sign</strong> greater than <strong>115</strong>.",
    hasFigure: false,
  },
  {
    id: "7cab9fe1",
    type: "mcq",
    questionHtml:
      "Which expression represents the result of increasing a positive quantity <strong>w</strong> by <strong>43 % sign</strong>?",
    choices: [
      { label: "A", text: "<strong>1.43 w</strong>" },
      { label: "B", text: "<strong>0.57 w</strong>" },
      { label: "C", text: "<strong>43 w</strong>" },
      { label: "D", text: "<strong>0.43 w</strong>" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. The result of increasing a positive quantity <strong>w</strong> by <strong>x % sign</strong> can be represented by the expression <strong>(1 + (x) / (100)) w</strong>. Therefore, the result of increasing a positive quantity <strong>w</strong> by <strong>43 % sign</strong> can be found by substituting <strong>43</strong> for <strong>x</strong> in the expression <strong>(1 + (x) / (100)) w</strong>, which gives <strong>(1 + (43) / (100)) w</strong>, or <strong>1.43 w</strong>. Thus, the expression <strong>1.43 w</strong> represents the result of increasing a positive quantity <strong>w</strong> by <strong>43 % sign</strong>.<br>Choice B is incorrect. This is the result of decreasing a positive quantity <strong>w</strong> by <strong>43 % sign</strong>.<br>Choice C is incorrect. This is the result of increasing a positive quantity <strong>w</strong> by <strong>4, 200 % sign</strong>.<br>Choice D is incorrect. This is the result of decreasing a positive quantity <strong>w</strong> by <strong>57 % sign</strong>.",
    hasFigure: false,
  },
  {
    id: "8a714fa1",
    type: "mcq",
    questionHtml:
      "Which of the following represents the result of increasing the quantity x by 9%, where <strong>x > 0</strong> ?",
    choices: [
      { label: "A", text: "<strong>1 . 0 9 x</strong>" },
      { label: "B", text: "<strong>0 . 0 9 x</strong>" },
      { label: "C", text: "<strong>x + 9</strong>" },
      { label: "D", text: "<strong>x + 0 . 0 9</strong>" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. Increasing the positive quantity x by 9% is the result of adding 9% of x to x. 9% of x can be represented algebraically as <strong>the fraction, 9 over 100, end fraction · x</strong>, or <strong>0 . 0 9 x</strong>. Adding this expression to x yields <strong>x + 0 . 0 9 x</strong>, or <strong>1 . 0 9 x</strong>.Choice B is incorrect. This represents 9% of x. Choice C is incorrect. This represents increasing x by 9, not by 9%. Choice D is incorrect. This represents increasing x by 0.09, not by 9%.",
    hasFigure: false,
  },
  {
    id: "8cbf1415",
    type: "mcq",
    questionHtml:
      "In a group, <em>(expression)</em>% of the items are red. Of all the red items in the group, <em>(expression)</em>% also have stripes. What percentage of the items in the group are red with stripes?",
    choices: [
      { label: "A", text: "<em>(expression)</em>%" },
      { label: "B", text: "<em>(expression)</em>%" },
      { label: "C", text: "<em>(expression)</em>%" },
      { label: "D", text: "<em>(expression)</em>%" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. It’s given that in a group, <strong>40 % sign</strong> of the items are red. It follows that the number of red items in the group can be represented by <strong>0 . 4 x</strong>, where <strong>x</strong> represents the total number of items in the group. It’s also given that of all the red items in the group, <strong>30 % sign</strong> also have stripes. It follows that the number of items in the group that are red and have stripes can be represented by <strong>0 . 3 (0 . 4 x)</strong>, or <strong>0 . 12 x</strong>. The expression <strong>0 . 12 x</strong> represents <strong>12 % sign</strong> of <strong>x</strong>. Since <strong>x</strong> represents the total number of items in the group, it follows that <strong>12 % sign</strong> of the items in the group are red and have stripes.<br>Choice A is incorrect and may result from subtracting <strong>30 % sign</strong> from <strong>40 % sign</strong> rather than calculating <strong>30 % sign</strong> of <strong>40 % sign</strong>.<br>Choice C is incorrect and may result from adding <strong>30 % sign</strong> and <strong>40 % sign</strong> rather than calculating <strong>30 % sign</strong> of <strong>40 % sign</strong>.<br>Choice D is incorrect and may result from calculating the percentage that <strong>30 % sign</strong> is of <strong>40 % sign</strong> rather than calculating <strong>30 % sign</strong> of <strong>40 % sign</strong>.",
    hasFigure: false,
  },
  {
    id: "8e2e424e",
    type: "mcq",
    questionHtml:
      "The number k is 36% greater than 50. If k is the product of 50 and r, what is the value of r ?",
    choices: [
      { label: "A", text: "36" },
      { label: "B", text: "3.6" },
      { label: "C", text: "1.36" },
      { label: "D", text: "0.36" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. It’s given that the number k is 36% greater than 50. Therefore, the value of k is the number 50 plus 36% of 50. This can be rewritten as <strong>k = 50 + the fraction 36 over 100, end fraction · 50</strong>. Multiplying the terms <strong>the fraction 36 over 100, end fraction · 50</strong> yields 18, so <strong>k = 50 + 18</strong>, or <strong>k = 68</strong>. It’s also given that k is the product of 50 and r, which can be rewritten as <strong>k = 50 r</strong>. Substituting 68 for k yields <strong>68 = 50 r</strong>. Dividing both sides of this equation by 50 yields <strong>r = 1 . 3 6</strong>.Choice A is incorrect. This is the percentage that k is greater than 50. Choice B is incorrect and may result from a calculation error. Choice D is incorrect. This would be the value of r if k were 36% of 50, instead of 36% greater than 50.",
    hasFigure: false,
  },
  {
    id: "94c65646",
    type: "spr",
    questionHtml:
      "<strong>432</strong> is <strong>96 % sign</strong> of what number?",
    choices: [],
    correctAnswer: "450",
    explanation:
      "The correct answer is <strong>450</strong>. Let <strong>x</strong> represent the number that <strong>432</strong> is <strong>96 % sign</strong> of. This can be written as <strong>((96) / (100)) x = 432</strong>, or <strong>0.96 x = 432</strong>. Dividing both sides of this equation by <strong>0.96</strong> yields <strong>x = 450</strong>. Therefore, <strong>432</strong> is <strong>96 % sign</strong> of <strong>450</strong>.",
    hasFigure: false,
  },
  {
    id: "96a45430",
    type: "mcq",
    questionHtml:
      "A number n is increased 6%. If the result is 318, what is the value of n ?",
    choices: [
      { label: "A", text: "199" },
      { label: "B", text: "299" },
      { label: "C", text: "300" },
      { label: "D", text: "337" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. The decimal equivalent of 6% is 0.06. Since increasing the number n by 6% yields the number 318, this situation can be represented by the equation <strong>n · (1 + 0 . 0 6, ) = 318</strong>, or <strong>n · 1 . 0 6 = 318</strong>. Dividing both sides of this equation by 1.06 yields <strong>n = 300</strong>.Choice A is incorrect. This is the result when n is increased by 60%, not by 6%. Choice B is incorrect. This is the approximate result of decreasing 318 by 6%. Choice D is incorrect. This is the approximate result of increasing 318 by 6%.",
    hasFigure: false,
  },
  {
    id: "b2f6f17d",
    type: "mcq",
    questionHtml:
      "A customer’s monthly water bill was $75.74. Due to a rate increase, her monthly bill is now $79.86. To the nearest tenth of a percent, by what percent did the amount of the customer’s water bill increase?",
    choices: [
      { label: "A", text: "4.1%" },
      { label: "B", text: "5.1%" },
      { label: "C", text: "5.2%" },
      { label: "D", text: "5.4%" },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. To find the percent increase of the customer’s water bill, the absolute increase of the bill, in dollars, is divided by the original amount of the bill, and the result is multiplied by 100%, as follows: <strong>the fraction with numerator 79 . 8 6 − 75 . 7 4, and denominator 75 . 7 4, is ≈, 0 . 0 5 4;</strong>; <strong>0 . 0 5 4 · 100 % = 5 . 4 %</strong>.Choice A is incorrect. This choice is the difference <strong>79 . 8 6 − 75 . 7 4</strong> rounded to the nearest tenth, which is the (absolute) increase of the bill’s amount, not its percent increase. Choice B is incorrect and may be the result of some calculation errors. Choice C is incorrect and is the result of dividing the difference between the two bill amounts by the new bill amount instead of the original bill amount.",
    hasFigure: false,
  },
  {
    id: "ba61d95f",
    type: "mcq",
    questionHtml:
      "The population of Greenville increased by <strong>7 % sign</strong> from <strong>2015</strong> to <strong>2016</strong>. If the <strong>2016</strong> population is <strong>k</strong> times the <strong>2015</strong> population, what is the value of <strong>k</strong>?",
    choices: [
      { label: "A", text: "<strong>0.07</strong>" },
      { label: "B", text: "<strong>0.7</strong>" },
      { label: "C", text: "<strong>1.07</strong>" },
      { label: "D", text: "<strong>1.7</strong>" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. Let <strong>x</strong> be the 2015 population of Greenville. It's given that the population increased by <strong>7 % sign</strong> from 2015 to 2016. The increase in population can be written as <strong>(0.07) x</strong>. The 2016 population of Greenville is given as the sum of the 2015 population of Greenville and the increase in population from 2015 to 2016. This can be rewritten as <strong>x + (0.07) x</strong>, or <strong>1.07 x</strong>. Therefore, the value of <strong>k</strong> is <strong>1.07</strong>.<br>Choice A is incorrect. This is the percent, represented as a decimal, that the population increased from 2015 to 2016, not the value of <strong>k</strong>.<br>Choice B is incorrect and may result from conceptual or calculation errors.<br>Choice D is incorrect. This is the value of <strong>k</strong> if the population increased by <strong>70 % sign</strong>, not <strong>7 % sign</strong>, from 2015 to 2016.",
    hasFigure: false,
  },
  {
    id: "d693f563",
    type: "spr",
    questionHtml:
      "Last year, Cedric had <strong>35</strong> plants in his garden. This year, the number of plants in Cedric’s garden is <strong>60 % sign</strong> greater than the number of plants in his garden last year. How many plants does Cedric have in his garden this year?",
    choices: [],
    correctAnswer: "56",
    explanation:
      "The correct answer is <strong>56</strong>. It’s given that Cedric had <strong>35</strong> plants in his garden last year and that the number of plants in Cedric's garden this year is <strong>60 % sign</strong> greater than the number of plants in his garden last year. It follows that the number of plants in Cedric’s garden this year is <strong>35</strong> plus <strong>60 % sign</strong> of <strong>35</strong>, which is equal to <strong>35 + 35 ((60) / (100))</strong>, or <strong>35 + 35 (0.6)</strong>. This expression is equivalent to <strong>35 + 21</strong>, or <strong>56</strong>. Therefore, Cedric has <strong>56</strong> plants in his garden this year.",
    hasFigure: false,
  },
  {
    id: "e9f4521a",
    type: "spr",
    questionHtml:
      "<strong>13</strong> is <strong>p % sign</strong> of <strong>25</strong>. What is the value of <strong>p</strong>?",
    choices: [],
    correctAnswer: "52",
    explanation:
      "The correct answer is <strong>52</strong>. It's given that <strong>13</strong> is <strong>p % sign</strong> of <strong>25</strong>. It follows that <strong>(13) / (25) = (p) / (100)</strong>. Multiplying both sides of this equation by <strong>100</strong> gives <strong>52 = p</strong>. Therefore, the value of <strong>p</strong> is <strong>52</strong>.",
    hasFigure: false,
  },
];

export const PERCENTAGES_HARD: PracticeQuestion[] = [
  {
    id: "0231050d",
    type: "spr",
    questionHtml:
      "<strong>The figure presents a line graph. The horizontal axis is labeled “Year, ” and the years 2003 through 2015 are indicated. The vertical axis is labeled “Annual snowfall, in inches, ” and the numbers 0 through 60, in increments of 10, are indicated. There are 13 points indicated on the graph. The data represented by the 13 points are as follows. Note that all values are approximate. Year, 2003. Number of inches, 40. Year, 2004. Number of inches, 12. Year, 2005. Number of inches, 13. Year, 2006. Number of inches, 14. Year, 2007. Number of inches, 10. Year, 2008. Number of inches, 5. Year, 2009. Number of inches, 8. Year, 2010. Number of inches, 56. Year, 2011. Number of inches, 10. Year, 2012. Number of inches, 3. Year, 2013. Number of inches, 4. Year, 2014. Number of inches, 32. Year, 2015. Number of inches, 19.</strong><br> <br><br>The line graph shows the total amount of snow, in inches, recorded each year in Washington, DC, from 2003 to 2015. If <strong>p %</strong> is the percent decrease in the annual snowfall from 2003 to 2007, what is the value of p ?",
    choices: [],
    correctAnswer: "",
    explanation:
      "The correct answer is 75. The percent decrease between two values is found by dividing the difference between the two values by the original value and multiplying by 100. The line graph shows that the annual snowfall in 2003 was 40 inches, and the annual snowfall in 2007 was 10 inches. Therefore, the percent decrease in the annual snowfall from 2003 to 2007 is <strong>(the fraction with numerator 40 − 10, and denominator 40, ) · 100</strong>, or 75. It’s given that this is equivalent to <strong>p %</strong>, so the value of p is 75.",
    hasFigure: true,
    figureUrl: "/practice-images/0231050d_img1.png",
  },
  {
    id: "040f2a84",
    type: "spr",
    questionHtml:
      "The regular price of a shirt at a store is <strong>dollar sign 11.70</strong>. The sale price of the shirt is <strong>80 % sign</strong> less than the regular price, and the sale price is <strong>30 % sign</strong> greater than the store's cost for the shirt. What was the store’s cost, in dollars, for the shirt? (Disregard the <strong>dollar sign</strong> sign when entering your answer. For example, if your answer is <strong>dollar sign 4.97</strong>, enter <strong>4.97</strong>)",
    choices: [],
    correctAnswer: "1.8, 9/5",
    explanation:
      "The correct answer is <strong>1.8</strong>. It’s given that the regular price of a shirt at a store is <strong>dollar sign 11.70</strong>, and the sale price of the shirt is <strong>80 % sign</strong> less than the regular price. It follows that the sale price of the shirt is <strong>dollar sign 11.70 (1 − (80) / (100))</strong>, or <strong>dollar sign 11.70 (1 − 0.8)</strong>, which is equivalent to <strong>dollar sign 2.34</strong>. It’s also given that the sale price of the shirt is <strong>30 % sign</strong> greater than the store’s cost for the shirt. Let <strong>x</strong> represent the store’s cost for the shirt. It follows that <strong>2.34 = (1 + (30) / (100)) x</strong>, or <strong>2.34 = 1.3 x</strong>. Dividing both sides of this equation by <strong>1.3</strong> yields <strong>x = 1.80</strong>. Therefore, the store’s cost, in dollars, for the shirt is <strong>1.80</strong>. Note that 1.8 and 9/5 are examples of ways to enter a correct answer.",
    hasFigure: false,
  },
  {
    id: "0ea56bb2",
    type: "mcq",
    questionHtml:
      "The manager of an online news service received the report above on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be double the percent increase from 2013 to 2014. How many subscriptions did the manager expect would be sold in 2014?",
    choices: [
      { label: "A", text: "6,020" },
      { label: "B", text: "6,027" },
      { label: "C", text: "6,440" },
      { label: "D", text: "6,468" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. The percent increase from 2012 to 2013 was <strong>the fraction with numerator 5, 880 − 5, 600, and denominator 5, 600 = 0 . 0 5</strong>, or 5%. Since the percent increase from 2012 to 2013 was estimated to be double the percent increase from 2013 to 2014, the percent increase from 2013 to 2014 was expected to be 2.5%.<br><br>Therefore, the number of subscriptions sold in 2014 is expected to be the number of subscriptions sold in 2013 multiplied by <strong>1 + 0 . 0 2 5</strong>, or <strong>5, 880 · 1 . 0 2 5 = 6, 027</strong>.Choice A is incorrect and is the result of adding half of the value of the increase from 2012 to 2013 to the 2013 result. Choice C is incorrect and is the result adding twice the value of the increase from 2012 to 2013 to the 2013 result. Choice D is incorrect and is the result of interpreting the percent increase from 2013 to 2014 as double the percent increase from 2012 to 2013.",
    hasFigure: false,
  },
  {
    id: "20845d36",
    type: "spr",
    questionHtml:
      "The number <strong>a</strong> is <strong>70 % sign</strong> less than the positive number <strong>b</strong>. The number <strong>c</strong> is <strong>60 % sign</strong> greater than <strong>a</strong>. The number <strong>c</strong> is how many times <strong>b</strong>?",
    choices: [],
    correctAnswer: ".48, 12/25",
    explanation:
      "The correct answer is <strong>.48</strong>. It's given that the number <strong>a</strong> is <strong>70 % sign</strong> less than the positive number <strong>b</strong>. Therefore, <strong>a = (1 − (70) / (100)) b</strong>, which is equivalent to <strong>a = (1 − 0.70) b</strong>, or <strong>a = 0.30 b</strong>. It's also given that the number <strong>c</strong> is <strong>60 % sign</strong> greater than <strong>a</strong>. Therefore, <strong>c = (1 + (60) / (100)) a</strong>, which is equivalent to <strong>c = (1 + 0.60) a</strong>, or <strong>c = 1.60 a</strong>. Since <strong>a = 0.30 b</strong>, substituting <strong>0.30 b</strong> for <strong>a</strong> in the equation <strong>c = 1.60 a</strong> yields <strong>c = 1.60 (0.30 b)</strong>, or <strong>c = 0.48 b</strong>. Thus, <strong>c</strong> is <strong>0.48</strong> times <strong>b</strong>. Note that .48 and 12/25 are examples of ways to enter a correct answer.",
    hasFigure: false,
  },
  {
    id: "25faa756",
    type: "spr",
    questionHtml:
      "The number <strong>a</strong> is <strong>60 % sign</strong> greater than the positive number <strong>b</strong>. The number <strong>c</strong> is <strong>45 % sign</strong> less than <strong>a</strong>. The number <strong>c</strong> is how many times <strong>b</strong>?",
    choices: [],
    correctAnswer: ".88, 22/25",
    explanation:
      "The correct answer is <strong>.88</strong>. It’s given that the number <strong>a</strong> is <strong>60 % sign</strong> greater than the positive number <strong>b</strong>. Therefore, <strong>a = (1 + (60) / (100)) b</strong>, which is equivalent to <strong>a = (1 + 0.60) b</strong>, or <strong>a = 1.60 b</strong>. It’s also given that the number <strong>c</strong> is <strong>45 % sign</strong> less than <strong>a</strong>. Therefore, <strong>c = (1 − (45) / (100)) a</strong>, which is equivalent to <strong>c = (1 − 0.45) a</strong>, or <strong>c = 0.55 a</strong>. Since <strong>a = 1.60 b</strong>, substituting <strong>1.60 b</strong> for <strong>a</strong> in the equation <strong>c = 0.55 a</strong> yields <strong>c = 0.55 (1.60 b)</strong>, or <strong>c = 0.88 b</strong>. Thus, the number <strong>c</strong> is <strong>0.88</strong> times the number <strong>b</strong>. Note that .88 and 22/25 are examples of ways to enter a correct answer.",
    hasFigure: false,
  },
  {
    id: "2e92cc21",
    type: "spr",
    questionHtml:
      "The number <strong>a</strong> is <strong>110 % sign</strong> greater than the number <strong>b</strong>. The number <strong>b</strong> is <strong>90 % sign</strong> less than <strong>47</strong>. What is the value of <strong>a</strong>?",
    choices: [],
    correctAnswer: "9.87, 987/100",
    explanation:
      "The correct answer is <strong>9.87</strong>. It’s given that the number <strong>a</strong> is <strong>110 % sign</strong> greater than the number <strong>b</strong>. It follows that <strong>a = (1 + (110) / (100)) b</strong>, or <strong>a = 2.1 b</strong>. It’s also given that the number <strong>b</strong> is <strong>90 % sign</strong> less than <strong>47</strong>. It follows that <strong>b = (1 − (90) / (100)) (47)</strong>, or <strong>b = 0.1 (47)</strong>, which yields <strong>b = 4.7</strong>. Substituting <strong>4.7</strong> for <strong>b</strong> in the equation <strong>a = 2.1 b</strong> yields <strong>a = 2.1 (4.7)</strong>, which is equivalent to <strong>a = 9.87</strong>. Therefore, the value of <strong>a</strong> is <strong>9.87</strong>.",
    hasFigure: false,
  },
  {
    id: "34f8cd89",
    type: "mcq",
    questionHtml:
      "<strong>37 % sign</strong> of the items in a box are green. Of those, <strong>37 % sign</strong> are also rectangular. Of the green rectangular items, <strong>42 % sign</strong> are also metal. Which of the following is closest to the percentage of the items in the box that are not rectangular green metal items?",
    choices: [
      { label: "A", text: "<strong>1.16 % sign</strong>" },
      { label: "B", text: "<strong>57.50 % sign</strong>" },
      { label: "C", text: "<strong>94.25 % sign</strong>" },
      { label: "D", text: "<strong>98.84 % sign</strong>" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. It's given that <strong>37 % sign</strong> of the items in a box are green. Let <strong>x</strong> represent the total number of items in the box. It follows that <strong>(37) / (100) x</strong>, or <strong>0.37 x</strong>, items in the box are green. It's also given that of those, <strong>37 % sign</strong> are also rectangular. Therefore, <strong>(37) / (100) (0.37 x)</strong>, or <strong>0.1369 x</strong>, items in the box are green rectangular items. It's also given that of the green rectangular items, <strong>42 % sign</strong> are also metal. Therefore, <strong>(42) / (100) (0.1369 x)</strong>, or <strong>0.057498 x</strong>, items in the box are rectangular green metal items. The number of the items in the box that are not rectangular green metal items is the total number of items in the box minus the number of rectangular green metal items in the box. Therefore, the number of items in the box that are not rectangular green metal items is <strong>x − 0.057498 x</strong>, or <strong>0.942502 x</strong>. The percentage of items in the box that are not rectangular green metal items is the percentage that <strong>0.942502 x</strong> is of <strong>x</strong>. If <strong>p % sign</strong> represents this percentage, the value of <strong>p</strong> is <strong>100 ((0.942502 x) / (x))</strong>, or <strong>94.2502</strong>. Of the given choices, <strong>94.25 % sign</strong> is closest to the percentage of items in the box that are not rectangular green metal items.<br>Choice A is incorrect and may result from conceptual or calculation errors.<br>Choice B is incorrect and may result from conceptual or calculation errors.<br>Choice D is incorrect and may result from conceptual or calculation errors.",
    hasFigure: false,
  },
  {
    id: "3d73a58b",
    type: "spr",
    questionHtml:
      "A gift shop buys souvenirs at a wholesale price of <strong>7.00</strong> dollars each and resells them each at a retail price that is <strong>290 % sign</strong> of the wholesale price. At the end of the season, any remaining souvenirs are marked at a discounted price that is <strong>80 % sign</strong> off the retail price. What is the discounted price of each remaining souvenir, in dollars?",
    choices: [],
    correctAnswer: "203/50, 4.06",
    explanation:
      "The correct answer is <strong>4.06</strong>. It's given that the retail price is <strong>290 % sign</strong> of the wholesale price of <strong>dollar sign 7.00</strong>. Thus, the retail price is <strong>dollar sign 7.00 ((290) / (100))</strong>, which is equivalent to <strong>dollar sign 7.00 (2.9)</strong>, or <strong>dollar sign 20.30</strong>. It's also given that the discounted price is <strong>80 % sign</strong> off the retail price. Thus, the discounted price is <strong>dollar sign 20.30 (1 − (80) / (100))</strong>, which is equivalent to <strong>dollar sign 20.30 (0.20)</strong>, or <strong>dollar sign 4.06</strong>.",
    hasFigure: false,
  },
  {
    id: "40e7a1a9",
    type: "spr",
    questionHtml:
      "<strong>210</strong> is <strong>p % sign</strong> greater than <strong>30</strong>. What is the value of <strong>p</strong>?",
    choices: [],
    correctAnswer: "600",
    explanation:
      "The correct answer is <strong>600</strong>. It’s given that <strong>210</strong> is <strong>p % sign</strong> greater than <strong>30</strong>. It follows that <strong>210 = (1 + (p) / (100)) (30)</strong>. Dividing both sides of this equation by <strong>30</strong> yields <strong>7 = 1 + (p) / (100)</strong>. Subtracting <strong>1</strong> from both sides of this equation yields <strong>6 = (p) / (100)</strong>. Multiplying both sides of this equation by <strong>100</strong> yields <strong>p = 600</strong>. Therefore, the value of <strong>p</strong> is <strong>600</strong>.",
    hasFigure: false,
  },
  {
    id: "55818046",
    type: "mcq",
    questionHtml:
      "Which of the following is closest to the difference between the percentage of adults aged 18–50 years who responded “warm” and the percentage of adults aged 51 years or greater who responded “warm”?",
    choices: [
      { label: "A", text: "4%" },
      { label: "B", text: "5%" },
      { label: "C", text: "10%" },
      { label: "D", text: "18%" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. The percentage of adults aged 18–50 who responded “warm” is <strong>the fraction with numerator 295 + 246, and denominator 508 + 410, end fraction = the fraction 541 over 918</strong>, or about 58.9%. The percentage of adults aged 51 years or greater who responded “warm” is <strong>the fraction with numerator 238 + 137, and denominator 403 + 279, end fraction = the fraction 375 over 682</strong>, or about 55.0%. The difference between 58.9% and 55.0% is 3.9%. Of the answer choices, 4% is closest to this number.Choices B, C, and D are incorrect and may result from calculation errors.",
    hasFigure: false,
  },
  {
    id: "65c49824",
    type: "spr",
    questionHtml:
      "A school district is forming a committee to discuss plans for the construction of a new high school. Of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. How many more teachers were invited to join the committee than school and district administrators?",
    choices: [],
    correctAnswer: "",
    explanation:
      "The correct answer is 8. The 6 students represent <strong>(100 − 15 − 45 − 25, ), % = 15 %</strong> of those invited to join the committee. If x people were invited to join the committee, then <strong>0 . 1 5 x = 6</strong>. Thus, there were <strong>6 over, 0 . 1 5 = 40</strong> people invited to join the committee. It follows that there were <strong>0 . 4 5 · 40 = 18</strong> teachers and <strong>0 . 2 5 · 40 = 10</strong> school and district administrators invited to join the committee. Therefore, there were 8 more teachers than school and district administrators invited to join the committee.",
    hasFigure: false,
  },
  {
    id: "67c0200a",
    type: "spr",
    questionHtml:
      "The number <strong>a</strong> is <strong>70 % sign</strong> less than the positive number <strong>b</strong>. The number <strong>c</strong> is <strong>80 % sign</strong> greater than <strong>a</strong>. The number <strong>c</strong> is how many times <strong>b</strong>?",
    choices: [],
    correctAnswer: ".54, 27/50",
    explanation:
      "The correct answer is <strong>.54</strong>. It's given that the number <strong>a</strong> is <strong>70 % sign</strong> less than the positive number <strong>b</strong>. Therefore, <strong>a = (1 − (70) / (100)) b</strong>, which is equivalent to <strong>a = (1 − 0.70) b</strong>, or <strong>a = 0.30 b</strong>. It's also given that the number <strong>c</strong> is <strong>80 % sign</strong> greater than <strong>a</strong>. Therefore, <strong>c = (1 + (80) / (100)) a</strong>, which is equivalent to <strong>c = (1 + 0.80) a</strong>, or <strong>c = 1.80 a</strong>. Since <strong>a = 0.30 b</strong>, substituting <strong>0.30 b</strong> for <strong>a</strong> in the equation <strong>c = 1.80 a</strong> yields <strong>c = 1.80 (0.30 b)</strong>, or <strong>c = 0.54 b</strong>. Thus, <strong>c</strong> is <strong>0.54</strong> times <strong>b</strong>. Note that .54 and 27/50 are examples of ways to enter a correct answer.",
    hasFigure: false,
  },
  {
    id: "8213b1b3",
    type: "spr",
    questionHtml:
      "According to a set of standards, a certain type of substance can contain a maximum of <strong>0.001 % sign</strong> phosphorus by mass. If a sample of this substance has a mass of <strong>140</strong> grams, what is the maximum mass, in grams, of phosphorus the sample can contain to meet these standards?",
    choices: [],
    correctAnswer: ".0014",
    explanation:
      "The correct answer is <strong>.0014</strong>. It's given that a certain type of substance can contain a maximum of <strong>0.001 % sign</strong> phosphorus by mass to meet a set of standards. If a sample of the substance has a mass of <strong>140</strong> grams, it follows that the maximum mass, in grams, of phosphorus the sample can contain to meet the standards is <strong>0.001 % sign</strong> of <strong>140</strong>, or <strong>(0.001) / (100) (140)</strong>, which is equivalent to <strong>(0.00001) (140)</strong>, or <strong>0.0014</strong>. Note that .0014 and 0.001 are examples of ways to enter a correct answer.",
    hasFigure: false,
  },
  {
    id: "8c5dbd3e",
    type: "spr",
    questionHtml:
      "The number <strong>w</strong> is <strong>110 % sign</strong> greater than the number <strong>z</strong>. The number <strong>z</strong> is <strong>55 % sign</strong> less than <strong>50</strong>. What is the value of <strong>w</strong>?",
    choices: [],
    correctAnswer: "189/4, 47.25",
    explanation:
      "The correct answer is <strong>47.25</strong>. It’s given that the number <strong>w</strong> is <strong>110 % sign</strong> greater than the number <strong>z</strong>. It follows that <strong>w = (1 + (110) / (100)) z</strong>, or <strong>w = 2.1 z</strong>. It’s also given that the number <strong>z</strong> is <strong>55 % sign</strong> less than <strong>50</strong>. It follows that <strong>z = (1 − (55) / (100)) (50)</strong>, or <strong>z = 0.45 (50)</strong>, which yields <strong>z = 22.5</strong>. Substituting <strong>22.5</strong> for <strong>z</strong> in the equation <strong>w = 2.1 z</strong> yields <strong>w = 2.1 (22.5)</strong>, which is equivalent to <strong>w = 47.25</strong>. Therefore, the value of <strong>w</strong> is <strong>47.25</strong>. Note that 47.25 and 189/4 are examples of ways to enter a correct answer.",
    hasFigure: false,
  },
  {
    id: "954943a4",
    type: "mcq",
    questionHtml:
      "Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that a serving size of the cereal is <strong>three fourths</strong> cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is 5% of the daily allowance for adults. If p percent of an adult’s daily allowance of potassium is provided by x servings of Crunchy Grain cereal per day, which of the following expresses p in terms of x ?",
    choices: [
      { label: "A", text: "<strong>p = 0 . 5 x</strong>" },
      { label: "B", text: "<strong>p = 5 x</strong>" },
      { label: "C", text: "<strong>p = (0 . 0 5, ), to the x power</strong>" },
      { label: "D", text: "<strong>p = (1 . 0 5, ), to the x power</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. It’s given that each serving of Crunchy Grain cereal provides 5% of an adult’s daily allowance of potassium, so x servings would provide x times 5%. The percentage of an adult’s daily allowance of potassium, p, is 5 times the number of servings, x. Therefore, the percentage of an adult’s daily allowance of potassium can be expressed as <strong>p = 5 x</strong>.Choices A, C, and D are incorrect and may result from incorrectly converting 5% to its decimal equivalent, which isn’t necessary since p is expressed as a percentage. Additionally, choices C and D are incorrect because the context should be represented by a linear relationship, not by an exponential relationship.",
    hasFigure: false,
  },
  {
    id: "ad911622",
    type: "mcq",
    questionHtml:
      "The value of a collectible comic book increased by <strong>167 % sign</strong> from the end of <strong>2011</strong> to the end of <strong>2012</strong> and then decreased by <strong>16 % sign</strong> from the end of <strong>2012</strong> to the end of <strong>2013</strong>. What was the net percentage increase in the value of the collectible comic book from the end of <strong>2011</strong> to the end of <strong>2013</strong>?",
    choices: [
      { label: "A", text: "<strong>124.28 % sign</strong>" },
      { label: "B", text: "<strong>140.28 % sign</strong>" },
      { label: "C", text: "<strong>151.00 % sign</strong>" },
      { label: "D", text: "<strong>209.72 % sign</strong>" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. It’s given that the value of the comic book increased by <strong>167 % sign</strong> from the end of <strong>2011</strong> to the end of <strong>2012</strong>. Therefore, if the value of the comic book at the end of <strong>2011</strong> was <strong>x</strong> dollars, then the value, in dollars, of the comic book at the end of <strong>2012</strong> was <strong>x + ((167) / (100)) x</strong>, which can be rewritten as <strong>1 x + 1.67 x</strong>, or <strong>2.67 x</strong>. It’s also given that the value of the comic book decreased by <strong>16 % sign</strong> from the end of <strong>2012</strong> to the end of <strong>2013</strong>. Therefore, the value, in dollars, of the comic book at the end of <strong>2013</strong> was <strong>2.67 x − 2.67 x ((16) / (100))</strong>, which can be rewritten as <strong>2.67 x − (2.67 x) (0.16)</strong>, or <strong>2.2428 x</strong>. Thus, if the value of the comic book at the end of <strong>2011</strong> was <strong>x</strong> dollars, and the value of the comic book at the end of <strong>2013</strong> was <strong>2.2428 x</strong> dollars, then from the end of <strong>2011</strong> to the end of <strong>2013</strong>, the value of the comic book increased by <strong>2.2428 x − 1 x</strong>, or <strong>1.2428 x</strong>, dollars. Therefore, the increase in the value of the comic book from the end of <strong>2011</strong> to the end of <strong>2013</strong> is equal to <strong>1.2428</strong> times the value of the comic book at the end of <strong>2011</strong>. It follows that from the end of <strong>2011</strong> to the end of <strong>2013</strong>, the net percentage increase in the value of the comic book was <strong>(1.2428) (100) % sign</strong>, or <strong>124.28 % sign</strong>.<br>Choice B is incorrect and may result from conceptual or calculation errors. <br>Choice C is incorrect. This is the difference between the net percentage increase in the value of the comic book from the end of <strong>2011</strong> to the end of <strong>2012</strong> and the net percentage decrease in the value of the comic book from the end of <strong>2012</strong> to the end of <strong>2013</strong>, not the net percentage increase in the value of the comic book from the end of <strong>2011</strong> to the end of <strong>2013</strong>.<br>Choice D is incorrect. This is the net percentage increase in the value of the comic book from the end of <strong>2011</strong> to the end of <strong>2013</strong>, if the value of the comic book increased by <strong>167 % sign</strong> from the end of <strong>2011</strong> to the end of <strong>2012</strong> and then increased, not decreased, by <strong>16 % sign</strong> from the end of <strong>2012</strong> to the end of <strong>2013</strong>.",
    hasFigure: false,
  },
];
