Pls check the following json for any duplicate ids. If there are any duplicate ids present, mention it's number:

[
  {
    "text": "If $f(x) = 2x^2 - 3x + 5$, what is the value of $f(-2)$?",
    "type": "multiple-choice-single-answer",
    "id": 1,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "To find $f(-2)$, substitute $-2$ for $x$ in the function:\n\n $f(-2) = 2(-2)^2 - 3(-2) + 5$. \n\n Simplify: $2(4) + 6 + 5 = 8 + 6 + 5 = 19$. \n\n The correct answer is $19$.",
    "options": [
      {
        "text": "$13$",
        "id": "a"
      },
      {
        "text": "$15$",
        "id": "b"
      },
      {
        "text": "$17$",
        "id": "c"
      },
      {
        "text": "$19$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The line $y = mx + b$ passes through the points $(2, 5)$ and $(4, 9)$. What is the value of $m$?",
    "type": "multiple-choice-single-answer",
    "id": 2,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "The slope $m$ can be calculated using the formula $m = \\frac{y_2 - y_1}{x_2 - x_1}$. \n\n Plugging in the given points: $m = \\frac{9 - 5}{4 - 2} = \\frac{4}{2} = 2$. \n\n The correct answer is $2$.",
    "options": [
      {
        "text": "$1$",
        "id": "a"
      },
      {
        "text": "$2$",
        "id": "b"
      },
      {
        "text": "$3$",
        "id": "c"
      },
      {
        "text": "$4$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $\\log_2 x = 5$, what is the value of $x$?",
    "type": "multiple-choice-single-answer",
    "id": 3,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "The equation $\\log_2 x = 5$ means that $2^5 = x$. \n\n Calculate $2^5$: $2 \\times 2 \\times 2 \\times 2 \\times 2 = 32$. \n\n Therefore, $x = 32$.",
    "options": [
      {
        "text": "$10$",
        "id": "a"
      },
      {
        "text": "$25$",
        "id": "b"
      },
      {
        "text": "$32$",
        "id": "c"
      },
      {
        "text": "$64$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In triangle ABC, angle C is a right angle. If $\\sin A = \\frac{3}{5}$, what is the value of $\\tan A$?",
    "type": "multiple-choice-single-answer",
    "id": 4,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "In a right-angled triangle, $\\sin A = \\frac{3}{5}$ means the side opposite angle A is $3$ units, and the hypotenuse is $5$ units. \n\n Using the Pythagorean theorem, the adjacent side to angle A is $\\sqrt{5^2 - 3^2} = \\sqrt{25 - 9} = \\sqrt{16} = 4$ units. \n\n Therefore, $\\tan A = \\frac{\\text{opposite}}{\\text{adjacent}} = \\frac{3}{4}$. \n\n The correct answer is $\\frac{3}{4}$.",
    "options": [
      {
        "text": "$\\frac{3}{4}$",
        "id": "a"
      },
      {
        "text": "$\\frac{4}{3}$",
        "id": "b"
      },
      {
        "text": "$\\frac{5}{3}$",
        "id": "c"
      },
      {
        "text": "$\\frac{5}{4}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $y = 3x + 7$ and $x = 4$, what is the value of $y$?",
    "type": "multiple-choice-single-answer",
    "id": 5,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To find y, substitute $x = 4$ into the equation $y = 3x + 7$. \n\n This gives $y = 3(4) + 7$. \n\n Simplify: $y = 12 + 7 = 19$. \n\n Therefore, the correct answer is $19$.",
    "options": [
      {
        "text": "$15$",
        "id": "a"
      },
      {
        "text": "$17$",
        "id": "b"
      },
      {
        "text": "$19$",
        "id": "c"
      },
      {
        "text": "$21$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Solve for $x$: $2x + 5 = 13$",
    "type": "multiple-choice-single-answer",
    "id": 6,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "To solve for $x$, first subtract $5$ from both sides: $2x = 8$. \n\n Then divide both sides by $2$: $x = 4$. \n\n The correct answer is $4$.",
    "options": [
      {
        "text": "$3$",
        "id": "a"
      },
      {
        "text": "$4$",
        "id": "b"
      },
      {
        "text": "$5$",
        "id": "c"
      },
      {
        "text": "$6$",
        "id": "d"
      }
    ]
  },
  {
    "text": "What is the value of $\\frac{1}{2} + \\frac{3}{4}$?",
    "type": "multiple-choice-single-answer",
    "id": 7,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To add fractions with different denominators, find a common denominator. \n\n Here, the LCD is $4$. \n\n Convert $\\frac{1}{2}$ to $\\frac{2}{4}$. \n\n Then add: $\\frac{2}{4} + \\frac{3}{4} = \\frac{5}{4}$ or $1.25$. \n\n The correct answer is $1.25$.",
    "options": [
      {
        "text": "$0.75$",
        "id": "a"
      },
      {
        "text": "$1$",
        "id": "b"
      },
      {
        "text": "$1.25$",
        "id": "c"
      },
      {
        "text": "$1.5$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $a^2 = 16$ and $a > 0$, what is the value of $a$?",
    "type": "multiple-choice-single-answer",
    "id": 8,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "The equation $a^2 = 16$ means that a is a square root of $16$. \n\n Since we're told $a > 0$, we're looking for the positive square root. \n\n  $\\sqrt{16} = 4$, so $a = 4$.",
    "options": [
      {
        "text": "$2$",
        "id": "a"
      },
      {
        "text": "$4$",
        "id": "b"
      },
      {
        "text": "$8$",
        "id": "c"
      },
      {
        "text": "$16$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A factory produces widgets at a constant rate. In $3$ hours, the factory produced $540$ widgets. If the factory continues at this rate, approximately how many widgets will it produce in $8$ hours?",
    "type": "multiple-choice-single-answer",
    "id": 9,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, calculate the rate of production:\n\n $540$ widgets ÷ $3$ hours = $180$ widgets per hour. \n\n Then, multiply this rate by $8$ hours: $180 \\times 8$ = $1,440$ widgets. \n\n The correct answer is $1,440$.",
    "options": [
      {
        "text": "$1,080$",
        "id": "a"
      },
      {
        "text": "$1,320$",
        "id": "b"
      },
      {
        "text": "$1,440$",
        "id": "c"
      },
      {
        "text": "$1,620$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A car travels from City A to City B, covering a distance of $360$ kilometers in $4$ hours. If the car maintains the same average speed, how long will it take to travel $495$ kilometers?",
    "type": "multiple-choice-single-answer",
    "id": 10,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Calculate the average speed:\n\n $360$ km ÷ $4$ hours = $90$ km/h. \n\n Then, use the formula Time = Distance ÷ Speed:\n\n $495$ km ÷ $90$ km/h = $5.5$ hours. \n\n The correct answer is $5.5$ hours.",
    "options": [
      {
        "text": "$5\\ \\text{hours}$",
        "id": "a"
      },
      {
        "text": "$5.5\\ \\text{hours}$",
        "id": "b"
      },
      {
        "text": "$6\\ \\text{hours}$",
        "id": "c"
      },
      {
        "text": "$6.5\\ \\text{hours}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A savings account earns interest at a constant rate. If the account balance increases from $\\$5,000$ to $\\$5,750$ in $2$ years, approximately how much will the balance be after $5$ years, assuming the same interest rate?",
    "type": "multiple-choice-single-answer",
    "id": 11,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, calculate the total interest earned in $2$ years:\n\n $\\$5,750 - \\$5,000 = \\$750$. \n\n The yearly interest is $\\$750 ÷ 2 = \\$375$. \n\n For $5$ years, the total interest would be $\\$375 \\times 5 = \\$1,875$. \n\n Add this to the initial balance:\n\n $\\$5,000 + \\$1,875 = \\$6,875$. \n\n The correct answer is $\\$6,875$.",
    "options": [
      {
        "text": "$\\$6,250$",
        "id": "a"
      },
      {
        "text": "$\\$6,500$",
        "id": "b"
      },
      {
        "text": "$\\$6,875$",
        "id": "c"
      },
      {
        "text": "$\\$7,125$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A bathtub is being filled at a constant rate. After $3$ minutes, the water level is $12$ cm deep. After $7$ minutes, the water level is $28$ cm deep. If this rate continues, how deep will the water be after $12$ minutes?",
    "type": "multiple-choice-single-answer",
    "id": 12,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Calculate the rate of water level increase:\n\n $(28\\text{ cm} - 12\\text{ cm}) \\div (7\\text{ min} - 3\\text{ min}) = 16\\text{ cm} \\div 4\\text{ min} = 4\\text{ cm/min}$. \n\n The water level increases by $4\\text{ cm}$ each minute. \n\n For $9$ additional minutes - from $3$ to $12$, the total increase would be $9 \\times 4 = 36\\text{ cm}$. \n\n Add this to the initial level:\n\n $12\\text{ cm} + 36\\text{ cm} = 48\\text{ cm}$. \n\n The correct answer is $48\\text{ cm}$.",
    "options": [
      {
        "text": "$48\\ \\text{cm}$",
        "id": "a"
      },
      {
        "text": "$52\\ \\text{cm}$",
        "id": "b"
      },
      {
        "text": "$56\\ \\text{cm}$",
        "id": "c"
      },
      {
        "text": "$60\\ \\text{cm}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Solve the system of equations:\n\n$2x + 3y = 12$\n$4x - y = 1$\n\nWhat is the value of $x + y$?",
    "type": "multiple-choice-single-answer",
    "id": 13,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Solving the system of equations:\n\n$2x + 3y = 12$\n$4x - y = 1$\n\nWe get: $x = \\frac{15}{14}$ and $y = \\frac{23}{7}$\n\nCalculating $x + y$:\n\n$\\frac{15}{14} + \\frac{23}{7} = \\frac{15}{14} + \\frac{46}{14} = \\frac{61}{14}$. \n\nThe correct answer is $\\frac{61}{14}$.",
    "options": [
      {
        "text": "$4$",
        "id": "a"
      },
      {
        "text": "$\\frac{61}{14}$",
        "id": "b"
      },
      {
        "text": "$\\frac{31}{7}$",
        "id": "c"
      },
      {
        "text": "$5$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Given the system of equations:\n\n$3x - 2y = 6$\n$5x + y = 29$\n\nWhat is the value of $2x - y$?",
    "type": "multiple-choice-single-answer",
    "id": 14,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Solving the system of equations:\n\n$3x - 2y = 6$\n$5x + y = 29$\n\nWe get: $x = \\frac{64}{13}$ and $y = \\frac{57}{13}$\n\nCalculating $2x - y$:\n\n$2\\left(\\frac{64}{13}\\right) - \\frac{57}{13} = \\frac{128}{13} - \\frac{57}{13} = \\frac{71}{13}$. \n\nThe correct answer is $\\frac{71}{13}$.",
    "options": [
      {
        "text": "$5$",
        "id": "a"
      },
      {
        "text": "$\\frac{16}{3}$",
        "id": "b"
      },
      {
        "text": "$\\frac{71}{13}$",
        "id": "c"
      },
      {
        "text": "$6$",
        "id": "d"
      }
    ]
  },
  {
    "text": "For the system of equations:\n\n$x + y = 10$\n$2x - y = 3$\n\nWhat is the value of $3x + 2y$?",
    "type": "multiple-choice-single-answer",
    "id": 15,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Solving the system of equations:\n\n$x + y = 10$\n$2x - y = 3$\n\nWe get: $x = \\frac{13}{3}$ and $y = \\frac{17}{3}$\n\nCalculating $3x + 2y$:\n\n$3\\left(\\frac{13}{3}\\right) + 2\\left(\\frac{17}{3}\\right) = 13 + \\frac{34}{3} = \\frac{73}{3}$. \n\nThe correct answer is $\\frac{73}{3}$.",
    "options": [
      {
        "text": "$23$",
        "id": "a"
      },
      {
        "text": "$24$",
        "id": "b"
      },
      {
        "text": "$\\frac{73}{3}$",
        "id": "c"
      },
      {
        "text": "$25$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Solve the system of equations:\n\n$7x - y = 14$\n$3x + 2y = 12$\n\nWhat is the value of $x - y$?",
    "type": "multiple-choice-single-answer",
    "id": 16,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Solving the system of equations:\n\n$7x - y = 14$\n$3x + 2y = 12$\n\nWe get: $x = \\frac{40}{17}$ and $y = \\frac{42}{17}$\n\nCalculating $x - y$:\n\n$\\frac{40}{17} - \\frac{42}{17} = -\\frac{2}{17}$. \n\nThe correct answer is $-\\frac{2}{17}$.",
    "options": [
      {
        "text": "$\\frac{-2}{17}$",
        "id": "a"
      },
      {
        "text": "$\\frac{-1}{8}$",
        "id": "b"
      },
      {
        "text": "$\\frac{1}{8}$",
        "id": "c"
      },
      {
        "text": "$\\frac{2}{17}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A charity organization's monthly donations can be modeled by the function $D(t) = 250t + 3000$, where $D(t)$ represents the total donations in dollars $t$ months after implementing a new fundraising strategy. How many months will it take for the total donations to reach $8500$?",
    "type": "multiple-choice-single-answer",
    "id": 17,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To find when the donations reach $\\$8500$, we set up the equation:\n\n$8500 = 250t + 3000$\n\nSubtracting 3000 from both sides:\n\n$8500 - 3000 = 250t$\n\nSimplifying:\n\n$5500 = 250t$\n\nDividing both sides by $250$:\n\n$t = \\dfrac{5500}{250}$\n\nSimplifying:\n\n$t = 22$\n\nTherefore, it will take $22$ months for the total donations to reach $\\$8500$.",
    "options": [
      {
        "text": "$18\\ \\text{months}$",
        "id": "a"
      },
      {
        "text": "$20\\ \\text{months}$",
        "id": "b"
      },
      {
        "text": "$22\\ \\text{months}$",
        "id": "c"
      },
      {
        "text": "$24\\ \\text{months}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The population of a small town is modeled by the function $P(y) = 150y + 5000$, where $P(y)$ represents the population $y$ years after a new factory opened. In how many years will the population reach $6800$?",
    "type": "multiple-choice-single-answer",
    "id": 18,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "To find when the population reaches $6800$, we set up the equation: \n\n$6800 = 150y + 5000$ \n\nSubtracting 5000 from both sides: \n\n$1800 = 150y$ \n\nDividing both sides by $150$: \n\n$12 = y$ \n\nTherefore, it will take $12$ years for the population to reach $6800$.",
    "options": [
      {
        "text": "$10\\ \\text{years}$",
        "id": "a"
      },
      {
        "text": "$12\\ \\text{years}$",
        "id": "b"
      },
      {
        "text": "$14\\ \\text{years}$",
        "id": "c"
      },
      {
        "text": "$16\\ \\text{years}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A company's profit can be modeled by the function $P(x) = 500x - 10000$, where $P(x)$ represents the total profit in dollars after selling $x$ units of their product. How many units need to be sold for the company to break even (reach $\\$0$ profit)?",
    "type": "multiple-choice-single-answer",
    "id": 19,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To find when the profit reaches $\\$0$, we set up the equation:\n\n$0 = 500x - 10000$\n\nAdding $10000$ to both sides:\n\n$0 + 10000 = 500x - 10000 + 10000$\n\nSimplifying:\n\n$10000 = 500x$\n\nDividing both sides by $500$:\n\n$x = \\dfrac{10000}{500}$\n\nSimplifying:\n\n$x = 20$\n\nTherefore, the company needs to sell $20$ units to break even.",
    "options": [
      {
        "text": "$15\\ \\text{units}$",
        "id": "a"
      },
      {
        "text": "$18\\ \\text{units}$",
        "id": "b"
      },
      {
        "text": "$20\\ \\text{units}$",
        "id": "c"
      },
      {
        "text": "$22\\ \\text{units}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The distance traveled by a car can be modeled by the function $D(h) = 65h - 5$, where $D(h)$ represents the distance in miles $h$ hours after starting a journey. How long will it take for the car to travel $450 miles?",
    "type": "multiple-choice-single-answer",
    "id": 20,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "To find when the distance reaches $450$ miles, we set up the equation: \n\n$450 = 65h - 5$ \n\nAdding $5$ to both sides: \n\n$455 = 65h$ \n\nDividing both sides by $65$: \n\n$7 = h$ \n\nTherefore, it will take $7$ hours for the car to travel $450$ miles.",
    "options": [
      {
        "text": "$6\\ \\text{hours}$",
        "id": "a"
      },
      {
        "text": "$7\\ \\text{hours}$",
        "id": "b"
      },
      {
        "text": "$8\\ \\text{hours}$",
        "id": "c"
      },
      {
        "text": "$9\\ \\text{hours}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $\\frac{3}{4}x - 2 = 7$, what is the value of $x$?",
    "type": "multiple-choice-single-answer",
    "id": 21,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Start by adding $2$ to both sides: $\\frac{3}{4}x = 9$. \n\n  Then, multiply both sides by $\\frac{4}{3}$ to solve for $x$:\n\n $x = 9 \\times \\frac{4}{3} = 12$.",
    "options": [
      {
        "text": "$9$",
        "id": "a"
      },
      {
        "text": "$10$",
        "id": "b"
      },
      {
        "text": "$12$",
        "id": "c"
      },
      {
        "text": "$15$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Equilateral triangle A has a perimeter that is twice the perimeter of equilateral triangle B. If one side of triangle B is $4$ inches long, what is the length, in inches, of one side of triangle A?",
    "type": "multiple-choice-single-answer",
    "id": 22,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, find the perimeter of triangle B: $4 \\times 3 = 12$ inches. \n\n  Since triangle A's perimeter is twice that of triangle B, it is $12 \\times 2 = 24$ inches. \n\n Each side of triangle A is $\\dfrac{24}{3} = 8$ inches long.",
    "options": [
      {
        "text": "$6$",
        "id": "a"
      },
      {
        "text": "$7$",
        "id": "b"
      },
      {
        "text": "$8$",
        "id": "c"
      },
      {
        "text": "$12$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The perimeter of equilateral triangle K is $18$ inches. If the side length of equilateral triangle L is $2$ inches longer than that of triangle K, what is the perimeter, in inches, of triangle L?",
    "type": "multiple-choice-single-answer",
    "id": 23,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Find the side length of triangle K: $\\dfrac{18}{3} = 6$ inches. \n\n Triangle L has sides that are $6 + 2 = 8$ inches long. \n\n Therefore, the perimeter of triangle L is $8 \\times 3 = 24$ inches.",
    "options": [
      {
        "text": "$14$",
        "id": "a"
      },
      {
        "text": "$18$",
        "id": "b"
      },
      {
        "text": "$20$",
        "id": "c"
      },
      {
        "text": "$24$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Equilateral triangle M and square N have the same perimeter. If one side of triangle M is $5$ inches long, what is the length, in inches, of one side of square N?",
    "type": "multiple-choice-single-answer",
    "id": 24,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Calculate the perimeter of triangle M: $5 \\times 3 = 15$ inches. \n\n Since square N has the same perimeter, each side is $\\dfrac{15}{4} = 3.75$ inches long.",
    "options": [
      {
        "text": "$3$",
        "id": "a"
      },
      {
        "text": "$3.75$",
        "id": "b"
      },
      {
        "text": "$4$",
        "id": "c"
      },
      {
        "text": "$5$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The perimeter of equilateral triangle P is half the perimeter of equilateral triangle Q. If one side of triangle P is $7$ inches long, what is the length, in inches, of one side of triangle Q?",
    "type": "multiple-choice-single-answer",
    "id": 25,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, find the perimeter of triangle P: $7 \\times 3 = 21$ inches. \n\n Triangle Q has a perimeter that is twice that of triangle P:\n\n $21 \\times 2 = 42$ inches. \n\n Each side of triangle Q is $\\dfrac{42}{3} = 14$ inches long.",
    "options": [
      {
        "text": "$7$",
        "id": "a"
      },
      {
        "text": "$10.5$",
        "id": "b"
      },
      {
        "text": "$14$",
        "id": "c"
      },
      {
        "text": "$21$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $|5x - 10| = 20$, what is one possible value of $x + 1$?",
    "type": "multiple-choice-single-answer",
    "id": 26,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To solve $|5x - 10| = 20$, consider both cases of the absolute value: \n\n1. $5x - 10 = 20$ \n\n   Solve for $x$: \n\n   $5x = 30$ \n   $x = 6$ \n\n   Then, $x + 1 = 6 + 1 = 7$.\n\n2. $5x - 10 = -20$ \n\n   Solve for $x$: \n\n   $5x = -10$ \n   $x = -2$ \n\n   Then, $x + 1 = -2 + 1 = -1$.\n\nTherefore, one possible value of $x + 1$ is $7$ or $-1$.",
    "options": [
      {
        "text": "$-3$",
        "id": "a"
      },
      {
        "text": "$-1$",
        "id": "b"
      },
      {
        "text": "$7$",
        "id": "c"
      },
      {
        "text": "$9$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $|2x + 8| = 12$, what is one possible value of $x - 4$?",
    "type": "multiple-choice-single-answer",
    "id": 27,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Solve the equation $|2x + 8| = 12$ by considering both cases:\n\n1. $2x + 8 = 12$ \n\n   Solve for $x$: \n\n   $2x = 4$ \n   $x = 2$ \n\n   Then, $x - 4 = 2 - 4 = -2$.\n\n2. $2x + 8 = -12$ \n\n   Solve for $x$: \n\n   $2x = -20$ \n   $x = -10$ \n\n   Then, $x - 4 = -10 - 4 = -14$.\n\nTherefore, one possible value of $x - 4$ is $-2$ or $-14$.",
    "options": [
      {
        "text": "$-2$",
        "id": "a"
      },
      {
        "text": "$2$",
        "id": "b"
      },
      {
        "text": "$-6$",
        "id": "c"
      },
      {
        "text": "$6$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $|6x - 12| = 18$, what is one possible value of $2x + 1$?",
    "type": "multiple-choice-single-answer",
    "id": 28,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Consider both cases for the absolute value equation $|6x - 12| = 18$:\n\n1. $6x - 12 = 18$ \n\n   Solve for $x$: \n\n   $6x = 30$ \n   $x = 5$ \n\n   Then, $2x + 1 = 2(5) + 1 = 11$.\n\n2. $6x - 12 = -18$ \n\n   Solve for $x$: \n\n   $6x = -6$ \n   $x = -1$ \n\n   Then, $2x + 1 = 2(-1) + 1 = -1$.\n\nTherefore, one possible value of $2x + 1$ is $11$ or $-1$.",
    "options": [
      {
        "text": "$-5$",
        "id": "a"
      },
      {
        "text": "$1$",
        "id": "b"
      },
      {
        "text": "$5$",
        "id": "c"
      },
      {
        "text": "$11$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $|x + 3| = 7$, what is one possible value of $3x$?",
    "type": "multiple-choice-single-answer",
    "id": 29,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Solve the equation $|x + 3| = 7$ by considering both cases:\n\n1. $x + 3 = 7$ \n\n   Solve for $x$: \n\n   $x = 4$ \n\n   Then, $3x = 3 \\times 4 = 12$.\n\n2. $x + 3 = -7$ \n\n   Solve for $x$: \n\n   $x = -10$ \n\n   Then, $3x = 3 \\times (-10) = -30$.\n\nTherefore, one possible value of $3x$ is $12$ or $-30$.",
    "options": [
      {
        "text": "$-7$",
        "id": "a"
      },
      {
        "text": "$12$",
        "id": "b"
      },
      {
        "text": "$-3$",
        "id": "c"
      },
      {
        "text": "$10$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The expression $(6x^2 - 5) + (mx^2 + 3)$ is equivalent to $9x^2 - 2$, where $m$ is a constant. What is the value of $m$?",
    "type": "multiple-choice-single-answer",
    "id": 30,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Simplify the expression:\n\n$(6x^2 - 5) + (mx^2 + 3) =$\n\n $(6x^2 + mx^2) + (-5 + 3) =$\n\n $(6 + m)x^2 -2$\n\nSet the expression equal to $9x^2 - 2$:\n\n$(6 + m)x^2 -2 = 9x^2 - 2$\n\nSince the constant terms are the same, set the coefficients of $x^2$ equal:\n\n$6 + m = 9$\n\nSolve for $m$:\n\n$m = 9 - 6 = 3$",
    "options": [
      {
        "text": "$-3$",
        "id": "a"
      },
      {
        "text": "$3$",
        "id": "b"
      },
      {
        "text": "$-9$",
        "id": "c"
      },
      {
        "text": "$9$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The expression $(5x^3 - 2x^2) + (kx^3 + 7x^2)$ is equivalent to $8x^3 + 5x^2$, where $k$ is a constant. What is the value of $k$?",
    "type": "multiple-choice-single-answer",
    "id": 31,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "First, combine like terms:\n\n$(5x^3 - 2x^2) + (kx^3 + 7x^2) =$\n\n $(5x^3 + kx^3) + (-2x^2 + 7x^2) =$\n\n $(5 + k)x^3 + 5x^2$\n\nSince this expression is equivalent to $8x^3 + 5x^2$, set the coefficients equal:\n\n$5 + k = 8$\n\nSolve for $k$:\n\n$k = 8 - 5 = 3$",
    "options": [
      {
        "text": "$3$",
        "id": "a"
      },
      {
        "text": "$-3$",
        "id": "b"
      },
      {
        "text": "$8$",
        "id": "c"
      },
      {
        "text": "$-8$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The expression $(4x^2 - 6x) - (2x^2 - cx)$ is equivalent to $2x^2 - 12x$, where $c$ is a constant. What is the value of $c$?",
    "type": "multiple-choice-single-answer",
    "id": 32,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Simplify the expression:\n\n$(4x^2 - 6x) - (2x^2 - cx) =$\n\n $4x^2 - 6x - 2x^2 + cx =$\n\n $(4x^2 - 2x^2) + (-6x + cx) =$\n\n $2x^2 + (-6x + cx)$\n\nSet the expression equal to $2x^2 - 12x$:\n\n$2x^2 + (-6x + cx) = 2x^2 - 12x$\n\nSubtract $2x^2$ from both sides:\n\n$-6x + cx = -12x$\n\nCombine like terms:\n\n$(-6 + c)x = -12x$\n\nSet coefficients equal:\n\n$-6 + c = -12$\n\nSolve for $c$:\n\n$c = -12 + 6 = -6$",
    "options": [
      {
        "text": "$-6$",
        "id": "a"
      },
      {
        "text": "$6$",
        "id": "b"
      },
      {
        "text": "$-18$",
        "id": "c"
      },
      {
        "text": "$18$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The expression $(7x^5 + 2x^3) - (9x^5 + 4x^3) + dx^5$ is equivalent to $-2x^5 - 2x^3$, where $d$ is a constant. What is the value of $d$?",
    "type": "multiple-choice-single-answer",
    "id": 33,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Simplify the expression:\n\n$(7x^5 + 2x^3) - (9x^5 + 4x^3) + dx^5 =$\n\n $7x^5 + 2x^3 - 9x^5 - 4x^3 + dx^5 =$\n\n $(7x^5 - 9x^5 + dx^5) + (2x^3 - 4x^3) =$\n\n $(-2x^5 + dx^5) - 2x^3$\n\nCombine like terms for $x^5$:\n\n$(-2 + d)x^5 - 2x^3$\n\nSet the expression equal to $-2x^5 - 2x^3$:\n\n$(-2 + d)x^5 - 2x^3 = -2x^5 - 2x^3$\n\nSince the coefficients of $x^5$ and $x^3$ terms are equal on both sides, we have:\n\n$-2 + d = -2$\n\nSolve for $d$:\n\n$d = -2 - (-2) = 0$",
    "options": [
      {
        "text": "$0$",
        "id": "a"
      },
      {
        "text": "$2$",
        "id": "b"
      },
      {
        "text": "$-2$",
        "id": "c"
      },
      {
        "text": "$4$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The variables $k$, $m$, and $n$ are related by the equation $\\frac{7k}{2} = \\frac{3m}{n},$ where $n \\ne 0$ and $m > 0$. Which equation correctly expresses $n$ in terms of $k$ and $m$?",
    "type": "multiple-choice-single-answer",
    "id": 34,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Cross-multiply to solve for $n$:\n\n$7k \\times n = 2 \\times 3m$\n\nSimplify:\n\n$7k n = 6m$\n\nIsolate $n$ by dividing both sides by $7k$:\n\n$n = \\frac{6m}{7k}.$",
    "options": [
      {
        "text": "$n = \\dfrac{6m}{7k}$",
        "id": "a"
      },
      {
        "text": "$n = \\dfrac{7k}{6m}$",
        "id": "b"
      },
      {
        "text": "$n = 14k m$",
        "id": "c"
      },
      {
        "text": "$n = \\dfrac{2k}{3m}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The equation $\\frac{a}{5b} = \\frac{2c}{3},$ where $b \\ne 0$ and $c > 0$, relates the numbers $a$, $b$, and $c$. Which equation correctly expresses $b$ in terms of $a$ and $c$?",
    "type": "multiple-choice-single-answer",
    "id": 35,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "To solve for $b$, cross-multiply the equation:\n\n$a \\times 3 = 5b \\times 2c$\n\nSimplify:\n\n$3a = 10b c$\n\nIsolate $b$ by dividing both sides by $10c$:\n\n$b = \\frac{3a}{10c}.$",
    "options": [
      {
        "text": "$b = \\dfrac{10a c}{3}$",
        "id": "a"
      },
      {
        "text": "$b = \\dfrac{3a}{10c}$",
        "id": "b"
      },
      {
        "text": "$b = \\dfrac{5a}{6c}$",
        "id": "c"
      },
      {
        "text": "$b = \\dfrac{2a c}{15}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Given the equation $\\frac{4p}{q} = \\frac{s}{2},$ where $q \\ne 0$ and $s > 0$, which equation correctly expresses $s$ in terms of $p$ and $q$?",
    "type": "multiple-choice-single-answer",
    "id": 36,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Cross-multiply to solve for $s$:\n\n$4p \\times 2 = q \\times s$\n\nSimplify:\n\n$8p = q s$\n\nIsolate $s$ by dividing both sides by $q$:\n\n$s = \\frac{8p}{q}.$",
    "options": [
      {
        "text": "$s = 2p q$",
        "id": "a"
      },
      {
        "text": "$s = \\dfrac{q}{8p}$",
        "id": "b"
      },
      {
        "text": "$s = \\dfrac{4p}{2q}$",
        "id": "c"
      },
      {
        "text": "$s = \\dfrac{8p}{q}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $\\frac{3x}{y} = \\frac{5}{2z},$ where $y \\ne 0$ and $z \\ne 0$, which equation correctly expresses $x$ in terms of $y$ and $z$?",
    "type": "multiple-choice-single-answer",
    "id": 37,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Cross-multiply to solve for $x$:\n\n$3x \\times 2z = y \\times 5$\n\nSimplify:\n\n$6x z = 5y$\n\nIsolate $x$ by dividing both sides by $6z$:\n\n$x = \\frac{5y}{6z}.$",
    "options": [
      {
        "text": "$x = \\dfrac{6y z}{5}$",
        "id": "a"
      },
      {
        "text": "$x = \\dfrac{5y}{2z}$",
        "id": "b"
      },
      {
        "text": "$x = \\dfrac{5y}{6z}$",
        "id": "c"
      },
      {
        "text": "$x = \\dfrac{y}{15z}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A certain virus infects a computer system, causing the number of corrupted files to increase by a factor of $3$ every $2$ hours. If there were initially $5$ corrupted files, how many corrupted files will there be after $8$ hours?",
    "type": "multiple-choice-single-answer",
    "id": 38,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "The number of corrupted files increases by a factor of $3$ every $2$ hours.  \n\n First, determine the number of times the files will triple in $8$ hours:\n\n $\\text{Number of periods} = \\frac{8 \\text{ hours}}{2 \\text{ hours/period}} = 4.$  \n\n The number of corrupted files after $8$ hours is calculated using the formula:\n\n $\\text{Final amount} = \\text{Initial amount} \\times (\\text{Multiplier})^{\\text{Number of periods}}.$  \n\n Here, the multiplier is $3$, so: $\\text{Final amount} = 5 \\times 3^4 = 5 \\times 81 = 405.$",
    "options": [
      {
        "text": "$135$",
        "id": "a"
      },
      {
        "text": "$243$",
        "id": "b"
      },
      {
        "text": "$324$",
        "id": "c"
      },
      {
        "text": "$405$",
        "id": "d"
      }
    ]
  },
  {
    "text": "An investment of $\\$10,000$ appreciates by $20\\%$ every year. What is the value of the investment after $3$ years?",
    "type": "multiple-choice-single-answer",
    "id": 39,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "The investment grows by $20\\%$ each year. \n\n  The multiplier for a $20\\%$ increase is $1 + 0.20 = 1.20.$ \n\n  The value after $3$ years is:\n\n $10,000 \\times (1.20)^3 =$\n\n $10,000 \\times 1.728 =$\n\n $17,280.$",
    "options": [
      {
        "text": "$14,400$",
        "id": "a"
      },
      {
        "text": "$17,280$",
        "id": "b"
      },
      {
        "text": "$20,736$",
        "id": "c"
      },
      {
        "text": "$24,000$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A radioactive substance decays at a rate of $25\\%$ every hour. If the initial mass of the substance is $80$ grams, how much remains after $6$ hours?",
    "type": "multiple-choice-single-answer",
    "id": 40,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "The substance decays by $25\\%$ each hour, so the multiplier is $1 - 0.25 = 0.75.$ \n\n  The amount remaining after $6$ hours is: $80 \\times (0.75)^6.$  \n\n Calculate: $0.75^6 \\approx 0.178.$  \n\n Then, $80 \\times 0.178 \\approx 14.22.$ \n\n  Therefore, approximately $14$ grams remain.",
    "options": [
      {
        "text": "Approximately $14$ grams",
        "id": "a"
      },
      {
        "text": "Approximately $18$ grams",
        "id": "b"
      },
      {
        "text": "Approximately $24$ grams",
        "id": "c"
      },
      {
        "text": "Approximately $30$ grams",
        "id": "d"
      }
    ]
  },
  {
    "text": "The population of a town increases by $10\\%$ every year. If the current population is $50,000$, what will be the population after $5$ years?",
    "type": "multiple-choice-single-answer",
    "id": 41,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "The population grows by $10\\%$ annually. \n\n  The growth multiplier is $1 + 0.10 = 1.10.$ \n\n  After $5$ years, the population will be:\n\n $50,000 \\times (1.10)^5.$ \n\n  Calculate:\n\n $ (1.10)^5 \\approx 1.61051.$ \n\n  So, $50,000 \\times 1.61051 \\approx 80,525.$ \n\n  Therefore, the population will be approximately $80,525$.",
    "options": [
      {
        "text": "Approximately $70,000$",
        "id": "a"
      },
      {
        "text": "Approximately $75,000$",
        "id": "b"
      },
      {
        "text": "Approximately $80,525$",
        "id": "c"
      },
      {
        "text": "Approximately $85,000$",
        "id": "d"
      }
    ]
  },
  {
    "text": "When the given system of inequalities is graphed in the xy-plane, one of the solutions is $(12, y)$. Which of the following could be the value of $y$?\n\n$x + 3y \\geq 21$\n$2x - y \\geq 14$",
    "type": "multiple-choice-single-answer",
    "id": 42,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "To determine the possible value of $y$ when $x = 12$, substitute $x = 12$ into both inequalities and solve for $y$.\n\n1. **First Inequality:**\n\n$12 + 3y \\geq 21$\n\nSubtract 12 from both sides:\n\n$3y \\geq 9$\n\nDivide both sides by 3:\n\n$y \\geq 3$\n\n2. **Second Inequality:**\n\n$2(12) - y \\geq 14$\n\nSimplify:\n\n$24 - y \\geq 14$\n\nSubtract 24 from both sides:\n\n$-y \\geq -10$\n\nMultiply both sides by -1 and reverse the inequality sign:\n\n$y \\leq 10$\n\nCombining both results, $y$ must satisfy:\n\n$y \\geq 3 \\quad \\text{and} \\quad y \\leq 10$\n\nThus, $y = 10$.\n\nAmong the provided options, $10$ is the only value that satisfies this condition. Therefore, the correct answer is $10$.",
    "options": [
      {
        "text": "$10$",
        "id": "a"
      },
      {
        "text": "$9$",
        "id": "b"
      },
      {
        "text": "$11$",
        "id": "c"
      },
      {
        "text": "$12$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Solve for $x$ in the equation $5(x - 4) = 3x + 8$. What is the value of $x$?",
    "type": "multiple-choice-single-answer",
    "id": 43,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To solve for $x$ in the equation $5(x - 4) = 3x + 8$, follow these steps:\n\n1. **Distribute the $5$ on the left side:**\n\n$5x - 20 = 3x + 8$\n\n2. **Subtract $3x$ from both sides to gather like terms:**\n\n$5x - 3x - 20 = 8$\n\nSimplify:\n\n$2x - 20 = 8$\n\n3. **Add $20$ to both sides to isolate the term with $x$:**\n\n$2x = 28$\n\n4. **Divide both sides by $2$:**\n\n$x = 14$\n\nTherefore, the value of $x$ is $14$.",
    "options": [
      {
        "text": "$10$",
        "id": "a"
      },
      {
        "text": "$12$",
        "id": "b"
      },
      {
        "text": "$14$",
        "id": "c"
      },
      {
        "text": "$16$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Given the equation $7y - 5 = 2y + 20$, what is the value of $y$?",
    "type": "multiple-choice-single-answer",
    "id": 44,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To solve for $y$ in the equation $7y - 5 = 2y + 20$, follow these steps:\n\n1. **Subtract $2y$ from both sides to gather like terms:**\n\n$5y - 5 = 20$\n\n2. **Add $5$ to both sides to isolate the term with $y$:**\n\n$5y = 25$\n\n3. **Divide both sides by $5$:**\n\n$y = 5$\n\nTherefore, the value of $y$ is $5$.",
    "options": [
      {
        "text": "$3$",
        "id": "a"
      },
      {
        "text": "$4$",
        "id": "b"
      },
      {
        "text": "$5$",
        "id": "c"
      },
      {
        "text": "$6$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The variables $a$, $b$, and $c$ are related by the equation $\\frac{5a}{c} = \\frac{4b}{3}$. Which equation correctly expresses $a$ in terms of $b$ and $c$?",
    "type": "multiple-choice-single-answer",
    "id": 45,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "To express $a$ in terms of $b$ and $c$ using the equation $\\frac{5a}{c} = \\frac{4b}{3}$, follow these steps:\n\n1. **Cross-multiply to eliminate the fractions:**\n\n$5a \\times 3 = 4b \\times c$\n\nSimplify:\n\n$15a = 4bc$\n\n2. **Divide both sides by $15$ to solve for $a$:**\n\n$a = \\frac{4bc}{15}$\n\nTherefore, the equation that correctly expresses $a$ in terms of $b$ and $c$ is:\n\n$a = \\frac{4bc}{15}$",
    "options": [
      {
        "text": "$a = \\dfrac{15bc}{4}$",
        "id": "a"
      },
      {
        "text": "$a = \\dfrac{4bc}{15}$",
        "id": "b"
      },
      {
        "text": "$a = \\dfrac{5bc}{12}$",
        "id": "c"
      },
      {
        "text": "$a = \\dfrac{3bc}{4}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A business has a cost function described by the equation $C(x) = 800 + 25x$, where $x$ is the number of units produced. If the company wants to achieve a profit of $5000$, and each unit is sold for $60$, how many units must they produce and sell?",
    "type": "multiple-choice-single-answer",
    "id": 46,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Profit $P$ is given by:\n\n$P = \\text{Revenue} - \\text{Cost}$\n\nGiven:\n\n$P = 5000$\n\n$\\text{Selling price per unit} = 60$\n\n$\\text{Cost function} = C(x) = 800 + 25x$\n\nFirst, express Revenue $R$ in terms of $x$:\n\n$R = 60x$\n\nSet up the profit equation:\n\n$5000 = 60x - (800 + 25x)$\n\nSimplify:\n\n$5000 = 35x - 800$\n\nAdd $800$ to both sides:\n\n$5800 = 35x$\n\nDivide both sides by $35$:\n\n$x = \\frac{5800}{35} \\approx 165.71$\n\nSince the company cannot produce a fraction of a unit, they must produce and sell at least **166 units**.\n\nTherefore, the company needs to produce and sell $166$ units to achieve a profit of $5000$.",
    "options": [
      {
        "text": "$166\\ \\text{units}$",
        "id": "a"
      },
      {
        "text": "$160\\ \\text{units}$",
        "id": "b"
      },
      {
        "text": "$170\\ \\text{units}$",
        "id": "c"
      },
      {
        "text": "$175\\ \\text{units}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In right triangle $XYZ$, side $XY = 30$, side $YZ = 40$, and side $XZ = 50$. Triangle $XYZ$ is similar to triangle $ABC$, where angle $X$ corresponds to angle $A$ and angle $Y$ corresponds to angle $B$. If the length of side $AB$ is $45$, what is the length of side $BC$?",
    "type": "multiple-choice-single-answer",
    "id": 47,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Since triangle $XYZ$ is similar to triangle $ABC$, the corresponding sides are proportional.\n\n**Given:**\n\n$XY = 30 \\quad \\text{corresponds to} \\quad AB = 45$\n\n$YZ = 40 \\quad \\text{corresponds to} \\quad BC$\n\n$XZ = 50 \\quad \\text{corresponds to} \\quad AC$\n\nThe ratio of similarity $k$ between triangle $ABC$ and triangle $XYZ$ is:\n\n$k = \\dfrac{AB}{XY} = \\dfrac{45}{30} = 1.5$\n\nTo find the length of side $BC$:\n\n$BC = k \\times YZ = 1.5 \\times 40 = 60$\n\nTherefore, the length of side $BC$ is $60$.",
    "options": [
      {
        "text": "$50$",
        "id": "a"
      },
      {
        "text": "$55$",
        "id": "b"
      },
      {
        "text": "$60$",
        "id": "c"
      },
      {
        "text": "$65$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The function $g(x)$ is defined as $g(x) = 4x^2 - 16x + 15$. What is the value of $g(3)$?",
    "type": "multiple-choice-single-answer",
    "id": 48,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "To find the value of $g(3)$, substitute $x = 3$ into the function:\n\n$g(3) = 4(3)^2 - 16(3) + 15$\n\nSimplify step-by-step:\n\n$g(3) = 4(9) - 48 + 15 =$\n\n $36 - 48 + 15 =$\n\n $-12 + 15 = 3$\n\nTherefore, the value of $g(3)$ is $3$.",
    "options": [
      {
        "text": "$1$",
        "id": "a"
      },
      {
        "text": "$3$",
        "id": "b"
      },
      {
        "text": "$5$",
        "id": "c"
      },
      {
        "text": "$7$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A rectangular playground has a length that is three times its width. If the perimeter of the playground is $64$ meters, what is the area of the playground?",
    "type": "multiple-choice-single-answer",
    "id": 49,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Let the width of the playground be $w$ meters. Then, the length is $3w$ meters.\n\nThe perimeter $P$ of a rectangle is given by:\n\n$P = 2 \\times (\\text{length} + \\text{width})$\n\nSubstitute the known values:\n\n$64 = 2 \\times (3w + w) = 8w$\n\nSolve for $w$:\n\n$w = 8 \\, \\text{meters}$\n\nNow, find the length:\n\n$\\text{Length} = 3w = 24 \\, \\text{meters}$\n\nThe area $A$ is:\n\n$A = \\text{length} \\times \\text{width} =$\n\n $24 \\times 8 = 192 \\, \\text{square meters}$\n\nTherefore, the area of the playground is $192$ square meters.",
    "options": [
      {
        "text": "$128\\ \\text{square meters}$",
        "id": "a"
      },
      {
        "text": "$144\\ \\text{square meters}$",
        "id": "b"
      },
      {
        "text": "$160\\ \\text{square meters}$",
        "id": "c"
      },
      {
        "text": "$192\\ \\text{square meters}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The maximum value of $m$ is $20$ less than $5$ times the value of $n$. Which inequality represents the relationship between $m$ and $n$?",
    "type": "multiple-choice-single-answer",
    "id": 50,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "The maximum value of $m$ is $20$ less than $5$ times the value of $n$ translates to $m \\leq 5n - 20$.\n\nBreaking it down:\n\n- '$5$ times the value of $n$' is $5n$.\n\n- '$20$ less than $5$ times the value of $n$' is $5n - 20$.\n\n- The phrase 'the maximum value of $m$' indicates that $m$ is at most $5n - 20$, which is represented by the inequality $m \\leq 5n - 20$.\n\nTherefore, the correct inequality is $m \\leq 5n - 20$.",
    "options": [
      {
        "text": "$m \\leq 5n - 20$",
        "id": "a"
      },
      {
        "text": "$m \\geq 5n - 20$",
        "id": "b"
      },
      {
        "text": "$m \\geq 20 - 5n$",
        "id": "c"
      },
      {
        "text": "$m \\leq 20 - 5n$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The total cost $C$ is at least $50$ more than twice the number of items $n$ produced. Which inequality represents the relationship between $C$ and $n$?",
    "type": "multiple-choice-single-answer",
    "id": 51,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "The statement 'The total cost $C$ is at least $50$ more than twice the number of items $n$ produced' translates to $C \\geq 2n + 50$.\n\nBreaking it down:\n\n- 'Twice the number of items $n$' is $2n$.\n\n- '$50$ more than twice the number of items $n$' is $2n + 50$.\n\n- 'At least' indicates that $C$ is greater than or equal to $2n + 50$.\n\nTherefore, the correct inequality is $C \\geq 2n + 50$.",
    "options": [
      {
        "text": "$C \\geq 2n + 50$",
        "id": "a"
      },
      {
        "text": "$C \\leq 2n + 50$",
        "id": "b"
      },
      {
        "text": "$C \\geq 50n + 2$",
        "id": "c"
      },
      {
        "text": "$C \\leq 50n + 2$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The speed $v$ of a vehicle is no more than $80$ miles per hour. Which inequality represents the relationship between $v$ and the speed limit?",
    "type": "multiple-choice-single-answer",
    "id": 52,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "The statement 'The speed $v$ of a vehicle is no more than $80$ miles per hour' translates to $v \\leq 80$.\n\nBreaking it down:\n\n- 'No more than' indicates that $v$ is less than or equal to $80$.\n\nTherefore, the correct inequality is $v \\leq 80$.",
    "options": [
      {
        "text": "$v > 80$",
        "id": "a"
      },
      {
        "text": "$v \\leq 80$",
        "id": "b"
      },
      {
        "text": "$v \\geq 80$",
        "id": "c"
      },
      {
        "text": "$v < 80$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The profit $P$ is at least $3$ times the cost $C$ minus $25$ dollars. Which inequality represents the relationship between $P$ and $C$?",
    "type": "multiple-choice-single-answer",
    "id": 53,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "The statement 'The profit $P$ is at least $3$ times the cost $C$ minus $25$ dollars' translates to $P \\geq 3C - 25$.\n\nBreaking it down:\n\n- '3 times the cost $C$' is $3C$.\n\n- '3 times the cost $C$ minus 25 dollars' is $3C - 25$.\n\n- 'At least' indicates that $P$ is greater than or equal to $3C - 25$.\n\nTherefore, the correct inequality is $P \\geq 3C - 25$.",
    "options": [
      {
        "text": "$P \\geq 3C - 25$",
        "id": "a"
      },
      {
        "text": "$P \\leq 3C - 25$",
        "id": "b"
      },
      {
        "text": "$P \\geq C - 75$",
        "id": "c"
      },
      {
        "text": "$P \\leq C - 75$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In $2024$, a bookstore reduced its inventory of fiction books by $15\\%$ compared to the number of fiction books in $2023$. If the number of fiction books available in $2024$ is represented by $n$ times the number of fiction books available in $2023$, what is the value of $n$?",
    "type": "multiple-choice-single-answer",
    "id": 54,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "The bookstore decreased its inventory by $15\\%$, meaning it retains $85\\%$ of its $2023$ inventory.\n\n Therefore, $n = 0.85$. To verify, if the number of fiction books in $2023$ is $100$, then in $2024$ it would be $100 \\times 0.85 = 85$, which is $85\\%$ of the original number.\n\nThus, $n = 0.85$.",
    "options": [
      {
        "text": "$0.15$",
        "id": "a"
      },
      {
        "text": "$0.85$",
        "id": "b"
      },
      {
        "text": "$1.15$",
        "id": "c"
      },
      {
        "text": "$1.85$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A company's revenue increased by $20\\%$ from $2021$ to $2022$. If the revenue in $2022$ is $r$ times the revenue in $2021$, what is the value of $r$?",
    "type": "multiple-choice-single-answer",
    "id": 55,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "An increase of $20\\%$ means the revenue in $2022$ is $120\\%$ of the revenue in $2021$.\n\nTherefore, $r = 1.20$.\n\nTo confirm, if the $2021$ revenue was $\\$100$, the $2022$ revenue would be $\\$100 \\times 1.20 = 120$, which reflects a $20\\%$ increase.\n\nThus, $r = 1.20$.",
    "options": [
      {
        "text": "$0.80$",
        "id": "a"
      },
      {
        "text": "$1.00$",
        "id": "b"
      },
      {
        "text": "$1.20$",
        "id": "c"
      },
      {
        "text": "$1.50$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In $2025$, a gym membership base declined by $12\\%$ from its $2024$ membership numbers. If the number of members in $2025$ is $k$ times the number of members in $2024$, what is the value of $k$?",
    "type": "multiple-choice-single-answer",
    "id": 56,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "A decline of $12\\%$ means the gym retains $88\\%$ of its $2024$ membership.\n\nTherefore, $k = 0.88$.\n\nTo verify, if there were $100$ members in $2024$, there would be $100 \\times 0.88 = 88$ members in $2025$, reflecting a $12\\%$ decrease.\n\nThus, $k = 0.88$.",
    "options": [
      {
        "text": "$0.88$",
        "id": "a"
      },
      {
        "text": "$0.12$",
        "id": "b"
      },
      {
        "text": "$1.12$",
        "id": "c"
      },
      {
        "text": "$1.88$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A smartphone manufacturer saw its production increase by $25\\%$ from $2022$ to $2023$. If the number of smartphones produced in $2023$ is $p$ times the number produced in $2022$, what is the value of $p$?",
    "type": "multiple-choice-single-answer",
    "id": 57,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "An increase of $25\\%$ means the production in $2023$ is $125\\%$ of the $2022$ production.\n\nTherefore, $p = 1.25$.\n\nTo confirm, if the production in $2022$ was $200$ units, in $2023$ it would be $200 \\times 1.25 = 250$ units, reflecting a $25\\%$ increase.\n\nThus, $p = 1.25$.",
    "options": [
      {
        "text": "$0.75$",
        "id": "a"
      },
      {
        "text": "$1.00$",
        "id": "b"
      },
      {
        "text": "$1.25$",
        "id": "c"
      },
      {
        "text": "$1.75$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A printer can print $30$ pages per minute. At this rate, how many pages can the printer print in $2$ hours?",
    "type": "multiple-choice-single-answer",
    "id": 58,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "First, convert the time from hours to minutes because the printer's rate is in pages per minute.\n\nThere are $60$ minutes in $1$ hour, so $2$ hours is $120$ minutes.\n\nThen, multiply the printing rate by the total time:\n\n$30\\ \\text{pages/minute} \\times 120\\ \\text{minutes} = 3,600\\ \\text{pages}$\n\nTherefore, the printer can print $3,600$ pages in $2$ hours.",
    "options": [
      {
        "text": "$2,400$",
        "id": "a"
      },
      {
        "text": "$3,000$",
        "id": "b"
      },
      {
        "text": "$3,200$",
        "id": "c"
      },
      {
        "text": "$3,600$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A water tank is being filled at a constant rate of $15$ liters per minute. How many liters of water will be in the tank after $3$ hours?",
    "type": "multiple-choice-single-answer",
    "id": 59,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, convert the time from hours to minutes:\n\n$3\\ \\text{hours} \\times 60\\ \\text{minutes/hour} = 180\\ \\text{minutes}$\n\nThen, multiply the filling rate by the total time:\n\n$15\\ \\text{liters/minute} \\times 180\\ \\text{minutes} = 2,700\\ \\text{liters}$\n\nThus, the tank will have $2,700$ liters of water after $3$ hours.",
    "options": [
      {
        "text": "$1,500$",
        "id": "a"
      },
      {
        "text": "$2,100$",
        "id": "b"
      },
      {
        "text": "$2,700$",
        "id": "c"
      },
      {
        "text": "$3,000$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A factory produces $500$ gadgets every $4$ hours. Working at the same rate, how many gadgets can it produce in $10$ hours?",
    "type": "multiple-choice-single-answer",
    "id": 60,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "First, find the production rate in gadgets per hour:\n\n$\\frac{500\\ \\text{gadgets}}{4\\ \\text{hours}} = 125\\ \\text{gadgets/hour}$\n\nThen, multiply the rate by the total time:\n\n$125\\ \\text{gadgets/hour} \\times 10\\ \\text{hours} = 1,250\\ \\text{gadgets}$\n\nTherefore, the factory can produce $1,250$ gadgets in $10$ hours.",
    "options": [
      {
        "text": "$1,000$",
        "id": "a"
      },
      {
        "text": "$1,250$",
        "id": "b"
      },
      {
        "text": "$1,500$",
        "id": "c"
      },
      {
        "text": "$2,000$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A typist can type $45$ words per minute. How many words can she type in $2$ hours, assuming she types continuously?",
    "type": "multiple-choice-single-answer",
    "id": 61,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "First, convert the time from hours to minutes:\n\n$2\\ \\text{hours} \\times 60\\ \\text{minutes/hour} = 120\\ \\text{minutes}$\n\nThen, multiply the typing rate by the total time:\n\n$45\\ \\text{words/minute} \\times 120\\ \\text{minutes} = 5,400\\ \\text{words}$\n\nTherefore, she can type $5,400$ words in $2$ hours.",
    "options": [
      {
        "text": "$4,800$",
        "id": "a"
      },
      {
        "text": "$5,000$",
        "id": "b"
      },
      {
        "text": "$5,200$",
        "id": "c"
      },
      {
        "text": "$5,400$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $4x + 2 = 18$, what is the value of $2x + 1$?",
    "type": "multiple-choice-single-answer",
    "id": 62,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "First, solve for $x$ in the equation:\n\n$4x + 2 = 18$\n\nSubtract $2$ from both sides:\n\n$4x = 16$\n\nDivide both sides by $4$:\n\n$x = 4$\n\nNow, find the value of $2x + 1$:\n\n$2(4) + 1 = 8 + 1 = 9$",
    "options": [
      {
        "text": "$7$",
        "id": "a"
      },
      {
        "text": "$9$",
        "id": "b"
      },
      {
        "text": "$10$",
        "id": "c"
      },
      {
        "text": "$12$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $\\frac{1}{2}y = 6$, what is the value of $y - 4$?",
    "type": "multiple-choice-single-answer",
    "id": 63,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, solve for $y$:\n\nMultiply both sides of $\\frac{1}{2}y = 6$ by $2$:\n\n$2 \\times \\frac{1}{2}y = 2 \\times 6$\n\n$y = 12$\n\nNow, compute $y - 4$:\n\n$12 - 4 = 8$",
    "options": [
      {
        "text": "$6$",
        "id": "a"
      },
      {
        "text": "$7$",
        "id": "b"
      },
      {
        "text": "$8$",
        "id": "c"
      },
      {
        "text": "$9$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $3(2z - 1) = 15$, what is the value of $z + 2$?",
    "type": "multiple-choice-single-answer",
    "id": 64,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "First, expand the equation:\n\n$3(2z - 1) = 15$\n\n$6z - 3 = 15$\n\nAdd $3$ to both sides:\n\n$6z = 18$\n\nDivide both sides by $6$:\n\n$z = 3$\n\nNow, find $z + 2$:\n\n$3 + 2 = 5$",
    "options": [
      {
        "text": "$3$",
        "id": "a"
      },
      {
        "text": "$4$",
        "id": "b"
      },
      {
        "text": "$6$",
        "id": "c"
      },
      {
        "text": "$5$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $5k - 10 = 15$, what is the value of $2k$?",
    "type": "multiple-choice-single-answer",
    "id": 65,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "First, solve for $k$:\n\nAdd $10$ to both sides:\n\n$5k = 25$\n\nDivide both sides by $5$:\n\n$k = 5$\n\nNow, calculate $2k$:\n\n$2 \\times 5 = 10$",
    "options": [
      {
        "text": "$10$",
        "id": "a"
      },
      {
        "text": "$12$",
        "id": "b"
      },
      {
        "text": "$14$",
        "id": "c"
      },
      {
        "text": "$15$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A bookstore purchased $500$ books and sold $25\\%$ of them in the first month. How many books did the bookstore sell in the first month?",
    "type": "multiple-choice-single-answer",
    "id": 66,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "To find $25\\%$ of $500$, convert the percentage to a decimal:\n\n $25\\% = 0.25$.\n\nMultiply this by the total number of books:\n\n$0.25 \\times 500 = 125$\n\nTherefore, the bookstore sold $125$ books in the first month.",
    "options": [
      {
        "text": "$100$",
        "id": "a"
      },
      {
        "text": "$125$",
        "id": "b"
      },
      {
        "text": "$150$",
        "id": "c"
      },
      {
        "text": "$200$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A tank contains $1,200$ liters of water. If $35\\%$ of the water is drained, how many liters of water are drained from the tank?",
    "type": "multiple-choice-single-answer",
    "id": 67,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, convert $35\\%$ to a decimal:\n\n $35\\% = 0.35$.\n\nThen multiply by the total volume:\n\n$0.35 \\times 1,200 = 420$\n\nThus, $420$ liters of water are drained from the tank.",
    "options": [
      {
        "text": "$350$",
        "id": "a"
      },
      {
        "text": "$400$",
        "id": "b"
      },
      {
        "text": "$420$",
        "id": "c"
      },
      {
        "text": "$450$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In a school of $800$ students, $60\\%$ participate in extracurricular activities. How many students participate in extracurricular activities?",
    "type": "multiple-choice-single-answer",
    "id": 68,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Convert $60\\%$ to a decimal:\n\n $60\\% = 0.60$.\n\nMultiply by the total number of students:\n\n$0.60 \\times 800 = 480$\n\nTherefore, $480$ students participate in extracurricular activities.",
    "options": [
      {
        "text": "$380$",
        "id": "a"
      },
      {
        "text": "$400$",
        "id": "b"
      },
      {
        "text": "$420$",
        "id": "c"
      },
      {
        "text": "$480$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Lisa received a commission of $8\\%$ on her sales amounting to $\\$15,000$. How much commission did Lisa earn?",
    "type": "multiple-choice-single-answer",
    "id": 69,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Convert $8\\%$ to a decimal:\n\n $8\\% = 0.08$.\n\nMultiply by the total sales amount:\n\n$0.08 \\times 15,000 = 1,200$\n\nLisa earned a commission of $\\$1,200$.",
    "options": [
      {
        "text": "$\\$1,000$",
        "id": "a"
      },
      {
        "text": "$\\$1,200$",
        "id": "b"
      },
      {
        "text": "$\\$1,400$",
        "id": "c"
      },
      {
        "text": "$\\$1,600$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Given the function $m(x) = 4 - 2x$, find the value of $m(-1)$.",
    "type": "multiple-choice-single-answer",
    "id": 70,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Substitute $x = -1$ into the function:\n\n$m(-1) = 4 - 2 \\times (-1) = 4 + 2 = 6$\n\nTherefore, $m(-1) = 6$.",
    "options": [
      {
        "text": "$2$",
        "id": "a"
      },
      {
        "text": "$6$",
        "id": "b"
      },
      {
        "text": "$-6$",
        "id": "c"
      },
      {
        "text": "$0$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $g(x) = 3x^2 + 2x - 1$, what is the value of $g(2)$?",
    "type": "multiple-choice-single-answer",
    "id": 71,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Substitute $x = 2$ into the function:\n\n$g(2) = 3(2)^2 + 2 \\times 2 - 1 =$\n\n $3 \\times 4 + 4 - 1 =$\n\n $ 12 + 4 - 1 = 15$\n\nTherefore, $g(2) = 15$.",
    "options": [
      {
        "text": "$11$",
        "id": "a"
      },
      {
        "text": "$15$",
        "id": "b"
      },
      {
        "text": "$17$",
        "id": "c"
      },
      {
        "text": "$19$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The function $h(t) = \\frac{20}{t+2}$ is defined above. What is the value of $h(3)$?",
    "type": "multiple-choice-single-answer",
    "id": 72,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Substitute $t = 3$ into the function:\n\n$h(3) = \\frac{20}{3+2} =$\n\n $ \\frac{20}{5} = 4$\n\nTherefore, $h(3) = 4$.",
    "options": [
      {
        "text": "$5$",
        "id": "a"
      },
      {
        "text": "$6$",
        "id": "b"
      },
      {
        "text": "$4$",
        "id": "c"
      },
      {
        "text": "$3$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $k(n) = n^2 - 4n + 7$, what is the value of $k(5)$?",
    "type": "multiple-choice-single-answer",
    "id": 73,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Substitute $n = 5$ into the function:\n\n$k(5) = (5)^2 - 4 \\times 5 + 7 =$\n\n $ 25 - 20 + 7 = 12$\n\nTherefore, $k(5) = 12$.",
    "options": [
      {
        "text": "$8$",
        "id": "a"
      },
      {
        "text": "$10$",
        "id": "b"
      },
      {
        "text": "$14$",
        "id": "c"
      },
      {
        "text": "$12$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A rectangle has a length of $14$ meters and a width of $9$ meters. What is the area of the rectangle?",
    "type": "multiple-choice-single-answer",
    "id": 74,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "To find the area of a rectangle, multiply its length by its width:\n\n$\\text{Area} = \\text{length} \\times \\text{width} =$\n\n $ 14 \\times 9 = 126\\ \\text{square meters}$\n\nTherefore, the area of the rectangle is $126$ square meters.",
    "options": [
      {
        "text": "$112$",
        "id": "a"
      },
      {
        "text": "$126$",
        "id": "b"
      },
      {
        "text": "$140$",
        "id": "c"
      },
      {
        "text": "$150$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The perimeter of a rectangle is $48$ centimeters. If the length of the rectangle is $16$ centimeters, what is its width?",
    "type": "multiple-choice-single-answer",
    "id": 75,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "The perimeter $P$ of a rectangle is calculated as:\n\n$P = 2(\\text{length} + \\text{width})$\n\nSubstitute the known values:\n\n$48 = 2(16 + w)$\n\nDivide both sides by $2$:\n\n$24 = 16 + w$\n\nSubtract $16$ from both sides:\n\n$w = 8\\ \\text{centimeters}$\n\nTherefore, the width of the rectangle is $8$ centimeters.",
    "options": [
      {
        "text": "$6$",
        "id": "a"
      },
      {
        "text": "$7$",
        "id": "b"
      },
      {
        "text": "$8$",
        "id": "c"
      },
      {
        "text": "$9$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A square garden has an area of $256$ square feet. What is the length of each side of the garden?",
    "type": "multiple-choice-single-answer",
    "id": 76,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "For a square, the area $A$ is given by:\n\n$A = s^2$\n\nSet up the equation:\n\n$256 = s^2$\n\nTake the square root of both sides:\n\n$s = \\sqrt{256} = 16\\ \\text{feet}$\n\nTherefore, each side of the garden is $16$ feet long.",
    "options": [
      {
        "text": "$16$",
        "id": "a"
      },
      {
        "text": "$18$",
        "id": "b"
      },
      {
        "text": "$20$",
        "id": "c"
      },
      {
        "text": "$22$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A rectangle has an area of $54$ square inches and a width of $6$ inches. What is the perimeter of the rectangle?",
    "type": "multiple-choice-single-answer",
    "id": 77,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "First, find the length of the rectangle using the area formula:\n\n$\\text{Area} = \\text{length} \\times \\text{width}$\n\n$54 = L \\times 6$\n\n$L = \\frac{54}{6} = 9\\ \\text{inches}$\n\nNow, calculate the perimeter:\n\n$P = 2(L + W) =$\n\n $ 2(9 + 6) = 2(15) = 30\\ \\text{inches}$\n\nTherefore, the perimeter of the rectangle is $30$ inches.",
    "options": [
      {
        "text": "$20$",
        "id": "a"
      },
      {
        "text": "$24$",
        "id": "b"
      },
      {
        "text": "$26$",
        "id": "c"
      },
      {
        "text": "$30$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A bag contains $15$ marbles, each numbered from $1$ to $15$. If one marble is selected at random, what is the probability that the number on the marble is a prime number?",
    "type": "multiple-choice-single-answer",
    "id": 78,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, identify the prime numbers between $1$ and $15$. \n\nThe prime numbers are $2$, $3$, $5$, $7$, $11$, and $13$. \n\nThis gives $6$ favorable outcomes. \n\nThe total number of possible outcomes is $15$. \n\nTherefore, the probability is:\n\n$\\text{Probability} = \\frac{\\text{Number of favorable outcomes}}{\\text{Total number of outcomes}} = \\frac{6}{15} = \\frac{2}{5}$",
    "options": [
      {
        "text": "$\\dfrac{2}{15}$",
        "id": "a"
      },
      {
        "text": "$\\dfrac{4}{15}$",
        "id": "b"
      },
      {
        "text": "$\\dfrac{2}{5}$",
        "id": "c"
      },
      {
        "text": "$\\dfrac{11}{15}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A box contains $20$ identical balls numbered from $1$ to $20$. If a ball is drawn at random, what is the probability that the number on the ball is a multiple of $4$?",
    "type": "multiple-choice-single-answer",
    "id": 79,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "First, list the multiples of $4$ between $1$ and $20$: $4$, $8$, $12$, $16$, and $20$.\n\nThere are $5$ multiples of $4$ in this range.\n\nThe total number of balls is $20$.\n\nThus, the probability is:\n\n$\\text{Probability} = \\frac{5}{20} = \\frac{1}{4}$",
    "options": [
      {
        "text": "$\\dfrac{1}{5}$",
        "id": "a"
      },
      {
        "text": "$\\dfrac{1}{4}$",
        "id": "b"
      },
      {
        "text": "$\\dfrac{1}{2}$",
        "id": "c"
      },
      {
        "text": "$\\dfrac{3}{4}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A spinner is divided into $8$ equal sections numbered from $1$ to $8$. When spun, what is the probability that the spinner lands on an even number?",
    "type": "multiple-choice-single-answer",
    "id": 80,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "The even numbers between $1$ and $8$ are $2$, $4$, $6$, and $8$.\n\nThere are $4$ favorable outcomes.\n\nThe total number of outcomes is $8$.\n\nTherefore, the probability is:\n\n$\\text{Probability} = \\frac{4}{8} = \\frac{1}{2}$",
    "options": [
      {
        "text": "$\\dfrac{1}{8}$",
        "id": "a"
      },
      {
        "text": "$\\dfrac{1}{4}$",
        "id": "b"
      },
      {
        "text": "$\\dfrac{1}{2}$",
        "id": "c"
      },
      {
        "text": "$\\dfrac{3}{4}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A jar contains $12$ slips of paper, each marked with a different letter from $A$ to $L$. If one slip is drawn at random, what is the probability that it is a vowel?",
    "type": "multiple-choice-single-answer",
    "id": 81,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "The vowels between $A$ and $L$ are $A$, $E$, and $I$.\n\nSo there are $3$ favorable outcomes.\n\nThe total number of slips is $12$.\n\nTherefore, the probability is:\n\n$\\text{Probability} = \\frac{3}{12} = \\frac{1}{4}$",
    "options": [
      {
        "text": "$\\dfrac{1}{6}$",
        "id": "a"
      },
      {
        "text": "$\\dfrac{1}{4}$",
        "id": "b"
      },
      {
        "text": "$\\dfrac{1}{3}$",
        "id": "c"
      },
      {
        "text": "$\\dfrac{1}{2}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A fitness trainer designs a workout plan consisting of running and cycling. The total calories burned can be represented by the equation $10r + 8c = 480$, where $r$ is the number of minutes running and $c$ is the number of minutes cycling. What does the number $10$ represent in this equation?",
    "type": "multiple-choice-single-answer",
    "id": 81,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "In the equation $10r + 8c = 480$, the term $10r$ represents the calories burned from running.\n\n The number $10$ is multiplied by $r$, indicating the calories burned per minute of running. \n\nTherefore, $10$ represents the number of calories burned per minute while running.",
    "options": [
      {
        "text": "The trainer plans $10$ minutes of running.",
        "id": "a"
      },
      {
        "text": "The calories burned per minute of running.",
        "id": "b"
      },
      {
        "text": "The calories burned per minute of cycling.",
        "id": "c"
      },
      {
        "text": "The trainer burns $10$ calories during the workout.",
        "id": "d"
      }
    ]
  },
  {
    "text": "A farmer has $p$ apple trees and $q$ orange trees in an orchard. Each apple tree yields $30$ kilograms of fruit, and each orange tree yields $20$ kilograms of fruit. The equation $30p + 20q = 600$ represents the total yield in kilograms. Which of the following is the best interpretation of the number $20$ in this context?",
    "type": "multiple-choice-single-answer",
    "id": 82,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "In the equation $30p + 20q = 600$, the term $20q$ represents the yield from orange trees. \n\nThe number $20$ is multiplied by $q$, the number of orange trees.\n\n Therefore, $20$ represents the kilograms of fruit yielded by each orange tree.",
    "options": [
      {
        "text": "The farmer has $20$ apple trees.",
        "id": "a"
      },
      {
        "text": "Each orange tree yields $20$ kilograms of fruit.",
        "id": "b"
      },
      {
        "text": "Each apple tree yields $20$ kilograms of fruit.",
        "id": "c"
      },
      {
        "text": "The farmer harvested a total of $20$ kilograms of fruit.",
        "id": "d"
      }
    ]
  },
  {
    "text": "A printing company charges a fixed setup fee of $50$ dollars and an additional $0.10$ dollars per page printed. The total cost $C$ (in dollars) for printing $n$ pages is given by the equation $C = 0.10n + 50$. What does the number $0.10$ represent in this equation?",
    "type": "multiple-choice-single-answer",
    "id": 83,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "In the equation $C = 0.10n + 50$, the term $0.10n$ represents the variable cost based on the number of pages printed.\n\n The number $0.10$ is multiplied by $n$, indicating the cost per page.\n\n Therefore, $0.10$ represents the cost in dollars for printing each page.",
    "options": [
      {
        "text": "The cost in dollars per page printed.",
        "id": "a"
      },
      {
        "text": "The fixed setup fee in dollars.",
        "id": "b"
      },
      {
        "text": "The total number of pages printed.",
        "id": "c"
      },
      {
        "text": "The total cost in dollars for $0.10$ pages.",
        "id": "d"
      }
    ]
  },
  {
    "text": "A delivery service charges based on the weight of packages. The total cost $T$ (in dollars) for delivering $l$ light packages and $h$ heavy packages is given by $T = 5l + 8h$. What does the number $8$ represent in this equation?",
    "type": "multiple-choice-single-answer",
    "id": 84,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "In the equation $T = 5l + 8h$, the term $8h$ represents the cost associated with heavy packages.\n\n The number $8$ is multiplied by $h$, the number of heavy packages.\n\n Therefore, $8$ represents the cost in dollars to deliver each heavy package.",
    "options": [
      {
        "text": "The service delivers $8$ heavy packages.",
        "id": "a"
      },
      {
        "text": "Each light package weighs $8$ pounds.",
        "id": "b"
      },
      {
        "text": "Each heavy package costs $8$ dollars to deliver.",
        "id": "c"
      },
      {
        "text": "Heavy packages weigh $8$ times more than light packages.",
        "id": "d"
      }
    ]
  },
  {
    "text": "How many real solutions are there to the equation $x^2 + x + 1 = 0$?",
    "type": "multiple-choice-single-answer",
    "id": 85,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Calculate the discriminant $D$ for the quadratic equation $x^2 + x + 1 = 0$, where $a = 1$, $b = 1$, and $c = 1$:\n\n$D = b^2 - 4ac =$\n\n $ (1)^2 - 4 \\times 1 \\times 1 = 1 - 4 = -3$\n\nSince $D$ is negative, the equation has $\\textbf{no real solutions}$.",
    "options": [
      {
        "text": "Exactly one",
        "id": "a"
      },
      {
        "text": "Exactly two",
        "id": "b"
      },
      {
        "text": "Infinitely many",
        "id": "c"
      },
      {
        "text": "Zero",
        "id": "d"
      }
    ]
  },
  {
    "text": "How many real solutions does the equation $x^2 + 4x + 5 = 0$ have?",
    "type": "multiple-choice-single-answer",
    "id": 86,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "To determine the number of real solutions, calculate the discriminant $D$ of the quadratic equation $ax^2 + bx + c = 0$, where $a = 1$, $b = 4$, and $c = 5$. The discriminant is:\n\n$D = b^2 - 4ac =$\n\n $ (4)^2 - 4 \\times 1 \\times 5 = 16 - 20 = -4$\n\nSince $D$ is negative, the equation has $\\textbf{no real solutions}$.",
    "options": [
      {
        "text": "Exactly one",
        "id": "a"
      },
      {
        "text": "Exactly two",
        "id": "b"
      },
      {
        "text": "Infinitely many",
        "id": "c"
      },
      {
        "text": "Zero",
        "id": "d"
      }
    ]
  },
  {
    "text": "How many distinct real solutions does the equation $2x^2 - 3x + 1 = 0$ have?",
    "type": "multiple-choice-single-answer",
    "id": 87,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Compute the discriminant $D$ for the quadratic equation $2x^2 - 3x + 1 = 0$, where $a = 2$, $b = -3$, and $c = 1$:\n\n$D = b^2 - 4ac =$\n\n $ (-3)^2 - 4 \\times 2 \\times 1 = 9 - 8 = 1$\n\nSince $D$ is positive, the equation has $\\textbf{exactly two real solutions}$.",
    "options": [
      {
        "text": "Exactly one",
        "id": "a"
      },
      {
        "text": "Exactly two",
        "id": "b"
      },
      {
        "text": "Infinitely many",
        "id": "c"
      },
      {
        "text": "Zero",
        "id": "d"
      }
    ]
  },
  {
    "text": "Determine the number of real solutions for the equation $x^2 - 6x + 9 = 0$.",
    "type": "multiple-choice-single-answer",
    "id": 88,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Find the discriminant $D$ of the quadratic equation $x^2 - 6x + 9 = 0$, where $a = 1$, $b = -6$, and $c = 9$:\n\n$D = b^2 - 4ac =$\n\n $ (-6)^2 - 4 \\times 1 \\times 9 = 36 - 36 = 0$\n\nSince $D$ is zero, the equation has $\\textbf{exactly one real solution}$.",
    "options": [
      {
        "text": "Exactly one",
        "id": "a"
      },
      {
        "text": "Exactly two",
        "id": "b"
      },
      {
        "text": "Infinitely many",
        "id": "c"
      },
      {
        "text": "Zero",
        "id": "d"
      }
    ]
  },
  {
    "text": "A farmer has a total of $45$ animals consisting of cows and chickens. If the animals have a total of $120$ legs, how many cows does the farmer have?",
    "type": "multiple-choice-single-answer",
    "id": 89,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Let the number of cows be $x$. Since there are $45$ animals in total, the number of chickens is $45 - x$.\n\n Cows have $4$ legs, and chickens have $2$ legs. \n\nThe total number of legs is $4x + 2(45 - x) = 120$.\n\n Simplify: $4x + 90 - 2x = 120$.\n\n Combine like terms: $2x + 90 = 120$.\n\n Subtract $90$ from both sides: $2x = 30$. \n\nDivide both sides by $2$: $x = 15$.\n\n Therefore, the farmer has $15$ cows.",
    "options": [
      {
        "text": "$10$",
        "id": "a"
      },
      {
        "text": "$12$",
        "id": "b"
      },
      {
        "text": "$14$",
        "id": "c"
      },
      {
        "text": "$15$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A bookstore sold a total of $50$ books consisting of novels and comic books. Each novel costs $\\$20$, and each comic book costs $\\$10$. If the total sales amount was $\\$800$, how many novels did the bookstore sell?",
    "type": "multiple-choice-single-answer",
    "id": 90,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Let the number of novels sold be $x$.\n\n Then the number of comic books sold is $50 - x$.\n\n The total sales amount is $20x + 10(50 - x) = 800$.\n\n Simplify: $20x + 500 - 10x = 800$.\n\n Combine like terms: $10x + 500 = 800$.\n\n Subtract $500$ from both sides: $10x = 300$.\n\n Divide both sides by $10$: $x = 30$.\n\n Therefore, the bookstore sold $30$ novels.",
    "options": [
      {
        "text": "$20$",
        "id": "a"
      },
      {
        "text": "$25$",
        "id": "b"
      },
      {
        "text": "$30$",
        "id": "c"
      },
      {
        "text": "$35$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A transportation company has a fleet of $25$ vehicles consisting of cars and buses. Each car can carry $4$ passengers, and each bus can carry $40$ passengers. If the entire fleet can carry a total of $280$ passengers, how many buses are in the fleet?",
    "type": "multiple-choice-single-answer",
    "id": 91,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Let the number of buses be $x$. \n\nThen the number of cars is $25 - x$.\n\n The total passenger capacity is $40x + 4(25 - x) = 280$.\n\n Simplify: $40x + 100 - 4x = 280$.\n\n Combine like terms: $36x + 100 = 280$.\n\n Subtract 100 from both sides: $36x = 180$.\n\n Divide both sides by 36: $x = \\dfrac{180}{36} = 5$.\n\n Therefore, there are $5$ buses in the fleet.",
    "options": [
      {
        "text": "$4$",
        "id": "a"
      },
      {
        "text": "$5$",
        "id": "b"
      },
      {
        "text": "$6$",
        "id": "c"
      },
      {
        "text": "$7$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A jeweler has a collection of $60$ rings made of gold and silver. Each gold ring weighs $8$ grams, and each silver ring weighs $5$ grams. If the total weight of the rings is $360$ grams, how many gold rings are there?",
    "type": "multiple-choice-single-answer",
    "id": 92,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Let the number of gold rings be $x$.\n\n Then the number of silver rings is $60 - x$.\n\n The total weight is $8x + 5(60 - x) = 360$. \n\nSimplify: $8x + 300 - 5x = 360$.\n\n Combine like terms: $3x + 300 = 360$.\n\n Subtract 300 from both sides: $3x = 60$.\n\n Divide both sides by 3: $x = 20$.\n\n Therefore, there are $20$ gold rings.",
    "options": [
      {
        "text": "$15$",
        "id": "a"
      },
      {
        "text": "$18$",
        "id": "b"
      },
      {
        "text": "$20$",
        "id": "c"
      },
      {
        "text": "$25$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A metal cylinder has a mass of $500$ kilograms. The cylinder has a radius of $0.2$ meters and a height of $0.5$ meters. To the nearest whole number, what is the density, in kilograms per cubic meter, of the metal cylinder?",
    "type": "multiple-choice-single-answer",
    "id": 93,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "First, calculate the volume of the cylinder using the formula $V = \\pi r^2 h$.\n\n Substitute the given values:$\n\n $ $V = \\pi (0.2)^2 (0.5) =$\n\n $ \\pi (0.04)(0.5) = $\n\n $\\pi (0.02) \\approx 0.0628$ cubic meters.\n\n Next, calculate the density using $D = \\dfrac{m}{V} =$\n\n $ \\dfrac{500}{0.0628} \\approx 7,957.75$ kilograms per cubic meter.\n\n Rounded to the nearest whole number, the density is $7,958$ kg/m³.",
    "options": [
      {
        "text": "$7,500$",
        "id": "a"
      },
      {
        "text": "$7,958$",
        "id": "b"
      },
      {
        "text": "$8,000$",
        "id": "c"
      },
      {
        "text": "$8,500$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A solid cube made of aluminum has a mass of $2,700$ grams. Each side of the cube is $10$ centimeters long. To the nearest whole number, what is the density, in grams per cubic centimeter, of the aluminum cube?",
    "type": "multiple-choice-single-answer",
    "id": 94,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Calculate the volume of the cube using $V = s^3$, where $s$ is the side length.\n\n So, $V = (10)^3 = 1,000$ cubic centimeters.\n\n The density is $D = \\dfrac{m}{V} =$\n\n $ \\dfrac{2,700}{1,000} = 2.7$ grams per cubic centimeter.",
    "options": [
      {
        "text": "$2.5$",
        "id": "a"
      },
      {
        "text": "$2.6$",
        "id": "b"
      },
      {
        "text": "$2.7$",
        "id": "c"
      },
      {
        "text": "$2.8$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A spherical balloon is filled with helium gas and has a radius of $0.5$ meters. The mass of the helium gas inside is $0.089$ kilograms. To the nearest whole number, what is the density, in kilograms per cubic meter, of the helium gas in the balloon?",
    "type": "multiple-choice-single-answer",
    "id": 95,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Calculate the volume of the sphere using $V = \\dfrac{4}{3}\\pi r^3$.\n\n Substitute the given radius:$\n\n $ $V = \\dfrac{4}{3}\\pi (0.5)^3 =$\n\n $ \\dfrac{4}{3}\\pi (0.125) \\approx 0.5236$ cubic meters.\n\n The density is $D = \\dfrac{m}{V} =$\n\n $ \\dfrac{0.089}{0.5236} \\approx 0.17$ kilograms per cubic meter. \n\nRounded to the nearest whole number, the density is $0$ kg/m³.",
    "options": [
      {
        "text": "$0$",
        "id": "a"
      },
      {
        "text": "$1$",
        "id": "b"
      },
      {
        "text": "$2$",
        "id": "c"
      },
      {
        "text": "$3$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A rectangular prism-shaped aquarium is filled with water and has dimensions of length $2$ meters, width $1.5$ meters, and height $1$ meter. The mass of the water is $3,000$ kilograms. To the nearest whole number, what is the density, in kilograms per cubic meter, of the water in the aquarium?",
    "type": "multiple-choice-single-answer",
    "id": 96,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Calculate the volume of the aquarium using $V = lwh =$\n\n $ (2)(1.5)(1) = 3$ cubic meters. \n\nThe density is $D = \\dfrac{m}{V} =$\n\n $ \\dfrac{3,000}{3} = 1,000$ kilograms per cubic meter.",
    "options": [
      {
        "text": "$900$",
        "id": "a"
      },
      {
        "text": "$950$",
        "id": "b"
      },
      {
        "text": "$980$",
        "id": "c"
      },
      {
        "text": "$1,000$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A granite statue in the shape of a rectangular prism has dimensions of length $0.5$ meters, width $0.4$ meters, and height $2$ meters. If the density of granite is approximately $2,700$ kilograms per cubic meter, to the nearest kilogram, what is the mass of the statue?",
    "type": "multiple-choice-single-answer",
    "id": 97,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "First, calculate the volume of the statue:\n\n  $V = lwh =$\n\n $ (0.5)(0.4)(2) = 0.4$ cubic meters.\n\n Next, calculate the mass using $m = D \\times V =$\n\n $ 2,700 \\times 0.4 = 1,080$ kilograms.",
    "options": [
      {
        "text": "$800$",
        "id": "a"
      },
      {
        "text": "$1,080$",
        "id": "b"
      },
      {
        "text": "$1,200$",
        "id": "c"
      },
      {
        "text": "$1,500$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The expression $x^2 + 5x + 6$ is equivalent to which of the following?",
    "type": "multiple-choice-single-answer",
    "id": 98,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "To factor the quadratic expression $x^2 + 5x + 6$, we need to find two numbers that multiply to $6$, which is the constant term, and add up to $5$, which is the coefficient of $x$.\n\n These numbers are $2$ and $3$ because $2 \\times 3 = 6$ and $2 + 3 = 5$.\n\n Therefore, the factored form is $(x + 2)(x + 3)$.",
    "options": [
      {
        "text": "$(x + 2)(x + 3)$",
        "id": "a"
      },
      {
        "text": "$(x - 2)(x + 3)$",
        "id": "b"
      },
      {
        "text": "$(x + 2)(x - 3)$",
        "id": "c"
      },
      {
        "text": "$(x - 2)(x - 3)$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The expression $2x^2 - 7x + 3$ is equivalent to which of the following?",
    "type": "multiple-choice-single-answer",
    "id": 99,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "To factor $2x^2 - 7x + 3$, we look for two numbers that multiply to the product of the leading coefficient and the constant term $(2)(3) = 6$ and add up to the middle coefficient $-7$.\n\n These numbers are $-6$ and $-1$ because $(-6)(-1) = 6$ and $-6 + (-1) = -7$.\n\n Rewrite the middle term using these numbers:\n\n$2x^2 - 6x - x + 3$. \n\nGroup the terms:\n\n$(2x^2 - 6x) - (x - 3)$. \n\nFactor out common factors from each group:\n\n$2x(x - 3) - 1(x - 3)$. \n\nFactor out $(x - 3)$:\n\n$(x - 3)(2x - 1)$. \n\nTherefore, the factored form is $(2x - 1)(x - 3)$.",
    "options": [
      {
        "text": "$(2x - 1)(x - 3)$",
        "id": "a"
      },
      {
        "text": "$(2x + 1)(x - 3)$",
        "id": "b"
      },
      {
        "text": "$(x - 1)(2x - 3)$",
        "id": "c"
      },
      {
        "text": "$(2x - 3)(x - 1)$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The expression $x^2 - 4x - 12$ is equivalent to which of the following?",
    "type": "multiple-choice-single-answer",
    "id": 100,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "To factor $x^2 - 4x - 12$, find two numbers that multiply to $-12$ and add up to $-4$.\n\n These numbers are $-6$ and $2$ because $(-6) \\times 2 = -12$ and $-6 + 2 = -4$.\n\n Therefore, the factored form is $(x - 6)(x + 2)$.",
    "options": [
      {
        "text": "$(x - 6)(x + 2)$",
        "id": "a"
      },
      {
        "text": "$(x + 6)(x - 2)$",
        "id": "b"
      },
      {
        "text": "$(x - 4)(x + 3)$",
        "id": "c"
      },
      {
        "text": "$(x + 4)(x - 3)$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The expression $9x^2 - 16$ is equivalent to which of the following?",
    "type": "multiple-choice-single-answer",
    "id": 101,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "The expression $9x^2 - 16$ is a difference of squares since $9x^2$ is $(3x)^2$ and $16$ is $(4)^2$. \n\nThe difference of squares formula states that $a^2 - b^2 = (a - b)(a + b)$. Applying this, we get:\n\n$9x^2 - 16 = (3x - 4)(3x + 4)$.",
    "options": [
      {
        "text": "$(3x - 4)(3x + 4)$",
        "id": "a"
      },
      {
        "text": "$(9x - 16)(x + 1)$",
        "id": "b"
      },
      {
        "text": "$(3x - 2)(3x + 8)$",
        "id": "c"
      },
      {
        "text": "$(x - 4)(9x + 4)$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Triangle XYZ is an equilateral triangle. What is the measure of angle X?",
    "type": "multiple-choice-single-answer",
    "id": 102,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "An equilateral triangle has all sides equal and all angles equal.\n\nSince the sum of the interior angles of a triangle is $180^{\\circ}$, each angle measures:\n\n$\\frac{180^{\\circ}}{3} = 60^{\\circ}$\n\nTherefore, the measure of angle X is $60^{\\circ}$.",
    "options": [
      {
        "text": "$45^{\\circ}$",
        "id": "a"
      },
      {
        "text": "$60^{\\circ}$",
        "id": "b"
      },
      {
        "text": "$75^{\\circ}$",
        "id": "c"
      },
      {
        "text": "$90^{\\circ}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In triangle DEF, angle D measures $x^{\\circ}$, angle E measures $2x^{\\circ}$, and angle F measures $3x^{\\circ}$. What is the value of $x$?",
    "type": "multiple-choice-single-answer",
    "id": 103,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "The sum of the angles in a triangle is $180^{\\circ}$. Set up the equation:\n\n$x^{\\circ} + 2x^{\\circ} + 3x^{\\circ} = 180^{\\circ}$\n\nCombine like terms:\n\n$6x^{\\circ} = 180^{\\circ}$\n\nDivide both sides by 6:\n\n$x = \\frac{180^{\\circ}}{6}$\n\n$x = 30^{\\circ}$\n\nTherefore, the value of $x$ is $30^{\\circ}$.",
    "options": [
      {
        "text": "$30^{\\circ}$",
        "id": "a"
      },
      {
        "text": "$36^{\\circ}$",
        "id": "b"
      },
      {
        "text": "$45^{\\circ}$",
        "id": "c"
      },
      {
        "text": "$60^{\\circ}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In triangle RST, angle R measures twice angle S, and angle T measures three times angle S. What is the measure of angle S?",
    "type": "multiple-choice-single-answer",
    "id": 104,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Let angle S be $x^{\\circ}$. Then angle R is $2x^{\\circ}$, and angle T is $3x^{\\circ}$.\n\nThe sum of the angles is:\n\n$x^{\\circ} + 2x^{\\circ} + 3x^{\\circ} = 180^{\\circ}$\n\nCombine like terms:\n\n$6x^{\\circ} = 180^{\\circ}$\n\nDivide both sides by 6:\n\n$x = \\frac{180^{\\circ}}{6}$\n\n$x = 30^{\\circ}$\n\nTherefore, the measure of angle S is $30^{\\circ}$.",
    "options": [
      {
        "text": "$30^{\\circ}$",
        "id": "a"
      },
      {
        "text": "$60^{\\circ}$",
        "id": "b"
      },
      {
        "text": "$90^{\\circ}$",
        "id": "c"
      },
      {
        "text": "$120^{\\circ}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In triangle ABC, angle A measures $45^{\\circ}$ and angle B measures $55^{\\circ}$. What is the measure of angle C?",
    "type": "multiple-choice-single-answer",
    "id": 105,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "In any triangle, the sum of the interior angles is $180^{\\circ}$. To find angle C, set up the equation:\n\n$45^{\\circ} + 55^{\\circ} + C = 180^{\\circ}$\n\nCombine like terms:\n\n$100^{\\circ} + C = 180^{\\circ}$\n\nSubtract $100^{\\circ}$ from both sides:\n\n$C = 180^{\\circ} - 100^{\\circ}$\n\n$C = 80^{\\circ}$\n\nTherefore, the measure of angle C is $80^{\\circ}$.",
    "options": [
      {
        "text": "$70^{\\circ}$",
        "id": "a"
      },
      {
        "text": "$75^{\\circ}$",
        "id": "b"
      },
      {
        "text": "$80^{\\circ}$",
        "id": "c"
      },
      {
        "text": "$85^{\\circ}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "What is the negative solution to the equation $\\dfrac{24}{x} = x - 5$?",
    "type": "multiple-choice-single-answer",
    "id": 106,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Begin by multiplying both sides of the equation by $x$ to eliminate the denominator:\n\n$24 = x(x - 5)$\n\nExpand the right side:\n\n$24 = x^2 - 5x$\n\nBring all terms to one side to set the quadratic equation to zero:\n\n$x^2 - 5x - 24 = 0$\n\nFactor the quadratic equation:\n\n$(x - 8)(x + 3) = 0$\n\nSet each factor equal to zero:\n\n1. $x - 8 = 0 \\quad \\Rightarrow \\quad x = 8$\n\n2. $x + 3 = 0 \\quad \\Rightarrow \\quad x = -3$\n\nThe negative solution is $x = -3$.",
    "options": [
      {
        "text": "$-1$",
        "id": "a"
      },
      {
        "text": "$-2$",
        "id": "b"
      },
      {
        "text": "$-3$",
        "id": "c"
      },
      {
        "text": "$-4$",
        "id": "d"
      }
    ]
  },
  {
    "text": "What is the negative solution to the equation $\\dfrac{15}{x} = x + 2$?",
    "type": "multiple-choice-single-answer",
    "id": 107,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Multiply both sides of the equation by $x$ to eliminate the denominator:\n\n$15 = x(x + 2)$\n\nExpand the right side:\n\n$15 = x^2 + 2x$\n\nBring all terms to one side:\n\n$x^2 + 2x - 15 = 0$\n\nFactor the quadratic equation:\n\n$(x + 5)(x - 3) = 0$\n\nSet each factor equal to zero:\n\n1. $x + 5 = 0 \\quad \\Rightarrow \\quad x = -5$\n\n2. $x - 3 = 0 \\quad \\Rightarrow \\quad x = 3$\n\nThe negative solution is $x = -5$.",
    "options": [
      {
        "text": "$-5$",
        "id": "a"
      },
      {
        "text": "$-2$",
        "id": "b"
      },
      {
        "text": "$-1$",
        "id": "c"
      },
      {
        "text": "$0$",
        "id": "d"
      }
    ]
  },
  {
    "text": "What is the negative solution to the equation $\\dfrac{16}{x} = x + 6$?",
    "type": "multiple-choice-single-answer",
    "id": 108,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Multiply both sides by $x$:\n\n$16 = x(x + 6)$\n\nExpand the right side:\n\n$16 = x^2 + 6x$\n\nBring all terms to one side:\n\n$x^2 + 6x - 16 = 0$\n\nFactor the quadratic equation:\n\n$(x + 8)(x - 2) = 0$\n\nSet each factor equal to zero:\n\n1. $x + 8 = 0 \\quad \\Rightarrow \\quad x = -8$\n\n2. $x - 2 = 0 \\quad \\Rightarrow \\quad x = 2$\n\nThe negative solution is $x = -8$.",
    "options": [
      {
        "text": "$-10$",
        "id": "a"
      },
      {
        "text": "$-8$",
        "id": "b"
      },
      {
        "text": "$-6$",
        "id": "c"
      },
      {
        "text": "$-4$",
        "id": "d"
      }
    ]
  },
  {
    "text": "What is the negative solution to the equation $x - \\dfrac{12}{x} = 4$?",
    "type": "multiple-choice-single-answer",
    "id": 109,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Multiply both sides of the equation by $x$ to eliminate the fraction:\n\n$x^2 - 12 = 4x$\n\nBring all terms to one side to form a quadratic equation:\n\n$x^2 - 4x - 12 = 0$\n\nFactor the quadratic equation:\n\n$(x - 6)(x + 2) = 0$\n\nSet each factor equal to zero:\n\n1. $x - 6 = 0 \\quad \\Rightarrow \\quad x = 6$\n\n2. $x + 2 = 0 \\quad \\Rightarrow \\quad x = -2$\n\nThe negative solution is $x = -2$.",
    "options": [
      {
        "text": "$-6$",
        "id": "a"
      },
      {
        "text": "$-2$",
        "id": "b"
      },
      {
        "text": "$-1$",
        "id": "c"
      },
      {
        "text": "$0$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A population of bacteria doubles every hour starting from $500$ bacteria. Which of the following best describes the function used to model the bacteria population over time?",
    "type": "multiple-choice-single-answer",
    "id": 110,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Since the bacteria population doubles every hour, it increases by a constant 'factor' of $2$ each hour.\n\nThis is characteristic of exponential growth, which can be modeled by the function $P(t) = 500 \\times 2^t,$ where $P(t)$ is the population after $t$ hours.\n\nTherefore, the function modeling the bacteria population over time is an 'increasing exponential' function.",
    "options": [
      {
        "text": "Increasing linear",
        "id": "a"
      },
      {
        "text": "Increasing exponential",
        "id": "b"
      },
      {
        "text": "Decreasing linear",
        "id": "c"
      },
      {
        "text": "Decreasing exponential",
        "id": "d"
      }
    ]
  },
  {
    "text": "A car depreciates in value by $15\\%$ each year after being purchased for $\\$20,000$. Which of the following best describes the function used to model the car's value over time?",
    "type": "multiple-choice-single-answer",
    "id": 111,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "The car's value decreases by a constant 'percentage' each year, meaning it decreases by a factor of $0.85$ annually, since $100\\% - 15\\% = 85\\% = 0.85$. \n\nThis is characteristic of exponential decay, modeled by the function $V(t) = 20,000 \\times (0.85)^t,$ where $V(t)$ is the value after $t$ years.\n\nTherefore, the function modeling the car's value over time is a 'decreasing exponential' function.",
    "options": [
      {
        "text": "Increasing linear",
        "id": "a"
      },
      {
        "text": "Increasing exponential",
        "id": "b"
      },
      {
        "text": "Decreasing linear",
        "id": "c"
      },
      {
        "text": "Decreasing exponential",
        "id": "d"
      }
    ]
  },
  {
    "text": "A tank is being filled with water at a constant rate of $10$ liters per minute, starting from an initial amount of $50$ liters. Which of the following best describes the function used to model the volume of water in the tank over time?",
    "type": "multiple-choice-single-answer",
    "id": 112,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "The volume of water increases by a constant 'amount' each minute, which is characteristic of linear growth.\n\nThe function can be modeled as $V(t) = 50 + 10t,$ where $V(t)$ is the volume after $t$ minutes.\n\nTherefore, the function modeling the volume of water over time is an 'increasing linear' function.",
    "options": [
      {
        "text": "Increasing linear",
        "id": "a"
      },
      {
        "text": "Increasing exponential",
        "id": "b"
      },
      {
        "text": "Decreasing linear",
        "id": "c"
      },
      {
        "text": "Decreasing exponential",
        "id": "d"
      }
    ]
  },
  {
    "text": "A radioactive substance decays such that it loses half of its mass every $5$ years. Which of the following best describes the function used to model the substance's mass over time?",
    "type": "multiple-choice-single-answer",
    "id": 113,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Since the substance loses half of its mass every $5$ years, it decreases by a constant 'factor' of $0.5$ at regular intervals.\n\nThis is exponential decay, modeled by the function $M(t) = M_0 \\times \\left(0.5\\right)^{t/5},$ where $M_0$ is the initial mass and $t$ is time in years.\n\nTherefore, the function modeling the substance's mass over time is a 'decreasing exponential' function.",
    "options": [
      {
        "text": "Increasing linear",
        "id": "a"
      },
      {
        "text": "Increasing exponential",
        "id": "b"
      },
      {
        "text": "Decreasing linear",
        "id": "c"
      },
      {
        "text": "Decreasing exponential",
        "id": "d"
      }
    ]
  },
  {
    "text": "The following data set represents the ages (in years) of participants in a workshop: $24$, $27$, $29$, $32$, $35$, $38$, $40$\n\nWhich of the following is the median age of the participants?",
    "type": "multiple-choice-single-answer",
    "id": 114,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To find the median, first ensure the data is in numerical order, if it not already.\n\nThere are $7$ data points, which is an odd number.\n\nThe median is the middle value, which is the $4^{\\text{th}}$ number in the list.\n\nThe $4^{\\text{th}}$ number is $32$.\n\nTherefore, the median age is $32$ years.",
    "options": [
      {
        "text": "$29$",
        "id": "a"
      },
      {
        "text": "$31$",
        "id": "b"
      },
      {
        "text": "$32$",
        "id": "c"
      },
      {
        "text": "$35$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A set of exam scores is as follows: $72$, $76$, $81$, $85$, $89$, $93$, $97$\n\nWhich of the following is the median exam score?",
    "type": "multiple-choice-single-answer",
    "id": 115,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "The data is already in order.\n\nThere are $7$ scores, so the median is the middle value, which is the $4^{\\text{th}}$ score.\n\nThe $4^{\\text{th}}$ score is $85$.\n\nTherefore, the median exam score is $85$.",
    "options": [
      {
        "text": "$81$",
        "id": "a"
      },
      {
        "text": "$85$",
        "id": "b"
      },
      {
        "text": "$89$",
        "id": "c"
      },
      {
        "text": "$93$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The heights (in centimeters) of plants in a study are: $54$, $56$, $59$, $63$, $67$, $70$\n\nWhat is the median height of the plants?",
    "type": "multiple-choice-single-answer",
    "id": 116,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "There are $6$ data points, which is an even number. \n\nThe median is the average of the $3^{\\text{rd}}$ and $4^{\\text{th}}$ values.\n\nThe $3^{\\text{rd}}$ value is $59$, and the $4^{\\text{th}}$ value is $63$.\n\nCalculate the average:\n\n$\\text{Median} = \\frac{59 + 63}{2} = \\frac{122}{2} = 61$\n\nTherefore, the median height is $61$ centimeters.",
    "options": [
      {
        "text": "$59$",
        "id": "a"
      },
      {
        "text": "$60$",
        "id": "b"
      },
      {
        "text": "$61$",
        "id": "c"
      },
      {
        "text": "$63$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Consider the following data set representing weekly sales (in units): $120$, $135$, $150$, $165$, $180$, $195$, $210$, $225$\n\nWhat is the median number of units sold per week?",
    "type": "multiple-choice-single-answer",
    "id": 117,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "There are $8$ data points, which is an even number.\n\nThe median is the average of the $4^{\\text{th}}$ and $5^{\\text{th}}$ values.\n\nThe $4^{\\text{th}}$ value is $165$, and the $5^{\\text{th}}$ value is $180$. \n\nCalculate the average:\n\n$\\text{Median} = \\frac{165 + 180}{2} = \\frac{345}{2} = 172.5$\n\nTherefore, the median number of units sold per week is $172.5$ units.",
    "options": [
      {
        "text": "$165$",
        "id": "a"
      },
      {
        "text": "$172.5$",
        "id": "b"
      },
      {
        "text": "$180$",
        "id": "c"
      },
      {
        "text": "$195$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In the linear function $f$, if $f(2) = 7$ and $f(4) = 11$, which of the following is the equation of function $f$?",
    "type": "multiple-choice-single-answer",
    "id": 118,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "To find the equation of the linear function $f$, we use the two given points: $(2, 7)$ and $(4, 11)$.\n\nFirst, find the slope $m$:\n\n$m = \\frac{y_2 - y_1}{x_2 - x_1} = \\frac{11 - 7}{4 - 2} = \\frac{4}{2} = 2$\n\nNext, use the point-slope form with one of the points, say $(2, 7)$:\n\n$y - y_1 = m(x - x_1)$\n\nPlug in the values:\n\n$y - 7 = 2(x - 2)$\n\nSimplify:\n\n$y - 7 = 2x - 4$\n\nAdd $7$ to both sides:\n\n$y = 2x - 4 + 7$\n\n$y = 2x + 3$\n\nTherefore, the equation of the function is $f(x) = 2x + 3$.",
    "options": [
      {
        "text": "$f(x) = 2x + 3$",
        "id": "a"
      },
      {
        "text": "$f(x) = 2x - 1$",
        "id": "b"
      },
      {
        "text": "$f(x) = x + 5$",
        "id": "c"
      },
      {
        "text": "$f(x) = 3x + 1$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In the linear function $g$, if $g(1) = 3$ and $g(5) = 11$, which of the following is the equation of function $g$?",
    "type": "multiple-choice-single-answer",
    "id": 119,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Use the given points $(1, 3)$ and $(5, 11)$ to find the slope $m$:\n\n$m = \\frac{11 - 3}{5 - 1} = \\frac{8}{4} = 2$\n\nUse point-slope form with point $(1, 3)$:\n\n$y - 3 = 2(x - 1)$\n\nSimplify:\n\n$y - 3 = 2x - 2$\n\nAdd $3$ to both sides:\n\n$y = 2x - 2 + 3$\n\n$y = 2x + 1$\n\nTherefore, the equation of the function is $g(x) = 2x + 1$.",
    "options": [
      {
        "text": "$g(x) = 2x + 3$",
        "id": "a"
      },
      {
        "text": "$g(x) = 2x + 1$",
        "id": "b"
      },
      {
        "text": "$g(x) = 3x + 1$",
        "id": "c"
      },
      {
        "text": "$g(x) = x + 2$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Function $h$ is linear, and it satisfies $h(-3) = -1$ and $h(5) = 15$. Which of the following is the equation of function $h$?",
    "type": "multiple-choice-single-answer",
    "id": 120,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Using the points $(-3, -1)$ and $(5, 15)$, calculate the slope $m$:\n\n$m = \\frac{15 - (-1)}{5 - (-3)} = \\frac{16}{8} = 2$\n\nUse point-slope form with $(-3, -1)$:\n\n$y - (-1) = 2(x - (-3))$\n\nSimplify:\n\n$y + 1 = 2(x + 3)$\n\nExpand:\n\n$y + 1 = 2x + 6$\n\nSubtract $1$ from both sides:\n\n$y = 2x + 6 - 1$\n\n$y = 2x + 5$\n\nTherefore, the equation of the function is $h(x) = 2x + 5$.",
    "options": [
      {
        "text": "$h(x) = 2x + 3$",
        "id": "a"
      },
      {
        "text": "$h(x) = 2x + 4$",
        "id": "b"
      },
      {
        "text": "$h(x) = 2x + 5$",
        "id": "c"
      },
      {
        "text": "$h(x) = -2x + 5$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The linear function $k$ satisfies $k(0) = -4$ and $k(6) = 8$. Which of the following is the equation of function $k$?",
    "type": "multiple-choice-single-answer",
    "id": 121,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Given points $(0, -4)$ and $(6, 8)$, find the slope $m$:\n\n$m = \\dfrac{8 - (-4)}{6 - 0} = \\dfrac{12}{6} = 2$\n\nUse point-slope form with point $(0, -4)$:\n\n$y - (-4) = 2(x - 0)$\n\nSimplify:\n\n$y + 4 = 2x$\n\nSubtract $4$ from both sides:\n\n$y = 2x - 4$\n\nTherefore, the equation of the function is $k(x) = 2x - 4$.",
    "options": [
      {
        "text": "$k(x) = -2x - 4$",
        "id": "a"
      },
      {
        "text": "$k(x) = -2x + 4$",
        "id": "b"
      },
      {
        "text": "$k(x) = 2x + 4$",
        "id": "c"
      },
      {
        "text": "$k(x) = 2x - 4$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In the equation $5(b + 2) - 12 = 7(b + 2)$, what is the value of $b + 2$?",
    "type": "multiple-choice-single-answer",
    "id": 122,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Start by subtracting $5(b + 2)$ from both sides:\n\n$-12 = 7(b + 2) - 5(b + 2)$\n\nSimplify the right side:\n\n$-12 = (7 - 5)(b + 2)$\n\n$-12 = 2(b + 2)$\n\nDivide both sides by $2$:\n\n$-6 = b + 2$\n\nTherefore, the value of $b + 2$ is $-6$.",
    "options": [
      {
        "text": "$-8$",
        "id": "a"
      },
      {
        "text": "$-6$",
        "id": "b"
      },
      {
        "text": "$-4$",
        "id": "c"
      },
      {
        "text": "$6$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $6(c - 5) + 8 = 4(c - 5)$, what is the value of $c - 5$?",
    "type": "multiple-choice-single-answer",
    "id": 123,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Subtract $4(c - 5)$ from both sides:\n\n$6(c - 5) + 8 - 4(c - 5) = 0$\n\nSimplify:\n\n$(6 - 4)(c - 5) + 8 = 0$\n\n$2(c - 5) + 8 = 0$\n\nSubtract $8$ from both sides:\n\n$2(c - 5) = -8$\n\nDivide both sides by $2$:\n\n$c - 5 = -4$\n\nTherefore, the value of $c - 5$ is $-4$.",
    "options": [
      {
        "text": "$-6$",
        "id": "a"
      },
      {
        "text": "$-5$",
        "id": "b"
      },
      {
        "text": "$-3$",
        "id": "c"
      },
      {
        "text": "$-4$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In the equation $7(d + 1) - 14 = 3(d + 1)$, what is the value of $d + 1$?",
    "type": "multiple-choice-single-answer",
    "id": 124,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Subtract $3(d + 1)$ from both sides:\n\n$7(d + 1) - 14 - 3(d + 1) = 0$\n\nSimplify:\n\n$(7 - 3)(d + 1) - 14 = 0$\n\n$4(d + 1) - 14 = 0$\n\nAdd $14$ to both sides:\n\n$4(d + 1) = 14$\n\nDivide both sides by $4$:\n\n$d + 1 = \\dfrac{14}{4} = 3.5$\n\nTherefore, the value of $d + 1$ is $3.5$.",
    "options": [
      {
        "text": "$3.5$",
        "id": "a"
      },
      {
        "text": "$2$",
        "id": "b"
      },
      {
        "text": "$-3.5$",
        "id": "c"
      },
      {
        "text": "$-2$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $5(e - 4) + 10 = 6(e - 4)$, what is the value of $e - 4$?",
    "type": "multiple-choice-single-answer",
    "id": 125,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Subtract $5(e - 4)$ from both sides:\n\n$10 = 6(e - 4) - 5(e - 4)$\n\nSimplify:\n\n$10 = (6 - 5)(e - 4)$\n\n$10 = 1(e - 4)$\n\nThus:\n\n$e - 4 = 10$\n\nTherefore, the value of $e - 4$ is $10$.",
    "options": [
      {
        "text": "$10$",
        "id": "a"
      },
      {
        "text": "$-10$",
        "id": "b"
      },
      {
        "text": "$0$",
        "id": "c"
      },
      {
        "text": "$4$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In the xy-plane, the equation $(x + 2)^2 + (y - 3)^2 = 100$ defines circle $C_1$, and the equation $(x + 2)^2 + (y - 3)^2 = k$ defines circle $C_2$. If the two circles have the same center, and the radius of circle $C_2$ is twice the radius of circle $C_1$, what is the value of the constant $k$?",
    "type": "multiple-choice-single-answer",
    "id": 126,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "The standard form of a circle's equation is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. \n\nFor circle $C_1$, we have $r_1^2 = 100$, so $r_1 = 10$.\n\nSince the radius of circle $C_2$ is twice that of $C_1$, we have $r_2 = 2r_1 = 20$.\n\nTherefore, the value of $k$ is $r_2^2 = (20)^2 = 400$.",
    "options": [
      {
        "text": "$150$",
        "id": "a"
      },
      {
        "text": "$200$",
        "id": "b"
      },
      {
        "text": "$300$",
        "id": "c"
      },
      {
        "text": "$400$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In the coordinate plane, circle $A$ is defined by the equation $(x - 4)^2 + (y + 5)^2 = 49$. Circle $B$ has the same center as circle $A$, and its equation is $(x - 4)^2 + (y + 5)^2 = m$. If the circumference of circle $B$ is half that of circle $A$, what is the value of $m$?",
    "type": "multiple-choice-single-answer",
    "id": 127,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "For circle $A$, the radius is $r_A$ where $r_A^2 = 49$, so $r_A = 7$.\n\nThe circumference is proportional to the radius.\n\nIf the circumference of circle $B$ is half that of circle $A$, then $r_B = \\dfrac{r_A}{2} = \\dfrac{7}{2} = 3.5$.\n\nTherefore, $m = r_B^2 = (3.5)^2 = 12.25$. \n\nThus, the value of $m$ is $12.25$.",
    "options": [
      {
        "text": "$24.5$",
        "id": "a"
      },
      {
        "text": "$12.25$",
        "id": "b"
      },
      {
        "text": "$7$",
        "id": "c"
      },
      {
        "text": "$3.5$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Circle $M$ is defined by the equation $(x - 1)^2 + (y - 2)^2 = 16$ in the xy-plane. Circle $N$ has the same center as circle $M$ and is defined by $(x - 1)^2 + (y - 2)^2 = p$. If the area of circle $N$ is $4$ times the area of circle $M$, what is the value of $p$?",
    "type": "multiple-choice-single-answer",
    "id": 128,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "The area of a circle is $A = \\pi r^2$.\n\nFor circle $M$, $r_M^2 = 16$, so $r_M = 4$, and $A_M = \\pi (4)^2 = 16\\pi$.\n\nSince $A_N = 4A_M = 64\\pi$, we find $r_N$ such that $\\pi r_N^2 = 64\\pi$, so $r_N^2 = 64$.\n\nTherefore, $p = r_N^2 = 64$.",
    "options": [
      {
        "text": "$32$",
        "id": "a"
      },
      {
        "text": "$48$",
        "id": "b"
      },
      {
        "text": "$54$",
        "id": "c"
      },
      {
        "text": "$64$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In the xy-plane, the circle defined by $(x + 3)^2 + (y - 4)^2 = 225$ is circle $Q$. Circle $R$ has the same center as circle $Q$ and is defined by $(x + 3)^2 + (y - 4)^2 = n$. If the diameter of circle $R$ is $10$ units less than the diameter of circle $Q$, what is the value of $n$?",
    "type": "multiple-choice-single-answer",
    "id": 129,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "For circle $Q$, the radius is $r_Q$ where $r_Q^2 = 225$, so $r_Q = 15$.\n\nThe diameter of circle $Q$ is $D_Q = 2r_Q = 30$. \n\nTherefore, the diameter of circle $R$ is $D_R = D_Q - 10 = 20$, so $r_R = \\dfrac{D_R}{2} = 10$.\n\nThus, $n = r_R^2 = (10)^2 = 100$.",
    "options": [
      {
        "text": "$50$",
        "id": "a"
      },
      {
        "text": "$100$",
        "id": "b"
      },
      {
        "text": "$150$",
        "id": "c"
      },
      {
        "text": "$200$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A library has a budget of $\\$15,000$ to purchase new books. Each book costs $\\$125$, and the publisher offers a $10\\%$ discount on orders of at least $100$ books. What is the maximum number of books the library can purchase within its budget?",
    "type": "multiple-choice-single-answer",
    "id": 130,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To find the maximum number of books the library can purchase, we need to consider whether the discount applies.\n\nLet's consider purchasing $120$ books.\n\n**Without discount:** Total cost $= 125 \\times 120 = \\$15,000$. Since the order is at least $100$ books, a $10\\%$ discount applies.\n\n**Discounted total cost:**\n\n$\\$15,000 - 0.10 \\times \\$15,000 =$\n\n $ \\$15,000 - \\$1,500 = \\$13,500$.\n\nThis is within the budget. Let's see if we can purchase more books.\n\n**Try $130$ books:**\n\nTotal cost without discount:\n\n$125 \\times 130 = \\$16,250$.\n\n Applying the discount:\n\n$\\$16,250 - 0.10 \\times \\$16,250 =$\n\n $ \\$16,250 - \\$1,625 = \\$14,625$.\n\nThis is within the budget. Next, try $140$ books:\n\nTotal cost:\n\n$125 \\times 140 = \\$17,500$.\n\n Discounted total cost:\n\n$\\$17,500 - 0.10 \\times \\$17,500 =$\n\n $ \\$17,500 - \\$1,750 = \\$15,750$.\n\nThis exceeds the budget. Therefore, the maximum number of books the library can purchase is $130$.",
    "options": [
      {
        "text": "$120$",
        "id": "a"
      },
      {
        "text": "$125$",
        "id": "b"
      },
      {
        "text": "$130$",
        "id": "c"
      },
      {
        "text": "$140$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A community center received a grant of $\\$10,000$ to buy new chairs. Each chair costs $\\$85$, and the supplier offers a $5\\%$ discount on orders of $80$ chairs or more. What is the maximum number of chairs the community center can purchase with the grant?",
    "type": "multiple-choice-single-answer",
    "id": 131,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, calculate the cost including the discount.\n\n**Test $120$ chairs:**\n\nTotal cost without discount:\n\n$85 \\times 120 = \\$10,200$. Since $120 \\geq 80$, a $5\\%$ discount applies.\n\n**Discounted total cost:**\n\n$\\$10,200 - 0.05 \\times \\$10,200 =$\n\n $ \\$10,200 - \\$510 = \\$9,690$.\n\nThis is within the budget of \\$10,000. Let's see if we can purchase more chairs.\n\n**Try $125$ chairs:**\n\nTotal cost:\n\n$85 \\times 125 = \\$10,625$.\n\n**Discounted total cost:**\n\n$\\$10,625 - 0.05 \\times \\$10,625 =$\n\n $ \\$10,625 - \\$531.25 = \\$10,093.75$.\n\nThis exceeds the budget. Therefore, the maximum number of chairs is $120$.",
    "options": [
      {
        "text": "$115$",
        "id": "a"
      },
      {
        "text": "$118$",
        "id": "b"
      },
      {
        "text": "$120$",
        "id": "c"
      },
      {
        "text": "$125$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A company has $\\$50,000$ to spend on new computers. Each computer costs $\\$1,200$, and the vendor offers an $8\\%$ discount on purchases of $40$ or more computers. What is the maximum number of computers the company can buy?",
    "type": "multiple-choice-single-answer",
    "id": 132,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, check if purchasing $42$ computers is within the budget.\n\n**Total cost without discount:**\n\n$1,200 \\times 42 = \\$50,400$. With an $8\\%$ discount:\n\n**Discounted total cost:**\n\n$\\$50,400 - 0.08 \\times \\$50,400 =$\n\n $ \\$50,400 - \\$4,032 = \\$46,368$.\n\nThis is within the budget. Next, try $45$ computers:\n\n**Total cost:**\n\n$1,200 \\times 45 = \\$54,000$.\n\n**Discounted total cost:**\n\n$\\$54,000 - 0.08 \\times \\$54,000 =$\n\n $ \\$54,000 - \\$4,320 = \\$49,680$.\n\nStill within budget. Try $46$ computers:\n\n**Total cost:**\n\n$1,200 \\times 46 = \\$55,200$.\n\n**Discounted total cost:**\n\n$\\$55,200 - 0.08 \\times \\$55,200 =$\n\n $ \\$55,200 - \\$4,416 = \\$50,784$.\n\nThis exceeds the budget. Therefore, the maximum number is $45$ computers.",
    "options": [
      {
        "text": "$42$",
        "id": "a"
      },
      {
        "text": "$44$",
        "id": "b"
      },
      {
        "text": "$45$",
        "id": "c"
      },
      {
        "text": "$46$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A charity organization wants to buy blankets for a donation drive with a budget of $\\$5,000$. Each blanket costs $\\$55$, and the supplier offers a $10\\%$ discount on orders of $90$ blankets or more. What is the maximum number of blankets the organization can purchase?",
    "type": "multiple-choice-single-answer",
    "id": 133,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, calculate the cost for $90$ blankets.\n\n**Total cost without discount:**\n\n$55 \\times 90 = \\$4,950$.\n\nApplying the $10\\%$ discount:\n\n$\\$4,950 - 0.10 \\times \\$4,950 =$\n\n $ \\$4,950 - \\$495 = \\$4,455$.\n\nUnder budget.\n\n**Try $100$ blankets:**\n\nTotal cost:\n\n$55 \\times 100 = \\$5,500$.\n\n**Discounted total cost:**\n\n$\\$5,500 - 0.10 \\times \\$5,500 =$\n\n $ \\$5,500 - \\$550 = \\$4,950$.\n\nStill under budget.\n\n**Try $105$ blankets:**\n\nTotal cost:\n\n$55 \\times 105 = \\$5,775$.\n\n**Discounted total cost:**\n\n$\\$5,775 - 0.10 \\times \\$5,775 =$\n\n $ \\$5,775 - \\$577.50 = \\$5,197.50$.\n\nExceeds budget. Therefore, the maximum number of blankets is $100$.",
    "options": [
      {
        "text": "$95$",
        "id": "a"
      },
      {
        "text": "$98$",
        "id": "b"
      },
      {
        "text": "$100$",
        "id": "c"
      },
      {
        "text": "$105$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A parabola represents the graph of the function $f$ in the $xy$-plane, where $y = f(x)$. If the vertex of the parabola is $(2, 6)$ and one of the $x$-intercepts is $(5, 0)$, what is the other $x$-intercept?",
    "type": "multiple-choice-single-answer",
    "id": 134,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "The parabola is symmetric about the vertical line passing through its vertex, known as the axis of symmetry.\n\nThe $x$-coordinate of the vertex is $2$.\n\nThe distance from the vertex to the known $x$-intercept is $5 - 2 = 3$ units. \n\nTherefore, the other $x$-intercept is located the same distance on the opposite side of the vertex: $2 - 3 = -1$. \n\nThus, the other $x$-intercept is at $(-1, 0)$.",
    "options": [
      {
        "text": "$(-1, 0)$",
        "id": "a"
      },
      {
        "text": "$(1, 0)$",
        "id": "b"
      },
      {
        "text": "$(2, 0)$",
        "id": "c"
      },
      {
        "text": "$(3, 0)$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The graph of the quadratic function $g$ has its vertex at $(-4, -5)$ and passes through the point $(0, 0)$. What is the other $x$-intercept of the graph?",
    "type": "multiple-choice-single-answer",
    "id": 135,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "The axis of symmetry of the parabola is $x = -4$. \n\nThe distance from the vertex to the known $x$-intercept is $0 - (-4) = 4$ units. \n\nTherefore, the other $x$-intercept is at $-4 - 4 = -8$.\n\nThus, the other $x$-intercept is at $(-8, 0)$.",
    "options": [
      {
        "text": "$(-2, 0)$",
        "id": "a"
      },
      {
        "text": "$(-4, 0)$",
        "id": "b"
      },
      {
        "text": "$(-6, 0)$",
        "id": "c"
      },
      {
        "text": "$(-8, 0)$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A parabola representing the function $h$ has its vertex at $(0, -16)$ in the $xy$-plane. If one of the $x$-intercepts is at $(4, 0)$, what is the other $x$-intercept?",
    "type": "multiple-choice-single-answer",
    "id": 136,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Since the vertex is at $(0, -16)$, the axis of symmetry is $x = 0$.\n\nThe distance from the vertex to the known $x$-intercept is $4 - 0 = 4$ units. \n\nThe other $x$-intercept is located $4$ units on the opposite side of the axis of symmetry, at $0 - 4 = -4$. \n\nTherefore, the other $x$-intercept is at $(-4, 0)$.",
    "options": [
      {
        "text": "$(-8, 0)$",
        "id": "a"
      },
      {
        "text": "$(-4, 0)$",
        "id": "b"
      },
      {
        "text": "$(0, 0)$",
        "id": "c"
      },
      {
        "text": "$(4, 0)$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The function $p$ represents a parabola in the $xy$-plane with vertex at $(6, 9)$. If one of the $x$-intercepts of the parabola is at $(2, 0)$, what is the other $x$-intercept?",
    "type": "multiple-choice-single-answer",
    "id": 137,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "The axis of symmetry is $x = 6$.\n\nThe distance from the vertex to the known $x$-intercept is $6 - 2 = 4$ units.\n\nThe other $x$-intercept is at $6 + 4 = 10$.\n\nTherefore, the other $x$-intercept is at $(10, 0)$.",
    "options": [
      {
        "text": "$(4, 0)$",
        "id": "a"
      },
      {
        "text": "$(8, 0)$",
        "id": "b"
      },
      {
        "text": "$(10, 0)$",
        "id": "c"
      },
      {
        "text": "$(12, 0)$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In triangle $ABC$, angles $A$, $B$, and $C$ measure $45^{\\circ}$, $45^{\\circ}$, and $90^{\\circ}$, respectively. If the hypotenuse $BC$ has a length of $10\\sqrt{2}$ centimeters, what is the perimeter of the triangle in centimeters?",
    "type": "multiple-choice-single-answer",
    "id": 138,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "In a $45^{\\circ}$-$45^{\\circ}$-$90^{\\circ}$ triangle, the sides are in the ratio $x : x : x\\sqrt{2}$, where $x\\sqrt{2}$ is the hypotenuse. Given that the hypotenuse is $10\\sqrt{2}$ cm, we have:\n\n$x\\sqrt{2} = 10\\sqrt{2}$\n\nDivide both sides by $\\sqrt{2}$:\n\n$x = 10$\n\nSo, the two legs are each $10$ cm. The perimeter is:\n\n$10 + 10 + 10\\sqrt{2} = 20 + 10\\sqrt{2}\\ \\text{cm}$",
    "options": [
      {
        "text": "$20$",
        "id": "a"
      },
      {
        "text": "$10 + 10\\sqrt{2}$",
        "id": "b"
      },
      {
        "text": "$20 + 20\\sqrt{2}$",
        "id": "c"
      },
      {
        "text": "$20 + 10\\sqrt{2}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Triangle $DEF$ is a right triangle with angles measuring $30^{\\circ}$, $60^{\\circ}$, and $90^{\\circ}$. If the side opposite the $60^{\\circ}$ angle has a length of $12\\sqrt{3}$ centimeters, what is the perimeter of the triangle in centimeters?",
    "type": "multiple-choice-single-answer",
    "id": 139,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "In a $30^{\\circ}$-$60^{\\circ}$-$90^{\\circ}$ triangle, the sides are in the ratio $x : x\\sqrt{3} : 2x$, where:\n\n- **$x$** is the side opposite the $30^{\\circ}$ angle.\n- **$x\\sqrt{3}$** is the side opposite the $60^{\\circ}$ angle.\n- **$2x$** is the hypotenuse opposite the $90^{\\circ}$ angle.\n\nGiven that the side opposite the $60^{\\circ}$ angle is $12\\sqrt{3}$ cm:\n\nSet up the equation:\n\n$x\\sqrt{3} = 12\\sqrt{3}$\n\nDivide both sides by $\\sqrt{3}$:\n\n$\\frac{x\\sqrt{3}}{\\sqrt{3}} = \\frac{12\\sqrt{3}}{\\sqrt{3}}\\quad \\implies\\quad x = 12$\n\nCalculate the lengths of all sides:\n\n- Side opposite $30^{\\circ}$ angle: $x = 12$ cm\n- Side opposite $60^{\\circ}$ angle: $x\\sqrt{3} = 12\\sqrt{3}$ cm\n- Hypotenuse opposite $90^{\\circ}$ angle: $2x = 2 \\times 12 = 24$ cm\n\nCompute the perimeter:\n\n$\\text{Perimeter} = 12 + 12\\sqrt{3} + 24 = (36 + 12\\sqrt{3})\\ \\text{cm}$",
    "options": [
      {
        "text": "$48 + 12\\sqrt{3}$",
        "id": "a"
      },
      {
        "text": "$36 + 24\\sqrt{3}$",
        "id": "b"
      },
      {
        "text": "$36 + 12\\sqrt{3}$",
        "id": "c"
      },
      {
        "text": "$24 + 12\\sqrt{3}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "In a triangle with angles measuring $45^{\\circ}$, $45^{\\circ}$, and $90^{\\circ}$, the length of the hypotenuse is $14$ centimeters. What is the perimeter of the triangle in centimeters?",
    "type": "multiple-choice-single-answer",
    "id": 140,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "For a $45^{\\circ}$-$45^{\\circ}$-$90^{\\circ}$ triangle, the sides are in the ratio $x : x : x\\sqrt{2}$, with the hypotenuse being $x\\sqrt{2}$. Given:\n\n$x\\sqrt{2} = 14$\n\nSolve for $x$:\n\n$x = \\dfrac{14}{\\sqrt{2}} = \\dfrac{14\\sqrt{2}}{2} = 7\\sqrt{2}$\n\nThe legs are each $7\\sqrt{2}$ cm. The perimeter is:\n\n$7\\sqrt{2} + 7\\sqrt{2} + 14 = 14\\sqrt{2} + 14\\ \\text{cm}$",
    "options": [
      {
        "text": "$14 + 7\\sqrt{2}$",
        "id": "a"
      },
      {
        "text": "$14 + 14\\sqrt{2}$",
        "id": "b"
      },
      {
        "text": "$14\\sqrt{2}$",
        "id": "c"
      },
      {
        "text": "$28 + 14\\sqrt{2}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Triangle $XYZ$ is a right triangle with angles measuring $30^{\\circ}$, $60^{\\circ}$, and $90^{\\circ}$. If the hypotenuse has a length of $26$ centimeters, what is the perimeter of the triangle in centimeters?",
    "type": "multiple-choice-single-answer",
    "id": 141,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "In a $30^{\\circ}$-$60^{\\circ}$-$90^{\\circ}$ triangle, the sides are in the ratio $x : x\\sqrt{3} : 2x$, where the hypotenuse is $2x$. Given:\n\n$2x = 26$\n\nSolve for $x$:\n\n$x = 13$\n\nSo, the sides are $13$ cm opposite $30^{\\circ}$, $13\\sqrt{3}$ cm opposite $60^{\\circ}$, and $26$ cm - hypotenuse. The perimeter is:\n\n$13 + 13\\sqrt{3} + 26 = 39 + 13\\sqrt{3}\\ \\text{cm}$",
    "options": [
      {
        "text": "$39 + 13\\sqrt{3}$",
        "id": "a"
      },
      {
        "text": "$26 + 13\\sqrt{3}$",
        "id": "b"
      },
      {
        "text": "$39 + 26\\sqrt{3}$",
        "id": "c"
      },
      {
        "text": "$26 + 26\\sqrt{3}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "$78$, $85$, $92$, $87$\n\nA data set consists of $5$ positive integers greater than $70$. What is the value of the smallest integer in the data set if the mean of the entire data set is an integer less than the mean of the four integers from the data set shown above?",
    "type": "multiple-choice-single-answer",
    "id": 142,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "First, find the mean of the four given integers.\n\n The total of these integers is $78 + 85 + 92 + 87 = 342$. \n\nThe mean is $\\dfrac{342}{4} = 85.5$.\n\n We need the mean of all five integers to be an integer less than $85.5$, so possible integer means are $85$, $84$, $83$, etc.\n\nAssuming the mean is $85$:\n\nTotal sum required: $5 \\times 85 = 425$\n\nFifth integer: $425 - 342 = 83$\n\nSince all integers must be greater than $70$, $83$ is acceptable. Try a lower mean.\n\nMean of $84$:\n\nTotal sum: $5 \\times 84 = 420$\n\nFifth integer: $420 - 342 = 78$\n\n$78$ is acceptable. Try a mean of $83$:\n\nTotal sum: $5 \\times 83 = 415$\n\nFifth integer: $415 - 342 = 73$\n\n$73$ is acceptable. Try a mean of $82$:\n\nTotal sum: $5 \\times 82 = 410$\n\nFifth integer: $410 - 342 = 68$\n\n$68$ is not greater than $70$, so it's invalid. Therefore, the smallest possible integer is $73$.",
    "options": [
      {
        "text": "$68$",
        "id": "a"
      },
      {
        "text": "$73$",
        "id": "b"
      },
      {
        "text": "$78$",
        "id": "c"
      },
      {
        "text": "$83$",
        "id": "d"
      }
    ]
  },
  {
    "text": "$56$, $62$, $58$, $60$\n\nA data set consists of $5$ positive integers greater than $50$. What is the value of the smallest integer in the data set if the mean of the entire data set is an integer less than the mean of the four integers from the data set shown above?",
    "type": "multiple-choice-single-answer",
    "id": 143,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "First, calculate the mean of the four given integers:\n\nTotal sum: $56 + 62 + 58 + 60 = 236$\n\nMean: $\\dfrac{236}{4} = 59$\n\nWe need the mean of all five integers to be an integer less than $59$, so possible means are $58$, $57$, etc.\n\nAssuming the mean is $58$:\n\nTotal sum required: $5 \\times 58 = 290$\n\nFifth integer: $290 - 236 = 54$\n\nSince all integers must be greater than $50$, $54$ is acceptable. Try a mean of $57$:\n\nTotal sum: $5 \\times 57 = 285$\n\nFifth integer: $285 - 236 = 49$\n\n$49$ is not greater than $50$, so it's invalid. Therefore, the smallest possible integer is $54$.",
    "options": [
      {
        "text": "$49$",
        "id": "a"
      },
      {
        "text": "$52$",
        "id": "b"
      },
      {
        "text": "$54$",
        "id": "c"
      },
      {
        "text": "$56$",
        "id": "d"
      }
    ]
  },
  {
    "text": "$132$, $138$, $140$, $136$\n\nA data set consists of $5$ positive integers greater than $130$. What is the value of the smallest integer in the data set if the mean of the entire data set is an integer less than the mean of the four integers from the data set shown above?",
    "type": "multiple-choice-single-answer",
    "id": 144,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Calculate the mean of the four given integers:\n\nTotal sum: $132 + 138 + 140 + 136 = 546$\n\nMean: $\\dfrac{546}{4} = 136.5$\n\nWe need the mean of all five integers to be an integer less than $136.5$, so possible means are $136$, $135$, etc.\n\nAssuming the mean is $136$:\n\nTotal sum required: $5 \\times 136 = 680$\n\nFifth integer: $680 - 546 = 134$\n\n$134$ is greater than $130$, so acceptable. Try a mean of $135$:\n\nTotal sum: $5 \\times 135 = 675$\n\nFifth integer: $675 - 546 = 129$\n\n$129$ is not greater than $130$, so invalid. Therefore, the smallest possible integer is $134$.",
    "options": [
      {
        "text": "$134$",
        "id": "a"
      },
      {
        "text": "$132$",
        "id": "b"
      },
      {
        "text": "$130$",
        "id": "c"
      },
      {
        "text": "$128$",
        "id": "d"
      }
    ]
  },
  {
    "text": "$205$, $210$, $215$, $220$\n\nA data set consists of $5$ positive integers greater than $200$. What is the value of the smallest integer in the data set if the mean of the entire data set is an integer less than the mean of the four integers from the data set shown above?",
    "type": "multiple-choice-single-answer",
    "id": 145,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Find the mean of the four given integers:\n\nTotal sum: $205 + 210 + 215 + 220 = 850$\n\nMean: $\\dfrac{850}{4} = 212.5$\n\nWe need the mean of all five integers to be an integer less than $212.5$, so possible means are $212$, $211$, etc.\n\nAssuming the mean is $212$:\n\nTotal sum required: $5 \\times 212 = 1,060$\n\nFifth integer: $1,060 - 850 = 210$\n\n$210$ is greater than $200$, so acceptable. Try a mean of $211$:\n\nTotal sum: $5 \\times 211 = 1,055$\n\nFifth integer: $1,055 - 850 = 205$\n\n$205$ is greater than $200$. Try a mean of $210$:\n\nTotal sum: $5 \\times 210 = 1,050$\n\nFifth integer: $1,050 - 850 = 200$\n\n$200$ is not greater than $200$, and the problem states numbers greater than $200$.\n\n Therefore, the smallest possible integer is $205$.",
    "options": [
      {
        "text": "$200$",
        "id": "a"
      },
      {
        "text": "$203$",
        "id": "b"
      },
      {
        "text": "$205$",
        "id": "c"
      },
      {
        "text": "$210$",
        "id": "d"
      }
    ]
  },
  {
    "text": "The height of a ball thrown upward from a platform is modeled by the equation $h = -4.9t^2 + 19.6t + 10$, where $h$ is the height in meters and $t$ is the time in seconds after the ball is thrown. Which of the following represents the initial height, in meters, of the platform from which the ball is thrown?",
    "type": "multiple-choice-single-answer",
    "id": 146,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "The initial height is the height when time $t = 0$. \n\nSubstitute $t = 0$ into the equation:\n\n $h = -4.9(0)^2 + 19.6(0) + 10 = 0 + 0 + 10 = 10$. \n\nTherefore, the platform is $10$ meters above the ground.",
    "options": [
      {
        "text": "$0$",
        "id": "a"
      },
      {
        "text": "$10$",
        "id": "b"
      },
      {
        "text": "$19.6$",
        "id": "c"
      },
      {
        "text": "$4.9$",
        "id": "d"
      }
    ]
  },
  {
    "text": "An object is projected upward from ground level, and its height above the ground, in meters, after $t$ seconds is given by the equation $h = -5t^2 + 30t$. What is the initial velocity, in meters per second, of the object when it was projected?",
    "type": "multiple-choice-single-answer",
    "id": 147,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "In the equation $h = -5t^2 + 30t$, the coefficient of the $t$ term represents the initial velocity. \n\nTherefore, the initial velocity is $30$ meters per second.",
    "options": [
      {
        "text": "$0$",
        "id": "a"
      },
      {
        "text": "$5$",
        "id": "b"
      },
      {
        "text": "$30$",
        "id": "c"
      },
      {
        "text": "$-5$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A firefighter aims a stream of water upward from the top of a fire truck, and the height of the water jet above the ground is modeled by $h = -16t^2 + 48t + 8$, where $h$ is the height in feet and $t$ is the time in seconds after the water leaves the nozzle. What does the constant term in the equation represent in this context?",
    "type": "multiple-choice-single-answer",
    "id": 148,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "The constant term in the equation represents the initial height when $t = 0$.\n\n Substituting $t = 0$ yields $h = -16(0)^2 + 48(0) + 8 = 8$.\n\n Therefore, the constant term $8$ represents the height of the nozzle above the ground.",
    "options": [
      {
        "text": "The height of the nozzle above the ground",
        "id": "a"
      },
      {
        "text": "The time when the water reaches its maximum height",
        "id": "b"
      },
      {
        "text": "The initial velocity of the water",
        "id": "c"
      },
      {
        "text": "The acceleration due to gravity",
        "id": "d"
      }
    ]
  },
  {
    "text": "The path of a projectile launched from the ground is given by the equation $y = -0.5x^2 + 4x$, where $y$ is the height in meters, and $x$ is the horizontal distance in meters from the launch point. What does the coefficient $-0.5$ represent in the context of the projectile's motion?",
    "type": "multiple-choice-single-answer",
    "id": 149,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "The coefficient of the $x^2$ term represents the effect of gravity on the projectile's vertical motion, causing the parabolic trajectory.\n\n The negative sign indicates that gravity is acting downward, pulling the projectile toward the ground.",
    "options": [
      {
        "text": "The initial height of the projectile",
        "id": "a"
      },
      {
        "text": "The effect of gravity on the projectile",
        "id": "b"
      },
      {
        "text": "The initial horizontal velocity",
        "id": "c"
      },
      {
        "text": "The maximum height reached",
        "id": "d"
      }
    ]
  },
  {
    "text": "For all positive values of $x$, the expression $\\dfrac{5}{x + k}$ is equivalent to $\\dfrac{10}{2x + 6}$. What is the value of the constant $k$?",
    "type": "multiple-choice-single-answer",
    "id": 150,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Set the two expressions equal to each other:\n\n$\\dfrac{5}{x + k} = \\dfrac{10}{2x + 6}$\n\nCross-multiply:\n\n$5(2x + 6) = 10(x + k)$\n\nSimplify both sides:\n\n**Left side:**\n\n$5(2x + 6) = 10x + 30$\n\n**Right side:**\n\n$10(x + k) = 10x + 10k$\n\nSet the expressions equal:\n\n$10x + 30 = 10x + 10k$\n\nSubtract $10x$ from both sides:\n\n$30 = 10k$\n\nDivide both sides by 10:\n\n$k = 3$\n\nTherefore, the value of $k$ is $3$.",
    "options": [
      {
        "text": "$2$",
        "id": "a"
      },
      {
        "text": "$3$",
        "id": "b"
      },
      {
        "text": "$4$",
        "id": "c"
      },
      {
        "text": "$5$",
        "id": "d"
      }
    ]
  },
  {
    "text": "For all positive values of $n$, the expression $\\dfrac{7}{n + m}$ is equivalent to $\\dfrac{21}{3n + 9}$. What is the value of the constant $m$?",
    "type": "multiple-choice-single-answer",
    "id": 151,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Set the two expressions equal:\n\n$\\dfrac{7}{n + m} = \\dfrac{21}{3n + 9}$\n\nCross-multiply:\n\n$7(3n + 9) = 21(n + m)$\n\nSimplify both sides:\n\n**Left side:**\n\n$7(3n + 9) = 21n + 63$\n\n**Right side:**\n\n$21(n + m) = 21n + 21m$\n\nSet the expressions equal:\n\n$21n + 63 = 21n + 21m$\n\nSubtract $21n$ from both sides:\n\n$63 = 21m$\n\nDivide both sides by 21:\n\n$m = 3$\n\nTherefore, the value of $m$ is $3$.",
    "options": [
      {
        "text": "$2$",
        "id": "a"
      },
      {
        "text": "$9$",
        "id": "b"
      },
      {
        "text": "$3$",
        "id": "c"
      },
      {
        "text": "$7$",
        "id": "d"
      }
    ]
  },
  {
    "text": "For all positive values of $t$, the expression $\\dfrac{2}{t + b}$ is equivalent to $\\dfrac{8}{4t + 16}$. What is the value of the constant $b$?",
    "type": "multiple-choice-single-answer",
    "id": 152,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Set the two expressions equal:\n\n$\\dfrac{2}{t + b} = \\dfrac{8}{4t + 16}$\n\nCross-multiply:\n\n$2(4t + 16) = 8(t + b)$\n\nSimplify both sides:\n\n**Left side:**\n\n$2(4t + 16) = 8t + 32$\n\n**Right side:**\n\n$8(t + b) = 8t + 8b$\n\nSet the expressions equal:\n\n$8t + 32 = 8t + 8b$\n\nSubtract $8t$ from both sides:\n\n$32 = 8b$\n\nDivide both sides by 8:\n\n$b = 4$\n\nTherefore, the value of $b$ is $4$.",
    "options": [
      {
        "text": "$4$",
        "id": "a"
      },
      {
        "text": "$8$",
        "id": "b"
      },
      {
        "text": "$2$",
        "id": "c"
      },
      {
        "text": "$16$",
        "id": "d"
      }
    ]
  },
  {
    "text": "For all positive values of $z$, the expression $\\dfrac{9}{z + d}$ is equivalent to $\\dfrac{27}{3z + 18}$. What is the value of the constant $d$?",
    "type": "multiple-choice-single-answer",
    "id": 153,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Set the two expressions equal:\n\n$\\dfrac{9}{z + d} = \\dfrac{27}{3z + 18}$\n\nCross-multiply:\n\n$9(3z + 18) = 27(z + d)$\n\nSimplify both sides:\n\n**Left side:**\n\n$9(3z + 18) = 27z + 162$\n\n**Right side:**\n\n$27(z + d) = 27z + 27d$\n\nSet the expressions equal:\n\n$27z + 162 = 27z + 27d$\n\nSubtract $27z$ from both sides:\n\n$162 = 27d$\n\nDivide both sides by 27:\n\n$d = 6$\n\nTherefore, the value of $d$ is $6$.",
    "options": [
      {
        "text": "$5$",
        "id": "a"
      },
      {
        "text": "$6$",
        "id": "b"
      },
      {
        "text": "$9$",
        "id": "c"
      },
      {
        "text": "$27$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Which equation represents the relationship between the numbers $p$ and $q$ if $p$ is three times $q$?",
    "type": "multiple-choice-single-answer",
    "id": 154,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "To translate the statement into an equation, interpret 'is' as '=', and 'three times' as '$3 \\times$'. \n\nTherefore, $p$ is three times $q$ translates to $p = 3q$.",
    "options": [
      {
        "text": "$p = q + 3$",
        "id": "a"
      },
      {
        "text": "$p = 3q$",
        "id": "b"
      },
      {
        "text": "$p = q - 3$",
        "id": "c"
      },
      {
        "text": "$p = \\dfrac{q}{3}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Which equation represents the relationship between $x$ and $y$ if $y$ is five less than $x$?",
    "type": "multiple-choice-single-answer",
    "id": 155,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Translating the statement, 'is' means '=', and 'five less than $x$' means '$x - 5$'.\n\n So, $y = x - 5$.",
    "options": [
      {
        "text": "$y = x + 5$",
        "id": "a"
      },
      {
        "text": "$y = 5x$",
        "id": "b"
      },
      {
        "text": "$y = x - 5$",
        "id": "c"
      },
      {
        "text": "$y = \\dfrac{x}{5}$",
        "id": "d"
      }
    ]
  },
  {
    "text": "If $m$ is directly proportional to $n$, which equation represents the relationship between $m$ and $n$?",
    "type": "multiple-choice-single-answer",
    "id": 156,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Directly proportional means $m = k n$, where $k$ is a constant of proportionality.\n\n Since no specific constant is given, the general form is $m = k n$.",
    "options": [
      {
        "text": "$m = k n$",
        "id": "a"
      },
      {
        "text": "$m = \\dfrac{k}{n}$",
        "id": "b"
      },
      {
        "text": "$m = n + k$",
        "id": "c"
      },
      {
        "text": "$m = n - k$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Which equation represents the relationship between $s$ and $t$ if $s$ is equal to the square of $t$?",
    "type": "multiple-choice-single-answer",
    "id": 157,
    "correctAnswer": "d",
    "quiztype": "satmath",
    "explanation": "Translate 'is equal to' as '=', and 'the square of $t$' as $t^2$. \n\nTherefore, $s = t^2$.",
    "options": [
      {
        "text": "$s = 2t$",
        "id": "a"
      },
      {
        "text": "$s = \\dfrac{t}{2}$",
        "id": "b"
      },
      {
        "text": "$s = t + 2$",
        "id": "c"
      },
      {
        "text": "$s = t^2$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Simplify the expression: $20e - (10e + 5e)$\n\nWhich of the following expressions is equivalent to the given expression?",
    "type": "multiple-choice-single-answer",
    "id": 158,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "First, simplify inside the parentheses:\n\n$10e + 5e = 15e$\n\nThen, the expression becomes:\n\n$20e - 15e = 5e$\n\nTherefore, the equivalent expression is $5e$.",
    "options": [
      {
        "text": "$35e$",
        "id": "a"
      },
      {
        "text": "$5e$",
        "id": "b"
      },
      {
        "text": "$-5e$",
        "id": "c"
      },
      {
        "text": "$25e$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Simplify the expression: $8b - (3b + 5b)$\n\nWhich of the following expressions is equivalent to the given expression?",
    "type": "multiple-choice-single-answer",
    "id": 159,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "First, simplify inside the parentheses:\n\n$3b + 5b = 8b$\n\nThen, the expression becomes:\n\n$8b - 8b = 0$\n\nTherefore, the equivalent expression is $0$.",
    "options": [
      {
        "text": "$16b$",
        "id": "a"
      },
      {
        "text": "$0$",
        "id": "b"
      },
      {
        "text": "$8b$",
        "id": "c"
      },
      {
        "text": "$1b$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Simplify the expression: $12c - (2c - 4c)$\n\nWhich of the following expressions is equivalent to the given expression?",
    "type": "multiple-choice-single-answer",
    "id": 160,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "First, simplify inside the parentheses:\n\n$2c - 4c = -2c$\n\nThen, the expression becomes:\n\n$12c - (-2c) = 12c + 2c = 14c$\n\nTherefore, the equivalent expression is $14c$.",
    "options": [
      {
        "text": "$10c$",
        "id": "a"
      },
      {
        "text": "$14c$",
        "id": "b"
      },
      {
        "text": "$16c$",
        "id": "c"
      },
      {
        "text": "$-14c$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Simplify the expression: $9d + (5d - 3d)$\n\nWhich of the following expressions is equivalent to the given expression?",
    "type": "multiple-choice-single-answer",
    "id": 161,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "First, simplify inside the parentheses:\n\n$5d - 3d = 2d$\n\nThen, the expression becomes:\n\n$9d + 2d = 11d$\n\nTherefore, the equivalent expression is $11d$.",
    "options": [
      {
        "text": "$7d$",
        "id": "a"
      },
      {
        "text": "$11d$",
        "id": "b"
      },
      {
        "text": "$12d$",
        "id": "c"
      },
      {
        "text": "$14d$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Simplify the expression: $10 - 2^3 \\times 2$\n\nWhich of the following is the value of the expression?",
    "type": "multiple-choice-single-answer",
    "id": 162,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Following PEMDAS:\n\n**Exponents:**\n\n$2^3 = 8$\n\n**Multiplication:**\n\n$8 \\times 2 = 16$\n\n**Subtraction:**\n\n$10 - 16 = -6$\n\nTherefore, the value of the expression is $-6$.",
    "options": [
      {
        "text": "$-6$",
        "id": "a"
      },
      {
        "text": "$-12$",
        "id": "b"
      },
      {
        "text": "$-2$",
        "id": "c"
      },
      {
        "text": "$6$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Simplify the expression: $(3 + 5) \\div [(4 - 2) \\times 2]$\n\nWhich of the following is the value of the expression?",
    "type": "multiple-choice-single-answer",
    "id": 163,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Following PEMDAS:\n\n**Parentheses:**\n\n$3 + 5 = 8$\n\n$4 - 2 = 2$\n\n**Multiplication, inside brackets:**\n\n$2 \\times 2 = 4$\n\n**Division:**\n\n$8 \\div 4 = 2$\n\nTherefore, the value of the expression is $2$.",
    "options": [
      {
        "text": "$1$",
        "id": "a"
      },
      {
        "text": "$2$",
        "id": "b"
      },
      {
        "text": "$4$",
        "id": "c"
      },
      {
        "text": "$8$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Simplify the expression: $[2^3 \\times (4 + 2)] \\div 4$\n\nWhich of the following is the value of the expression?",
    "type": "multiple-choice-single-answer",
    "id": 164,
    "correctAnswer": "a",
    "quiztype": "satmath",
    "explanation": "Following PEMDAS:\n\n**Parentheses:**\n\n$4 + 2 = 6$\n\n**Exponents:**\n\n$2^3 = 8$\n\n**Multiplication:**\n\n$8 \\times 6 = 48$\n\n**Division:**\n\n$48 \\div 4 = 12$\n\nTherefore, the value of the expression is $12$.",
    "options": [
      {
        "text": "$12$",
        "id": "a"
      },
      {
        "text": "$16$",
        "id": "b"
      },
      {
        "text": "$8$",
        "id": "c"
      },
      {
        "text": "$24$",
        "id": "d"
      }
    ]
  },
  {
    "text": "Simplify the expression: $8 + 2 \\times (5 - 3)^2$\n\nWhich of the following is the value of the expression?",
    "type": "multiple-choice-single-answer",
    "id": 165,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Following the order of operations (PEMDAS):\n\n**Parentheses:**\n\n$5 - 3 = 2$\n\n**Exponents:**\n\n$2^2 = 4$\n\n**Multiplication:**\n\n$2 \\times 4 = 8$\n\n**Addition:**\n\n$8 + 8 = 16$\n\nTherefore, the value of the expression is $16$.",
    "options": [
      {
        "text": "$12$",
        "id": "a"
      },
      {
        "text": "$16$",
        "id": "b"
      },
      {
        "text": "$24$",
        "id": "c"
      },
      {
        "text": "$20$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A cylinder has a volume of $200\\pi\\, \\text{cm}^3$ and a radius of $5\\, \\text{cm}$. What is the height of the cylinder in centimeters?",
    "type": "multiple-choice-single-answer",
    "id": 166,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "To find the height of the cylinder, use the formula for the volume of a cylinder: $V = \\pi r^2 h$. \n\nPlug in the given values:\n\n$200\\pi = \\pi (5)^2 h$\n\nSimplify:\n\n$200\\pi = \\pi (25) h$\n\nDivide both sides by $25\\pi$:\n\n$\\dfrac{200\\pi}{25\\pi} = h$\n\nSimplify:\n\n$h = 8$\n\nTherefore, the height of the cylinder is $8$ centimeters.",
    "options": [
      {
        "text": "$4$",
        "id": "a"
      },
      {
        "text": "$6$",
        "id": "b"
      },
      {
        "text": "$8$",
        "id": "c"
      },
      {
        "text": "$10$",
        "id": "d"
      }
    ]
  },
  {
    "text": "What is the radius, in meters (m), of a cylinder that has a volume of $150\\pi\\, \\text{m}^3$ and a height of $6\\, \\text{m}$?",
    "type": "multiple-choice-single-answer",
    "id": 167,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "Use the formula for the volume of a cylinder: $V = \\pi r^2 h$. Plug in the given values:\n\n$150\\pi = \\pi r^2 \\times 6$\n\nDivide both sides by $6\\pi$:\n\n$\\dfrac{150\\pi}{6\\pi} = r^2$\n\nSimplify:\n\n$25 = r^2$\n\nTake the square root of both sides:\n\n$r = 5$\n\nTherefore, the radius of the cylinder is $5$ meters.",
    "options": [
      {
        "text": "$4$",
        "id": "a"
      },
      {
        "text": "$5$",
        "id": "b"
      },
      {
        "text": "$6$",
        "id": "c"
      },
      {
        "text": "$10$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A cylinder has a radius of $3\\, \\text{inches}$ and a height of $7\\, \\text{inches}$. What is the volume of the cylinder, in cubic inches?",
    "type": "multiple-choice-single-answer",
    "id": 168,
    "correctAnswer": "c",
    "quiztype": "satmath",
    "explanation": "Use the formula for the volume of a cylinder: $V = \\pi r^2 h$.\n\n Plug in the given values:\n\n$V = \\pi (3)^2 \\times 7$\n\nSimplify:\n\n$V = \\pi \\times 9 \\times 7 = \\pi \\times 63$\n\nTherefore, the volume of the cylinder is $63\\pi$ cubic inches.",
    "options": [
      {
        "text": "$21\\pi$",
        "id": "a"
      },
      {
        "text": "$45\\pi$",
        "id": "b"
      },
      {
        "text": "$63\\pi$",
        "id": "c"
      },
      {
        "text": "$126\\pi$",
        "id": "d"
      }
    ]
  },
  {
    "text": "A cylinder has a diameter of $10\\, \\text{cm}$ and a height of $12\\, \\text{cm}$. What is the volume of the cylinder, in cubic centimeters?",
    "type": "multiple-choice-single-answer",
    "id": 169,
    "correctAnswer": "b",
    "quiztype": "satmath",
    "explanation": "First, find the radius by dividing the diameter by 2:\n\n$r = \\dfrac{10}{2} = 5\\, \\text{cm}$\n\nUse the formula for the volume of a cylinder:\n\n$V = \\pi r^2 h$\n\nPlug in the values:\n\n$V = \\pi (5)^2 \\times 12$\n\nSimplify:\n\n$V = \\pi \\times 25 \\times 12 = \\pi \\times 300$\n\nTherefore, the volume of the cylinder is $300\\pi$ cubic centimeters.",
    "options": [
      {
        "text": "$150\\pi$",
        "id": "a"
      },
      {
        "text": "$300\\pi$",
        "id": "b"
      },
      {
        "text": "$600\\pi$",
        "id": "c"
      },
      {
        "text": "$750\\pi$",
        "id": "d"
      }
    ]
  },
    {
      "text": "At Bella's Bakery, the owner sometimes arranges small tables to display pastries. If she arranges 2 tables together, she can display 18 pastries. If she arranges 4 tables together, she can display 34 pastries. Which equation best describes the relationship between the number of pastries, P, that can be displayed on t tables arranged together?",
      "type": "multiple-choice-single-answer",
      "id": 170,
      "correctAnswer": "d",
      "quiztype": "satmath",
      "explanation": "First, observe the relationship between the number of tables and pastries:\n\nWhen $t = 2$, $P = 18$.\n\nWhen $t = 4$, $P = 34$.\n\nLet's find the linear equation in the form $P = mt + b$.\n\nSet up two equations based on the given information:\n\n1. $18 = m(2) + b$\n\n2. $34 = m(4) + b$\n\nSubtract the first equation from the second to eliminate $b$:\n\n$34 - 18 = m(4 - 2)$\n\n$16 = 2m$\n\nSolve for $m$:\n\n$m = 8$\n\nPlug the value of $m$ back into the first equation to find $b$:\n\n$18 = 8(2) + b$\n\n$18 = 16 + b$\n\n$b = 18 - 16$\n\n$b = 2$\n\nTherefore, the equation that describes the relationship is $P = 8t + 2$.",
      "options": [
        {
          "text": "$P = 8t - 2$",
          "id": "a"
        },
        {
          "text": "$P = 9t$",
          "id": "b"
        },
        {
          "text": "$P = 8t$",
          "id": "c"
        },
        {
          "text": "$P = 8t + 2$",
          "id": "d"
        }
      ]
    },
    {
      "text": "In a theater, rows of seats are being added to accommodate more guests. If 3 rows can seat 60 people, and 5 rows can seat 100 people, which equation best describes the relationship between the number of people, P, who can be seated in r rows?",
      "type": "multiple-choice-single-answer",
      "id": 171,
      "correctAnswer": "b",
      "quiztype": "satmath",
      "explanation": "Given the two data points:\n\n- When $r = 3$, $P = 60$.\n\n- When $r = 5$, $P = 100$.\n\nWe can model the relationship with a linear equation of the form $P = mr + b$.\n\nSet up two equations:\n\n1. $60 = m(3) + b$\n\n2. $100 = m(5) + b$\n\nSubtract the first equation from the second:\n\n$100 - 60 = m(5 - 3)$\n\n$40 = 2m$\n\nSolve for $m$:\n\n$m = 20$\n\nUse the value of $m$ to find $b$ by substituting back into the first equation:\n\n$60 = 20(3) + b$\n\n$60 = 60 + b$\n\n$b = 60 - 60$\n\n$b = 0$\n\nTherefore, the equation is $P = 20r$.",
      "options": [
        {
          "text": "$P = 15r + 5$",
          "id": "a"
        },
        {
          "text": "$P = 20r$",
          "id": "b"
        },
        {
          "text": "$P = 20r + 5$",
          "id": "c"
        },
        {
          "text": "$P = 25r$",
          "id": "d"
        }
      ]
    },
    {
      "text": "A school's playground fence is made by connecting sections. If 4 sections create a fence 28 meters long, and 7 sections create a fence 49 meters long, which equation best describes the relationship between the length of the fence, L, in meters, and the number of sections, s?",
      "type": "multiple-choice-single-answer",
      "id": 172,
      "correctAnswer": "c",
      "quiztype": "satmath",
      "explanation": "Using the information provided:\n\n- When $s = 4$, $L = 28$.\n\n- When $s = 7$, $L = 49$.\n\nWe assume a linear relationship of the form $L = ms + b$.\n\nSet up two equations:\n\n1. $28 = m(4) + b$\n\n2. $49 = m(7) + b$\n\nSubtract the first equation from the second:\n\n$49 - 28 = m(7 - 4)$\n\n$21 = 3m$\n\nSolve for $m$:\n\n$m = 7$\n\nNow, find $b$ using the first equation:\n\n$28 = 7(4) + b$\n\n$28 = 28 + b$\n\n$b = 28 - 28$\n\n$b = 0$\n\nTherefore, the equation is $L = 7s$.",
      "options": [
        {
          "text": "$L = 7s + 1$",
          "id": "a"
        },
        {
          "text": "$L = 6s + 4$",
          "id": "b"
        },
        {
          "text": "$L = 7s$",
          "id": "c"
        },
        {
          "text": "$L = 8s - 2$",
          "id": "d"
        }
      ]
    },
    {
      "text": "At a function hall, rectangular tables are arranged end to end to form longer tables. If connecting 3 tables seats 24 guests and connecting 5 tables seats 40 guests, which equation best represents the number of guests, G, that can be seated at t tables?",
      "type": "multiple-choice-single-answer",
      "id": 173,
      "correctAnswer": "a",
      "quiztype": "satmath",
      "explanation": "From the given data:\n\n- When $t = 3$, $G = 24$.\n\n- When $t = 5$, $G = 40$.\n\nLet's find a linear equation of the form $G = mt + b$.\n\nSet up two equations:\n\n1. $24 = m(3) + b$\n\n2. $40 = m(5) + b$\n\nSubtract the first equation from the second:\n\n$40 - 24 = m(5 - 3)$\n\n$16 = 2m$\n\nSolve for $m$:\n\n$m = 8$\n\nFind $b$ by substituting $m$ back into the first equation:\n\n$24 = 8(3) + b$\n\n$24 = 24 + b$\n\n$b = 24 - 24$\n\n$b = 0$\n\nTherefore, the equation is $G = 8t$.",
      "options": [
        {
          "text": "$G = 8t$",
          "id": "a"
        },
        {
          "text": "$G = 7t + 3$",
          "id": "b"
        },
        {
          "text": "$G = 8t - 4$",
          "id": "c"
        },
        {
          "text": "$G = 9t$",
          "id": "d"
        }
      ]
    },
    {
      "text": "The table below shows the distribution of hats by color and style in a store inventory. If a hat is selected at random, what is the probability that it is a **blue beanie**?",
      "type": "chartsquestion",
      "id": 174,
      "correctAnswer": "c",
      "quiztype": "satmath",
      "explanation": "To find the probability of selecting a blue beanie, use the formula:\n\n$\\text{Probability} = \\frac{\\text{Number of blue beanies}}{\\text{Total number of hats}}$\n\nFrom the table:\n\n- **Total number of hats:** $400$\n\n- **Number of blue beanies:** $50$\n\nCalculate the probability:\n\n$\\text{Probability} = \\frac{50}{400} = \\frac{5}{40} = \\frac{1}{8} = 0.125$\n\nTherefore, the probability that a randomly selected hat is a blue beanie is $\\dfrac{1}{8}$.",
      "options": [
        {
          "text": "$\\dfrac{1}{4}$",
          "id": "a"
        },
        {
          "text": "$\\dfrac{1}{5}$",
          "id": "b"
        },
        {
          "text": "$\\dfrac{1}{8}$",
          "id": "c"
        },
        {
          "text": "$\\dfrac{1}{10}$",
          "id": "d"
        }
      ],
      "chartData": {
        "type": "table",
        "data": {
          "title": "Distribution of Hats by Color and Style",
          "headers": [
            "Color",
            "Baseball Cap",
            "Beanie",
            "Fedora",
            "Total"
          ],
          "rows": [
            {
              "Color": "Red",
              "Baseball Cap": "60",
              "Beanie": "40",
              "Fedora": "20",
              "Total": "120"
            },
            {
              "Color": "Blue",
              "Baseball Cap": "80",
              "Beanie": "50",
              "Fedora": "30",
              "Total": "160"
            },
            {
              "Color": "Black",
              "Baseball Cap": "40",
              "Beanie": "50",
              "Fedora": "30",
              "Total": "120"
            },
            {
              "Color": "Total",
              "Baseball Cap": "180",
              "Beanie": "140",
              "Fedora": "80",
              "Total": "400"
            }
          ]
        }
      }
    },
    {
      "text": "The table below shows the number of students by grade level and elective course enrollment at Central High School. If a student is selected at random, what is the probability that the student is a **senior enrolled in Art**?",
      "type": "chartsquestion",
      "id": 175,
      "correctAnswer": "b",
      "quiztype": "satmath",
      "explanation": "To determine the probability, use the formula:\n\n$\\text{Probability} = \\frac{\\text{Number of seniors enrolled in Art}}{\\text{Total number of students}}$\n\nFrom the table:\n\n- **Total number of students:** $800$\n\n- **Number of seniors enrolled in Art:** $50$\n\nCalculate the probability:\n\n$\\text{Probability} = \\frac{50}{800} = \\frac{5}{80} = \\frac{1}{16} \\approx 0.0625$\n\nTherefore, the probability that a randomly selected student is a senior enrolled in Art is $\\dfrac{1}{16}$.",
      "options": [
        {
          "text": "$\\dfrac{1}{20}$",
          "id": "a"
        },
        {
          "text": "$\\dfrac{1}{16}$",
          "id": "b"
        },
        {
          "text": "$\\dfrac{1}{10}$",
          "id": "c"
        },
        {
          "text": "$\\dfrac{1}{8}$",
          "id": "d"
        }
      ],
      "chartData": {
        "type": "table",
        "data": {
          "title": "Number of Students by Grade Level and Elective Course Enrollment",
          "headers": [
            "Grade Level",
            "Art",
            "Music",
            "Drama",
            "Computers",
            "Total"
          ],
          "rows": [
            {
              "Grade Level": "Freshmen",
              "Art": "80",
              "Music": "60",
              "Drama": "40",
              "Computers": "20",
              "Total": "200"
            },
            {
              "Grade Level": "Sophomores",
              "Art": "70",
              "Music": "50",
              "Drama": "60",
              "Computers": "20",
              "Total": "200"
            },
            {
              "Grade Level": "Juniors",
              "Art": "60",
              "Music": "40",
              "Drama": "70",
              "Computers": "30",
              "Total": "200"
            },
            {
              "Grade Level": "Seniors",
              "Art": "50",
              "Music": "30",
              "Drama": "50",
              "Computers": "70",
              "Total": "200"
            },
            {
              "Grade Level": "Total",
              "Art": "260",
              "Music": "180",
              "Drama": "220",
              "Computers": "140",
              "Total": "800"
            }
          ]
        }
      }
    },
    {
      "text": "The following table shows the number of smartphones sold in different categories in a store. If a smartphone is selected at random from the store's inventory, what is the probability that it is a **brand A smartphone with 128 GB storage**?",
      "type": "chartsquestion",
      "id": 176,
      "correctAnswer": "d",
      "quiztype": "satmath",
      "explanation": "To find the probability of selecting a brand A smartphone with 128 GB storage, use:\n\n$\\text{Probability} = \\frac{\\text{Number of brand A smartphones with 128 GB}}{\\text{Total number of smartphones}}$\n\nFrom the table:\n\n- **Total number of smartphones:** $600$\n\n- **Brand A with 128 GB storage:** $150$\n\nCalculate the probability:\n\n$\\text{Probability} = \\frac{150}{600} = \\frac{15}{60} = \\frac{1}{4} = 0.25$\n\nTherefore, the probability is $\\dfrac{1}{4}$.",
      "options": [
        {
          "text": "$\\dfrac{1}{6}$",
          "id": "a"
        },
        {
          "text": "$\\dfrac{1}{3}$",
          "id": "b"
        },
        {
          "text": "$\\dfrac{1}{5}$",
          "id": "c"
        },
        {
          "text": "$\\dfrac{1}{4}$",
          "id": "d"
        }
      ],
      "chartData": {
        "type": "table",
        "data": {
          "title": "Smartphones Sold by Brand and Storage Capacity",
          "headers": [
            "Brand Name",
            "64 GB",
            "128 GB",
            "256 GB",
            "Total"
          ],
          "rows": [
            {
              "Brand Name": "Brand A",
              "64 GB": "100",
              "128 GB": "150",
              "256 GB": "50",
              "Total": "300"
            },
            {
              "Brand Name": "Brand B",
              "64 GB": "80",
              "128 GB": "120",
              "256 GB": "50",
              "Total": "250"
            },
            {
              "Brand Name": "Brand C",
              "64 GB": "20",
              "128 GB": "20",
              "256 GB": "10",
              "Total": "50"
            },
            {
              "Brand Name": "Total",
              "64 GB": "200",
              "128 GB": "290",
              "256 GB": "110",
              "Total": "600"
            }
          ]
        }
      }
    },
    {
      "text": "A market research company conducted a survey on favorite fruit preferences among different age groups. The results are summarized in the table below. If a person is selected at random from those surveyed, what is the probability that the person is **aged 30-39 and prefers apples**?",
      "type": "chartsquestion",
      "id": 177,
      "correctAnswer": "a",
      "quiztype": "satmath",
      "explanation": "To calculate the probability, use the formula:\n\n$\\text{Probability} = \\frac{\\text{Number of people aged 30-39 who prefer apples}}{\\text{Total number of people surveyed}}$\n\nFrom the table:\n\n- **Total number of people surveyed:** $1,000$\n\n- **Number of people aged 30-39 who prefer apples:** $80$\n\nCalculate the probability:\n\n$\\text{Probability} = \\frac{80}{1,000} = \\frac{8}{100} = \\frac{2}{25} = 0.08$\n\nTherefore, the probability that a randomly selected person is aged 30-39 and prefers apples is $\\dfrac{2}{25}$.",
      "options": [
        {
          "text": "$\\dfrac{2}{25}$",
          "id": "a"
        },
        {
          "text": "$\\dfrac{3}{25}$",
          "id": "b"
        },
        {
          "text": "$\\dfrac{1}{10}$",
          "id": "c"
        },
        {
          "text": "$\\dfrac{1}{5}$",
          "id": "d"
        }
      ],
      "chartData": {
        "type": "table",
        "data": {
          "title": "Fruit Preferences by Age Group",
          "headers": [
            "Age Group",
            "Apples",
            "Bananas",
            "Oranges",
            "Grapes",
            "Total"
          ],
          "rows": [
            {
              "Age Group": "Under 20",
              "Apples": "70",
              "Bananas": "80",
              "Oranges": "50",
              "Grapes": "30",
              "Total": "230"
            },
            {
              "Age Group": "20-29",
              "Apples": "90",
              "Bananas": "60",
              "Oranges": "70",
              "Grapes": "30",
              "Total": "250"
            },
            {
              "Age Group": "30-39",
              "Apples": "80",
              "Bananas": "50",
              "Oranges": "70",
              "Grapes": "50",
              "Total": "250"
            },
            {
              "Age Group": "40 and above",
              "Apples": "60",
              "Bananas": "40",
              "Oranges": "100",
              "Grapes": "70",
              "Total": "270"
            },
            {
              "Age Group": "Total",
              "Apples": "300",
              "Bananas": "230",
              "Oranges": "290",
              "Grapes": "180",
              "Total": "1,000"
            }
          ]
        }
      }
    },
    {
      "text": "The table below shows the exponential decay of a radioactive substance over time $t$, in hours. The remaining mass $M$ of the substance is measured in grams. Which equation represents the relationship between the remaining mass and time, assuming no external interference?",
      "type": "chartsquestion",
      "id": 178,
      "correctAnswer": "a",
      "quiztype": "satmath",
      "explanation": "To find the equation representing the relationship, examine the data in the table and identify the pattern.\n\nFrom the table:\n\n- When $t = 0$, $M = 80$\n\n- When $t = 1$, $M = 40$\n\n- When $t = 2$, $M = 20$\n\n- When $t = 3$, $M = 10$\n\nObserving the pattern, the mass halves every hour. This suggests an exponential decay where the remaining mass at time $t$ is given by:\n\n$M = 80 \\times \\left(\\dfrac{1}{2}\\right)^t$\n\nSimplifying the decay factor $\\dfrac{1}{2}$, we have:\n\n$M = 80 \\times (0.5)^t$\n\nTherefore, the equation that represents this relationship is $M = 80 \\times (0.5)^t$.",
      "options": [
        {
          "text": "$M = 80 \\times (0.5)^t$",
          "id": "a"
        },
        {
          "text": "$M = 80 \\times 2^t$",
          "id": "b"
        },
        {
          "text": "$M = 80 \\times (0.25)^t$",
          "id": "c"
        },
        {
          "text": "$M = 80 \\times (1.5)^t$",
          "id": "d"
        }
      ],
      "chartData": {
        "type": "table",
        "data": {
          "title": "Radioactive Decay Over Time",
          "headers": [
            "Time (hours)",
            "Remaining Mass (grams)"
          ],
          "rows": [
            {
              "Time (hours)": "0",
              "Remaining Mass (grams)": "80"
            },
            {
              "Time (hours)": "1",
              "Remaining Mass (grams)": "40"
            },
            {
              "Time (hours)": "2",
              "Remaining Mass (grams)": "20"
            },
            {
              "Time (hours)": "3",
              "Remaining Mass (grams)": "10"
            }
          ]
        }
      }
    },
    {
      "text": "The table below shows the population $P$ of a certain species of bacteria over time $t$, in days. What is the equation that represents this exponential growth, assuming no external factors affect the growth?",
      "type": "chartsquestion",
      "id": 179,
      "correctAnswer": "b",
      "quiztype": "satmath",
      "explanation": "Analyzing the data from the table:\n\n- At $t = 0$, $P = 500$\n\n- At $t = 1$, $P = 1,000$\n\n- At $t = 2$, $P = 2,000$\n\n- At $t = 3$, $P = 4,000$\n\nThe population doubles each day. This pattern suggests an exponential growth function of the form:\n\n$P = 500 \\times 2^t$\n\nTherefore, the equation representing this relationship is $P = 500 \\times 2^t$.",
      "options": [
        {
          "text": "$P = 500 \\times 3^t$",
          "id": "a"
        },
        {
          "text": "$P = 500 \\times 2^t$",
          "id": "b"
        },
        {
          "text": "$P = 500 \\times 4^t$",
          "id": "c"
        },
        {
          "text": "$P = 500 \\times 2^{t+1}$",
          "id": "d"
        }
      ],
      "chartData": {
        "type": "table",
        "data": {
          "title": "Bacterial Population Over Time",
          "headers": [
            "Time (days)",
            "Population"
          ],
          "rows": [
            {
              "Time (days)": "0",
              "Population": "500"
            },
            {
              "Time (days)": "1",
              "Population": "1000"
            },
            {
              "Time (days)": "2",
              "Population": "2000"
            },
            {
              "Time (days)": "3",
              "Population": "4000"
            }
          ]
        }
      }
    },
    {
      "text": "The table below shows the depreciation of a car's value over time $t$, in years. The value $V$ is measured in thousands of dollars. Which equation best represents this relationship, assuming a consistent rate of depreciation?",
      "type": "chartsquestion",
      "id": 180,
      "correctAnswer": "c",
      "quiztype": "satmath",
      "explanation": "From the table:\n\n- When $t = 0$, $V = 20$\n\n- When $t = 1$, $V = 16$\n\n- When $t = 2$, $V = 12.8$\n\n- When $t = 3$, $V = 10.24$\n\nObserving the pattern, the car's value decreases by $20\\%$ each year, retaining $80\\%$ of its value each year. This suggests an exponential decay function:\n\n$V = 20 \\times (0.8)^t$\n\nTherefore, the equation that represents this relationship is $V = 20 \\times (0.8)^t$.",
      "options": [
        {
          "text": "$V = 20 \\times (0.9)^t$",
          "id": "a"
        },
        {
          "text": "$V = 20 \\times (0.85)^t$",
          "id": "b"
        },
        {
          "text": "$V = 20 \\times (0.8)^t$",
          "id": "c"
        },
        {
          "text": "$V = 20 \\times (0.75)^t$",
          "id": "d"
        }
      ],
      "chartData": {
        "type": "table",
        "data": {
          "title": "Car Value Depreciation Over Time",
          "headers": [
            "Time (years)",
            "Value (thousands of dollars)"
          ],
          "rows": [
            {
              "Time (years)": "0",
              "Value (thousands of dollars)": "20"
            },
            {
              "Time (years)": "1",
              "Value (thousands of dollars)": "16"
            },
            {
              "Time (years)": "2",
              "Value (thousands of dollars)": "12.8"
            },
            {
              "Time (years)": "3",
              "Value (thousands of dollars)": "10.24"
            }
          ]
        }
      }
    },
    {
      "text": "The table below shows the number of views $V$ a viral video receives over time $t$, in days. Assuming the growth continues exponentially, what is the equation that models this relationship?",
      "type": "chartsquestion",
      "id": 181,
      "correctAnswer": "d",
      "quiztype": "satmath",
      "explanation": "Analyzing the data from the table:\n\n- At $t = 0$, $V = 1,000$\n\n- At $t = 1$, $V = 3,000$\n\n- At $t = 2$, $V = 9,000$\n\n- At $t = 3$, $V = 27,000$\n\nThe number of views triples each day. This pattern suggests an exponential growth function:\n\n$V = 1,000 \\times 3^t$\n\nTherefore, the equation that models this relationship is $V = 1,000 \\times 3^t$.",
      "options": [
        {
          "text": "$V = 1,000 \\times 2^t$",
          "id": "a"
        },
        {
          "text": "$V = 3,000 \\times 3^{t}$",
          "id": "b"
        },
        {
          "text": "$V = 1,000 \\times 3^{t+1}$",
          "id": "c"
        },
        {
          "text": "$V = 1,000 \\times 3^t$",
          "id": "d"
        }
      ],
      "chartData": {
        "type": "table",
        "data": {
          "title": "Viral Video Views Over Time",
          "headers": [
            "Time (days)",
            "Views"
          ],
          "rows": [
            {
              "Time (days)": "0",
              "Views": "1000"
            },
            {
              "Time (days)": "1",
              "Views": "3000"
            },
            {
              "Time (days)": "2",
              "Views": "9000"
            },
            {
              "Time (days)": "3",
              "Views": "27000"
            }
          ]
        }
      }
    },
      {
        "text": "A linear function $y = g(x)$ is graphed in the $xy$-plane. The function passes through the corresponding values of $x$ and $g(x)$ shown in the table below. Which of the following could represent the function?",
        "type": "chartsquestion",
        "id": 182,
        "correctAnswer": "c",
        "quiztype": "satmath",
        "explanation": "To determine the function that represents the data, examine the values in the table and find the pattern.\n\nFrom the table:\n\n- When $x = -2$, $g(x) = 5$\n\n- When $x = 0$, $g(x) = 9$\n\n- When $x = 2$, $g(x) = 13$\n\n- When $x = 4$, $g(x) = 17$\n\nCalculate the rate of change (slope):\n\nUsing $x = 2$ and $x = 0$:\n\n$\\text{Slope} = \\frac{g(2) - g(0)}{2 - 0} = \\frac{13 - 9}{2 - 0} = \\frac{4}{2} = 2$\n\nAlternatively, using $x = 4$ and $x = 2$:\n\n$\\text{Slope} = \\frac{g(4) - g(2)}{4 - 2} = \\frac{17 - 13}{4 - 2} = \\frac{4}{2} = 2$\n\nThe slope is consistent at $2$.\n\nFind the $y$-intercept using $x = 0$:\n\n$g(0) = 2(0) + b = b$\n\nSince $g(0) = 9$, we have:\n\n$9 = b$\n\nTherefore, the equation of the line is $g(x) = 2x + 9$.",
        "options": [
          {
            "text": "$g(x) = 2x + 5$",
            "id": "a"
          },
          {
            "text": "$g(x) = 4x + 5$",
            "id": "b"
          },
          {
            "text": "$g(x) = 2x + 9$",
            "id": "c"
          },
          {
            "text": "$g(x) = 4x + 9$",
            "id": "d"
          }
        ],
        "chartData": {
          "type": "table",
          "data": {
            "headers": [
              "$x$",
              "$g(x)$"
            ],
            "rows": [
              {
                "$x$": "$-2$",
                "$g(x)$": "$5$"
              },
              {
                "$x$": "$0$",
                "$g(x)$": "$9$"
              },
              {
                "$x$": "$2$",
                "$g(x)$": "$13$"
              },
              {
                "$x$": "$4$",
                "$g(x)$": "$17$"
              }
            ]
          }
        }
      },
      {
        "text": "The linear function $y = h(x)$ is graphed in the $xy$-plane, containing the values of $x$ and $h(x)$ given in the table below. Which function could represent $h(x)$?",
        "type": "chartsquestion",
        "id": 183,
        "correctAnswer": "a",
        "quiztype": "satmath",
        "explanation": "From the table, we can determine the slope and $y$-intercept.\n\nValues from the table:\n\n- $x = -3$, $h(x) = 11$\n\n- $x = -1$, $h(x) = 7$\n\n- $x = 1$, $h(x) = 3$\n\n- $x = 3$, $h(x) = -1$\n\nCalculate the slope using any two points. Let's use $x = -1$ and $x = 1$:\n\n$\\text{Slope} = \\frac{h(1) - h(-1)}{1 - (-1)} = \\frac{3 - 7}{1 + 1} = \\frac{-4}{2} = -2$\n\nVerify the slope with another pair, $x = -3$ and $x = -1$:\n\n$\\text{Slope} = \\frac{h(-1) - h(-3)}{-1 - (-3)} = \\frac{7 - 11}{-1 + 3} = \\frac{-4}{2} = -2$\n\nThe slope is consistently $-2$.\n\nFind the $y$-intercept using $x = 1$ and $h(1) = 3$:\n\n$3 = (-2)(1) + b$\n\n$3 = -2 + b$\n\n$b = 5$\n\nTherefore, the equation of the function is $h(x) = -2x + 5$.",
        "options": [
          {
            "text": "$h(x) = -2x + 5$",
            "id": "a"
          },
          {
            "text": "$h(x) = -2x - 5$",
            "id": "b"
          },
          {
            "text": "$h(x) = 2x + 5$",
            "id": "c"
          },
          {
            "text": "$h(x) = 2x - 5$",
            "id": "d"
          }
        ],
        "chartData": {
          "type": "table",
          "data": {
            "headers": [
              "$x$",
              "$h(x)$"
            ],
            "rows": [
              {
                "$x$": "$-3$",
                "$h(x)$": "$11$"
              },
              {
                "$x$": "$-1$",
                "$h(x)$": "$7$"
              },
              {
                "$x$": "$1$",
                "$h(x)$": "$3$"
              },
              {
                "$x$": "$3$",
                "$h(x)$": "$-1$"
              }
            ]
          }
        }
      },
      {
        "text": "The table below shows selected values of the linear function $y = k(x)$. Which of the following functions could represent $k(x)$?",
        "type": "chartsquestion",
        "id": 184,
        "correctAnswer": "d",
        "quiztype": "satmath",
        "explanation": "Using the data from the table:\n\n- $x = 0$, $k(x) = -2$\n\n- $x = 2$, $k(x) = 4$\n\n- $x = 4$, $k(x) = 10$\n\n- $x = 6$, $k(x) = 16$\n\nCalculate the slope:\n\nUsing $x = 2$ and $x = 0$:\n\n$\\text{Slope} = \\frac{k(2) - k(0)}{2 - 0} = \\frac{4 - (-2)}{2} = \\frac{6}{2} = 3$\n\nVerify the slope with $x = 6$ and $x = 4$:\n\n$\\text{Slope} = \\frac{k(6) - k(4)}{6 - 4} = \\frac{16 - 10}{2} = \\frac{6}{2} = 3$\n\nThe slope is consistently $3$.\n\nFind the $y$-intercept using $x = 0$:\n\n$k(0) = 3(0) + b = b$\n\nSince $k(0) = -2$, we find:\n\n$-2 = b$\n\nTherefore, the equation is $k(x) = 3x - 2$.",
        "options": [
          {
            "text": "$k(x) = 2x - 2$",
            "id": "a"
          },
          {
            "text": "$k(x) = 3x + 2$",
            "id": "b"
          },
          {
            "text": "$k(x) = 2x + 2$",
            "id": "c"
          },
          {
            "text": "$k(x) = 3x - 2$",
            "id": "d"
          }
        ],
        "chartData": {
          "type": "table",
          "data": {
            "headers": [
              "$x$",
              "$k(x)$"
            ],
            "rows": [
              {
                "$x$": "$0$",
                "$k(x)$": "$-2$"
              },
              {
                "$x$": "$2$",
                "$k(x)$": "$4$"
              },
              {
                "$x$": "$4$",
                "$k(x)$": "$10$"
              },
              {
                "$x$": "$6$",
                "$k(x)$": "$16$"
              }
            ]
          }
        }
      },
      {
        "text": "A function $y = m(x)$ is linear and passes through the points given in the table below. Which of the following equations could represent $m(x)$?",
        "type": "chartsquestion",
        "id": 185,
        "correctAnswer": "b",
        "quiztype": "satmath",
        "explanation": "From the table:\n\n- $x = -2$, $m(x) = -5$\n\n- $x = 0$, $m(x) = -1$\n\n- $x = 2$, $m(x) = 3$\n\n- $x = 4$, $m(x) = 7$\n\nCalculate the slope:\n\nUsing $x = 2$ and $x = 0$:\n\n$\\text{Slope} = \\frac{m(2) - m(0)}{2 - 0} = \\frac{3 - (-1)}{2} = \\frac{4}{2} = 2$\n\nVerify the slope with $x = 4$ and $x = 2$:\n\n$\\text{Slope} = \\frac{m(4) - m(2)}{4 - 2} = \\frac{7 - 3}{2} = \\frac{4}{2} = 2$\n\nThe slope is consistently $2$.\n\nFind the $y$-intercept using $x = 0$:\n\n$m(0) = 2(0) + b = b$\n\nSince $m(0) = -1$, we have:\n\n$-1 = b$\n\nTherefore, the equation is $m(x) = 2x - 1$.",
        "options": [
          {
            "text": "$m(x) = -2x - 1$",
            "id": "a"
          },
          {
            "text": "$m(x) = 2x - 1$",
            "id": "b"
          },
          {
            "text": "$m(x) = -2x + 1$",
            "id": "c"
          },
          {
            "text": "$m(x) = 2x + 1$",
            "id": "d"
          }
        ],
        "chartData": {
          "type": "table",
          "data": {
            "headers": [
              "$x$",
              "$m(x)$"
            ],
            "rows": [
              {
                "$x$": "$-2$",
                "$m(x)$": "$-5$"
              },
              {
                "$x$": "$0$",
                "$m(x)$": "$-1$"
              },
              {
                "$x$": "$2$",
                "$m(x)$": "$3$"
              },
              {
                "$x$": "$4$",
                "$m(x)$": "$7$"
              }
            ]
          }
        }
      },
      {
        "text": "The bar graph below shows the number of books sold by a bookstore over a $7$-day period. According to the graph, how many books were sold on Day $5$?",
        "type": "chartsquestion",
        "id": 187,
        "correctAnswer": "c",
        "quiztype": "satmath",
        "explanation": "To find the number of books sold on Day $5$, locate 'Day $5$' on the $x$-axis of the bar graph. Then, look at the height of the bar corresponding to Day $5$ and read the value on the $y$-axis.\n\nThe bar for Day $5$ reaches up to $80$. Therefore, $80$ books were sold on Day $5$.\n\nThe correct answer is $80$.",
        "options": [
          {
            "text": "$60$",
            "id": "a"
          },
          {
            "text": "$70$",
            "id": "b"
          },
          {
            "text": "$80$",
            "id": "c"
          },
          {
            "text": "$90$",
            "id": "d"
          }
        ],
        "chartData": {
          "type": "bar",
          "data": {
            "title": "Number of Books Sold Over 7 Days",
            "xAxisLabel": "Day",
            "yAxisLabel": "Number of Books Sold",
            "headers": [
              "Day",
              "Number of Books Sold"
            ],
            "bars": [
              {
                "Day": "1",
                "Number of Books Sold": "50"
              },
              {
                "Day": "2",
                "Number of Books Sold": "60"
              },
              {
                "Day": "3",
                "Number of Books Sold": "70"
              },
              {
                "Day": "4",
                "Number of Books Sold": "65"
              },
              {
                "Day": "5",
                "Number of Books Sold": "80"
              },
              {
                "Day": "6",
                "Number of Books Sold": "75"
              },
              {
                "Day": "7",
                "Number of Books Sold": "85"
              }
            ]
          }
        }
      },
      {
        "text": "The bar graph below displays the number of cars produced by a factory each month over a $6$-month period. Based on the graph, during which month was the greatest number of cars produced?",
        "type": "chartsquestion",
        "id": 188,
        "correctAnswer": "d",
        "quiztype": "satmath",
        "explanation": "To determine the month with the greatest number of cars produced, examine the heights of the bars for each month and identify the one that reaches the highest value on the $y$-axis.\n\nThe production numbers are as follows:\n\n- Month $1$: $200$ cars\n\n- Month $2$: $250$ cars\n\n- Month $3$: $240$ cars\n\n- Month $4$: $260$ cars\n\n- Month $5$: $255$ cars\n\n- Month $6$: $265$ cars\n\nThe highest number is $265$ cars in Month $6$. Therefore, the greatest number of cars was produced in Month $6$.",
        "options": [
          {
            "text": "Month $2$",
            "id": "a"
          },
          {
            "text": "Month $4$",
            "id": "b"
          },
          {
            "text": "Month $5$",
            "id": "c"
          },
          {
            "text": "Month $6$",
            "id": "d"
          }
        ],
        "chartData": {
          "type": "bar",
          "data": {
            "title": "Cars Produced Over 6 Months",
            "xAxisLabel": "Month",
            "yAxisLabel": "Number of Cars Produced",
            "headers": [
              "Month",
              "Number of Cars Produced"
            ],
            "bars": [
              {
                "Month": "1",
                "Number of Cars Produced": "200"
              },
              {
                "Month": "2",
                "Number of Cars Produced": "250"
              },
              {
                "Month": "3",
                "Number of Cars Produced": "240"
              },
              {
                "Month": "4",
                "Number of Cars Produced": "260"
              },
              {
                "Month": "5",
                "Number of Cars Produced": "255"
              },
              {
                "Month": "6",
                "Number of Cars Produced": "265"
              }
            ]
          }
        }
      },
      {
        "text": "The bar graph below represents the number of visitors to a museum over an $8$-day period. According to the graph, what was the average number of visitors per day over this period?",
        "type": "chartsquestion",
        "id": 189,
        "correctAnswer": "b",
        "quiztype": "satmath",
        "explanation": "To find the average number of visitors per day, sum the number of visitors for all $8$ days and divide by $8$.\n\nVisitors per day:\n\n- Day $1$: $150$\n\n- Day $2$: $160$\n\n- Day $3$: $155$\n\n- Day $4$: $165$\n\n- Day $5$: $170$\n\n- Day $6$: $160$\n\n- Day $7$: $175$\n\n- Day $8$: $165$\n\nTotal visitors $= 150 + 160 + 155 + 165 + 170 + 160 + 175 + 165 = 1{,}300$\n\nAverage $= \\dfrac{\\text{Total visitors}}{\\text{Number of days}} = \\dfrac{1{,}300}{8} = 162.5$\n\nTherefore, the average number of visitors per day is $162.5$.",
        "options": [
          {
            "text": "$160$",
            "id": "a"
          },
          {
            "text": "$162.5$",
            "id": "b"
          },
          {
            "text": "$165$",
            "id": "c"
          },
          {
            "text": "$167.5$",
            "id": "d"
          }
        ],
        "chartData": {
          "type": "bar",
          "data": {
            "title": "Number of Visitors to the Museum Over 8 Days",
            "xAxisLabel": "Day",
            "yAxisLabel": "Number of Visitors",
            "headers": [
              "Day",
              "Number of Visitors"
            ],
            "bars": [
              {
                "Day": "1",
                "Number of Visitors": "150"
              },
              {
                "Day": "2",
                "Number of Visitors": "160"
              },
              {
                "Day": "3",
                "Number of Visitors": "155"
              },
              {
                "Day": "4",
                "Number of Visitors": "165"
              },
              {
                "Day": "5",
                "Number of Visitors": "170"
              },
              {
                "Day": "6",
                "Number of Visitors": "160"
              },
              {
                "Day": "7",
                "Number of Visitors": "175"
              },
              {
                "Day": "8",
                "Number of Visitors": "165"
              }
            ]
          }
        }
      },
      {
        "text": "The bar graph below shows the amount of rainfall **in millimeters** recorded in City $X$ over a $10$-month period. In which month did City $X$ experience the lowest rainfall?",
        "type": "chartsquestion",
        "id": 190,
        "correctAnswer": "a",
        "quiztype": "satmath",
        "explanation": "To find the month with the lowest rainfall, examine the heights of the bars for each month and identify the one with the smallest value on the $y$-axis.\n\nThe rainfall amounts are as follows:\n\n- Month $1$: $80$ mm\n\n- Month $2$: $85$ mm\n\n- Month $3$: $75$ mm\n\n- Month $4$: $70$ mm\n\n- Month $5$: $90$ mm\n\n- Month $6$: $95$ mm\n\n- Month $7$: $100$ mm\n\n- Month $8$: $85$ mm\n\n- Month $9$: $90$ mm\n\n- Month $10$: $80$ mm\n\nThe lowest rainfall was $70$ mm in Month $4$. Therefore, City $X$ experienced the lowest rainfall in Month $4$.",
        "options": [
          {
            "text": "Month $4$",
            "id": "a"
          },
          {
            "text": "Month $3$",
            "id": "b"
          },
          {
            "text": "Month $1$",
            "id": "c"
          },
          {
            "text": "Month $2$",
            "id": "d"
          }
        ],
        "chartData": {
          "type": "bar",
          "data": {
            "title": "Rainfall in City X Over 10 Months",
            "xAxisLabel": "Month",
            "yAxisLabel": "Rainfall (mm)",
            "headers": [
              "Month",
              "Rainfall (mm)"
            ],
            "bars": [
              {
                "Month": "1",
                "Rainfall (mm)": "80"
              },
              {
                "Month": "2",
                "Rainfall (mm)": "85"
              },
              {
                "Month": "3",
                "Rainfall (mm)": "75"
              },
              {
                "Month": "4",
                "Rainfall (mm)": "70"
              },
              {
                "Month": "5",
                "Rainfall (mm)": "90"
              },
              {
                "Month": "6",
                "Rainfall (mm)": "95"
              },
              {
                "Month": "7",
                "Rainfall (mm)": "100"
              },
              {
                "Month": "8",
                "Rainfall (mm)": "85"
              },
              {
                "Month": "9",
                "Rainfall (mm)": "90"
              },
              {
                "Month": "10",
                "Rainfall (mm)": "80"
              }
            ]
          }
        }
      }
  ]