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70
[ "28" ]
[ { "content": "Tony loved to solve difficult pen and paper puzzles. He did a warm-up puzzle that only took 10 minutes and after that he did 2 puzzles that each took 3 times as long. How long did he spend solving puzzles?", "role": "user" }, { "content": "Let's solve this problem using Python code.\...
[ { "content": "Tony loved to solve difficult pen and paper puzzles. He did a warm-up puzzle that only took 10 minutes and after that he did 2 puzzles that each took 3 times as long. How long did he spend solving puzzles?", "role": "user" }, { "content": "Let's solve this problem using Python code.\...
103
[ "78" ]
[ { "content": "If $6543_{10}$ is converted to base 8, then each digit of the result is squared, and finally, the squared digits are summed, what is the final result?", "role": "user" }, { "content": "Let's convert the decimal number $6543_{10}$ to base 8:\n```python\nfrom sympy import Integer, floor\...
[ { "content": "If $6543_{10}$ is converted to base 8, then each digit of the result is squared, and finally, the squared digits are summed, what is the final result?", "role": "user" }, { "content": "Let's calculate all the steps.\n```python\nimport math\n\n# convert number to base 8\ndef convert_to_...
10.5
[ "\\frac{63}{2}" ]
[ { "content": "The sum of three numbers is $66$. The first number is $3$ times the third number, and the second number is $24$. What is the third number?", "role": "user" }, { "content": "Let's use sympy to find the solution.\n```python\nfrom sympy import symbols, Eq, solve\n\n# define the variables\...
[ { "content": "The sum of three numbers is $66$. The first number is $3$ times the third number, and the second number is $24$. What is the third number?", "role": "user" }, { "content": "To solve this problem, we can use Python's sympy library.\n```python\nfrom sympy import symbols, Eq, solve\n\n# D...
1
[ "" ]
[ { "content": "The line segment connecting $(-2,7)$ and $(3,11)$ can be parameterized by the equations\n\\begin{align*}\nx &= at + b, \\\\\ny &= ct + d,\n\\end{align*}where $0 \\le t \\le X and $t = 0$ corresponds to the point $(-2,7).$ Find $a^2 + b^2 + c^2 + d^2. 94. What is the value of unknown variable X?",...
[ { "content": "The line segment connecting $(-2,7)$ and $(3,11)$ can be parameterized by the equations\n\\begin{align*}\nx &= at + b, \\\\\ny &= ct + d,\n\\end{align*}where $0 \\le t \\le X and $t = 0$ corresponds to the point $(-2,7).$ Find $a^2 + b^2 + c^2 + d^2. 94. What is the value of unknown variable X?",...
5
[ "12" ]
[ { "content": "I have X marbles numbered 1 through 5 in a bag. Suppose I take out two different marbles at random. What is the expected value of the sum of the numbers on the marbles?\nIf we know the answer to the above question is 6, what is the value of unknown variable X?", "role": "user" }, { "...
[ { "content": "I have X marbles numbered 1 through 5 in a bag. Suppose I take out two different marbles at random. What is the expected value of the sum of the numbers on the marbles?\nIf we know the answer to the above question is 6, what is the value of unknown variable X?", "role": "user" }, { "...
-15
[ "7" ]
[ { "content": "Given the functions $f(x) = 3x^2 - 7$, $g(t) = 4t + c$, $h(x) = g(f(x))$ and $j(y) = y^3 + h(y)$, if $h(2) = 5$ and $j(2) = 13$, what is the value of $c$?", "role": "user" }, { "content": "Let's use sympy to solve for $c$.\n```python\nimport sympy as sp\n\n# define the symbols\nx, t, y...
[ { "content": "Given the functions $f(x) = 3x^2 - 7$, $g(t) = 4t + c$, $h(x) = g(f(x))$ and $j(y) = y^3 + h(y)$, if $h(2) = 5$ and $j(2) = 13$, what is the value of $c$?", "role": "user" }, { "content": "Let's write down an equation for $h(x)$ and $j(y)$ and solve for $c$.\n```python\nfrom sympy impo...
3108
[ "3112" ]
[ { "content": "What is the sum of the least common multiple and the greatest common divisor of the numbers 1332 and 888?", "role": "user" }, { "content": "Let's use sympy to calculate the least common multiple (LCM) and the greatest common divisor (GCD) of 1332 and 888.\n```python\nfrom sympy import ...
[ { "content": "What is the sum of the least common multiple and the greatest common divisor of the numbers 1332 and 888?", "role": "user" }, { "content": "Let's find the least common multiple (LCM) and greatest common divisor (GCD) of the numbers 1332 and 888.\nWe can use sympy to find the LCM as fol...
60
[ "75" ]
[ { "content": "If a 40-foot tree is casting a 10-foot shadow, and Andrea is casting a 15-inch shadow at the same time, how tall is Andrea in inches?", "role": "user" }, { "content": "To solve this, we can use Python's sympy library.\n```python\nimport sympy as sp\n\n# Let's assume that Andrea's heigh...
[ { "content": "If a 40-foot tree is casting a 10-foot shadow, and Andrea is casting a 15-inch shadow at the same time, how tall is Andrea in inches?", "role": "user" }, { "content": "To find the height of Andrea in inches, we need to use the given information.\nLet's set some variables to represent t...
1461
[ "" ]
[ { "content": "If one were to begin counting from the start of 2001 to the end of 2004, how many days would have passed?", "role": "user" }, { "content": "Let's write a simple Python program to count the number of days from the start of 2001 to the end of 2004.\n```python\nfrom datetime import dateti...
[ { "content": "If one were to begin counting from the start of 2001 to the end of 2004, how many days would have passed?", "role": "user" }, { "content": "I can find out this by calculating the total number of days in 2001, 2002, 2003 and 2004.\nLet's use Python's pandas library for that.\n```python\...
63
[ "103" ]
[ { "content": "If Molly and her parents spent most of the day at the beach and were joined by 100 people, but then 40 people left at 5:00, what is the total number of people at the beach if everyone stayed until evening?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n`...
[ { "content": "If Molly and her parents spent most of the day at the beach and were joined by 100 people, but then 40 people left at 5:00, what is the total number of people at the beach if everyone stayed until evening?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n`...
120
[ "1.2" ]
[ { "content": "What is $\\frac{1}{4}\\%$ of X? Express your answer as a decimal. The answer is 0.3. What is the value of unknown variable X?", "role": "user" }, { "content": "Let's use sympy:\n```python\nfrom sympy import Symbol, Eq, solve\n\nx = Symbol('x')\n\neq = Eq(0.25 * 0.01 * x, 0.3)\n\nsoluti...
[ { "content": "What is $\\frac{1}{4}\\%$ of X? Express your answer as a decimal. The answer is 0.3. What is the value of unknown variable X?", "role": "user" }, { "content": "Let's first rewrite the equation with percent in terms of decimals, and use Python's sympy library to solve for $X$.\n```pytho...
10
[ "1" ]
[ { "content": "A fan can create an airflow of x liters per second. If the fan works for 10 minutes each day, calculate the amount of airflow it will create in one week.\nIf we know the answer to the above question is 42000, what is the value of unknown variable x?", "role": "user" }, { "content": "Le...
[ { "content": "A fan can create an airflow of x liters per second. If the fan works for 10 minutes each day, calculate the amount of airflow it will create in one week.\nIf we know the answer to the above question is 42000, what is the value of unknown variable x?", "role": "user" }, { "content": "Le...
-12
[ "2" ]
[ { "content": "For $x=-3$, $y=5$, and $z=-4$, find the outcome of the algebraic expression $x^2+y^2-z^2+2xy$.", "role": "user" }, { "content": "Let's calculate the final value using sympy.\n```python\nfrom sympy import Symbol, Integer, Eq, solve\n\n# Let $x$, $y$, $z$ be the variables\nx = Symbol('x'...
[ { "content": "For $x=-3$, $y=5$, and $z=-4$, find the outcome of the algebraic expression $x^2+y^2-z^2+2xy$.", "role": "user" }, { "content": "Plug in -3 for x, 5 for y, and -4 for z in the expression and compute.\n```python\n# Given variables\nx = -3\ny = 5\nz = -4\n\n# Original expression\norig_ex...
58
[ "64" ]
[ { "content": "Find the value of $x + y + z + w$ if $x$, $y$, $z$, and $w$ are positive integers, $x + y + xy = 76$, $z$ is the greatest prime number less than $20$, and $w$ is the smallest prime number greater than $20$.", "role": "user" }, { "content": "We know that $x$, $y$, $z$, and $w$ are posit...
[ { "content": "Find the value of $x + y + z + w$ if $x$, $y$, $z$, and $w$ are positive integers, $x + y + xy = 76$, $z$ is the greatest prime number less than $20$, and $w$ is the smallest prime number greater than $20$.", "role": "user" }, { "content": "Let's use sympy and numpy to solve this probl...
\sqrt{3}
[ "1" ]
[ { "content": "Suppose $z$ and $w$ are complex numbers such that\n\\[|z| = |w| = z \\overline{w} + \\overline{z} w= 1.\\]Find the largest possible value of the real part of $z + w.$", "role": "user" }, { "content": "We can use sympy for this:\n```python\nfrom sympy import Poly, symbols, solve\n\nx = ...
[ { "content": "Suppose $z$ and $w$ are complex numbers such that\n\\[|z| = |w| = z \\overline{w} + \\overline{z} w= 1.\\]Find the largest possible value of the real part of $z + w.$", "role": "user" }, { "content": "Let's consider z = x + yi and w = a + bi, where x, y, a, b are real numbers.\nGiven t...
8
[ "2" ]
[ { "content": "Let $a$, $b$, $c$, $m$, $n$, and $p$ be integers with $m$ and $n$ odd, $n < m$, $c$ even, and $p$ a prime number such that $a^2 + b^2 + c^2 + p = m^2 - n^2 + c^2 + p$. Find the largest integer that divides $a^2 + b^2 + c^2 + p$ for any such $m$, $n$, $c$, and $p$.\n$\\textbf{(A)}\\ 2\\qquad \\text...
[ { "content": "Let $a$, $b$, $c$, $m$, $n$, and $p$ be integers with $m$ and $n$ odd, $n < m$, $c$ even, and $p$ a prime number such that $a^2 + b^2 + c^2 + p = m^2 - n^2 + c^2 + p$. Find the largest integer that divides $a^2 + b^2 + c^2 + p$ for any such $m$, $n$, $c$, and $p$.\n$\\textbf{(A)}\\ 2\\qquad \\text...
\frac{3}{2}
[ "0" ]
[ { "content": "Find the value(s) of $x$ such that $8xy-12y+2x-3=0$ is true for all values of $y$.", "role": "user" }, { "content": "Let's solve for $x$ using sympy.\n```python\nimport sympy as sp\n\nx, y = sp.symbols('x y')\n\nsolve_for_x = sp.solve(8 * x * y - 12 * y + 2 * x - 3, x)\nprint(solve_for...
[ { "content": "Find the value(s) of $x$ such that $8xy-12y+2x-3=0$ is true for all values of $y$.", "role": "user" }, { "content": "To find the value of $x$, we set $y$ to an array of values ranging from $-100$ to $100$. We do this by creating a Python array with values from $-100$ to $100$ using lis...
34
[ "6" ]
[ { "content": "If $a \\triangle b = 2a^2 + 4b^2$ for all $a$ and $b$, then what is the value of $3 \\triangle 2$?", "role": "user" }, { "content": "Since $a \\triangle b = 2a^2 + 4b^2$, we can simply substitute $a$ with $3$ and $b$ with $2$.\n```python\na = 3\nb = 2\n\nresult = 2 * a**2 + 4 * b**2\nr...
[ { "content": "If $a \\triangle b = 2a^2 + 4b^2$ for all $a$ and $b$, then what is the value of $3 \\triangle 2$?", "role": "user" }, { "content": "To answer this, we can use Python's sympy library.\n```python\nfrom sympy import symbols, Eq, solve\n\na, b = symbols('a b')\n\n# Define the equation\neq...
7
[ "\\frac{7}{30}" ]
[ { "content": "Find the number that when added to the numerator and denominator of the fraction $\\frac{3}{5}$ will make it equal to $\\frac{5}{6}$. What is this number?", "role": "user" }, { "content": "Let's call the number $x$ and let's set up an equation based on the information we are given.\n``...
[ { "content": "Find the number that when added to the numerator and denominator of the fraction $\\frac{3}{5}$ will make it equal to $\\frac{5}{6}$. What is this number?", "role": "user" }, { "content": "To solve this problem, we define the number that needs to be added to both the numerator and deno...
19
[ "9" ]
[ { "content": "The average of three positive integers is 26, with the central number being 27. Knowing that the largest of these numbers is 5 greater than the median, determine the smallest integer in the sequence.", "role": "user" }, { "content": "Since the central number is 27, that makes it the me...
[ { "content": "The average of three positive integers is 26, with the central number being 27. Knowing that the largest of these numbers is 5 greater than the median, determine the smallest integer in the sequence.", "role": "user" }, { "content": "Let's call the three numbers $a$, $b$, and $c$ where...
\frac{1}{16}
[ "0.0608740214809736" ]
[ { "content": "What is the value of $\\sin 6^\\circ \\sin 42^\\circ \\sin 66^\\circ \\sin 78^\\circ$?", "role": "user" }, { "content": "Let's use sympy to solve this problem.\n```python\nfrom sympy import sin, pi\n\nangle_list = [6, 42, 66, 78]\nproduct = 1\n\nfor angle in angle_list:\n product *=...
[ { "content": "What is the value of $\\sin 6^\\circ \\sin 42^\\circ \\sin 66^\\circ \\sin 78^\\circ$?", "role": "user" }, { "content": "We can compute the value of $\\sin x$ for all the angles using sympy.\n```python\nimport sympy as sp\n\nx = sp.symbols('x')\n\nsolutions = sp.solve([sp.sin(x)], [x])...
360
[ "358" ]
[ { "content": "Stan drove 300 miles in 5 hours, 20 minutes. Next, he drove X miles in 6 hours, 40 minutes. What was Stan's average speed in miles per hour for the total trip?\nIf we know the answer to the above question is 55, what is the value of unknown variable X?", "role": "user" }, { "content": ...
[ { "content": "Stan drove 300 miles in 5 hours, 20 minutes. Next, he drove X miles in 6 hours, 40 minutes. What was Stan's average speed in miles per hour for the total trip?\nIf we know the answer to the above question is 55, what is the value of unknown variable X?", "role": "user" }, { "content": ...
343
[ "" ]
[ { "content": "Calculate the volume of a cube that has a surface area of 294 square inches.", "role": "user" }, { "content": "To calculate the volume of a cube given the surface area, we can use the following formula:\n```python\nfrom sympy import sqrt\n\n# Define the surface area\nsurface_area = 294...
[ { "content": "Calculate the volume of a cube that has a surface area of 294 square inches.", "role": "user" }, { "content": "The number of faces a cube has is 6.\nThe surface area of the cube can be calculated by multiplying the area of a face by the number of faces, i.e., $6a$.\nWe are given that t...
12
[ "16" ]
[ { "content": "Adam and Tom are brothers. Adam is 8 years old and Tom is x years old. Their combined age will be 44 years old in 12 years. What is the value of unknown variable x?", "role": "user" }, { "content": "Let's use Python code to solve this problem.\n```python\nx = 8\nx_12 = x + 12\nadam_age...
[ { "content": "Adam and Tom are brothers. Adam is 8 years old and Tom is x years old. Their combined age will be 44 years old in 12 years. What is the value of unknown variable x?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\n# Adam is 8 years old and Tom i...
3
[ "10.1" ]
[ { "content": "Determine the maximum value possible for the expression $x+\\frac{1}{x}$ provided that $7=x^2+\\frac{1}{x^2}$.", "role": "user" }, { "content": "Since $7=x^2+\\frac{1}{x^2}$, we have \\begin{align*} x^2+\\frac{1}{x^2}&=7 \\\\ (x + \\frac{1}{x})^2 &= x^2 + 2 + \\frac{1}{x^2} \\\\ (x + ...
[ { "content": "Determine the maximum value possible for the expression $x+\\frac{1}{x}$ provided that $7=x^2+\\frac{1}{x^2}$.", "role": "user" }, { "content": "We can solve it using calculus:\nwe need to find stationary points and evaluate the function on these points to find maximum value.\n```pytho...
20
[ "3510003" ]
[ { "content": "Given that $f(x) = 3x^2-2$ and we have another function $g(f(x))$ which equals $x^2 + x +1$, evaluate and sum up all the possible values for $g(25)$.", "role": "user" }, { "content": "To evaluate $g(25)$, we first need to find a value of $x$ for which $f(x) = 25$.\nWe'll use sympy to d...
[ { "content": "Given that $f(x) = 3x^2-2$ and we have another function $g(f(x))$ which equals $x^2 + x +1$, evaluate and sum up all the possible values for $g(25)$.", "role": "user" }, { "content": "Since $g(f(x)) = x^2+x+1$, we can use a Python's sympy library to get the possible values of $g(25)$ b...
28
[ "21" ]
[ { "content": "If there exists an integer $p$ in the range $0 < 4p < 30$, can you determine the sum of all the distinct integer values that $p$ could take?", "role": "user" }, { "content": "We can use sympy to iterate over the range of values for $p$ and then sum up all the unique values.\n```python\...
[ { "content": "If there exists an integer $p$ in the range $0 < 4p < 30$, can you determine the sum of all the distinct integer values that $p$ could take?", "role": "user" }, { "content": "To solve this, we can use Python's sympy library.\n```python\nfrom sympy import divisors\n\nN = 30 // 4\nQ = li...
20
[ "60" ]
[ { "content": "Mary is going on a business trip. It takes 10 minutes for her Uber to get to her house and 5 times longer to get to the airport. It takes 15 minutes to check her bag and three times as long to get through security. Then she has to wait for x minutes for her flight to start boarding and twice as lo...
[ { "content": "Mary is going on a business trip. It takes 10 minutes for her Uber to get to her house and 5 times longer to get to the airport. It takes 15 minutes to check her bag and three times as long to get through security. Then she has to wait for x minutes for her flight to start boarding and twice as lo...
3
[ "5" ]
[ { "content": "In a school garden, there are flowers in different colors. In total there are 96 flowers of four colors: green, red, blue, and yellow. There are 9 green flowers and x times more red flowers. Blue flowers make up to 50% of the total flower count. There are 12 yellow flowers. What is the value of un...
[ { "content": "In a school garden, there are flowers in different colors. In total there are 96 flowers of four colors: green, red, blue, and yellow. There are 9 green flowers and x times more red flowers. Blue flowers make up to 50% of the total flower count. There are 12 yellow flowers. What is the value of un...
4
[ "3" ]
[ { "content": "At the zoo, there are 5 different types of animals. Seeing each animal type takes around 6 minutes. How much time would it take to see each animal type if the zoo decided to import x new species?\nIf we know the answer to the above question is 54, what is the value of unknown variable x?", "ro...
[ { "content": "At the zoo, there are 5 different types of animals. Seeing each animal type takes around 6 minutes. How much time would it take to see each animal type if the zoo decided to import x new species?\nIf we know the answer to the above question is 54, what is the value of unknown variable x?", "ro...
18
[ "900" ]
[ { "content": "When you take the square root of $\\frac{y}{50}$ you get $\\frac{3}{5}$. What does $y$ equal?", "role": "user" }, { "content": "Let's use sympy to solve for y.\n```python\nimport sympy as sp\n\n# define the symbols\ny = sp.symbols('y')\n\n# solve for y\ny_answer = sp.solve(sp.Eq(sp.sqr...
[ { "content": "When you take the square root of $\\frac{y}{50}$ you get $\\frac{3}{5}$. What does $y$ equal?", "role": "user" }, { "content": "Let's write down an equation and solve for $y$ using sympy.\n```python\nfrom sympy import Eq, symbols, solve\n\n# defining the symbol y\ny = symbols('y')\n\ne...
12
[ "6" ]
[ { "content": "Mr. and Mrs. Lopez have two children. When they get into their family car, two people sit in the front, and the other two sit in the back. Either Mr. Lopez or Mrs. Lopez must sit in the driver's seat. How many seating arrangements are possible?", "role": "user" }, { "content": "Sinc...
[ { "content": "Mr. and Mrs. Lopez have two children. When they get into their family car, two people sit in the front, and the other two sit in the back. Either Mr. Lopez or Mrs. Lopez must sit in the driver's seat. How many seating arrangements are possible?", "role": "user" }, { "content": "We c...
10500
[ "0" ]
[ { "content": "Determine the independent term of $x$ when expanding the binomial $\\left(\\sqrt{x} + \\frac{5}{x}\\right)^9$.", "role": "user" }, { "content": "We can solve this problem using sympy library.\n```python\nfrom sympy import expand, sqrt, symbols\n\n# Define the symbol for x\nx = symbols(...
[ { "content": "Determine the independent term of $x$ when expanding the binomial $\\left(\\sqrt{x} + \\frac{5}{x}\\right)^9$.", "role": "user" }, { "content": "We can use sympy to expand the binomial and then print the independent term of $x$.\n```python\nfrom sympy import sqrt, symbols, binomial, ex...
30
[ "15" ]
[ { "content": "Janice has been working part-time at a convenience store 5 days a week. She can earn $x per day and can earn $15 more when she works a 2 hour overtime shift. If she works three overtime shifts this week, She will earn 195 this week. What is the value of unknown variable x?", "role": "user" }...
[ { "content": "Janice has been working part-time at a convenience store 5 days a week. She can earn $x per day and can earn $15 more when she works a 2 hour overtime shift. If she works three overtime shifts this week, She will earn 195 this week. What is the value of unknown variable x?", "role": "user" }...
3
[ "6" ]
[ { "content": "Frank went to a shop to buy some food for his breakfast. He bought 10 buns for $0.1 each, two bottles of milk, for $2 each, and a carton of eggs, which was x times more expensive than one bottle of milk. How much did Frank pay for his breakfast shopping?\nIf we know the answer to the above questio...
[ { "content": "Frank went to a shop to buy some food for his breakfast. He bought 10 buns for $0.1 each, two bottles of milk, for $2 each, and a carton of eggs, which was x times more expensive than one bottle of milk. How much did Frank pay for his breakfast shopping?\nIf we know the answer to the above questio...
-1
[ "0" ]
[ { "content": "If $g(x) = f(x) + \\cos(x)$ and $f(x) = 2\\arcsin(\\sin(x))$, find the value of $g(7\\pi)$. Express your answer in radians.", "role": "user" }, { "content": "Let's break down the problem into smaller steps. First, we need to find the value of $f(x)$. We can do this using sympy.\n```pyt...
[ { "content": "If $g(x) = f(x) + \\cos(x)$ and $f(x) = 2\\arcsin(\\sin(x))$, find the value of $g(7\\pi)$. Express your answer in radians.", "role": "user" }, { "content": "To solve this problem, we define the function $g(x)$ in Python using Python's sympy library and then compute $g(7\\pi).$\n```pyt...
340
[ "324" ]
[ { "content": "Mary chose an even $4$-digit number $n$. She wrote down all the divisors of $n$ in increasing order from left to right: $1,2,...,\\dfrac{n}{2},n$. At some moment Mary wrote $323$ as a divisor of $n$. What is the smallest possible value of the next divisor written to the right of $323$?\n$\\textbf{...
[ { "content": "Mary chose an even $4$-digit number $n$. She wrote down all the divisors of $n$ in increasing order from left to right: $1,2,...,\\dfrac{n}{2},n$. At some moment Mary wrote $323$ as a divisor of $n$. What is the smallest possible value of the next divisor written to the right of $323$?\n$\\textbf{...
610
[ "607" ]
[ { "content": "What is the sum of all distinct prime factors of 5463?", "role": "user" }, { "content": "Let's use sympy to prime factorize 5463 and then find the sum of the distinct prime factors.\n```python\nimport sympy as sp\n\n# prime factorize 5463 using sympy\nfactors = sp.factorint(5463)\n\n# ...
[ { "content": "What is the sum of all distinct prime factors of 5463?", "role": "user" }, { "content": "A prime number is a natural number that is greater than one and has no positive divisors other than 1 and itself.\nWe can find all divisors of 5463 using sympy library and then calculate the sum of...
56
[ "42" ]
[ { "content": "A koala's diet consists of 75\\% fiber. Koalas absorb only $25\\%$ of the fiber they eat. If a koala absorbed 10.5 ounces of fiber in one day, how many ounces of koala's total food did he eat that day?", "role": "user" }, { "content": "Let $x$ be the total amount of food that the koala...
[ { "content": "A koala's diet consists of 75\\% fiber. Koalas absorb only $25\\%$ of the fiber they eat. If a koala absorbed 10.5 ounces of fiber in one day, how many ounces of koala's total food did he eat that day?", "role": "user" }, { "content": "Let $x$ be the amount of food that the koala eats ...
14
[ "2.6" ]
[ { "content": "June's house and Julia's residence are separated by a distance of 1 mile. June can cycle to Julia's place in 4 minutes. How long will it take her to bike 3.5 miles to visit Bernard's house if she maintains the same cycling speed?", "role": "user" }, { "content": "Let's use Python to so...
[ { "content": "June's house and Julia's residence are separated by a distance of 1 mile. June can cycle to Julia's place in 4 minutes. How long will it take her to bike 3.5 miles to visit Bernard's house if she maintains the same cycling speed?", "role": "user" }, { "content": "Let's write down an eq...
5
[ "25" ]
[ { "content": "Given the equation $(a + b)^2 = 45$ and the product $ab = 10$, calculate the value of $(a - b)^2$.", "role": "user" }, { "content": "Let's use sympy to solve the system of equations.\n```python\nimport sympy as sp\n\na, b = sp.symbols('a b')\n\nequation_1 = sp.Eq((a + b)**2, 45)\nequat...
[ { "content": "Given the equation $(a + b)^2 = 45$ and the product $ab = 10$, calculate the value of $(a - b)^2$.", "role": "user" }, { "content": "To solve this problem, we can expand the square of a binomial\n$(a + b)^2 = 45$, which gives us a quadratic equation in terms of $a$ and $b$:\n$a^2 + 2ab...
7
[ "4" ]
[ { "content": "Jimmy is going to sell pizzas at the carnival to make some money. The carnival only gave him x hours to do so. He bought a 22kg sack of flour to make his pizzas and he takes 10 min to make each pizza for the customers. At the end of the 7 hours, he saw some flour was left. Knowing that each pizza ...
[ { "content": "Jimmy is going to sell pizzas at the carnival to make some money. The carnival only gave him x hours to do so. He bought a 22kg sack of flour to make his pizzas and he takes 10 min to make each pizza for the customers. At the end of the 7 hours, he saw some flour was left. Knowing that each pizza ...
10800
[ "43200" ]
[ { "content": "If Jack goes hunting 6 times a month during the hunting season, which lasts for 1 quarter of the year, and he catches 2 deer each time weighing 600 pounds each, how many pounds of deer does he keep in a year, keeping half the weight?", "role": "user" }, { "content": "Let's solve this p...
[ { "content": "If Jack goes hunting 6 times a month during the hunting season, which lasts for 1 quarter of the year, and he catches 2 deer each time weighing 600 pounds each, how many pounds of deer does he keep in a year, keeping half the weight?", "role": "user" }, { "content": "Let's solve this p...
6
[ "24" ]
[ { "content": "For every 4 apple trees in Ben's orchard, he can collect 36 baskets of apples. If he exchanges 9 baskets for 1 pumpkin, how many apple trees are needed to collect enough apples for 6 pumpkins?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\n# B...
[ { "content": "For every 4 apple trees in Ben's orchard, he can collect 36 baskets of apples. If he exchanges 9 baskets for 1 pumpkin, how many apple trees are needed to collect enough apples for 6 pumpkins?", "role": "user" }, { "content": "Let's solve this problem using Python's sympy library.\n```...
20
[ "300" ]
[ { "content": "A farmer planted 30 rows of tomatoes with 10 plants in each row. Each tomato plant yields x pieces of tomatoes. How many pieces of tomatoes can the farmer get from all his planted tomatoes?\nIf we know the answer to the above question is 6000, what is the value of unknown variable x?", "role":...
[ { "content": "A farmer planted 30 rows of tomatoes with 10 plants in each row. Each tomato plant yields x pieces of tomatoes. How many pieces of tomatoes can the farmer get from all his planted tomatoes?\nIf we know the answer to the above question is 6000, what is the value of unknown variable x?", "role":...
-17
[ "" ]
[ { "content": "Let $f(x) = ax^7 + bx^3 + cx - 5.$ If $f(-7) = 7,$ then find $f(7).$", "role": "user" }, { "content": "To solve this, we can use Python's sympy library.\n```python\nfrom sympy import symbols, Eq, solve\n\nx = symbols('x')\na, b, c = symbols('a b c')\nf = a*x**7 + b*x**3 + c*x - 5\n\n#...
[ { "content": "Let $f(x) = ax^7 + bx^3 + cx - 5.$ If $f(-7) = 7,$ then find $f(7).$", "role": "user" }, { "content": "I will find $a, b, c$ from the equation $f(-7) = 7$.\nThen I will use these values of $a, b, c$ to solve for $f(7)$.\n```python\nimport sympy as sp\nfrom sympy import I, pi, exp, sqr...
742
[ "200" ]
[ { "content": "If Susan is making jewelry with a repeating pattern consisting of 3 green beads, 5 purple beads, and twice as many red beads as green beads, and the pattern repeats three times per bracelet and five times per necklace, how many beads does she need to make 1 bracelet and 10 necklaces in total?", ...
[ { "content": "If Susan is making jewelry with a repeating pattern consisting of 3 green beads, 5 purple beads, and twice as many red beads as green beads, and the pattern repeats three times per bracelet and five times per necklace, how many beads does she need to make 1 bracelet and 10 necklaces in total?", ...
163
[ "225" ]
[ { "content": "In a stem-and-leaf plot detailing the ride times in minutes and seconds for the 17 most popular roller coasters, the entry $2 \\ 20$ corresponds to a duration of 2 minutes and 20 seconds, or 140 seconds. Which number represents the median value of the times listed in the dataset? Your answer shoul...
[ { "content": "In a stem-and-leaf plot detailing the ride times in minutes and seconds for the 17 most popular roller coasters, the entry $2 \\ 20$ corresponds to a duration of 2 minutes and 20 seconds, or 140 seconds. Which number represents the median value of the times listed in the dataset? Your answer shoul...
15.17
[ "15.14" ]
[ { "content": "Consider a single roll of an unbiased six-sided die with faces numbered 1 to 6. For the outcome $n$, my prize will be the square of $n$ in dollars. What is the expected value of the prize I will receive? Round off your answer to the nearest two decimal points.", "role": "user" }, { "co...
[ { "content": "Consider a single roll of an unbiased six-sided die with faces numbered 1 to 6. For the outcome $n$, my prize will be the square of $n$ in dollars. What is the expected value of the prize I will receive? Round off your answer to the nearest two decimal points.", "role": "user" }, { "co...
50
[ "82" ]
[ { "content": "In Zeoland the fine for speeding is $16 for each mile per hour the driver is traveling over the posted speed limit. In Zeoland, Jed was fined $256 for speeding on a road with a posted speed limit of x mph. Jed was fined for traveling at what speed in miles per hour?\nIf we know the answer to the a...
[ { "content": "In Zeoland the fine for speeding is $16 for each mile per hour the driver is traveling over the posted speed limit. In Zeoland, Jed was fined $256 for speeding on a road with a posted speed limit of x mph. Jed was fined for traveling at what speed in miles per hour?\nIf we know the answer to the a...
1
[ "4" ]
[ { "content": "Determine the positive real number $t$ for which the equation $|t + 2i\\sqrt{3}| \\times |6 - 4i| = 26$ holds true.", "role": "user" }, { "content": "We can use sympy to solve this question.\n```python\nimport sympy as sp\n\nt = sp.symbols('t')\nr = sp.sqrt(t**2 + 12) * sp.sqrt(36 + 16...
[ { "content": "Determine the positive real number $t$ for which the equation $|t + 2i\\sqrt{3}| \\times |6 - 4i| = 26$ holds true.", "role": "user" }, { "content": "Let's substitute values and try to simplify the equation.\n```python\nfrom sympy import symbols, simplify, sqrt, re, im, Eq\n\n# symboli...
2
[ "4" ]
[ { "content": "Let $f$ be a function with domain and codomain as the set of real numbers. It follows that for all $x, y \\in \\mathbb{R}$:\n\\[f(f(x) + y) = f(x + y) + xf(y) - xy - x + 1\\]\n\nLet the number of conceivable values of $f(1)$ be denoted by $n$, and the sum of these values is $s$. Determine the valu...
[ { "content": "Let $f$ be a function with domain and codomain as the set of real numbers. It follows that for all $x, y \\in \\mathbb{R}$:\n\\[f(f(x) + y) = f(x + y) + xf(y) - xy - x + 1\\]\n\nLet the number of conceivable values of $f(1)$ be denoted by $n$, and the sum of these values is $s$. Determine the valu...
31
[ "-1" ]
[ { "content": "Let $r$ and $s$ be the solutions to $2x^2 - 3x = 11.$ Compute the value of $(4r^3 - 4s^3)(r - s)^{-1}.$", "role": "user" }, { "content": "We can compute this directly using sympy.\n```python\nimport sympy as sp\n\n# define the symbols\nx, r, s = sp.symbols('x r s')\n\n# the equation 2...
[ { "content": "Let $r$ and $s$ be the solutions to $2x^2 - 3x = 11.$ Compute the value of $(4r^3 - 4s^3)(r - s)^{-1}.$", "role": "user" }, { "content": "Let's solve for $r$ and $s$ using sympy.\n```python\nfrom sympy import *\n\nx = symbols('x')\nr, s = symbols('r s')\n\n# Define the equation\nequat...
100000
[ "80000" ]
[ { "content": "Denny, an Instagram influencer, has x followers and gets 1000 new followers every day. How many followers will he have if 20000 people unfollowed him in a year?\nIf we know the answer to the above question is 445000, what is the value of unknown variable x?", "role": "user" }, { "conte...
[ { "content": "Denny, an Instagram influencer, has x followers and gets 1000 new followers every day. How many followers will he have if 20000 people unfollowed him in a year?\nIf we know the answer to the above question is 445000, what is the value of unknown variable x?", "role": "user" }, { "conte...
2
[ "4" ]
[ { "content": "In the diagram, what is the perimeter of polygon $PQRST$? [asy]\n\nimport olympiad;\n\nsize(6cm); // ADJUST\n\npair p = (0, 6);\npair q = (3, 6);\n\npair r = (3, 3);\npair t = (0, 0);\npair s = (7, 0);\n\ndraw(p--q--r--s--t--cycle);\nlabel(\"$P$\", p, NW);\nlabel(\"$Q$\", q, NE);\nlabel(\"$R$\", r...
[ { "content": "In the diagram, what is the perimeter of polygon $PQRST$? [asy]\n\nimport olympiad;\n\nsize(6cm); // ADJUST\n\npair p = (0, 6);\npair q = (3, 6);\n\npair r = (3, 3);\npair t = (0, 0);\npair s = (7, 0);\n\ndraw(p--q--r--s--t--cycle);\nlabel(\"$P$\", p, NW);\nlabel(\"$Q$\", q, NE);\nlabel(\"$R$\", r...
10
[ "0.1" ]
[ { "content": "Calculate the expense in dollars for purchasing 1000 peppermint gums, each priced at 1 cent.", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\nprice_per_gum = 0.01\nnumber_of_gums = 1000\ntotal_expense = number_of_gums * price_per_gum\ntotal_expe...
[ { "content": "Calculate the expense in dollars for purchasing 1000 peppermint gums, each priced at 1 cent.", "role": "user" }, { "content": "To answer this, we need to first calculate the total number of cents required to purchase 1000 gums, and then convert that to dollars. We can use Python's symp...
4
[ "" ]
[ { "content": "If $y = 8x + 2$ and $y = (2c)x - 4$ represent two parallel lines, what is $c$?", "role": "user" }, { "content": "Since the lines are parallel, they have the same slope.\nLet's find the slope of each line and set them equal to each other.\n```python\nimport sympy as sp\n\nx, y, c = sp.s...
[ { "content": "If $y = 8x + 2$ and $y = (2c)x - 4$ represent two parallel lines, what is $c$?", "role": "user" }, { "content": "We can use Python's sympy library to solve the problem.\n```python\nfrom sympy import symbols, Eq, solve\n\nx, y, c = symbols('x y c')\n# Define the two equations\neq1 = Eq(...
\frac{25}{4}
[ "11" ]
[ { "content": "The function $f(x)$ satisfies\n\\[f(x + y) = f(x) + f(y)\\]for all real numbers $x$ and $y,$ and $f(4) = 5.$ Find $f(5).$", "role": "user" }, { "content": "Since $f(x)$ is linear in $x$, $f(x) = kx$, where $k$ is a constant.\nWe know that $f(4) = 5$, so $4k = 5$, and $k = 5/4$.\nSo we...
[ { "content": "The function $f(x)$ satisfies\n\\[f(x + y) = f(x) + f(y)\\]for all real numbers $x$ and $y,$ and $f(4) = 5.$ Find $f(5).$", "role": "user" }, { "content": "This is an interesting mathematical riddle! Let's just evaluate it using the given constraints.\n```python\ndef f(x):\n return...
x^2+4x-12
[ "" ]
[ { "content": "Expand the product ${(x-2)(x+6)}$.", "role": "user" }, { "content": "To expand the product ${(x-2)(x+6)}$ we need to apply the distributive law for multiplication over addition.\nThis means that we need to multiply each factor in the first binomial by each factor in the second binomial...
[ { "content": "Expand the product ${(x-2)(x+6)}$.", "role": "user" }, { "content": "I will expand the product and use sympy to simplify the expression.\n```python\nfrom sympy import simplify\n\n# Expansion of (x-2)(x+6)\nexpr = \"(x-2)*(x+6)\"\nexpanded = simplify(expr)\nprint(expanded)\n```", "r...
6
[ "1" ]
[ { "content": "What is the units digit of $6^{1999}$?", "role": "user" }, { "content": "Let's find the pattern of units digits for 6 raised to a power of k.\n```python\nimport numpy as np\nk_list = [i for i in range(20)]\nunits_digit_list = [6**i % 10 for i in k_list]\nprint(units_digit_list)\n```", ...
[ { "content": "What is the units digit of $6^{1999}$?", "role": "user" }, { "content": "The number $6^{1999}$ has a units digit equal to the units digit of $6^1 * 6^{1998}$.\nLet's simplify $6^n$ for small $n$ using sympy.\n```python\nfrom sympy import factorial, Mod, binomial, summation, oo, Symbol\...
8
[ "120" ]
[ { "content": "If you want to split 40 apples and 48 oranges into groups of equal quantity without any leftovers, how many fruits will be in each group?", "role": "user" }, { "content": "The maximum number of groups will be formed by the number of apples.\nWe need to find a number that divides both 4...
[ { "content": "If you want to split 40 apples and 48 oranges into groups of equal quantity without any leftovers, how many fruits will be in each group?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\nnum_apples = 40\nnum_oranges = 48\nnum_groups = 2\n\n# fin...
3
[ "0" ]
[ { "content": "If Paige bought new stickers and wants to divide a sheet of 100 space stickers and a sheet of 50 cat stickers equally among her 3 friends, how many stickers will she have remaining?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\n# number of sp...
[ { "content": "If Paige bought new stickers and wants to divide a sheet of 100 space stickers and a sheet of 50 cat stickers equally among her 3 friends, how many stickers will she have remaining?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\nspace_stickers...
4
[ "2" ]
[ { "content": "If 52 cards are dealt to 8 people as evenly as possible, how many people will end up with fewer than 7 cards?", "role": "user" }, { "content": "To see how many people will have fewer than 7 cards, we can use the Python code below to calculate the modulus of the ratio of a given integer...
[ { "content": "If 52 cards are dealt to 8 people as evenly as possible, how many people will end up with fewer than 7 cards?", "role": "user" }, { "content": "We can use sympy to calculate the modulus of a number.\n```python\nfrom sympy import Mod\n\n# number of cards and number of people\ncards = 52...
93
[ "48" ]
[ { "content": "Let $f(x)=x+3$, $g(x)=3x+5$, and $h(x)=2x-1$. If $k(x) = f(g(h(x)))$, calculate $k(2) + h(f(g(2))) + g(h(f(2))) + f(g(h(2)))$.", "role": "user" }, { "content": "Let's use sympy to evaluate $k(x) + h(f(g(2))) + g(h(f(2))) + f(g(h(2)))$.\n```python\nfrom sympy import symbols, Add\n\n# De...
[ { "content": "Let $f(x)=x+3$, $g(x)=3x+5$, and $h(x)=2x-1$. If $k(x) = f(g(h(x)))$, calculate $k(2) + h(f(g(2))) + g(h(f(2))) + f(g(h(2)))$.", "role": "user" }, { "content": "Let's calculate $f(g(h(x)))$ and use sympy to calculate the values for the desired expressions.\n```python\nfrom sympy import...
1
[ "4" ]
[ { "content": "If we divide $5^{2010}$ evenly into 7 parts, what will be the leftover?", "role": "user" }, { "content": "Let's use Python's sympy library to compute the remainder.\n```python\nfrom sympy import symbols, Mod\n\nx = symbols('x')\n\n# The number of parts we have to divide 5^2010 into\nn_...
[ { "content": "If we divide $5^{2010}$ evenly into 7 parts, what will be the leftover?", "role": "user" }, { "content": "Since $5^{2010} = 5^{2008} \\cdot 5^2 = (5^4)^{502} \\cdot 25 = (625)^{502} \\cdot 25$, the result will have the same remainder as $25$ in division by $7$.\nThe result is:\n```pyth...
110
[ "125" ]
[ { "content": "A group of 5 children are taken to an amusement park. Only 3 of them were daring enough to get on the Ferris wheel which cost $5 per child. Everyone had a go at the merry-go-round (at $3 per child). On their way home, they bought 2 cones of ice cream each (each cone cost $8). How much did they spe...
[ { "content": "A group of 5 children are taken to an amusement park. Only 3 of them were daring enough to get on the Ferris wheel which cost $5 per child. Everyone had a go at the merry-go-round (at $3 per child). On their way home, they bought 2 cones of ice cream each (each cone cost $8). How much did they spe...
4
[ "24" ]
[ { "content": "Oliver needs to create a wire frame for a cube with a minimum volume of 64 cubic centimeters. What should the edge of the cube be to use the least amount of wire?", "role": "user" }, { "content": "The minimum volume of a cube is achieved when the edge length is the smallest possible, i...
[ { "content": "Oliver needs to create a wire frame for a cube with a minimum volume of 64 cubic centimeters. What should the edge of the cube be to use the least amount of wire?", "role": "user" }, { "content": "Let's write a python script to find the minimum amount of wire needed to form a cube with...
3x^3-7x^2+8x-31
[ "-31x^3+8x^2-7x+3" ]
[ { "content": "If $f(x) = x(3x^2-2)-5(x^2-2x+7)$ and $g(x) = 2x^2 - 4$, find $f(x) - g(x)$. Express your answer in the form $Ax^3+Bx^2+Cx+D.$", "role": "user" }, { "content": "Let's use sympy to solve this problem.\n```python\nfrom sympy import symbols, simplify\n\n# define the variables\nx = symbols...
[ { "content": "If $f(x) = x(3x^2-2)-5(x^2-2x+7)$ and $g(x) = 2x^2 - 4$, find $f(x) - g(x)$. Express your answer in the form $Ax^3+Bx^2+Cx+D.$", "role": "user" }, { "content": "Let's write down the expressions of $f(x)$ and $g(x)$ and then use sympy to find $f(x) - g(x)$.\n```python\nfrom sympy import...
-3
[ "-\\frac{9}{2}" ]
[ { "content": "The sum of the squares of the roots of the quadratic equation $3x^2 + 4x - 9 = 0$ is known to be $\\frac{70}{9}$. What is the product of the roots of this quadratic equation?", "role": "user" }, { "content": "The correct answer is 9/4.\nTo get this answer, we need to solve for x using ...
[ { "content": "The sum of the squares of the roots of the quadratic equation $3x^2 + 4x - 9 = 0$ is known to be $\\frac{70}{9}$. What is the product of the roots of this quadratic equation?", "role": "user" }, { "content": "Let's calculate the sum and product of roots using sympy.\n```python\nimport ...
40
[ "25" ]
[ { "content": "Jake agrees to work part of his debt off. He owed someone $100 but paid them $x before agreeing to work off the rest. He worked for $15 an hour. How many hours did he have to work?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?", "role": "user" ...
[ { "content": "Jake agrees to work part of his debt off. He owed someone $100 but paid them $x before agreeing to work off the rest. He worked for $15 an hour. How many hours did he have to work?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?", "role": "user" ...
\frac{1}{64}
[ "0.046875" ]
[ { "content": "The probability of snow for each of the next three days is $\\frac{3}{4}$. What is the probability that it will not snow at all during the next three days? Express your answer as a common fraction.", "role": "user" }, { "content": "To find the probability that it will not snow at all d...
[ { "content": "The probability of snow for each of the next three days is $\\frac{3}{4}$. What is the probability that it will not snow at all during the next three days? Express your answer as a common fraction.", "role": "user" }, { "content": "Let's compute this probability using Python's sympy li...
-4-6i
[ "-6-6i" ]
[ { "content": "What do you get when you subtract the second complex number (1 + 4i) from the first one (-3 - 2i)?", "role": "user" }, { "content": "To find the difference between two complex numbers, we just subtract each of the real and imaginary parts.\nThe expression in sympy looks like this:\n```...
[ { "content": "What do you get when you subtract the second complex number (1 + 4i) from the first one (-3 - 2i)?", "role": "user" }, { "content": "We can use sympy to subtract the two complex numbers.\n```python\nfrom sympy import I, symbols, pprint\n\n# Define the variables\na, b, c, d = symbols('a...
2
[ "8" ]
[ { "content": "Last night, Jim bought a $7 lamp and a bulb which cost $4 less. If he bought x lamps and 6 bulbs, Jim paid 32 in all. What is the value of unknown variable x?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\ncost_of_lamp = 7\ncost_of_bulb = cost...
[ { "content": "Last night, Jim bought a $7 lamp and a bulb which cost $4 less. If he bought x lamps and 6 bulbs, Jim paid 32 in all. What is the value of unknown variable x?", "role": "user" }, { "content": "Let's solve this problem using Python's sympy library.\n```python\nimport sympy as sp\n\n# ji...
73
[ "25" ]
[ { "content": "Given vectors $\\mathbf{v}$ and $\\mathbf{w}$ with $\\|\\mathbf{v}\\| = 4$, $\\|\\mathbf{w}\\| = 3$, $\\mathbf{v} \\perp \\mathbf{w}$, and $\\mathbf{u} = 2\\mathbf{v} - \\mathbf{w}$, find $\\mathbf{u} \\cdot \\mathbf{u}$.", "role": "user" }, { "content": "Using the formula for the dot ...
[ { "content": "Given vectors $\\mathbf{v}$ and $\\mathbf{w}$ with $\\|\\mathbf{v}\\| = 4$, $\\|\\mathbf{w}\\| = 3$, $\\mathbf{v} \\perp \\mathbf{w}$, and $\\mathbf{u} = 2\\mathbf{v} - \\mathbf{w}$, find $\\mathbf{u} \\cdot \\mathbf{u}$.", "role": "user" }, { "content": "Since $\\mathbf{v} \\perp \\ma...
6
[ "3" ]
[ { "content": "Using the digits 2, 4, and 7, how many unique two-digit positive integers can be formed without repeating any digits?", "role": "user" }, { "content": "We can use Python's itertools library to generate all possible permutations of 2, 4, and 7.\nWe then discard any permutation that star...
[ { "content": "Using the digits 2, 4, and 7, how many unique two-digit positive integers can be formed without repeating any digits?", "role": "user" }, { "content": "The trick is to enumerate all possible combinations of 2 digits that we can construct from these numbers.\nThis is a combinatorics pro...
\frac{9}{2}
[ "3.4286" ]
[ { "content": "What is the combined sum of the roots of the cubic polynomials \\(2x^3 + x^2 - 8x + 20\\) and \\(5x^3 - 25x^2 + 19\\) if they are set to equal zero?", "role": "user" }, { "content": "Let's find the roots of the given equations and then use sympy to find the sum of the roots.\n```python...
[ { "content": "What is the combined sum of the roots of the cubic polynomials \\(2x^3 + x^2 - 8x + 20\\) and \\(5x^3 - 25x^2 + 19\\) if they are set to equal zero?", "role": "user" }, { "content": "Let's combine the two polynomials into one and solve it using sympy.\n```python\nfrom sympy import symb...
19440
[ "44*22*4*12" ]
[ { "content": "Suppose there are four distinct positive integers, $P$, $Q$, $R$, and $S$, which when added together give a total of 64. Moreover, these integers satisfy $P + 3 = Q - 3 = R \\times 3 = S \\div 3$. Can you determine the product $P \\times Q \\times R \\times S$?", "role": "user" }, { "c...
[ { "content": "Suppose there are four distinct positive integers, $P$, $Q$, $R$, and $S$, which when added together give a total of 64. Moreover, these integers satisfy $P + 3 = Q - 3 = R \\times 3 = S \\div 3$. Can you determine the product $P \\times Q \\times R \\times S$?", "role": "user" }, { "c...
20
[ "12" ]
[ { "content": "Hannah is making banana bread. She needs to use 3 cups of flour for every cup of banana mush. It takes 4 bananas to make one cup of mush. If Hannah uses x bananas, how many cups of flour should she use?\nIf we know the answer to the above question is 15, what is the value of unknown variable x?", ...
[ { "content": "Hannah is making banana bread. She needs to use 3 cups of flour for every cup of banana mush. It takes 4 bananas to make one cup of mush. If Hannah uses x bananas, how many cups of flour should she use?\nIf we know the answer to the above question is 15, what is the value of unknown variable x?", ...
9
[ "8" ]
[ { "content": "Marcus has two numbers, $a$ and $b$. When he divides $a$ by 45 he gets a remainder of 37. When he divides $b$ by 30 he gets a remainder of X$. What remainder does he get when he divides $a+b$ by 15?\nIf we know the answer to the above question is 1, what is the value of unknown variable X?", ...
[ { "content": "Marcus has two numbers, $a$ and $b$. When he divides $a$ by 45 he gets a remainder of 37. When he divides $b$ by 30 he gets a remainder of X$. What remainder does he get when he divides $a+b$ by 15?\nIf we know the answer to the above question is 1, what is the value of unknown variable X?", ...
91
[ "76" ]
[ { "content": "If $h(x) = g(x) + x^3$ where $g(x) = 2f(x) + 3$ and $f(x) = x^2 - x$, what is $h(4)$?", "role": "user" }, { "content": "To compute $h(4)$ we need to first compute $f(x)$ and $g(x)$.\nNoting that $f(x) = x^2 - x$ and $g(x) = 2f(x) + 3$ we can use sympy to write the following code:\n```p...
[ { "content": "If $h(x) = g(x) + x^3$ where $g(x) = 2f(x) + 3$ and $f(x) = x^2 - x$, what is $h(4)$?", "role": "user" }, { "content": "We can compute $h(4)$ as $g(4) + 64$, where $g(x) = 2f(x) + 3$.\n```python\nimport sympy as sp\nfrom sympy.parsing.sympy_parser import parse_expr\n\nx = sp.symbols('x...
2
[ "-\\frac{2}{3}" ]
[ { "content": "Find the slope of a line that is parallel to the line represented by the equation $3y - 6x = 9$. Give your answer as a fraction.", "role": "user" }, { "content": "First, we will rewrite the equation of the line in the form $y = mx + c$.\nThe equation in the slope-intercept form can be ...
[ { "content": "Find the slope of a line that is parallel to the line represented by the equation $3y - 6x = 9$. Give your answer as a fraction.", "role": "user" }, { "content": "We can use sympy to get the canonical form of the equation and then print out the slope.\n```python\nimport sympy as sp\n\n...
3
[ "6" ]
[ { "content": "How many unordered pairs of prime numbers have a sum of 40?", "role": "user" }, { "content": "To calculate the answer, we will iterate over all primes below 40 using Python's sympy library and find pairs whose sum is 40.\n```python\nfrom sympy import isprime, sieve\n\n# Initialize a li...
[ { "content": "How many unordered pairs of prime numbers have a sum of 40?", "role": "user" }, { "content": "Let's use sympy to get a list of prime numbers with a sum of 40.\n```python\nfrom sympy import isprime, primepi\n\ndef find_primes_with_sum(n):\n primes = []\n for i in range(2, n+1):\n ...
15
[ "13" ]
[ { "content": "There are x tables in the school's cafeteria. Each table can seat 10 people. Usually, only 1/10 of the seats are left unseated. Usually, 135 seats are taken. What is the value of unknown variable x?", "role": "user" }, { "content": "Let's solve this problem using Python's sympy library...
[ { "content": "There are x tables in the school's cafeteria. Each table can seat 10 people. Usually, only 1/10 of the seats are left unseated. Usually, 135 seats are taken. What is the value of unknown variable x?", "role": "user" }, { "content": "Let's solve this problem using Python's sympy library...
5
[ "" ]
[ { "content": "What is the highest integer $n$ that can be used in $n^2 - 9n + 18 < 0$ to still have a negative result?", "role": "user" }, { "content": "Let's first check whether sympy has an analytical solution to this inequality.\n```python\nimport sympy as sp\n\nn = sp.symbols('n')\nequation = n*...
[ { "content": "What is the highest integer $n$ that can be used in $n^2 - 9n + 18 < 0$ to still have a negative result?", "role": "user" }, { "content": "I can find it using sympy:\n```python\nfrom sympy import symbols, solve\n\nn = symbols('n')\n# Define the expression\nexpr = n**2 - 9*n + 18\n\n# F...
4
[ "5" ]
[ { "content": "If there are 32 students in a class and each student needs 5 minutes to present their project, with each period being 40 minutes long, how many periods will it take for every student to present their project?", "role": "user" }, { "content": "Let's solve this problem using Python code....
[ { "content": "If there are 32 students in a class and each student needs 5 minutes to present their project, with each period being 40 minutes long, how many periods will it take for every student to present their project?", "role": "user" }, { "content": "Let's solve this problem using Python code....
8
[ "72" ]
[ { "content": "On the first day of the week, David is able to assemble $w$ units every hour, working for a total of $t$ hours. Feeling worn out, he decides to shorten his workday on the following day by $2$ hours, although his productivity increases by $4$ units per hour. Given that $w = 2t$, what is the differe...
[ { "content": "On the first day of the week, David is able to assemble $w$ units every hour, working for a total of $t$ hours. Feeling worn out, he decides to shorten his workday on the following day by $2$ hours, although his productivity increases by $4$ units per hour. Given that $w = 2t$, what is the differe...
50
[ "" ]
[ { "content": "Kyle bikes for 2 hours to work every day. Ten times the time he takes to travel to work and back is the same as the cost of buying a pack of snacks (in dollars). How much will Ryan pay, in dollars, to buy x packs of snacks?\nIf we know the answer to the above question is 2000, what is the value of...
[ { "content": "Kyle bikes for 2 hours to work every day. Ten times the time he takes to travel to work and back is the same as the cost of buying a pack of snacks (in dollars). How much will Ryan pay, in dollars, to buy x packs of snacks?\nIf we know the answer to the above question is 2000, what is the value of...
\frac{-1}{4}
[ "\\frac{1}{4}" ]
[ { "content": "If $\\det \\mathbf{B} = -4,$ then evaluate $ \\det (\\mathbf{B}^{-1}).$", "role": "user" }, { "content": "To find the determinant of the inverse of a matrix, we can use the fact that $\\det(\\mathbf{B}^{-1}) = \\frac{1}{\\det \\mathbf{B}}.$\n```python\ndet_B = -4\n\n# Calculate the det...
[ { "content": "If $\\det \\mathbf{B} = -4,$ then evaluate $ \\det (\\mathbf{B}^{-1}).$", "role": "user" }, { "content": "Let's write down the determinant of the inverse of the matrix using sympy.\n```python\nimport sympy as sp\n\n# define symbols for the matrix entries\na, b, c, d = sp.symbols('a b c...
10
[ "20" ]
[ { "content": "If Mary wants to split her 60 characters according to their initials, with half of them having the initial A and half of that amount having the initial C, and she wants the remaining characters to have the initials D and E, with twice as many characters having the initial D as the initial E, how m...
[ { "content": "If Mary wants to split her 60 characters according to their initials, with half of them having the initial A and half of that amount having the initial C, and she wants the remaining characters to have the initials D and E, with twice as many characters having the initial D as the initial E, how m...
{Sunday}
[ "" ]
[ { "content": "What day of the week will it be 40 days from Tuesday?", "role": "user" }, { "content": "Let's use Python to solve this problem.\n```python\nimport datetime\n\n# define the initial date and the number of days\ndate = datetime.date(2021, 1, 19) # a Tuesday\ndays = 40\n\n# compute the ne...
[ { "content": "What day of the week will it be 40 days from Tuesday?", "role": "user" }, { "content": "Let's break down this problem into two steps. First, we will compute the day of the week that is 40 days from Tuesday. Second, we will use this to find out the day of the week for a given day number...
36
[ "50" ]
[ { "content": "Jenny wants to know whether bone meal or cow manure makes better fertilizer. The control plant with no fertilizer grows x inches high, the plant with bone meal grows to 125% of the height of the control plant, and the cow manure plant grows to 200% of the height of the bone meal plant. The cow man...
[ { "content": "Jenny wants to know whether bone meal or cow manure makes better fertilizer. The control plant with no fertilizer grows x inches high, the plant with bone meal grows to 125% of the height of the control plant, and the cow manure plant grows to 200% of the height of the bone meal plant. The cow man...
53
[ "100" ]
[ { "content": "In a survey about common animal carriers of diseases, 86.8% of the participants marked rats as potential disease carriers. Within this group, a fraction of 45.7% incorrectly identified rats as frequent carriers of rabies. This misconception was held by 21 of the respondents. Can you calculate the ...
[ { "content": "In a survey about common animal carriers of diseases, 86.8% of the participants marked rats as potential disease carriers. Within this group, a fraction of 45.7% incorrectly identified rats as frequent carriers of rabies. This misconception was held by 21 of the respondents. Can you calculate the ...
5
[ "7" ]
[ { "content": "How many integers $n$ are there that satisfy the inequality $(n-2)(n+4) < 0$?", "role": "user" }, { "content": "Let's use sympy to solve the inequality $(n-2)(n+4) < 0$.\n```python\nfrom sympy import solve, Symbol\n\n# define the variable n as a symbol\nn = Symbol('n', real=True)\n\n# ...
[ { "content": "How many integers $n$ are there that satisfy the inequality $(n-2)(n+4) < 0$?", "role": "user" }, { "content": "To solve this inequality, we need to find values of $n$ that make the left-hand side negative.\nTherefore we need to solve the equation to 0 and analyze the signs.\nLet's use...
10
[ "2" ]
[ { "content": "In the prime factorization of $24!$, what is the exponent of $3$? (Reminder: The number $n!$ is the product of the integers from 1 to $n$. For example, $5!=5\\cdot 4\\cdot3\\cdot2\\cdot 1= 120$.)", "role": "user" }, { "content": "We can use sympy to compute the prime factorization of...
[ { "content": "In the prime factorization of $24!$, what is the exponent of $3$? (Reminder: The number $n!$ is the product of the integers from 1 to $n$. For example, $5!=5\\cdot 4\\cdot3\\cdot2\\cdot 1= 120$.)", "role": "user" }, { "content": "To compute the exponent of $3$ in the prime factorizat...
144
[ "104" ]
[ { "content": "For every bike Henry sells, he is paid $8 more than he is paid to paint the bike. If Henry gets $5 to paint the bike, how much does he get paid to sell and paint 8 bikes?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\npaint_per_bike = 5\nsell_...
[ { "content": "For every bike Henry sells, he is paid $8 more than he is paid to paint the bike. If Henry gets $5 to paint the bike, how much does he get paid to sell and paint 8 bikes?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\npaint_price = 5\nsell_pri...
5
[ "" ]
[ { "content": "There are x times as many swordfish as pufferfish in an aquarium exhibit. If there are 90 fish total, There are 15 pufferfish. What is the value of unknown variable x?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\nnumber_of_swordfish = 90 - 1...
[ { "content": "There are x times as many swordfish as pufferfish in an aquarium exhibit. If there are 90 fish total, There are 15 pufferfish. What is the value of unknown variable x?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\n# Because the number of swor...
2
[ "" ]
[ { "content": "For $a$ being a positive real number, calculate $a$ if $p(q(a)) = 8$ and the functions are defined as $p(x) = x^2 + 8$ and $q(x) = x^2 - 4$.", "role": "user" }, { "content": "Let's define the functions and use sympy to solve for $a$.\n```python\nfrom sympy import *\n\nx, y, a = symbols...
[ { "content": "For $a$ being a positive real number, calculate $a$ if $p(q(a)) = 8$ and the functions are defined as $p(x) = x^2 + 8$ and $q(x) = x^2 - 4$.", "role": "user" }, { "content": "Since $p(x)$ is $x^2$ plus a constant, and $q(x)$ is $x^2$ minus a constant, their composition $p(q(x))$ must b...
3
[ "5" ]
[ { "content": "Mia is buying Christmas gifts for her family. She has spent $30 on each of her x siblings, and the rest of her spending was for her parents. If Mia spent a total of $150 on Christmas gifts and each of her parents received gifts of equal value, how much money, in dollars, did she spend on each pare...
[ { "content": "Mia is buying Christmas gifts for her family. She has spent $30 on each of her x siblings, and the rest of her spending was for her parents. If Mia spent a total of $150 on Christmas gifts and each of her parents received gifts of equal value, how much money, in dollars, did she spend on each pare...
6720
[ "560" ]
[ { "content": "8 distinct tokens are in a bag. In how many ways can 5 tokens be selected, in order, from the bag, if each token is not returned to the bag after it is selected?", "role": "user" }, { "content": "Let's use sympy to calculate the number of permutations.\n```python\nfrom sympy import fac...
[ { "content": "8 distinct tokens are in a bag. In how many ways can 5 tokens be selected, in order, from the bag, if each token is not returned to the bag after it is selected?", "role": "user" }, { "content": "Let's solve it recursively using list slicing and deletion.\n```python\ndef permutations(n...
99
[ "9" ]
[ { "content": "Determine the largest multiple of 9 that, when negated, is greater than -100.", "role": "user" }, { "content": "To answer this, we can use Python's sympy library.\n```python\nfrom sympy import divisors, sympify\n\nn = 9\ntarget_negation = -100\n\n# To find the largest multiple of 9 tha...
[ { "content": "Determine the largest multiple of 9 that, when negated, is greater than -100.", "role": "user" }, { "content": "Let's write a simple Python program to check the values until we find a number that fits the criteria.\n```python\nimport numpy as np\n\n# Initially set num = 1\nnum = 1\n\n#...