gt stringlengths 1 44 | rej listlengths 1 1 | chosen listlengths 4 12 | rejected listlengths 4 14 |
|---|---|---|---|
80 | [
"136"
] | [
{
"content": "Honey earned $x a day. Every day, she spent part of her pay and saved the rest. After 20 days of work, she spent $1360. How much did Honey save in 20 days?\nIf we know the answer to the above question is 240, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Le... | [
{
"content": "Honey earned $x a day. Every day, she spent part of her pay and saved the rest. After 20 days of work, she spent $1360. How much did Honey save in 20 days?\nIf we know the answer to the above question is 240, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Le... |
\frac{20}{3} | [
"\\frac{-80}{123}"
] | [
{
"content": "Solve for $x$: $\\sqrt{3x+5}$ is to $\\sqrt{6x+5}$ as $\\sqrt{5}$ is to $3$. Your answer should be written as an irreducible fraction.",
"role": "user"
},
{
"content": "Let's write down an equation and solve for $x$ using sympy.\n```python\nimport sympy as sp\n\nx = sp.symbols('x')\n\n... | [
{
"content": "Solve for $x$: $\\sqrt{3x+5}$ is to $\\sqrt{6x+5}$ as $\\sqrt{5}$ is to $3$. Your answer should be written as an irreducible fraction.",
"role": "user"
},
{
"content": "If the statement is true, then $\\sqrt{3x+5}$ and $\\sqrt{6x+5}$ must be proportional.\nIf $\\sqrt{3x+5}$ is to $\\sq... |
75 | [
"35"
] | [
{
"content": "A car rental company charges a daily rate of $\\$20.00$ plus $\\$0.10$ per mile driven. How much, in dollars, does it cost to rent the car for 3 days and drive it for 150 miles?",
"role": "user"
},
{
"content": "Let's calculate the cost using sympy.\n```python\nfrom sympy import symbol... | [
{
"content": "A car rental company charges a daily rate of $\\$20.00$ plus $\\$0.10$ per mile driven. How much, in dollars, does it cost to rent the car for 3 days and drive it for 150 miles?",
"role": "user"
},
{
"content": "Let's write down the cost of renting the car for 3 days and driving it for... |
120000 | [
"3200000002"
] | [
{
"content": "A rectangular room has an area of $2^{12} \\times 5^8$ square units and a length that is twice its width. What is the perimeter of the room?",
"role": "user"
},
{
"content": "If the length of the room is $x$ and width is $y$, then $x = 2y$.\nSince the area is 2^12 * 5^8 we can make thi... | [
{
"content": "A rectangular room has an area of $2^{12} \\times 5^8$ square units and a length that is twice its width. What is the perimeter of the room?",
"role": "user"
},
{
"content": "Let the length of the room be $x$ and the width $y$. We know that $x = 2y$.\nArea of the room is given as $x \\... |
3 | [
"4"
] | [
{
"content": "In a certain arithmetic series, the combined value of the 2nd and 4th terms is $6$. Identify what the 3rd term in this series is.",
"role": "user"
},
{
"content": "Let's write down the definitions of the arithmetic sequence.\n$$\na, a+d, a+2d, a+3d, a+4d, ...\n$$\nGiven that $a + (a + ... | [
{
"content": "In a certain arithmetic series, the combined value of the 2nd and 4th terms is $6$. Identify what the 3rd term in this series is.",
"role": "user"
},
{
"content": "Let $a$ be the first term and $d$ the common difference.\nThen we get the following equations:\n$a + d = 2$\n$a + 2d = 4$\... |
12 | [
"18"
] | [
{
"content": "The sum of the $x$-coordinates of the vertices of a square in the Cartesian plane is $12$. Find the sum of the $x$-coordinates of the center of each side of the square.",
"role": "user"
},
{
"content": "Let $x_1, x_2, x_3, x_4$ denote the $x$-coordinates of the vertices of the square. ... | [
{
"content": "The sum of the $x$-coordinates of the vertices of a square in the Cartesian plane is $12$. Find the sum of the $x$-coordinates of the center of each side of the square.",
"role": "user"
},
{
"content": "The sum of the $x$-coordinates of the vertices is equal to the sum of the $x$-coord... |
\frac{3}{4} | [
"\\frac{4}{5}"
] | [
{
"content": "Among the numbers $\\frac{7}{10}, \\frac{4}{5}$ and $\\frac{3}{4}$, which number is the average of the other two?",
"role": "user"
},
{
"content": "The average of two numbers is the sum of the numbers divided by 2.\nTo find which number is the average, we need to calculate the sum of t... | [
{
"content": "Among the numbers $\\frac{7}{10}, \\frac{4}{5}$ and $\\frac{3}{4}$, which number is the average of the other two?",
"role": "user"
},
{
"content": "Since $\\frac{3}{4} = \\frac{6}{8}$ and $\\frac{4}{5} = \\frac{8}{10}$ the average is simply the middle value.\n```python\nprint('4/5')\n`... |
511 | [
"1"
] | [
{
"content": "What is the greatest common divisor of $2^{1998}-1$ and $2^{1989}-1$?",
"role": "user"
},
{
"content": "The gcd of two numbers can be calculated using sympy's gcd function.\n```python\nfrom sympy import gcd\n\na = 2**1998 - 1\nb = 2**1989 - 1\n\nresult = gcd(a, b)\nprint(result)\n```",... | [
{
"content": "What is the greatest common divisor of $2^{1998}-1$ and $2^{1989}-1$?",
"role": "user"
},
{
"content": "To calculate the greatest common divisor of $2^{1998}-1$ and $2^{1989}-1$, we need to find the value of $N-1$ and $N-M_0$ in the below euclidean algorithm.\n```python\nfrom sympy imp... |
30 | [
"630"
] | [
{
"content": "In how many unique ways can the characters of the term 'MADAM' be rearranged, considering the repeated letters?",
"role": "user"
},
{
"content": "The correct answer is 60. Here's the Python code to compute this value:\n```python\nfrom sympy import factorial\n\nletters = ['M', 'A', 'D',... | [
{
"content": "In how many unique ways can the characters of the term 'MADAM' be rearranged, considering the repeated letters?",
"role": "user"
},
{
"content": "In order to compute the number of ways the characters can be rearranged, we first need to compute the number of ways the repeated letters ca... |
500 | [
"2"
] | [
{
"content": "Bill's roof can bear x pounds of weight. If 100 leaves fall on his roof every day, and 1000 leaves weighs 1 pound, It will take 5000 days for his roof to collapse. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n``... | [
{
"content": "Bill's roof can bear x pounds of weight. If 100 leaves fall on his roof every day, and 1000 leaves weighs 1 pound, It will take 5000 days for his roof to collapse. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sympy l... |
1711_8 | [
""
] | [
{
"content": "Convert $969_{10}$ to base 8.",
"role": "user"
},
{
"content": "We can use this formula:\n```python\ndef change_base(num, base=10):\n if num == 0:\n return '0'\n nums = []\n while num:\n num, r = divmod(num, base)\n nums.append(str(r))\n return ''.join(... | [
{
"content": "Convert $969_{10}$ to base 8.",
"role": "user"
},
{
"content": "In Python, we can use built-in function int to convert decimal number to octal number.\nThis function takes two arguments: the number to convert and the base to convert to.\nSince we need to convert to octal number (base=8... |
5 | [
"1531"
] | [
{
"content": "What is the remainder when the base-12 integer $1531_{12}$ is divided by $8$?",
"role": "user"
},
{
"content": "Let's write a python program to convert the base-12 integer to a decimal integer and then use sympy to find the remainder.\n```python\nimport sympy\n\n# define function to co... | [
{
"content": "What is the remainder when the base-12 integer $1531_{12}$ is divided by $8$?",
"role": "user"
},
{
"content": "We need to find the remainder when the base-12 integer $1531_{12}$ is divided by $8$.\nThe base-12 number system uses 11 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A (representin... |
0 | [
"84"
] | [
{
"content": "In an educational circle game involving 42 contenders, including Lily, everyone takes turns using three particular calculators. These calculators have starting values of 1, 0, and -1. Lily goes first and performs the following on each: she raises the first calculator's display to the power of thre... | [
{
"content": "In an educational circle game involving 42 contenders, including Lily, everyone takes turns using three particular calculators. These calculators have starting values of 1, 0, and -1. Lily goes first and performs the following on each: she raises the first calculator's display to the power of thre... |
12 | [
"0"
] | [
{
"content": "In the equation $\\displaystyle\\sqrt[3]{4 - \\frac{p^2}{3}} = -2$, find the positive difference between the two values of p that satisfy the equation.",
"role": "user"
},
{
"content": "Let's use sympy to rewrite the equation and solve it.\n```python\nfrom sympy import solve, Symbol, E... | [
{
"content": "In the equation $\\displaystyle\\sqrt[3]{4 - \\frac{p^2}{3}} = -2$, find the positive difference between the two values of p that satisfy the equation.",
"role": "user"
},
{
"content": "We can solve this problem using algebraic manipulation.\n```python\nfrom sympy import symbols, Eq, s... |
26 | [
"37"
] | [
{
"content": "What is the minimum number of rides you need to take every month so that the cost per ride of a 30-day pass, which costs $50, is less than the cost of a one-way ticket, which costs $2 per ride?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\n# ... | [
{
"content": "What is the minimum number of rides you need to take every month so that the cost per ride of a 30-day pass, which costs $50, is less than the cost of a one-way ticket, which costs $2 per ride?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\nri... |
4989600 | [
"831600"
] | [
{
"content": "Assuming all letters are unique, how many possible combinations of the word COMBINATION can be formed?",
"role": "user"
},
{
"content": "To find the number of possible combinations of the word COMBINATION,\nwe can first rearrange the word into alphabetical order to find the total numbe... | [
{
"content": "Assuming all letters are unique, how many possible combinations of the word COMBINATION can be formed?",
"role": "user"
},
{
"content": "The number of possible combinations of the word COMBINATION can be computed using Python.\n```python\nfrom sympy import factorial\n\n# Number of uniq... |
18 | [
"2"
] | [
{
"content": "Nikki's garden has a ratio of irises to roses to tulips of 2:5:3. She currently has 25 roses and 15 tulips. If she plans to add 20 roses and a certain number of irises to maintain the ratio of irises to roses while adding 10 tulips, how many irises will she have in total?",
"role": "user"
},... | [
{
"content": "Nikki's garden has a ratio of irises to roses to tulips of 2:5:3. She currently has 25 roses and 15 tulips. If she plans to add 20 roses and a certain number of irises to maintain the ratio of irises to roses while adding 10 tulips, how many irises will she have in total?",
"role": "user"
},... |
124 | [
"152"
] | [
{
"content": "Sarah, Greg, and Lisa went bowling together. Sarah's score was 40 points more than Greg's, and Lisa's score was 10 points less than Greg's. If the average of their three scores was 94, what was Sarah's score?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sym... | [
{
"content": "Sarah, Greg, and Lisa went bowling together. Sarah's score was 40 points more than Greg's, and Lisa's score was 10 points less than Greg's. If the average of their three scores was 94, what was Sarah's score?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sym... |
1200 | [
"14400"
] | [
{
"content": "A rectangular silver block has dimensions $n\\times m\\times p$ inches. Given that a two-inch cube ($2\\times2\\times2$) of silver weighs 3 pounds and is worth $\\$200$, how much is the silver block worth when $n=4, m=6, p=2$? Round your answer to the nearest dollar.",
"role": "user"
},
{
... | [
{
"content": "A rectangular silver block has dimensions $n\\times m\\times p$ inches. Given that a two-inch cube ($2\\times2\\times2$) of silver weighs 3 pounds and is worth $\\$200$, how much is the silver block worth when $n=4, m=6, p=2$? Round your answer to the nearest dollar.",
"role": "user"
},
{
... |
2 | [
"\\frac{1}{\\sqrt{3}}"
] | [
{
"content": "Let $\\alpha$, $\\beta$, and $\\gamma$ be complex numbers such that $|\\beta| = 1$, $|\\gamma| = 2$, and $\\overline{\\alpha} \\beta \\neq 1.$ Find the maximum value of\n\\[\\left| \\frac{\\gamma(\\beta - \\alpha)}{1 - \\overline{\\alpha} \\beta} \\right|.\\]",
"role": "user"
},
{
"co... | [
{
"content": "Let $\\alpha$, $\\beta$, and $\\gamma$ be complex numbers such that $|\\beta| = 1$, $|\\gamma| = 2$, and $\\overline{\\alpha} \\beta \\neq 1.$ Find the maximum value of\n\\[\\left| \\frac{\\gamma(\\beta - \\alpha)}{1 - \\overline{\\alpha} \\beta} \\right|.\\]",
"role": "user"
},
{
"co... |
1 | [
"4"
] | [
{
"content": "What is the remainder when $2^{2013}$ is divided by 7?",
"role": "user"
},
{
"content": "Let's write a python function to find the remainder when $2^n$ is divided by 7 for any $n$.\n```python\ndef modulo(n):\n if n == 0:\n return 1\n elif n == 1:\n return 2\n els... | [
{
"content": "What is the remainder when $2^{2013}$ is divided by 7?",
"role": "user"
},
{
"content": "We have $2^6 \\equiv 1 \\pmod{7}$, so we have the following equivalences.\n```python\n# using sympy\nfrom sympy import Mod\n\n# equivalences\n[Mod(2**i, 7) for i in range(1, 7)]\n```",
"role": ... |
2 | [
"2b-8"
] | [
{
"content": "Given $h(x) = 2x + b$ and $p(x) = bx - 1.$ If $h(p(x)) = 8x + e,$ what is the value of $e$?",
"role": "user"
},
{
"content": "To compute the value of $e$, let's use sympy.\n```python\nfrom sympy import symbols, solve\n\nx = symbols('x')\nb = symbols('b')\ne = symbols('e')\n\nh = 2*x + ... | [
{
"content": "Given $h(x) = 2x + b$ and $p(x) = bx - 1.$ If $h(p(x)) = 8x + e,$ what is the value of $e$?",
"role": "user"
},
{
"content": "Let's define h(x) and p(x) and the given equation in sympy.\n```python\nfrom sympy import Symbol, Eq, solve\n\nx = Symbol('x')\n\n# Given functions\nh = lambda ... |
4 | [
"6"
] | [
{
"content": "Billy has four horses. Each one eats x pounds of oats, twice a day. How many pounds of oats does he need to feed his horses for 3 days?\nIf we know the answer to the above question is 96, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's use Python code t... | [
{
"content": "Billy has four horses. Each one eats x pounds of oats, twice a day. How many pounds of oats does he need to feed his horses for 3 days?\nIf we know the answer to the above question is 96, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this proble... |
110 | [
"29"
] | [
{
"content": "Alex starts a new routine where he runs 2 miles on the first day and increases his distance by 2 miles each subsequent day. How many miles will he have run after 10 days?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\n# Alex runs 2 miles a day... | [
{
"content": "Alex starts a new routine where he runs 2 miles on the first day and increases his distance by 2 miles each subsequent day. How many miles will he have run after 10 days?",
"role": "user"
},
{
"content": "We have an arithmetic progression where the initial term is 2, and the difference... |
50 | [
"20"
] | [
{
"content": "A park has x benches with a capacity of 4 people each. On a Sunday afternoon, 80 people were sitting on the benches. What's the number of available spaces on the benches that other people can sit on before the carrying capacity of the benches is full?\nIf we know the answer to the above question i... | [
{
"content": "A park has x benches with a capacity of 4 people each. On a Sunday afternoon, 80 people were sitting on the benches. What's the number of available spaces on the benches that other people can sit on before the carrying capacity of the benches is full?\nIf we know the answer to the above question i... |
64 | [
"88"
] | [
{
"content": "If Carlos randomly selects a chocolate from a box containing 50 chocolates, where 3 are caramels, twice as many are nougats, the number of truffles is equal to the number of caramels plus 6, and the remaining chocolates are peanut clusters, what is the percentage chance that he will pick a peanut ... | [
{
"content": "If Carlos randomly selects a chocolate from a box containing 50 chocolates, where 3 are caramels, twice as many are nougats, the number of truffles is equal to the number of caramels plus 6, and the remaining chocolates are peanut clusters, what is the percentage chance that he will pick a peanut ... |
50 | [
"48"
] | [
{
"content": "Bill decides to bring donuts to work for a meeting that day. He buys a box of donuts that has x in total in them. He eats 2 on the ride in because he's hungry. When he gets to the office, the secretary takes another 4 out of the box when he's not looking. Lastly, right before the meeting Bill ... | [
{
"content": "Bill decides to bring donuts to work for a meeting that day. He buys a box of donuts that has x in total in them. He eats 2 on the ride in because he's hungry. When he gets to the office, the secretary takes another 4 out of the box when he's not looking. Lastly, right before the meeting Bill ... |
50 | [
"100"
] | [
{
"content": "Out of all the gingerbread cookies that Anna is making, some have red hats, some have blue boots, and some have both red hats and blue boots. What percentage of the gingerbread men have red hats?",
"role": "user"
},
{
"content": "Let's use Python code to solve this problem.\n```python\... | [
{
"content": "Out of all the gingerbread cookies that Anna is making, some have red hats, some have blue boots, and some have both red hats and blue boots. What percentage of the gingerbread men have red hats?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sympy library.\n... |
15 | [
"3\\sqrt{73}"
] | [
{
"content": "Find the difference between the larger and the smaller root of the quadratic equation $$(x-3)(x+3) = 21x - 63.$$",
"role": "user"
},
{
"content": "We can solve this problem using Python's sympy library.\n```python\nfrom sympy import symbols, solve\n\n# Define the equation as a string\n... | [
{
"content": "Find the difference between the larger and the smaller root of the quadratic equation $$(x-3)(x+3) = 21x - 63.$$",
"role": "user"
},
{
"content": "To find the roots of the quadratic equation, we use a method called the quadratic formula.\nThe quadratic formula allows us to find the roo... |
7 | [
"11"
] | [
{
"content": "For how many integers $n$ does the condition $n^3 > -50$ and $n^3 < 50$ apply?",
"role": "user"
},
{
"content": "To solve this problem, we need to find integers $n$ such that $n^3$ is greater than $-50$ and less than $50$.\nWe can use sympy to solve this problem using the following cod... | [
{
"content": "For how many integers $n$ does the condition $n^3 > -50$ and $n^3 < 50$ apply?",
"role": "user"
},
{
"content": "The condition $n^3 > -50$ is equivalent to $n > -50^{1/3}$.\nThe condition $n^3 < 50$ is equivalent to $n < 50^{1/3}$.\nSo we need to find the number of integers $n$ between... |
-3 | [
"-log(8)"
] | [
{
"content": "Evaluate $\\log_{\\frac{1}{2}}8$.",
"role": "user"
},
{
"content": "To evaluate $\\log_{1/2} 8$, we can use the logarithm rules:\n```python\nfrom sympy import log, symbols\n\n# Define the symbol x\nx = symbols('x')\n\n# Define the logarithm and calculate its value\nlog_value = log(8, 1... | [
{
"content": "Evaluate $\\log_{\\frac{1}{2}}8$.",
"role": "user"
},
{
"content": "We can use sympy to compute this directly.\n```python\nfrom sympy import log, Pow\n\nlog(8, Pow(1/2, 1))\n```",
"role": "assistant"
},
{
"content": "```output\n-1.44269504088896*log(8)\n```",
"role": "u... |
4 | [
"2"
] | [
{
"content": "Suppose $a,$ $b,$ and $c$ are real numbers with $a + 2b + c = 4.$ Determine the highest value of\n\\[ab + ac + bc.\\]",
"role": "user"
},
{
"content": "Let's define the equation and use sympy to find the solution.\n```python\nimport sympy as sp\n\n# define the equation\na, b, c = sp.s... | [
{
"content": "Suppose $a,$ $b,$ and $c$ are real numbers with $a + 2b + c = 4.$ Determine the highest value of\n\\[ab + ac + bc.\\]",
"role": "user"
},
{
"content": "We can solve it using computer algebra system:\n```python\nimport sympy\n\na, b, c = sympy.symbols('a b c')\n\neq = a + 2 * b + c - 4... |
350 | [
"362"
] | [
{
"content": "Calculate the number of trailing zeros in the number $2000^{100} \\times 5^{50}$.",
"role": "user"
},
{
"content": "I will find the answer by writing a Python function to perform the multiplication, then find the number of trailing zeros in the result.\n```python\ndef multiply_and_find... | [
{
"content": "Calculate the number of trailing zeros in the number $2000^{100} \\times 5^{50}$.",
"role": "user"
},
{
"content": "The number of trailing zeros in $2000^{100} \\times 5^{50}$ is the number of trailing zeros in $2000^{100}$ plus the number of trailing zeros in $5^{50}$.\nLet's find the... |
92 | [
"\\frac{300}{7}"
] | [
{
"content": "Three-fourths of the parrots on Bird Island are green, and the remainder are blue. If there are X parrots total on Bird Island, how many of those parrots are blue?\nIf we know the answer to the above question is 23, what is the value of unknown variable X?",
"role": "user"
},
{
"conten... | [
{
"content": "Three-fourths of the parrots on Bird Island are green, and the remainder are blue. If there are X parrots total on Bird Island, how many of those parrots are blue?\nIf we know the answer to the above question is 23, what is the value of unknown variable X?",
"role": "user"
},
{
"conten... |
(-\infty,-\frac{1}{5}) | [
"[-1/5,\\infty)"
] | [
{
"content": "Find all values of $k$ so that the domain of\n\\[b(x) = \\frac{kx^2 + 2x - 5}{-5x^2 + 2x + k}\\]is the set of all real numbers.",
"role": "user"
},
{
"content": "To ensure that the domain of a function $f$ is the set of all real numbers, we need to ensure that the denominator is non-ze... | [
{
"content": "Find all values of $k$ so that the domain of\n\\[b(x) = \\frac{kx^2 + 2x - 5}{-5x^2 + 2x + k}\\]is the set of all real numbers.",
"role": "user"
},
{
"content": "Let's write down an equation for the denominator and use sympy to solve for $k$.\n```python\nimport sympy as sp\n\nx, k = sp... |
11 | [
"10"
] | [
{
"content": "Suppose that $g$ is a function and $g^{-1}$ is the inverse of $g$. If $g(4)=2$, $g(6)=3$, and $g(7)=8$, evaluate $g^{-1}\\left(g^{-1}(8)+g^{-1}(2)\\right)$.",
"role": "user"
},
{
"content": "Since $g$ is a function $g(x) = y$ is equivalent to $g^{-1}(y) = x$.\nTherefore, we have the fo... | [
{
"content": "Suppose that $g$ is a function and $g^{-1}$ is the inverse of $g$. If $g(4)=2$, $g(6)=3$, and $g(7)=8$, evaluate $g^{-1}\\left(g^{-1}(8)+g^{-1}(2)\\right)$.",
"role": "user"
},
{
"content": "Let's find the inverse function $g^{-1}$ by examining the table of values of $g$.\n$$g^{-1}(g(4... |
37 | [
"36"
] | [
{
"content": "Anna, Alison, and Jeff collect stamps. Anna had x stamps in her collection, Alison had 28 stamps in her collection, and Jeff had 31 stamps in his collection. Alison gave Anna half of her collection in exchange for a novel, and then Anna traded Jeff two bluebird stamps for one mountain stamp. Anna ... | [
{
"content": "Anna, Alison, and Jeff collect stamps. Anna had x stamps in her collection, Alison had 28 stamps in her collection, and Jeff had 31 stamps in his collection. Alison gave Anna half of her collection in exchange for a novel, and then Anna traded Jeff two bluebird stamps for one mountain stamp. Anna ... |
77 | [
"27"
] | [
{
"content": "Ms. Mitsuko told the class that if the average score on their quiz is higher than 75% then they will get a pizza party. There are 25 students in the class. One student is absent and has to take the test the next day. The average score of the students who took the test was x%. The lowest grade the ... | [
{
"content": "Ms. Mitsuko told the class that if the average score on their quiz is higher than 75% then they will get a pizza party. There are 25 students in the class. One student is absent and has to take the test the next day. The average score of the students who took the test was x%. The lowest grade the ... |
1025024 | [
"0"
] | [
{
"content": "What is the coefficient of $x^5$ in the expansion of $(x+2)^{14}$?",
"role": "user"
},
{
"content": "We can use sympy's expand() function to expand the given binomial and find the coefficient of $x^5$.\nHere's the Python solution.\n```python\nfrom sympy import expand, symbols\n\n# Defi... | [
{
"content": "What is the coefficient of $x^5$ in the expansion of $(x+2)^{14}$?",
"role": "user"
},
{
"content": "We can use sympy to get the polynomial for $(x+2)^{14}$.\n```python\nimport sympy as sp\n\nx = sp.Symbol('x')\nexpr = sp.sympify('(x+2)**14')\nprint(expr)\n```",
"role": "assistant"... |
6 | [
"8"
] | [
{
"content": "Consider a numbering system with base $b$. In this system, there are a total of 100 (one hundred in base 10) unique three-digit numbers that consist of distinct digits for each number. What is the value of the base $b$?",
"role": "user"
},
{
"content": "We can iterate through all possi... | [
{
"content": "Consider a numbering system with base $b$. In this system, there are a total of 100 (one hundred in base 10) unique three-digit numbers that consist of distinct digits for each number. What is the value of the base $b$?",
"role": "user"
},
{
"content": "Let's define a function that fin... |
66 | [
"58"
] | [
{
"content": "During the lunch rush, a taco truck is selling soft tacos for $2 each and hard shell tacos for $5 each. The first group of customers, a family, purchases four hard shell tacos and three soft tacos. The remaining customers in the lunch rush each buy two soft tacos. If there were a total of ten cust... | [
{
"content": "During the lunch rush, a taco truck is selling soft tacos for $2 each and hard shell tacos for $5 each. The first group of customers, a family, purchases four hard shell tacos and three soft tacos. The remaining customers in the lunch rush each buy two soft tacos. If there were a total of ten cust... |
\frac{56.25\sqrt{3}}{2} | [
"\\frac{225}{2}"
] | [
{
"content": "A right triangle has a hypotenuse of 15 inches and one of the non-right angles measures $30^{\\circ}$. What is the area of this triangle?",
"role": "user"
},
{
"content": "To calculate the area of the triangle, we need the length of the two sides that form the right angle.\nWe can use ... | [
{
"content": "A right triangle has a hypotenuse of 15 inches and one of the non-right angles measures $30^{\\circ}$. What is the area of this triangle?",
"role": "user"
},
{
"content": "The correct answer is 25, but we will prove it mathematically.\nLet us denote the triangle's catheti by a and b.\n... |
202 | [
"203"
] | [
{
"content": "If $a = 10^{5} \\cdot 10^{-3}$, $b = 10^{3} \\cdot 10^{-1}$, and $c = 10^{2} \\cdot 10^{-2}$, calculate the value of $7a + 5b + 3c \\pmod{1001}$. Express your answer as a residue from $0$ to $1000$, inclusive.",
"role": "user"
},
{
"content": "We'll use sympy to perform the calculation... | [
{
"content": "If $a = 10^{5} \\cdot 10^{-3}$, $b = 10^{3} \\cdot 10^{-1}$, and $c = 10^{2} \\cdot 10^{-2}$, calculate the value of $7a + 5b + 3c \\pmod{1001}$. Express your answer as a residue from $0$ to $1000$, inclusive.",
"role": "user"
},
{
"content": "Let's first calculate $a$, $b$, and $c$ an... |
83 | [
"165"
] | [
{
"content": "If Nathan purchased a large box of bananas consisting of six bunches with eight bananas in each bunch and five bunches with seven bananas in each bunch, what is the total number of bananas that Nathan has?",
"role": "user"
},
{
"content": "The number of bananas is simply 6 multiplied b... | [
{
"content": "If Nathan purchased a large box of bananas consisting of six bunches with eight bananas in each bunch and five bunches with seven bananas in each bunch, what is the total number of bananas that Nathan has?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n`... |
1 | [
"3"
] | [
{
"content": "The Grammar club has 20 members: 10 boys and 10 girls. A 4-person committee is chosen at random. What is the probability that the committee has at least 1 boy and at least X girl?\nIf we know the answer to the above question is \\frac{295}{323}, what is the value of unknown variable X?",
"ro... | [
{
"content": "The Grammar club has 20 members: 10 boys and 10 girls. A 4-person committee is chosen at random. What is the probability that the committee has at least 1 boy and at least X girl?\nIf we know the answer to the above question is \\frac{295}{323}, what is the value of unknown variable X?",
"ro... |
1.5 | [
"3"
] | [
{
"content": "Amanda charges $20.00 per hour to help clean out and organize a person's home. She has 5 x hours appointments on Monday, a 3-hours appointment on Tuesday and 2 2-hours appointments on Thursday. On Saturday, she will spend 6 hours at one client's house. How much money will she make this week?\nI... | [
{
"content": "Amanda charges $20.00 per hour to help clean out and organize a person's home. She has 5 x hours appointments on Monday, a 3-hours appointment on Tuesday and 2 2-hours appointments on Thursday. On Saturday, she will spend 6 hours at one client's house. How much money will she make this week?\nI... |
2 | [
"7"
] | [
{
"content": "The solution of $8x+1\\equiv 5 \\pmod{12}$ is $x\\equiv a\\pmod{m}$ for some positive integers $m\\geq X and $a<m$. Find $a+m$. The answer is 5. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "Let's solve this problem using sympy:\n```python\nfrom sympy impor... | [
{
"content": "The solution of $8x+1\\equiv 5 \\pmod{12}$ is $x\\equiv a\\pmod{m}$ for some positive integers $m\\geq X and $a<m$. Find $a+m$. The answer is 5. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "Let's use sympy to solve the congruence equation i.e. $8x + 1 \\eq... |
3 | [
"0.5"
] | [
{
"content": "James buys a jar of hot sauce. Each serving is .5 ounces. He uses x servings every day. The container will last for 20 days if it is 2 ounces less than 1 quart. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sympy l... | [
{
"content": "James buys a jar of hot sauce. Each serving is .5 ounces. He uses x servings every day. The container will last for 20 days if it is 2 ounces less than 1 quart. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sympy l... |
3 | [
"9"
] | [
{
"content": "What single digit replaces $\\star$ in the equation $\\star4_7 = \\star1_{8}$ to make it true?",
"role": "user"
},
{
"content": "Let's write a python script to iterate through the possible digits to see which one makes the equation true.\n```python\nfor star in range(10):\n # conver... | [
{
"content": "What single digit replaces $\\star$ in the equation $\\star4_7 = \\star1_{8}$ to make it true?",
"role": "user"
},
{
"content": "We can write a python program to find the correct digit using the modulo operator and simple integer arithmetic.\n```python\nfor digit in range(10):\n if ... |
0 | [
"2"
] | [
{
"content": "What is the modulo $4$ remainder of the sum $2+4+6+8+10+ \\ldots + 244+246+248?$",
"role": "user"
},
{
"content": "I will find the answer by writing a Python program to perform modular arithmetic.\n```python\ndef modulo(num, mod):\n return num % mod\n\nsum = 0\nfor i in range(2, 249... | [
{
"content": "What is the modulo $4$ remainder of the sum $2+4+6+8+10+ \\ldots + 244+246+248?$",
"role": "user"
},
{
"content": "Let's break down the problem into smaller chunks.\n```python\nlst = list(range(2, 249, 2))\nlst_sum = sum(lst)\nlst_remainder = lst_sum % 4\nlst_remainder\n```",
"role... |
2 | [
"1"
] | [
{
"content": "If $x = \\frac{9 \\pi}{4} + \\pi n$ and $y = \\frac{5 \\pi}{4} + \\pi m$ for any integers $n$ and $m$, find the value of $\\tan(x) \\cdot \\tan(y) + \\tan^2(x)$.",
"role": "user"
},
{
"content": "```python\nfrom sympy import tan, pi, simplify\n\nx = (9 * pi) / 4 + pi * 2\ny = (5 * pi) ... | [
{
"content": "If $x = \\frac{9 \\pi}{4} + \\pi n$ and $y = \\frac{5 \\pi}{4} + \\pi m$ for any integers $n$ and $m$, find the value of $\\tan(x) \\cdot \\tan(y) + \\tan^2(x)$.",
"role": "user"
},
{
"content": "For this one we can actually use sympy to calculate the exact answer.\n```python\nfrom sym... |
\sqrt{10} | [
"2r"
] | [
{
"content": "Determine the diameter of the circle that is inscribed in triangle ABC, given that AB = 11, AC = 6, and BC = 7. Express your answer in simplest radical form.",
"role": "user"
},
{
"content": "We can use Heron's formula to calculate the area of the triangle and then the radius of the in... | [
{
"content": "Determine the diameter of the circle that is inscribed in triangle ABC, given that AB = 11, AC = 6, and BC = 7. Express your answer in simplest radical form.",
"role": "user"
},
{
"content": "Let's use sympy to find the area of the triangle.\n```python\nimport sympy as sp\n\n# define t... |
120 | [
""
] | [
{
"content": "Given matrices $A = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}$, $B = \\begin{pmatrix} e & f \\\\ g & h \\end{pmatrix}$, and $C = \\begin{pmatrix} j & k \\\\ l & m \\end{pmatrix}$ with $\\det(A) = 4$, $\\det(B) = 5$, and $\\det(C) = 6$, find the determinant of the matrix $M = \\begin{pmatrix... | [
{
"content": "Given matrices $A = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}$, $B = \\begin{pmatrix} e & f \\\\ g & h \\end{pmatrix}$, and $C = \\begin{pmatrix} j & k \\\\ l & m \\end{pmatrix}$ with $\\det(A) = 4$, $\\det(B) = 5$, and $\\det(C) = 6$, find the determinant of the matrix $M = \\begin{pmatrix... |
-5 | [
"2-\\sqrt{29}"
] | [
{
"content": "Find the least integer whose square is 25 more than four times the integer.",
"role": "user"
},
{
"content": "Let's denote the integer as $n$.\nWe need to solve the following equation:\n$n^2 = 4n + 25$.\nWe can rearrange the equation as $n^2 - 4n - 25 = 0$.\nNow we need to find the roo... | [
{
"content": "Find the least integer whose square is 25 more than four times the integer.",
"role": "user"
},
{
"content": "Let's denote unknown number by $x$.\nThen according to the problem $x ^ 2 = 4x + 25$.\nLet's solve this equation using sympy.\n```python\nfrom sympy import symbols, solve\n\nx ... |
2 | [
""
] | [
{
"content": "Stella’s antique shop has 3 dolls, x clocks and 5 glasses for sale. She sells the dolls for $5 each. The clocks are priced at $15 each. The glasses are priced at $4 each. If she spent $40 to buy everything and she sells all of her merchandise, She will make 25 profit. What is the value of unknown ... | [
{
"content": "Stella’s antique shop has 3 dolls, x clocks and 5 glasses for sale. She sells the dolls for $5 each. The clocks are priced at $15 each. The glasses are priced at $4 each. If she spent $40 to buy everything and she sells all of her merchandise, She will make 25 profit. What is the value of unknown ... |
\frac{2}{15} | [
"0.53333"
] | [
{
"content": "Don is holding a bottle containing $\\frac{1}{5}$ gallon of milk. His friend Rachel sips $\\frac{2}{3}$ of the milk from the bottle. What is the volume of milk that Rachel consumed?",
"role": "user"
},
{
"content": "```python\nfrom fractions import Fraction\n\ndon_amount = Fraction(1, ... | [
{
"content": "Don is holding a bottle containing $\\frac{1}{5}$ gallon of milk. His friend Rachel sips $\\frac{2}{3}$ of the milk from the bottle. What is the volume of milk that Rachel consumed?",
"role": "user"
},
{
"content": "Let's first calculate the total volume of the milk in the bottle. We k... |
20 | [
"16"
] | [
{
"content": "Consider Rural School USA, with an enrollment of 105 students - 60 of them boys and the remaining 45 girls. If on a particular school day, $\\frac{1}{10}$ of the boys and $\\frac{1}{3}$ of the girls are absent, how much of the school population does not show up, when expressed as a percentage?",
... | [
{
"content": "Consider Rural School USA, with an enrollment of 105 students - 60 of them boys and the remaining 45 girls. If on a particular school day, $\\frac{1}{10}$ of the boys and $\\frac{1}{3}$ of the girls are absent, how much of the school population does not show up, when expressed as a percentage?",
... |
11 | [
"12"
] | [
{
"content": "Linda owns a store. She sells jeans at x dollars each and tees at 8 dollars each. If she sold 7 tees and 4 jeans in a day, how much money, in dollars, did she have at the end of the day?\nIf we know the answer to the above question is 100, what is the value of unknown variable x?",
"role": "us... | [
{
"content": "Linda owns a store. She sells jeans at x dollars each and tees at 8 dollars each. If she sold 7 tees and 4 jeans in a day, how much money, in dollars, did she have at the end of the day?\nIf we know the answer to the above question is 100, what is the value of unknown variable x?",
"role": "us... |
56 | [
"88"
] | [
{
"content": "An open-air party is scheduled for tomorrow, and Sheila has been invited; the event will proceed irrespective of the weather. Sheila is considering whether to attend, with a $20\\%$ chance of her going if it is raining and an $80\\%$ chance if it is sunny. With a forecast indicating a $40\\%$ chan... | [
{
"content": "An open-air party is scheduled for tomorrow, and Sheila has been invited; the event will proceed irrespective of the weather. Sheila is considering whether to attend, with a $20\\%$ chance of her going if it is raining and an $80\\%$ chance if it is sunny. With a forecast indicating a $40\\%$ chan... |
10 | [
"2"
] | [
{
"content": "Mr. Reyansh has a dairy farm with 40 cows. Each cow on the farm drinks 80 liters of water daily. He also has a sheep ranch with x times the number of cows, with each sheep drinking 1/4 times as much water as a cow does. How many liters of water does Mr. Reyansh used to water all of his animals in ... | [
{
"content": "Mr. Reyansh has a dairy farm with 40 cows. Each cow on the farm drinks 80 liters of water daily. He also has a sheep ranch with x times the number of cows, with each sheep drinking 1/4 times as much water as a cow does. How many liters of water does Mr. Reyansh used to water all of his animals in ... |
194 | [
"4"
] | [
{
"content": "Assume $f(x)=3x^3+2$ and you know that $f^{-1}(y)=4$ for some number $y$. What is the value of $y$?",
"role": "user"
},
{
"content": "To solve for $y$, we can use Python's sympy library.\n```python\nfrom sympy import symbols, solve\n\ny = symbols('y')\nf_inv = 4\n\n# Define function f(... | [
{
"content": "Assume $f(x)=3x^3+2$ and you know that $f^{-1}(y)=4$ for some number $y$. What is the value of $y$?",
"role": "user"
},
{
"content": "We can solve this problem using algebraic substitution.\n```python\nfrom sympy import symbols, Eq, solve, simplify\n\n# Define the functions and given v... |
12 | [
"3"
] | [
{
"content": "To achieve the same efficacy as before, how many green tea leaves should Anderson add to a new batch of mud if he adds three sprigs of mint for every batch, and he adds two green tea leaves for every sprig of mint, but the other ingredients he adds are now only half as effective due to switching t... | [
{
"content": "To achieve the same efficacy as before, how many green tea leaves should Anderson add to a new batch of mud if he adds three sprigs of mint for every batch, and he adds two green tea leaves for every sprig of mint, but the other ingredients he adds are now only half as effective due to switching t... |
-\frac{25}{4} | [
"-12.5"
] | [
{
"content": "The quadratic $x^2 - 5x$ is converted to vertex form, which is represented by $a(x - h)^2 + k$. What does $k$ equal to in this case?",
"role": "user"
},
{
"content": "Let's find the vertex form of the quadratic function $f(x) = x^2 - 5x$ using sympy.\n```python\nfrom sympy import symbo... | [
{
"content": "The quadratic $x^2 - 5x$ is converted to vertex form, which is represented by $a(x - h)^2 + k$. What does $k$ equal to in this case?",
"role": "user"
},
{
"content": "We can use sympy to convert the quadratic function into the vertex form.\n```python\nfrom sympy import symbols, Eq, sol... |
15 | [
"1101"
] | [
{
"content": "Compute the smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4.",
"role": "user"
},
{
"content": "Let's iterate over the numbers greater than 5 and check if they are palindromes in both base 2 and base 4.\n```python\nnum = 5\n\nwhile... | [
{
"content": "Compute the smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4.",
"role": "user"
},
{
"content": "Let's iterate over all numbers greater than 5, convert them to binary and check if they're palindromes:\n```python\ndef is_palindrome(n... |
-\frac{15}{4} | [
"2+534+614"
] | [
{
"content": "Calculate the value of $p^2 + q^2 + r^2$ where $p$, $q$, and $r$ are the solutions to the polynomial \\[2x^3 - x^2 + 4x + 10 = 0.\\]",
"role": "user"
},
{
"content": "We can solve this problem using sympy library.\n```python\nfrom sympy import solve, symbols, simplify\n\n# Define the s... | [
{
"content": "Calculate the value of $p^2 + q^2 + r^2$ where $p$, $q$, and $r$ are the solutions to the polynomial \\[2x^3 - x^2 + 4x + 10 = 0.\\]",
"role": "user"
},
{
"content": "We have found the roots of the polynomial in the previous question.\nLet's calculate $p^2 + q^2 + r^2$ using sympy:\n``... |
1 | [
"-31"
] | [
{
"content": "Let \\[f(x) = \\left\\{\n\\begin{array}{cl} 2x+3 & \\text{ if }x < 5, \\\\\nx-10 & \\text{ if } x \\geq 5.\n\\end{array}\n\\right.\\] What is $f(f(f(3)))$?",
"role": "user"
},
{
"content": "Let's apply the function three times using sympy.\n```python\nfrom sympy import Piecewise\n\n# d... | [
{
"content": "Let \\[f(x) = \\left\\{\n\\begin{array}{cl} 2x+3 & \\text{ if }x < 5, \\\\\nx-10 & \\text{ if } x \\geq 5.\n\\end{array}\n\\right.\\] What is $f(f(f(3)))$?",
"role": "user"
},
{
"content": "Let's calculate all the values $f(3)$, $f(f(3))$ and $f(f(f(3)))$.\n```python\nfrom sympy import... |
10 | [
""
] | [
{
"content": "Javier is selling donuts to raise money for a new game. He wants to raise $96. He buys each dozen donuts for $2.40 and then sells each donut for $1. How many dozen donuts does he need to buy and sell to reach his goal?",
"role": "user"
},
{
"content": "Let's solve this problem using Py... | [
{
"content": "Javier is selling donuts to raise money for a new game. He wants to raise $96. He buys each dozen donuts for $2.40 and then sells each donut for $1. How many dozen donuts does he need to buy and sell to reach his goal?",
"role": "user"
},
{
"content": "Let's solve this problem using Py... |
3 | [
"-12"
] | [
{
"content": "For the lines with equations $y = 2x + 13$ and $6y + ax = 6$, find the value of $a$ that makes these lines form a 90 degree angle.",
"role": "user"
},
{
"content": "To find the value of $a$ that makes the lines form a 90 degree angle, we first need to determine the slopes of the lines.... | [
{
"content": "For the lines with equations $y = 2x + 13$ and $6y + ax = 6$, find the value of $a$ that makes these lines form a 90 degree angle.",
"role": "user"
},
{
"content": "Two lines form a 90 degree angle when their slopes are negative reciprocals of each other.\nLet's find the equation $y = ... |
10 | [
"26"
] | [
{
"content": "Last week, Charles bought a t-shirt for $30, a backpack for x, and a blue cap for $5. The store gave him a discount and, in total, he only spent $43. How much of a discount did they give him, in dollars?\nIf we know the answer to the above question is 2, what is the value of unknown variable x?",
... | [
{
"content": "Last week, Charles bought a t-shirt for $30, a backpack for x, and a blue cap for $5. The store gave him a discount and, in total, he only spent $43. How much of a discount did they give him, in dollars?\nIf we know the answer to the above question is 2, what is the value of unknown variable x?",
... |
8 | [
"4"
] | [
{
"content": "Vivian plays 10 Spotify songs every day. Her best friend Clara plays 2 fewer songs each day. If in June they didn't play any song during the weekends only, and there were x weekend days in June, The total number of songs they both listened to in that month is 396. What is the value of unknown vari... | [
{
"content": "Vivian plays 10 Spotify songs every day. Her best friend Clara plays 2 fewer songs each day. If in June they didn't play any song during the weekends only, and there were x weekend days in June, The total number of songs they both listened to in that month is 396. What is the value of unknown vari... |
85 | [
"95"
] | [
{
"content": "Gretchen, Mitzi, and Beth went bowling together. Gretchen bowled a 120. Mitzi bowled a 113. Beth bowled an x. What was their average bowling score?\nIf we know the answer to the above question is 106, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's use ... | [
{
"content": "Gretchen, Mitzi, and Beth went bowling together. Gretchen bowled a 120. Mitzi bowled a 113. Beth bowled an x. What was their average bowling score?\nIf we know the answer to the above question is 106, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solv... |
57 | [
""
] | [
{
"content": "What is the largest divisor of 342 that is also a factor of 285?",
"role": "user"
},
{
"content": "To compute the largest common divisor of the two numbers, we can use Python's sympy library.\n```python\nfrom sympy import gcd\n\nnum1 = 342\nnum2 = 285\n\ngcd(num1, num2)\n```",
"rol... | [
{
"content": "What is the largest divisor of 342 that is also a factor of 285?",
"role": "user"
},
{
"content": "Since we're looking for the largest divisor of 342 that is also a factor of 285, let's compute all its factors and then check whether it divides 285.\nWe will use sympy to get the divisor... |
\frac{3}{5} | [
"30.46"
] | [
{
"content": "A cylindrical water tank is $\\frac{1}{5}$ full with 4 liters of water. If eight liters were added to the tank, to what fraction of its full capacity would it be filled?",
"role": "user"
},
{
"content": "Since $\\frac{1}{5}$th of the tank is filled with 4 liters, we know that the tank ... | [
{
"content": "A cylindrical water tank is $\\frac{1}{5}$ full with 4 liters of water. If eight liters were added to the tank, to what fraction of its full capacity would it be filled?",
"role": "user"
},
{
"content": "Let's define `height_of_water_1` to be the height of the water when it is $\\frac{... |
10 | [
"60"
] | [
{
"content": "How many different combinations are there for choosing three socks from a drawer containing blue, brown, black, red, and purple socks, without considering the order of the socks?",
"role": "user"
},
{
"content": "We have 5 color choices for the first sock, 4 for the second sock and 3 f... | [
{
"content": "How many different combinations are there for choosing three socks from a drawer containing blue, brown, black, red, and purple socks, without considering the order of the socks?",
"role": "user"
},
{
"content": "The number of combinations is the total number of ways to choose 3 socks ... |
-11 | [
""
] | [
{
"content": "What is the minimum value of x that makes the equation |3x + 7| = 26 true?",
"role": "user"
},
{
"content": "To solve this problem, we can start by noticing that |3x + 7| = 26 implies that either 3x + 7 = 26 or 3x + 7 = -26.\nLet's use sympy to find the values of x that satisfy these t... | [
{
"content": "What is the minimum value of x that makes the equation |3x + 7| = 26 true?",
"role": "user"
},
{
"content": "The equation |3x + 7| = 26 is equivalent to either 3x + 7 = 26 or 3x + 7 = -26.\nLet's find the solution for each equation using sympy.\n```python\nfrom sympy import symbols, Eq... |
20 | [
""
] | [
{
"content": "Given $\\|\\mathbf{p}\\| = 5,$ find $\\|-4 \\mathbf{p}\\|.$",
"role": "user"
},
{
"content": "To calculate the value of $\\|-4 \\mathbf{p}\\|$, we can use Python's numerical libraries.\n```python\nfrom sympy import Rational\n\n# value of $\\|\\mathbf{p}\\|$\np = 5\n\n# value of $\\|-4 ... | [
{
"content": "Given $\\|\\mathbf{p}\\| = 5,$ find $\\|-4 \\mathbf{p}\\|.$",
"role": "user"
},
{
"content": "I am not sure what is meant by \"find\" here. But I can find it if you want me to.\nLet's define the vector in sympy and compute its magnitude.\n```python\nimport sympy as sp\nfrom sympy impor... |
200 | [
"140"
] | [
{
"content": "James listens to super-fast music. It is x beats per minute. He listens to 2 hours of music a day. How many beats does he hear per week?\nIf we know the answer to the above question is 168000, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve thi... | [
{
"content": "James listens to super-fast music. It is x beats per minute. He listens to 2 hours of music a day. How many beats does he hear per week?\nIf we know the answer to the above question is 168000, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve thi... |
2010 | [
"1995"
] | [
{
"content": "Which multiple of 15 is the closest to 2009?",
"role": "user"
},
{
"content": "To find the closest multiple of 15 to 2009, we can use Python's sympy library to iterate over multiples of 15 and check their distance to 2009.\n```python\nfrom sympy import symbols, Symbol\n\nx = Symbol('x'... | [
{
"content": "Which multiple of 15 is the closest to 2009?",
"role": "user"
},
{
"content": "Let's write a simple python program to check the closest number to 2009 that is divisible by 15.\n```python\nclosest_num = 2009\n\nnum = closest_num\nwhile num % 15 != 0:\n num -= 1\nprint(num)\n```",
... |
12 | [
"5"
] | [
{
"content": "Find the smallest positive integer $c$ such that there exist positive integers $a$ and $b$ satisfying $a-b=6$, $c-a=3$, and $\\text{gcd}\\left(\\frac{a^3+b^3+c^3-3abc}{a+b+c}, abc\\right) = 27$.",
"role": "user"
},
{
"content": "Let's find the solutions for $a$, $b$, and $c$ using symp... | [
{
"content": "Find the smallest positive integer $c$ such that there exist positive integers $a$ and $b$ satisfying $a-b=6$, $c-a=3$, and $\\text{gcd}\\left(\\frac{a^3+b^3+c^3-3abc}{a+b+c}, abc\\right) = 27$.",
"role": "user"
},
{
"content": "Let's write some code to test values of $c$ and return th... |
7 | [
"6"
] | [
{
"content": "If Juanita orders a \"Build Your Own Hot Brownie\" dessert from a local restaurant, which includes a brownie for $2.50, 2 scoops of ice cream for $1.00 each, double syrup for $0.50 each, and nuts for $1.50, what will be the total cost of her dessert?",
"role": "user"
},
{
"content": "L... | [
{
"content": "If Juanita orders a \"Build Your Own Hot Brownie\" dessert from a local restaurant, which includes a brownie for $2.50, 2 scoops of ice cream for $1.00 each, double syrup for $0.50 each, and nuts for $1.50, what will be the total cost of her dessert?",
"role": "user"
},
{
"content": "L... |
29 | [
"\\frac{18}{25}"
] | [
{
"content": "If $n$ is an integer and $0 \\leq n < 101$, what is the value of $n$ for which $100n$ is congruent to $72$ modulo $101$?",
"role": "user"
},
{
"content": "Let's try to solve this problem in python:\n```python\nN = 101\n\n# Try all values of n between 0 and 100 (inclusive)\nfor n in ran... | [
{
"content": "If $n$ is an integer and $0 \\leq n < 101$, what is the value of $n$ for which $100n$ is congruent to $72$ modulo $101$?",
"role": "user"
},
{
"content": "Let $M = 100$ and $O = 101$.\nBy definition of congruence, if $100n \\equiv 72 \\pmod{101}$, then $100n-72$ is divisible by 101. \n... |
70 | [
""
] | [
{
"content": "Two buses leave a pick-up point station with 60% and x% of capacity full, respectively. If the people in the buses are all employees of a company, and the buses have a capacity of 150, calculate the total number of the employees in the two buses combined?\nIf we know the answer to the above questi... | [
{
"content": "Two buses leave a pick-up point station with 60% and x% of capacity full, respectively. If the people in the buses are all employees of a company, and the buses have a capacity of 150, calculate the total number of the employees in the two buses combined?\nIf we know the answer to the above questi... |
5 | [
"\\frac{16}{5}"
] | [
{
"content": "A line with slope 3 intersects a line with slope X at the point $(10,15)$. The distance between the $x$-intercepts of these two lines is 2. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "I can find the answer by solving a system of equations. Let's assume we... | [
{
"content": "A line with slope 3 intersects a line with slope X at the point $(10,15)$. The distance between the $x$-intercepts of these two lines is 2. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "Let's use sympy to solve for $X$.\n```python\nimport sympy as sp\n\nx, ... |
20 | [
"50"
] | [
{
"content": "Mark wants to tip his server x% on a $200 check. If his friend agrees to kick in $10, how much should Mark add?\nIf we know the answer to the above question is 30, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sympy l... | [
{
"content": "Mark wants to tip his server x% on a $200 check. If his friend agrees to kick in $10, how much should Mark add?\nIf we know the answer to the above question is 30, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n``... |
6 | [
"28"
] | [
{
"content": "How many ways are there to divide a group of 6 friends among the basketball team, the soccer team, and the track team? (Each team could have anywhere from 0 to X of the friends on it. Assume the friends are distinguishable.)\nIf we know the answer to the above question is 729, what is the value ... | [
{
"content": "How many ways are there to divide a group of 6 friends among the basketball team, the soccer team, and the track team? (Each team could have anywhere from 0 to X of the friends on it. Assume the friends are distinguishable.)\nIf we know the answer to the above question is 729, what is the value ... |
56 | [
"54.5"
] | [
{
"content": "Two days ago, the temperature in the morning went up 1.5 degrees every 2 hours. If the temperature was 50 degrees at 3 A.M., what was the temperature at 11 A.M.?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\ninitial_temp = 50\ndegree_per_two_... | [
{
"content": "Two days ago, the temperature in the morning went up 1.5 degrees every 2 hours. If the temperature was 50 degrees at 3 A.M., what was the temperature at 11 A.M.?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\ninitial_temperature = 50\nmorning_... |
50 | [
"150"
] | [
{
"content": "April went to a concert that has two bands. 2/3 of the audience was there for the second band and 1/3 was there for the first band. x% of the audience there for the second band is under the age of 30. Of this group, 60% are women and there are 20 men. How many people are at the concert?\nIf we kno... | [
{
"content": "April went to a concert that has two bands. 2/3 of the audience was there for the second band and 1/3 was there for the first band. x% of the audience there for the second band is under the age of 30. Of this group, 60% are women and there are 20 men. How many people are at the concert?\nIf we kno... |
110 | [
"500"
] | [
{
"content": "Each of the three Morales sisters owns an orange grove that has x trees. Each orange tree produces medium-sized oranges. At harvest time, Gabriela's grove produced 600 oranges per tree, while Alba harvested 400 per tree. Each of Maricela's trees produced 500 oranges. With such a huge harvest, the ... | [
{
"content": "Each of the three Morales sisters owns an orange grove that has x trees. Each orange tree produces medium-sized oranges. At harvest time, Gabriela's grove produced 600 oranges per tree, while Alba harvested 400 per tree. Each of Maricela's trees produced 500 oranges. With such a huge harvest, the ... |
320 | [
"648"
] | [
{
"content": "If you list all the odd numbers with three distinct digits between $100$ and $999$, how many such numbers would there be?",
"role": "user"
},
{
"content": "Let's list out all odd numbers between 100 and 999 with distinct digits.\n```python\ndef has_repeated_digits(num):\n digits = [... | [
{
"content": "If you list all the odd numbers with three distinct digits between $100$ and $999$, how many such numbers would there be?",
"role": "user"
},
{
"content": "We can iterate through all numbers from 100 to 999 and count only ones with 3 distinct digits:\n```python\ncount = 0\n\nfor num in... |
20 | [
"24"
] | [
{
"content": "Triangle $ABC$ has sides of $6$ units, $8$ units, and $10$ units. The width of a rectangle, whose area is equal to the area of the triangle, is $4$ units. What is the perimeter of this rectangle, in units?",
"role": "user"
},
{
"content": "We can use sympy to solve this problem.\n```py... | [
{
"content": "Triangle $ABC$ has sides of $6$ units, $8$ units, and $10$ units. The width of a rectangle, whose area is equal to the area of the triangle, is $4$ units. What is the perimeter of this rectangle, in units?",
"role": "user"
},
{
"content": "Let's first check whether it is a right triang... |
(1,3) | [
"(1,1)"
] | [
{
"content": "Determine the ordered pair $(m,n)$, where $m$ and $n$ are positive integers that satisfy the equation $14mn = 55 - 7m - 2n$.",
"role": "user"
},
{
"content": "I will represent the answer in a tuple $(m, n)$.\nLet's solve the equation symbolically using sympy.\n```python\nfrom sympy imp... | [
{
"content": "Determine the ordered pair $(m,n)$, where $m$ and $n$ are positive integers that satisfy the equation $14mn = 55 - 7m - 2n$.",
"role": "user"
},
{
"content": "To solve this problem, we need to find integer solutions to the given equation $14mn = 55 - 7m - 2n$.\nWe can rewrite the equat... |
2.4875 | [
"1.4875"
] | [
{
"content": "John and Emily are having a pizza party. John has $\\frac{37}{80}$ of a pizza and buys another pizza and a half, then gives $\\frac{3}{5}$ of a pizza to his friend. Emily has $2$ pizzas and eats $\\frac{7}{8}$ of one. How much pizza do they have left in total in decimal form?",
"role": "user"
... | [
{
"content": "John and Emily are having a pizza party. John has $\\frac{37}{80}$ of a pizza and buys another pizza and a half, then gives $\\frac{3}{5}$ of a pizza to his friend. Emily has $2$ pizzas and eats $\\frac{7}{8}$ of one. How much pizza do they have left in total in decimal form?",
"role": "user"
... |
500 | [
"100"
] | [
{
"content": "Maria found a store that sells handmade sweaters for $30 and a handmade scarf for $20. She wants to buy one for everyone in her family. She will buy 6 sweaters and 6 scarves. If she has saved x, how much will be left in her savings after buying all these?\nIf we know the answer to the above questi... | [
{
"content": "Maria found a store that sells handmade sweaters for $30 and a handmade scarf for $20. She wants to buy one for everyone in her family. She will buy 6 sweaters and 6 scarves. If she has saved x, how much will be left in her savings after buying all these?\nIf we know the answer to the above questi... |
6 | [
"10"
] | [
{
"content": "A certain ellipse is tangent to both the $x$-axis and the $y$-axis, and its foci are at $(2, -3 + \\sqrt{5})$ and $(2, -3 - \\sqrt{5}).$ Find the length of the major axis.",
"role": "user"
},
{
"content": "The focii of an ellipse are the points $F_1$ and $F_2$ lying on opposite sides ... | [
{
"content": "A certain ellipse is tangent to both the $x$-axis and the $y$-axis, and its foci are at $(2, -3 + \\sqrt{5})$ and $(2, -3 - \\sqrt{5}).$ Find the length of the major axis.",
"role": "user"
},
{
"content": "The ellipse is symmetrical with respect to the axis passing through the foci.\n... |
4 | [
"1"
] | [
{
"content": "The local aquarium has x dolphins that each require 3 hours of training daily. The aquarium has 2 trainers and they want to split the hours they spend training the dolphins equally. Each trainer will spend 6 hours training the dolphins. What is the value of unknown variable x?",
"role": "user"... | [
{
"content": "The local aquarium has x dolphins that each require 3 hours of training daily. The aquarium has 2 trainers and they want to split the hours they spend training the dolphins equally. Each trainer will spend 6 hours training the dolphins. What is the value of unknown variable x?",
"role": "user"... |
16 | [
"21"
] | [
{
"content": "If the combined length of Jenna's and Bill's eels is 64 inches and Jenna's eel is 1/3 the length of Bill's eel, what is the length of Jenna's eel?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\n# define a variable to represent the total length... | [
{
"content": "If the combined length of Jenna's and Bill's eels is 64 inches and Jenna's eel is 1/3 the length of Bill's eel, what is the length of Jenna's eel?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\nlength_total = 64\nlength_jenna = 1 / 3\nlength_b... |
3 | [
""
] | [
{
"content": "Circles of radius X and $6$ are externally tangent to each other and are internally tangent to a circle of radius $9$. The circle of radius $9$ has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.\n[asy] pointpen = black; pathpen = bl... | [
{
"content": "Circles of radius X and $6$ are externally tangent to each other and are internally tangent to a circle of radius $9$. The circle of radius $9$ has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.\n[asy] pointpen = black; pathpen = bl... |
\frac{29}{32} | [
"0.847412109375"
] | [
{
"content": "In the first week of January, the probability of it snowing on any of the first three days is one-third, and for each of the following four days, the probability is one-fourth. Determine the probability that it snows on at least one day during this first week.",
"role": "user"
},
{
"co... | [
{
"content": "In the first week of January, the probability of it snowing on any of the first three days is one-third, and for each of the following four days, the probability is one-fourth. Determine the probability that it snows on at least one day during this first week.",
"role": "user"
},
{
"co... |
4 | [
"24"
] | [
{
"content": "When $19^{1999}$ is divided by a quarter century, what is the residual value?",
"role": "user"
},
{
"content": "We can use modular arithmetic to solve this problem.\n```python\nfrom sympy import Rational\n\nnum = 19**1999\nmodulus = 25\n\nresidue = num % modulus\n\nprint(residue)\n```"... | [
{
"content": "When $19^{1999}$ is divided by a quarter century, what is the residual value?",
"role": "user"
},
{
"content": "Let's first find out how many times 19 goes into 1999.\nWe can do this by repeatedly subtracting 19 from 1999 until we can't anymore.\n```python\n# Let's use sympy to find th... |
51 | [
"57"
] | [
{
"content": "If Susan is 15 years old, Arthur is 2 years older than Susan, and Bob is 11 years old, with Tom being 3 years younger than Bob, what is the total age of all four siblings in the family, including Susan, Arthur, Tom, and Bob?",
"role": "user"
},
{
"content": "Let's solve this problem us... | [
{
"content": "If Susan is 15 years old, Arthur is 2 years older than Susan, and Bob is 11 years old, with Tom being 3 years younger than Bob, what is the total age of all four siblings in the family, including Susan, Arthur, Tom, and Bob?",
"role": "user"
},
{
"content": "Let's solve this problem us... |
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