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gt stringlengths 1 39	rej listlengths 1 1	chosen listlengths 4 12	rejected listlengths 4 14
\frac{1}{4}	[ "\\frac{1}{2}" ]	[ { "content": "What is the sum of the following infinite geometric series: $\\frac{1}{3} - \\frac{1}{9} + \\frac{1}{27} - \\frac{1}{81} + \\frac{1}{243} - \\frac{1}{729} + \\frac{1}{2187} - \\cdots$?", "role": "user" }, { "content": "Since this is a geometric series we can use the sum formula for a g...	[ { "content": "What is the sum of the following infinite geometric series: $\\frac{1}{3} - \\frac{1}{9} + \\frac{1}{27} - \\frac{1}{81} + \\frac{1}{243} - \\frac{1}{729} + \\frac{1}{2187} - \\cdots$?", "role": "user" }, { "content": "Let's use sympy to calculate the sum of this infinite geometric ser...
4	[ "10" ]	[ { "content": "A line segment $\\overline{AB}$ has its midpoint at $M(4,4)$. If the coordinates of point A are known to be $(8,4)$, calculate the total of the x and y coordinates for the other endpoint, point $B$.", "role": "user" }, { "content": "Let's use sympy to solve this problem.\n```python\nfr...	[ { "content": "A line segment $\\overline{AB}$ has its midpoint at $M(4,4)$. If the coordinates of point A are known to be $(8,4)$, calculate the total of the x and y coordinates for the other endpoint, point $B$.", "role": "user" }, { "content": "Let's write down the midpoint formula as an equation ...
187	[ "131" ]	[ { "content": "What is the remainder when $2x^3 - x^2 - 17x + 47$ is divided by $x-5$?", "role": "user" }, { "content": "Let's use sympy to solve this problem.\n```python\nfrom sympy import symbols, poly\n\n# define the variables\nx, r = symbols('x r')\n\n# define the polynomial\np = poly(2 * x**3 - ...	[ { "content": "What is the remainder when $2x^3 - x^2 - 17x + 47$ is divided by $x-5$?", "role": "user" }, { "content": "We can use sympy to calculate the remainder:\n```python\nfrom sympy import sympify\n\n# Define the polynomial to divide\npoly_to_divide = sympify(\"2x3 - x2 - 17x + 47\")\ndi...
5	[ "\\frac{43}{4}" ]	[ { "content": "At a particular school with 43 students, each student takes chemistry, biology, or both. The chemistry class is three times as large as the biology class, and X students are taking both classes. How many people are in the chemistry class?\nIf we know the answer to the above question is 36, what is...	[ { "content": "At a particular school with 43 students, each student takes chemistry, biology, or both. The chemistry class is three times as large as the biology class, and X students are taking both classes. How many people are in the chemistry class?\nIf we know the answer to the above question is 36, what is...
8	[ "40" ]	[ { "content": "If Suzy is currently 20 years old and in four years she will be twice Mary's age at that time, what is Mary's current age?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\ncurrent_age_of_suzy = 20\n\n# in four years suzy will be twice as old as ...	[ { "content": "If Suzy is currently 20 years old and in four years she will be twice Mary's age at that time, what is Mary's current age?", "role": "user" }, { "content": "Let's solve this problem using Python's sympy library.\n```python\nimport sympy as sp\n\n# the age of Suzy\nM = 20\n\n# her age i...
2	[ "1.5" ]	[ { "content": "Alexia designed a logo X inches wide and 1.5 inches tall to be used on her school's notebooks. The school wants the logo on the notebook to be 8 inches wide. How tall, in inches, It will be 6 if it is enlarged proportionately. What is the value of unknown variable X?", "role": "user" }, { ...	[ { "content": "Alexia designed a logo X inches wide and 1.5 inches tall to be used on her school's notebooks. The school wants the logo on the notebook to be 8 inches wide. How tall, in inches, It will be 6 if it is enlarged proportionately. What is the value of unknown variable X?", "role": "user" }, { ...
234	[ "338" ]	[ { "content": "If Flynn watches 30 minutes of TV every night on weekdays and an additional 2 hours in total on weekends, how many hours of TV does she watch in 52 weeks?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\nweekday_TV_time = 30 # minutes\nweekend_T...	[ { "content": "If Flynn watches 30 minutes of TV every night on weekdays and an additional 2 hours in total on weekends, how many hours of TV does she watch in 52 weeks?", "role": "user" }, { "content": "The number of hours of television watched every week equals to 30 minutes of television watched p...
90	[ "" ]	[ { "content": "In a right triangle, the ratio of the measures of the acute angles is 8:1. What is the measure, in degrees, of the largest angle in the triangle?", "role": "user" }, { "content": "Let's use sympy to find the solutions for the equations.\n```python\nimport sympy as sp\n\n# define the an...	[ { "content": "In a right triangle, the ratio of the measures of the acute angles is 8:1. What is the measure, in degrees, of the largest angle in the triangle?", "role": "user" }, { "content": "Since we're looking at a right triangle, we know one of the angles is a right angle. So the remaining two ...
0	[ "\\frac{-1}{6}" ]	[ { "content": "If $z = 2y$ and $y = \\displaystyle\\frac{1}{3x+1}$, what is the value of $x$ when $z = 2$?", "role": "user" }, { "content": "Let's write down an equation for $z$ as a function of $x$ and solve it for $x$.\n```python\nfrom sympy import Eq, symbols, solve\n\n# define the variables\nx, y...	[ { "content": "If $z = 2y$ and $y = \\displaystyle\\frac{1}{3x+1}$, what is the value of $x$ when $z = 2$?", "role": "user" }, { "content": "Let's write down the definitions of $z$ and $y$ and solve for $x$ using sympy.\n```python\nimport sympy as sp\n\nx, y, z = sp.symbols('x y z')\n\neq1 = sp.Eq(z,...
2	[ "13" ]	[ { "content": "How many natural-number factors does $N$ have if $N = 2^4 \\cdot 3^3 \\cdot 5^2 \\cdot X$? The answer is 180. What is the value of unknown variable X?", "role": "user" }, { "content": "Let's write a python code to find the value of X.\n```python\ndef get_num_factors(N):\n '''Returns...	[ { "content": "How many natural-number factors does $N$ have if $N = 2^4 \\cdot 3^3 \\cdot 5^2 \\cdot X$? The answer is 180. What is the value of unknown variable X?", "role": "user" }, { "content": "We can compute the number of natural-number factors of $N$ using the following code.\n```python\n# TO...
5040	[ "-560" ]	[ { "content": "What is the product of the whole number values for $c$ that make the quadratic equation $8x^2+15x+c=0$ have two different real roots?", "role": "user" }, { "content": "Let's write down the discriminant of the quadratic equation $8x^2+15x+c=0$, which is equal to $b^2-4ac = 15^2 - 4 \\ti...	[ { "content": "What is the product of the whole number values for $c$ that make the quadratic equation $8x^2+15x+c=0$ have two different real roots?", "role": "user" }, { "content": "A quadratic equation $ax^2 + bx + c = 0$ has two roots in the real domain when the discriminant is greater than or equ...
60	[ "6" ]	[ { "content": "If a number is the product of 6! and 2^5, how many positive divisors does it have?", "role": "user" }, { "content": "Let's write this number as $6!\\cdot 2^5$ in prime factorization and then use this to find the number of positive divisors of the number using sympy.\n```python\nfrom sy...	[ { "content": "If a number is the product of 6! and 2^5, how many positive divisors does it have?", "role": "user" }, { "content": "Let's break down the number into prime factors.\n```python\nfrom sympy import factorint, prod\n\n# let's find the prime factors\nnum = 6 * 2 ** 5\nfactors = factorint(nu...
131	[ "104" ]	[ { "content": "The city's environmental division is expanding and needs to employ professionals who can handle multiple environmental concerns. Specifically, they need 85 workers to tackle issues related to water, another 73 to address problems with air quality, but they've found that 27 individuals are qualifie...	[ { "content": "The city's environmental division is expanding and needs to employ professionals who can handle multiple environmental concerns. Specifically, they need 85 workers to tackle issues related to water, another 73 to address problems with air quality, but they've found that 27 individuals are qualifie...
\frac{4}{3}	[ "4" ]	[ { "content": "The following line is parameterized, so that its direction vector is of the form $\\begin{pmatrix} 2 \\\\ b \\end{pmatrix}.$ Find $b.$\n\n[asy]\nunitsize(0.4 cm);\n\npair A, B, L, R;\nint i, n;\n\nfor (i = -8; i <= 8; ++i) {\n draw((i,-8)--(i,8),gray(0.7));\n draw((-8,i)--(8,i),gray(0.7));\n}\n...	[ { "content": "The following line is parameterized, so that its direction vector is of the form $\\begin{pmatrix} 2 \\\\ b \\end{pmatrix}.$ Find $b.$\n\n[asy]\nunitsize(0.4 cm);\n\npair A, B, L, R;\nint i, n;\n\nfor (i = -8; i <= 8; ++i) {\n draw((i,-8)--(i,8),gray(0.7));\n draw((-8,i)--(8,i),gray(0.7));\n}\n...
18	[ "" ]	[ { "content": "Given the matrix \\[A = \\begin{pmatrix} 9 & 18 \\\\ -6 & -12 \\end{pmatrix}\\], scalar \\[k = 3\\], and matrix \\[B = \\begin{pmatrix} 2 & 0 \\\\ 0 & 2 \\end{pmatrix}\\], calculate the determinant of matrix \\[D = k \\cdot B + A\\].", "role": "user" }, { "content": "Let's use sympy to...	[ { "content": "Given the matrix \\[A = \\begin{pmatrix} 9 & 18 \\\\ -6 & -12 \\end{pmatrix}\\], scalar \\[k = 3\\], and matrix \\[B = \\begin{pmatrix} 2 & 0 \\\\ 0 & 2 \\end{pmatrix}\\], calculate the determinant of matrix \\[D = k \\cdot B + A\\].", "role": "user" }, { "content": "Let's expand the d...
12	[ "192" ]	[ { "content": "The total mass of seven bowling balls is equivalent to that of three identical canoes. Knowing that one canoe has a mass of 28 pounds, compute the mass of an individual bowling ball.", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\nmass_of_a_can...	[ { "content": "The total mass of seven bowling balls is equivalent to that of three identical canoes. Knowing that one canoe has a mass of 28 pounds, compute the mass of an individual bowling ball.", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\nnumber_of_bal...
3000	[ "1300" ]	[ { "content": "Mr. Jesiah is a dairy cow farmer with cows producing 200 gallons of milk every day. The expenses for maintenance of the dairy farm and purchase of feeds is $x per month. Calculate his total income in June if he sells 1 gallon of milk at $3.55. The answer is 18300. What is the value of unknown vari...	[ { "content": "Mr. Jesiah is a dairy cow farmer with cows producing 200 gallons of milk every day. The expenses for maintenance of the dairy farm and purchase of feeds is $x per month. Calculate his total income in June if he sells 1 gallon of milk at $3.55. The answer is 18300. What is the value of unknown vari...
20	[ "70" ]	[ { "content": "Ali had a stock of 800 books in his Room. He sold 60 on Monday, 10 on Tuesday, x on Wednesday, 44 on Thursday and 66 on Friday. 600 books were not sold. What is the value of unknown variable x?", "role": "user" }, { "content": "Let's use Python code to solve this problem.\n```python\nx...	[ { "content": "Ali had a stock of 800 books in his Room. He sold 60 on Monday, 10 on Tuesday, x on Wednesday, 44 on Thursday and 66 on Friday. 600 books were not sold. What is the value of unknown variable x?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\nbo...
\frac{189}{2}\sqrt{3}	[ "22.3345" ]	[ { "content": "In the diagram, $\\triangle ABE$, $\\triangle BCE$ and $\\triangle CDE$ are right-angled, with $\\angle AEB=\\angle BEC = \\angle CED = 60^\\circ$, and $AE=24$. [asy]\npair A, B, C, D, E;\nA=(0,20.785);\nB=(0,0);\nC=(9,-5.196);\nD=(13.5,-2.598);\nE=(12,0);\ndraw(A--B--C--D--E--A);\ndraw(B--E);\ndr...	[ { "content": "In the diagram, $\\triangle ABE$, $\\triangle BCE$ and $\\triangle CDE$ are right-angled, with $\\angle AEB=\\angle BEC = \\angle CED = 60^\\circ$, and $AE=24$. [asy]\npair A, B, C, D, E;\nA=(0,20.785);\nB=(0,0);\nC=(9,-5.196);\nD=(13.5,-2.598);\nE=(12,0);\ndraw(A--B--C--D--E--A);\ndraw(B--E);\ndr...
0.5	[ "4" ]	[ { "content": "On a Sunday morning, Josephine sold milk in the farm stall. The buyers brought their containers. She filled three containers with two liters each, two containers with 0.75 liters each, and five containers with x liters each. How many liters of milk did Josephine sell in total?\nIf we know the answ...	[ { "content": "On a Sunday morning, Josephine sold milk in the farm stall. The buyers brought their containers. She filled three containers with two liters each, two containers with 0.75 liters each, and five containers with x liters each. How many liters of milk did Josephine sell in total?\nIf we know the answ...
22	[ "92" ]	[ { "content": "Trisha needed to buy some groceries for herself and her dog. She spent $17 on meat, $x on chicken, $43 on all the veggies, $5 on the eggs, and finally $45 on her dog’s food. When she left the store, she had only $35 left. She brought 167 money with her at the beginning. What is the value of unknow...	[ { "content": "Trisha needed to buy some groceries for herself and her dog. She spent $17 on meat, $x on chicken, $43 on all the veggies, $5 on the eggs, and finally $45 on her dog’s food. When she left the store, she had only $35 left. She brought 167 money with her at the beginning. What is the value of unknow...
11	[ "15" ]	[ { "content": "What is the largest number, all of whose digits are 3 or 2, and whose digits add up to X$?\nIf we know the answer to the above question is 32222, what is the value of unknown variable X?", "role": "user" }, { "content": "We can define a function which returns the sum of a number's digi...	[ { "content": "What is the largest number, all of whose digits are 3 or 2, and whose digits add up to X$?\nIf we know the answer to the above question is 32222, what is the value of unknown variable X?", "role": "user" }, { "content": "Let's use sympy to find the number we want.\n```python\nfrom symp...
17	[ "24" ]	[ { "content": "Within the drama society, there are 60 actors. Among them, 36 are attending math lectures, 27 are taking physics, and there is an overlap of 20 students who are engaged in both subjects. How many members of the drama society are not attending any math or physics lectures?", "role": "user" },...	[ { "content": "Within the drama society, there are 60 actors. Among them, 36 are attending math lectures, 27 are taking physics, and there is an overlap of 20 students who are engaged in both subjects. How many members of the drama society are not attending any math or physics lectures?", "role": "user" },...
3	[ "" ]	[ { "content": "Determine the number of nonzero terms in the expansion of $$(x+4)(2x^2+3x+9)-3(x^3-2x^2+7x)?$$", "role": "user" }, { "content": "We can solve this problem by doing the multiplication of the two polynomials and counting the number of non-zero terms. Here is how I did it:\n```python\nfro...	[ { "content": "Determine the number of nonzero terms in the expansion of $$(x+4)(2x^2+3x+9)-3(x^3-2x^2+7x)?$$", "role": "user" }, { "content": "I will use python's sympy library to solve the question.\n```python\nfrom sympy import expand, collect, Mul, Symbol\n\n# Initialize a symbol for x\nx = Symbo...
\frac{11}{15}	[ "\\frac{1}{3}" ]	[ { "content": "From the integers between 1 and 6 inclusive, two distinct numbers are chosen at random. Determine the probability that their highest common divisor is 1. Provide your answer as a simplified fraction.", "role": "user" }, { "content": "Let's use sympy to find the number of pairs of integ...	[ { "content": "From the integers between 1 and 6 inclusive, two distinct numbers are chosen at random. Determine the probability that their highest common divisor is 1. Provide your answer as a simplified fraction.", "role": "user" }, { "content": "To solve this problem, we can consider the number of...
7	[ "32" ]	[ { "content": "Joe’s mother gave him $56 to go to the store. Joe bought x notebooks and 2 books. Each notebook costs $4 and each book costs $7. How much money does Joe have left?\nIf we know the answer to the above question is 14, what is the value of unknown variable x?", "role": "user" }, { "conten...	[ { "content": "Joe’s mother gave him $56 to go to the store. Joe bought x notebooks and 2 books. Each notebook costs $4 and each book costs $7. How much money does Joe have left?\nIf we know the answer to the above question is 14, what is the value of unknown variable x?", "role": "user" }, { "conten...
6	[ "5+\\sqrt{61}" ]	[ { "content": "In a right-angled triangle, called $GHI$, with angle $H$ being 90 degrees, it is given that the hypotenuse $GI$ is $\\sqrt{61}$ units long, while leg $GH$ is 5 units. A circle, drawn with its center positioned on $GH$, gently touches both the hypotenuse $GI$ and side $HI$. When we name the touchpo...	[ { "content": "In a right-angled triangle, called $GHI$, with angle $H$ being 90 degrees, it is given that the hypotenuse $GI$ is $\\sqrt{61}$ units long, while leg $GH$ is 5 units. A circle, drawn with its center positioned on $GH$, gently touches both the hypotenuse $GI$ and side $HI$. When we name the touchpo...
\frac{8}{7}	[ "7" ]	[ { "content": "The solution of the equation $7^{x+7} = 8^x$ can be expressed in the form $x = \\log_b 7^7$. What is $b$?", "role": "user" }, { "content": "Let's first check whether there is a unique solution using sympy.\n```python\nimport sympy as sp\n\nx = sp.symbols('x')\n\neq = sp.Eq(7*(x+7), 8...	[ { "content": "The solution of the equation $7^{x+7} = 8^x$ can be expressed in the form $x = \\log_b 7^7$. What is $b$?", "role": "user" }, { "content": "Let's write down the equation and solve it.\n```python\nfrom sympy import log\nfrom sympy.abc import x\n\nequation = 7(x+7) - 8x\n\nsolutions ...
208000	[ "80" ]	[ { "content": "If the number of people living per cubic yard in a city is 80, how many additional people are there in a city with 9000 cubic yards compared to a city with 6400 cubic yards?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\nnumber_people_per_cubi...	[ { "content": "If the number of people living per cubic yard in a city is 80, how many additional people are there in a city with 9000 cubic yards compared to a city with 6400 cubic yards?", "role": "user" }, { "content": "Let's solve this problem using Python's sympy library.\n```python\nimport symp...
3	[ "4" ]	[ { "content": "Maria has 4 dimes, 4 quarters, and 7 nickels in her piggy bank. Her mom gives her 5 quarters. How much money, in dollars, does Maria have now?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\n# value of each coin\ndime_value = 0.1\nquarter_value...	[ { "content": "Maria has 4 dimes, 4 quarters, and 7 nickels in her piggy bank. Her mom gives her 5 quarters. How much money, in dollars, does Maria have now?", "role": "user" }, { "content": "Let's solve this problem using Python's sympy library.\n```python\nimport sympy as sp\n\n# Maria has 4 dimes,...
84	[ "63" ]	[ { "content": "If Dave has $46 and Kyle has $12 less than 3 times what Dave has, how much money does Kyle have after spending one-third of it on snowboarding?", "role": "user" }, { "content": "Let's solve this problem using Python code.\n```python\n# Dave has 46 dollars\ndave_has = 46\n# Kyle has 12 ...	[ { "content": "If Dave has $46 and Kyle has $12 less than 3 times what Dave has, how much money does Kyle have after spending one-third of it on snowboarding?", "role": "user" }, { "content": "Let's use symbolic variables to solve this problem using Python code.\n```python\nimport sympy as sp\n\n# we...
14	[ "9" ]	[ { "content": "What is the number of diagonals in a regular seven-sided polygon?", "role": "user" }, { "content": "The number of diagonals in a convex $n$-sided polygon is given by the formula:\n$$ \\frac{n(n-3)}{2} $$\nThe given polygon is a regular polygon, so all sides are equal. Thus the given po...	[ { "content": "What is the number of diagonals in a regular seven-sided polygon?", "role": "user" }, { "content": "Let's use sympy to count the number of diagonals in a regular polygon with $n$ sides.\n```python\nfrom sympy import factorial, Rational\n\n# for the regular polygon with n sides\nn = 7\n...
16	[ "9700" ]	[ { "content": "What is the largest four-digit number whose digits add up to X? The answer is 9700. What is the value of unknown variable X?", "role": "user" }, { "content": "Let's try to solve this problem in python:\n```python\nN = 9700\n\nM = N - 1\nM = '970'\nX = len(M)\n\nX = 9 + 7 + 0 + 0\nX\n``...	[ { "content": "What is the largest four-digit number whose digits add up to X? The answer is 9700. What is the value of unknown variable X?", "role": "user" }, { "content": "Let's go digits-first and build up from the lowest possible value for the four digits.\nUsing Python, we can loop through all c...
6	[ "7" ]	[ { "content": "If Alexa spent a week and 2 days on vacation, which is equivalent to 3/4ths of the time it took Ethan to learn 12 fencing tricks, and Joey spent half as much time as Ethan learning to swim, how many days did it take Joey to learn swimming?", "role": "user" }, { "content": "Let's solve ...	[ { "content": "If Alexa spent a week and 2 days on vacation, which is equivalent to 3/4ths of the time it took Ethan to learn 12 fencing tricks, and Joey spent half as much time as Ethan learning to swim, how many days did it take Joey to learn swimming?", "role": "user" }, { "content": "Let's solve ...
1	[ "e^{2\\pii/7}" ]	[ { "content": "Let $\\omega$ be a complex number such that $\\omega^7 = 1$ and $\\omega \\ne X Compute\n\\[\\omega^{16} + \\omega^{18} + \\omega^{20} + \\dots + \\omega^{54}.\\]\nIf we know the answer to the above question is -1, what is the value of unknown variable X?", "role": "user" }, { "conten...	[ { "content": "Let $\\omega$ be a complex number such that $\\omega^7 = 1$ and $\\omega \\ne X Compute\n\\[\\omega^{16} + \\omega^{18} + \\omega^{20} + \\dots + \\omega^{54}.\\]\nIf we know the answer to the above question is -1, what is the value of unknown variable X?", "role": "user" }, { "conten...
\frac{8}{16575}	[ "0.01" ]	[ { "content": "Imagine dealing three cards one after the other from a complete set of 52 cards, without returning them to the deck. What is the likelihood that you will pull a Jack first, followed by a Queen, and then a King?", "role": "user" }, { "content": "In a set of 52 cards, there are 4 of each...	[ { "content": "Imagine dealing three cards one after the other from a complete set of 52 cards, without returning them to the deck. What is the likelihood that you will pull a Jack first, followed by a Queen, and then a King?", "role": "user" }, { "content": "Let's write code to simulate drawing card...
-1	[ "1" ]	[ { "content": "Calculate $\\tan \\frac{3 \\pi}{4}.$", "role": "user" }, { "content": "Let's solve it using python:\n```python\nimport math\n\ndegree_pi = math.pi\n# Convert angle to radians\nradian_ang = degree_pi * 3 / 4\n\n# Calculate tan(angle)\nradian_ang_val = math.tan(radian_ang)\n\n# Convert f...	[ { "content": "Calculate $\\tan \\frac{3 \\pi}{4}.$", "role": "user" }, { "content": "We can use the following Mathematica script to do the calculations:\n```python\nfrom sympy import pi, tan\n\n# TODO: Use sympy to calculate value of tan(3 * pi / 4)\nresult = 1.0\nprint(result)\n```", "role": "a...
\frac{7}{24}	[ "0.6162" ]	[ { "content": "Find $\\tan Y$ in the right triangle shown below.\n\n[asy]\npair X,Y,Z;\nX = (0,0);\nY = (24,0);\nZ = (0,7);\ndraw(X--Y--Z--X);\ndraw(rightanglemark(Y,X,Z,23));\nlabel(\"$X$\",X,SW);\nlabel(\"$Y$\",Y,SE);\nlabel(\"$Z$\",Z,N);\nlabel(\"$25$\",(Y+Z)/2,NE);\nlabel(\"$24$\",Y/2,S);\n[/asy]", "role...	[ { "content": "Find $\\tan Y$ in the right triangle shown below.\n\n[asy]\npair X,Y,Z;\nX = (0,0);\nY = (24,0);\nZ = (0,7);\ndraw(X--Y--Z--X);\ndraw(rightanglemark(Y,X,Z,23));\nlabel(\"$X$\",X,SW);\nlabel(\"$Y$\",Y,SE);\nlabel(\"$Z$\",Z,N);\nlabel(\"$25$\",(Y+Z)/2,NE);\nlabel(\"$24$\",Y/2,S);\n[/asy]", "role...
1112	[ "306" ]	[ { "content": "If the arithmetic mean of two real numbers $x$ and $y$ is 18, and their geometric mean is $\\sqrt{92}$, what is the value of $x^2 + y^2$?", "role": "user" }, { "content": "Let's use sympy to find $x^2 + y^2$.\n```python\nfrom sympy import symbols, Eq, solve, simplify, sqrt\n\n# define ...	[ { "content": "If the arithmetic mean of two real numbers $x$ and $y$ is 18, and their geometric mean is $\\sqrt{92}$, what is the value of $x^2 + y^2$?", "role": "user" }, { "content": "Let's let AM be the arithmetic mean and GM be the geometric mean.\nThe arithmetic mean is $\\frac{x + y}{2} = 18$,...
16	[ "\\frac{1}{4}" ]	[ { "content": "Given that $x=64^{1/2}\\cdot27^{-1/3}\\cdot16^{1/4}$, find the value of $y = \\left(\\frac{3x}{4}\\right)^2$.", "role": "user" }, { "content": "Let's first check the value of $x$:\n```python\nfrom sympy import Symbol, Eq, simplify, sqrt\n\nx = Symbol('x')\ny = Symbol('y')\n\n# Define t...	[ { "content": "Given that $x=64^{1/2}\\cdot27^{-1/3}\\cdot16^{1/4}$, find the value of $y = \\left(\\frac{3x}{4}\\right)^2$.", "role": "user" }, { "content": "Let's use sympy to find $x$ and then calculate $y$.\n```python\nfrom sympy import Integer, Rational, Pow, log, sqrt\n\nx = Rational(1,2)*Integ...