prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "Expand and simplify the expression: $(2 + 3i)(4 - 5i)$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "23+2i",
"style": "rule"
}
|
numina_math
|
{
"index": 1900,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Johnny has a collection of nickels and dimes that total $2.65. If the total number of coins is 40, how many of each type of coin does he have? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 1901,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Max bought 12 packs of pencils and 7 packs of pens. Each pack of pencils costs $3, and each pack of pens costs $5. If he paid with a $100 bill, how much change did he receive? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "29",
"style": "rule"
}
|
numina_math
|
{
"index": 1902,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Farmer Dunphy has $100$ meters of fencing to create a closed rectangular pen. He will use an existing long wall for one of the sides of the pen, meaning he only needs to fence three sides. Each side of the pen must be a whole number of meters. What is the largest possible area of the pen? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1250",
"style": "rule"
}
|
numina_math
|
{
"index": 1903,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "For the quadratic function \\( f(x) = -x^2 + 4x + 5 \\):\n1. Find the roots of the quadratic equation.\n2. Determine the vertex of the quadratic function.\n3. Identify the x-intercepts and y-intercept.\n4. Determine the range of the function. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 1904,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical can has a radius of 3 inches and a height of 10 inches. The can is perfectly fitted inside a square box such that the top and bottom bases of the cylinder are parallel and aligned with the top and bottom faces of the box. What is the area of one face of the square box in square inches? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 1905,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Suppose the time \\( t \\) it takes to complete a task is inversely proportional to the number of workers \\( w \\). If 5 workers can complete the task in 8 hours, how long will it take for 10 workers to complete the same task? Additionally, what is the probability that it will rain tomorrow if the complementary probability of raining tomorrow is \\(\\frac{1}{4}\\)? Express your answer as a common fraction. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{3}{4}",
"style": "rule"
}
|
numina_math
|
{
"index": 1906,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom is buying multiple packs of pens for his office. Each pack of pens costs $4.50. He buys three times as many packs of pens as packs of notebooks. Each pack of notebooks costs $2.75. If Tom spends a total of $54.75, how many packs of pens and packs of notebooks does he buy? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 1907,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length that is 3 meters longer than its width. If the product of the length and width is 180 square meters, what are the dimensions of the garden? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{width} = 12 \\text{ meters}, \\text{length} = 15 \\text{ meters}",
"style": "rule"
}
|
numina_math
|
{
"index": 1908,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many two-digit numbers, when divided by 9, leave a remainder of 4? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 1909,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the decimal number 346 to its binary equivalent. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "101011010_2",
"style": "rule"
}
|
numina_math
|
{
"index": 1910,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) by completing the square: \\( x^2 + 8x + 7 = 0 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-7",
"style": "rule"
}
|
numina_math
|
{
"index": 1911,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Five standard six-sided dice are rolled. We are told there is no three-of-a-kind, but there is a pair of dice that show the same number. These two dice are set aside, and the other three dice are re-rolled. What is the probability that after re-rolling these three dice, at least three of the five dice show the same value? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{91}{216}",
"style": "rule"
}
|
numina_math
|
{
"index": 1912,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lucy is organizing a book fair. She has 200 books and wants to arrange them into 5 equal sections. However, she also needs to reserve 10 books for a special display. How many books will be in each section? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "38",
"style": "rule"
}
|
numina_math
|
{
"index": 1913,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $\\mathbf{M}$ be a $2 \\times 2$ matrix such that\n\\[\\mathbf{M} \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix} = \\begin{pmatrix} 2 \\\\ 3 \\end{pmatrix} \\quad \\text{and} \\quad \\mathbf{M} \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix} = \\begin{pmatrix} -1 \\\\ 4 \\end{pmatrix}.\\]\nCompute the magnitude of the vector $\\mathbf{M} \\begin{pmatrix} 3 \\\\ -2 \\end{pmatrix}$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\sqrt{65}",
"style": "rule"
}
|
numina_math
|
{
"index": 1914,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(\\mathbf{A}\\) be a \\(2 \\times 2\\) matrix such that\n\\[\\mathbf{A} = \\begin{pmatrix} 2 & 3 \\\\ -1 & 4 \\end{pmatrix}.\\]\nFind scalars \\(\\alpha\\) and \\(\\beta\\) such that \n\\[\\mathbf{A}^2 + \\alpha \\mathbf{A} + \\beta \\mathbf{I} = \\mathbf{0},\\]\nwhere \\(\\mathbf{I}\\) is the \\(2 \\times 2\\) identity matrix and \\(\\mathbf{0}\\) is the \\(2 \\times 2\\) zero matrix. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\alpha=-6\\beta=11",
"style": "rule"
}
|
numina_math
|
{
"index": 1915,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels a distance of 180 miles at a constant speed of 60 miles per hour. How much time, in hours, does it take for the car to complete the journey? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 1916,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If Maria's current age is 60% of her brother's age and the difference in their ages is 12 years, how old are Maria and her brother? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 1917,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a survey of 800 students, 25% of them are enrolled in a math class, and 15% of the students who are enrolled in a math class are also enrolled in a science class. How many students are enrolled in both a math and a science class? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 1918,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the equations \\(9s + 5t = 108\\) and \\(s = t - 2\\), solve for \\(t\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 1919,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence where each term is the product of its position in the sequence and the number of divisors of that position. For example, the first few terms are: \\(1\\), \\(4\\), \\(9\\), \\(8\\), and so on. What is the 5th term in this sequence? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 1920,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale on two products. Product A is originally priced at $150, and Product B is originally priced at $80. Both products are being offered at a 25% discount. If you buy both products, what is the total amount you will pay after the discount? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "172.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1921,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\[ g(x) = \n\\begin{cases}\n2x + 3 & \\text{if } x < 2, \\\\\nbx^2 - 4 & \\text{if } 2 \\le x < 5, \\\\\n3x - c & \\text{if } x \\ge 5\n\\end{cases}\n\\]\nFind the values of \\( b \\) and \\( c \\) such that the function \\( g(x) \\) is continuous. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "b=\\frac{11}{4}c=-\\frac{199}{4}",
"style": "rule"
}
|
numina_math
|
{
"index": 1922,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In triangle \\(XYZ\\), the measure of \\(\\angle X\\) is three times the measure of \\(\\angle Y\\), and the measure of \\(\\angle Z\\) is 10 degrees more than twice the measure of \\(\\angle Y\\). What is the measure, in degrees, of \\(\\angle Y\\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "28.33",
"style": "rule"
}
|
numina_math
|
{
"index": 1923,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( t \\) is a real number such that \\(\\sqrt{2t - 1} + \\sqrt{t + 4} = 5\\), find the value of \\( t \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 1924,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the parametric equations given by:\n\\[ x = t^2 + 3t + 2 \\]\n\\[ y = 4t + 5 \\]\nwhere \\( t \\) is a positive integer. Determine the sum of all possible values of \\( y \\) when \\( x \\) is a perfect square. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{nopossiblevaluesof}y",
"style": "rule"
}
|
numina_math
|
{
"index": 1925,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily has a monthly budget of $2400. She spends half of her budget on rent, a fifth of her budget on groceries, and the rest on entertainment. How much does she spend on entertainment each month? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "720",
"style": "rule"
}
|
numina_math
|
{
"index": 1926,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "An electronics store is offering a 25% discount on all items. If the discounted price of a laptop is $600, what was the original price of the laptop? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "800",
"style": "rule"
}
|
numina_math
|
{
"index": 1927,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Rachel works as a freelance graphic designer. She charges $45 per hour for her services. Last week, she worked on three different projects. For the first project, she worked for 5 hours. For the second project, she worked for 7 hours. For the third project, she worked for 3 hours. How much did Rachel earn in total last week? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "675",
"style": "rule"
}
|
numina_math
|
{
"index": 1928,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If June $15$ of a certain year is a Wednesday, what day of the week will July $10$ be in the same year? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{sunday}",
"style": "rule"
}
|
numina_math
|
{
"index": 1929,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial equation \\(x^3 - 6x^2 + 11x - 6 = 0\\) and the determinant of the following matrix:\n\\[\n\\begin{vmatrix}\n1 & x & x^2 \\\\\n1 & 2 & 4 \\\\\n1 & 3 & 9\n\\end{vmatrix}\n\\]\nfind all integer values of \\(x\\) that satisfy both the polynomial equation and make the determinant equal to zero. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "x=2\\text{and}x=3",
"style": "rule"
}
|
numina_math
|
{
"index": 1930,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the following system of congruences and find the value of \\( x \\):\n\\[ x \\equiv 3 \\pmod{5} \\]\n\\[ x \\equiv 4 \\pmod{7} \\]\n\\[ x \\equiv 2 \\pmod{9} \\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "263",
"style": "rule"
}
|
numina_math
|
{
"index": 1931,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A right triangular prism has a height of 8 cm and its base is a right-angled triangle with legs of 6 cm and 8 cm. Determine the volume of the prism. Additionally, the prism is placed in a coordinate plane with one of its triangular faces on the xy-plane. Find the coordinates of the vertices of the triangular face if one vertex is at the origin and the legs are aligned along the x and y axes. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "192",
"style": "rule"
}
|
numina_math
|
{
"index": 1932,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two friends, Jack and Jill, decide to meet up. Jack lives 5000 steps north of a park while Jill lives 6000 steps south of the same park. If they decide to meet at Jill's house, how many total steps will Jack need to walk to get there and then return home? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22000",
"style": "rule"
}
|
numina_math
|
{
"index": 1933,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires $\\frac{3}{4}$ cup of sugar, but you only have a $\\frac{1}{3}$ cup measuring tool. How many times must you use the $\\frac{1}{3}$ cup measuring tool to get the exact amount of sugar needed for the recipe? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2\\frac{1}{4}",
"style": "rule"
}
|
numina_math
|
{
"index": 1934,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If $0.\\overline{25}$ is expressed as a fraction and simplified to its lowest terms, then raised to the power of 2, what is the simplified form of the resulting fraction? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{625}{9801}",
"style": "rule"
}
|
numina_math
|
{
"index": 1935,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels a distance of 360 miles, consuming fuel at a rate of 30 miles per gallon. The cost of fuel is $3.50 per gallon. What is the total fuel cost for the trip? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "42",
"style": "rule"
}
|
numina_math
|
{
"index": 1936,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The sum of the first 10 terms of an arithmetic series is 155. If the first term is 5, what is the common difference of the series? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{7}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 1937,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha practices piano every day. She starts her practice with a 15-minute warm-up, then practices scales for 20 minutes, and finally spends 25 minutes playing pieces. If she keeps this schedule for 6 days in a week, how many minutes does she spend practicing piano in a week? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "360",
"style": "rule"
}
|
numina_math
|
{
"index": 1938,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Rachel is saving money and decides to deposit a fixed amount into her savings account every month. She starts by depositing $\\frac{2}{3}$ of a dollar in the first month and increases her deposit by $\\frac{1}{3}$ of a dollar each subsequent month. How much will she have deposited in total after the sixth month? Express your answer in simplest form. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 1939,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: \\((2x^{\\frac{1}{2}} + 3x^{\\frac{1}{3}})(4x^{\\frac{1}{2}} - x^{\\frac{1}{3}})\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8x+10x^{\\frac{5}{6}}-3x^{\\frac{2}{3}}",
"style": "rule"
}
|
numina_math
|
{
"index": 1940,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store sells gift bags in packs of 12. Each gift bag contains a number of candies equal to a perfect square. If the store wants to create packs containing exactly 144 candies without including any bag that contains 36 candies, how many different ways can the store create these packs? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 1941,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: $\\frac{x^5 \\cdot x^{-3}}{x^2 \\cdot x^{-4}}$. Your answer should contain only positive exponents. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "x^4",
"style": "rule"
}
|
numina_math
|
{
"index": 1942,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bacteria culture doubles in size every 3 hours. If the initial size of the culture is 500 bacteria, and it takes 24 hours for the culture to grow to a certain size, find the size of the culture after 24 hours. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "128000",
"style": "rule"
}
|
numina_math
|
{
"index": 1943,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anna has a certain number of candies. When she puts the candies in groups of 7, she has 3 candies left over. When she puts them in groups of 5, she has 2 candies left over. Additionally, the sum of the digits of the total number of candies is 12. How many candies does Anna have? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "192",
"style": "rule"
}
|
numina_math
|
{
"index": 1944,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the following \\(2 \\times 2\\) matrix:\n\\[ A = \\begin{pmatrix}\n\\cos \\theta & -\\sin \\theta \\\\\n\\sin \\theta & \\cos \\theta\n\\end{pmatrix}. \\]\nGiven that \\(\\theta = \\frac{\\pi}{3}\\), compute \\(A^3\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "a^3=\\begin{pmatrix}-1&0\\0&-1\\end{pmatrix}",
"style": "rule"
}
|
numina_math
|
{
"index": 1945,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A map has a scale of 1:100,000, which means 1 centimeter on the map equals 100,000 centimeters in real life. If the distance between two cities on the map is 7.5 centimeters, how far apart are the cities in real life in kilometers? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1946,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces widgets and gadgets. Each widget takes 8 minutes to produce, while each gadget takes 10 minutes. Last week, the factory produced 60% of its time making widgets and the rest making gadgets. If the factory operates 40 hours a week, how many widgets and gadgets were produced? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "96",
"style": "rule"
}
|
numina_math
|
{
"index": 1947,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah commutes to work by train and bus. The total distance she travels is 50 miles. The train travels at a speed of 40 miles per hour, while the bus travels at 20 miles per hour. The train ride takes 45 minutes, and she waits for the bus for 15 minutes before boarding. How long does the entire commute take, including the bus ride? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 1948,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anna wants to buy several items for her art project. She buys 5 packs of markers, each costing 12.5 yuan, and 3 sketchbooks, each costing 20.75 yuan. She also gets a discount of 15 yuan on her total purchase. How much does she pay in total? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "109.75",
"style": "rule"
}
|
numina_math
|
{
"index": 1949,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \n\\[\\mathbf{M} = \\begin{pmatrix} 1 & 2 & 2 \\\\ 2 & 1 & -2 \\\\ a & b & c \\end{pmatrix}.\\]\nIf $\\mathbf{M} \\mathbf{M}^T = 10 \\mathbf{I}$, find the values of $a$, $b$, and $c$.\n\nNote: For a matrix $\\mathbf{A}$, $\\mathbf{A}^T$ is the transpose of $\\mathbf{A}$, which is generated by reflecting the matrix $\\mathbf{A}$ over the main diagonal, going from the upper-left to the lower-right. So here,\n\\[\\mathbf{M}^T = \\begin{pmatrix} 1 & 2 & a \\\\ 2 & 1 & b \\\\ 2 & -2 & c \\end{pmatrix}.\\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "a=\\pm\\frac{2\\sqrt{10}}{3}b=\\mp\\frac{2\\sqrt{10}}{3}c=\\pm\\frac{\\sqrt{10}}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 1950,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company manufactures and sells widgets. The cost to produce each widget is $20, and the company sells each widget for $50. The company wants to maximize its profit by selling a certain number of widgets. If the company offers a 10% discount on the selling price for orders of more than 100 widgets, how many widgets should the company sell to maximize its profit if they are producing no more than 200 widgets? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "200",
"style": "rule"
}
|
numina_math
|
{
"index": 1951,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The sum of the first 15 terms of an arithmetic sequence is 195. If the first term is 3, what is the common difference? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{10}{7}",
"style": "rule"
}
|
numina_math
|
{
"index": 1952,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the range of the function \\( h(x) = \\frac{2}{x-1} + 3 \\). Express your answer in interval notation. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(-\\infty3)\\cup(3\\infty)",
"style": "rule"
}
|
numina_math
|
{
"index": 1953,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the population of a certain species of bacteria doubles every 5 hours, and you start with 200 bacteria, how many hours will it take for the population to reach 3200 bacteria? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 1954,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Roger bought a house for $120,000. He was able to pay 25% down, and his parents paid off an additional 40% of the remaining balance. How much money does Roger still owe on his house? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "54000",
"style": "rule"
}
|
numina_math
|
{
"index": 1955,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John and Sara are working together to complete a project. John can complete the project on his own in 10 hours, while Sara can complete it on her own in 15 hours. If they work together, how many hours will it take them to complete the project? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1956,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that \\(x + \\frac{1}{x} = 3\\), express \\(x^4 + \\frac{1}{x^4}\\) in terms of \\(x + \\frac{1}{x}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "47",
"style": "rule"
}
|
numina_math
|
{
"index": 1957,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the symmetric function \\( f(a, b) = \\frac{a^2 + b^2}{a + b} \\), simplify the expression for the specific values \\( a = x + 1 \\) and \\( b = x - 1 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{x^2+1}{x}",
"style": "rule"
}
|
numina_math
|
{
"index": 1958,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A hiking trail is shown on a map with a scale of 1:25,000. If the trail is represented by a length of 7.2 centimeters on the map, what is the actual length of the hiking trail in kilometers? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.8\\\\text{km}",
"style": "rule"
}
|
numina_math
|
{
"index": 1959,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the fraction $\\frac{7}{8}$ to a decimal and calculate the average speed if a car travels 280 miles in 4 hours. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "70",
"style": "rule"
}
|
numina_math
|
{
"index": 1960,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma is training for a marathon and follows a strict running schedule. She runs at a pace of 6 miles per hour. She increases her running time by 10 minutes each week, starting at 30 minutes in the first week. If she continues this pattern for 8 weeks, how many total miles will she have run by the end of the 8 weeks? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "52",
"style": "rule"
}
|
numina_math
|
{
"index": 1961,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the function \\( f(x) = 6x^2 + 11x - 10 \\), factor the quadratic expression completely and then evaluate \\( f(-2) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-8",
"style": "rule"
}
|
numina_math
|
{
"index": 1962,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex and Ben are two friends who decide to go on a hiking trip. Alex starts hiking from the trailhead towards a mountain peak at a speed of 3 miles per hour. After covering half the distance, he realizes he forgot something important and rushes back to the trailhead at a speed of 5 miles per hour. Meanwhile, Ben starts hiking from the trailhead 30 minutes after Alex at a constant speed of 4 miles per hour. If both meet at the trailhead when Alex returns, what was the total distance they each covered? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 1963,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a function \\( f : \\mathbb{R} \\to \\mathbb{R} \\) such that \\( f(x) \\) is an even function. Also, you have a right rectangular prism where the areas of three of its faces are \\( 15 \\, \\mathrm{cm}^2 \\), \\( 20 \\, \\mathrm{cm}^2 \\), and \\( 12 \\, \\mathrm{cm}^2 \\). Find the volume of the prism and determine if \\( f(x) = \\frac{1}{x^2 + 1} \\) is even, odd, or neither. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60\\\\mathrm{cm}^3",
"style": "rule"
}
|
numina_math
|
{
"index": 1964,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical tank has a radius of 4 meters and a height of 10 meters. If the tank is filled with water to a height of 6 meters, what is the ratio of the volume of water in the tank to the total volume of the tank? Simplify the ratio. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{3}{5}",
"style": "rule"
}
|
numina_math
|
{
"index": 1965,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A local bookstore is having a clearance sale. They have a total of 150 books, which they have divided into two categories: novels and textbooks. The novels are priced at $8 each, and the textbooks are priced at $12 each. If the total value of all the books is $1,320, how many novels and textbooks are there? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "n=120\\t=30",
"style": "rule"
}
|
numina_math
|
{
"index": 1966,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels from City X to City Y, which takes him 7 hours. On the return trip, he travels 3/4 of the speed he used to travel from City X to City Y, and it takes him 9 hours. How many hours in total did the cyclist take to travel from City X to City Y and back to City X? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 1967,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Nina, Omar, and Liam each donated a certain amount of money to a charity. The total amount donated by all three was $180. Nina donated $20 more than twice the amount donated by Omar, and Liam donated $10 less than the amount donated by Omar. How much did each person donate? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1968,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex, Bailey, and Casey each contributed different amounts to a charity fund. Alex contributed $150. Bailey contributed 30% more than Alex, and Casey contributed 50% more than Bailey. Calculate the total amount contributed by all three individuals to the charity fund. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "637.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1969,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A class conducted a survey to determine the number of hours students spend on homework each week. The bar graph below shows the results. How many more hours did the student who spent the most time on homework spend compared to the student who spent the least time?\n\n[asy]\ndefaultpen(linewidth(1pt)+fontsize(10pt));\npair[] yaxis = new pair[11];\nfor( int i = 0 ; i < 11 ; ++i ){\nyaxis[i] = (0,i);\ndraw(yaxis[i]--yaxis[i]+(13,0));\n}\ndraw((0,0)--(0,10));\ndraw((13,10)--(13,0));\nfill((1,0)--(1,7)--(2,7)--(2,0)--cycle,grey);\nfill((3,0)--(3,5)--(4,5)--(4,0)--cycle,grey);\nfill((5,0)--(5,9)--(6,9)--(6,0)--cycle,grey);\nfill((7,0)--(7,6)--(8,6)--(8,0)--cycle,grey);\nfill((9,0)--(9,4)--(10,4)--(10,0)--cycle,grey);\nfill((11,0)--(11,3)--(12,3)--(12,0)--cycle,grey);\nlabel(\"0\",yaxis[0],W);\nlabel(\"1\",yaxis[1],W);\nlabel(\"2\",yaxis[2],W);\nlabel(\"3\",yaxis[3],W);\nlabel(\"4\",yaxis[4],W);\nlabel(\"5\",yaxis[5],W);\nlabel(\"6\",yaxis[6],W);\nlabel(\"7\",yaxis[7],W);\nlabel(\"8\",yaxis[8],W);\nlabel(\"9\",yaxis[9],W);\nlabel(\"10\",yaxis[10],W);\nlabel(\"Students\",(6.5,0),S);\nlabel(\"Hours Spent on Homework\",(6.5,10),N);\nlabel(rotate(90)*\"Hours\",(0,5),W);\n[/asy] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1970,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lily is planning a birthday party and needs to buy cupcakes for her guests. Each cupcake costs $2.50. If she has invited 15 guests and wants to buy 2 cupcakes for each guest, how much will she spend on cupcakes in total? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 1971,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenna and Kate are planning a trip together. They have planned their budget and need to book hotel rooms. Each hotel room costs $\\$120$ per night. They plan to stay for $5$ nights. They also estimate that they will spend $\\$200$ on food and $\\$100$ on activities. Jenna has saved $\\$300$, and Kate has saved $\\$550$. If they decide to split the total cost equally, how much more money does each need to save to afford the trip? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 1972,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "When 7 is subtracted from three times a number, the result is equal to twice the number plus 5. What is the number? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 1973,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What integer is closest to the value of \\( \\sqrt[3]{9^3 + 10^3} \\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 1974,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical tank has a radius of 5 meters and a height of 10 meters. Calculate the volume of the tank in cubic meters and then convert this volume into liters. (Note: 1 cubic meter = 1000 liters) Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "785397.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1975,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The median of the set of numbers $\\{8, 15, 22, 35, y\\}$ is equal to twice the mean of the set. If $y$ is an integer, what is the value of $y$? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-25",
"style": "rule"
}
|
numina_math
|
{
"index": 1976,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A garden is divided into sections for different types of vegetables. One section, which is $\\frac{2}{5}$ of the entire garden, is dedicated to tomatoes. Another section, which is $\\frac{1}{4}$ of the remaining garden, is for cucumbers. The rest of the garden is used for peppers. If the garden's total area is 200 square meters, what is the area dedicated to peppers? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 1977,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A line passes through the points (2, 3) and (4, 7). Find the x-intercept of the line. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 1978,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah runs a small business selling handmade candles. She sells each candle for $15. Last week, she sold 30 candles. Her total cost to make the candles was $270. What was Sarah's profit for the week? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 1979,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a speed of 60 kilometers per hour. A cyclist travels at one-fourth the speed of the car. If both the car and the cyclist start from the same point and travel for 3 hours, how many more kilometers does the car travel compared to the cyclist? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "135",
"style": "rule"
}
|
numina_math
|
{
"index": 1980,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The midpoint of a line segment is located at $(3, 4)$. If one of the endpoints is $(5, 6)$, what is the other endpoint? Express your answer as an ordered pair. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(12)",
"style": "rule"
}
|
numina_math
|
{
"index": 1981,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends decided to go to a theme park. They planned their visit such that they would spend 2/5 of their time on rides, 1/4 of their time eating, and the remaining time watching shows. If they spent a total of 8 hours at the theme park, how much time did they spend watching shows? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.8",
"style": "rule"
}
|
numina_math
|
{
"index": 1982,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the number of bottles ordered in May from base 10 to base 5. The store owner ordered 30 cases in May, with 20 bottles per case. How many bottles of soda did the store owner order in May in base 5? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4400_5",
"style": "rule"
}
|
numina_math
|
{
"index": 1983,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is shopping for school supplies. He buys 5 notebooks at $3 each, 2 packs of pens at $4 each, and a backpack that costs $25. How much does John spend in total? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 1984,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The temperature in City A is 20 degrees Celsius higher than in City B. If the temperature in City A is 30 degrees Celsius, what is the temperature in City B in both Celsius and Fahrenheit? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 1985,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company buys 5 computers at a unit cost of \\( \\$600 \\) each. They also purchase 3 printers at a unit cost of \\( \\$150 \\) each. If the company uses a 10% discount on the total purchase, what is the final amount they need to pay? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3105",
"style": "rule"
}
|
numina_math
|
{
"index": 1986,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given a parallelogram with vertices \\( A(2, 3) \\), \\( B(8, 3) \\), \\( C(6, 8) \\), and \\( D(0, 8) \\). A line passing through the origin intersects the parallelogram such that it divides the parallelogram into two congruent triangles. The slope of this line is \\( \\frac{m}{n} \\), where \\( m \\) and \\( n \\) are relatively prime positive integers. Find \\( m+n \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "19",
"style": "rule"
}
|
numina_math
|
{
"index": 1987,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the range of the function \\(f(x) = -x^2 + 4x + 5\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(-\\infty9]",
"style": "rule"
}
|
numina_math
|
{
"index": 1988,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is on a weight loss program. She weighed 150 pounds at the beginning of the program. Every week, she loses 3 pounds. If she continues at this rate, how much will she weigh after 8 weeks? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "126",
"style": "rule"
}
|
numina_math
|
{
"index": 1989,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two lines in the coordinate plane are perpendicular to each other. The first line has a slope of \\( \\frac{3}{4} \\). What is the slope of the second line? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-\\frac{4}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 1990,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Compare the two values $\\frac{2}{3}$ and $0.\\overline{666}$ and determine which is greater. Express your answer as a common fraction and a repeating decimal. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{thetwovaluesareequal:}\\frac{2}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 1991,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the polynomial expression \\(4x^3 + 8x^2 - 10x - 20\\) by factoring it completely. Then, using the Remainder Theorem, find the remainder when this polynomial is divided by \\(x + 2\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 1992,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $f$ be a function taking the positive integers to the positive integers, such that\n(i) $f$ is multiplicative (i.e., $f(mn) = f(m) f(n)$ for all positive integers $m$ and $n$),\n(ii) $f(2^k) = 2^{f(k)}$ for all positive integers $k$, and\n(iii) $f(p^k) = p^{f(k)}$ for any prime $p$ and positive integer $k$.\nIf $f(27) = 81$, find $f(3)$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 1993,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, there are 25 students and 6 different types of colored markers. Each student must have at least one marker. What is the minimum number of students that must have the same colored marker, according to the Pigeonhole Principle? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1994,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the following limit: \\(\\lim_{{x \\to 2}} \\frac{x^2 - 4}{x - 2}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 1995,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Three workers, A, B, and C, are hired to complete a project. Worker A can complete the project alone in 15 days, worker B in 20 days, and worker C in 30 days. If all three workers start working together, how many days will it take for them to complete the project? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6\\frac{2}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 1996,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The product of three positive integers $a$, $b$, and $c$ is $180$. If $a \\leq b \\leq c$, what is the sum of these integers? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17",
"style": "rule"
}
|
numina_math
|
{
"index": 1997,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence of functions defined by \\( f_n(x) \\) where \\( f_1(x) = 2x + 1 \\) and \\( f_{n+1}(x) = f(f_n(x)) \\) for \\( n \\geq 1 \\). Find the explicit form of \\( f_3(x) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "f_3(x)=8x+7",
"style": "rule"
}
|
numina_math
|
{
"index": 1998,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a perimeter of 72 meters, and the ratio of its length to its width is 7:5. What is the area of the garden? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "315",
"style": "rule"
}
|
numina_math
|
{
"index": 1999,
"name": "numina_math",
"split": "train"
}
|
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