rkumar1999/Llama3.2-3B-Prover-Math-openr1-distill-SFT
Text Generation • 175k • Updated • 2
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"content": "## Task B-1.3.\n\nA ship traveling along a river has covered $24 \\mathrm{~km}$ upstream and $28 \\mathrm{~km}$ downstream. For this journey, it took half an hour less than for traveling $30 \\mathrm{~km}$ upstream and $21 \\mathrm{~km}$ downstream, or half an hour more than for traveling $15 \\ma... | 3,117 | open-r1/OpenR1-Math-220k |
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"content": "3. (6 points) A construction company was building a tunnel. When $\\frac{1}{3}$ of the tunnel was completed at the original speed, they started using new equipment, which increased the construction speed by $20 \\%$ and reduced the working hours to $80 \\%$ of the original. As a result, it took a ... | 2,708 | open-r1/OpenR1-Math-220k |
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"content": "4. Given the three sides of an obtuse triangle are 3, $4, x$, then the range of values for $x$ is ( ).\n(A) $1<x<7$.\n(B) $5 \\ll x<7$.\n(C) $1<x<\\sqrt{7}$.\n(D) $5<x<7$ or $1<x<\\sqrt{7}$.",
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"content": "<think>\nOkay, so I have this problem here where I need to fi... | 2,101 | open-r1/OpenR1-Math-220k |
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"content": "1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$.",
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"content": "<think>\nOkay, so I need to solve this equation: (8x + 13)/3 = (19 - 12x)/2 - (16x - (7 - 4x)/6). Hmm, that looks a bit complicated with all the fractio... | 1,749 | open-r1/OpenR1-Math-220k |
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"content": "Task B-4.2. Let $n$ be the number obtained by writing 2013 zeros between every two digits of the number 14641. Determine all solutions of the equation $x^{4}=n$ in the set $\\mathbb{C}$.",
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"content": "<think>\nOkay, let's see. I need to find all complex solutions to... | 3,739 | open-r1/OpenR1-Math-220k |
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"content": "## Problem Statement\n\nCalculate the definite integral:\n\n$$\n\\int_{0}^{3 / 2} \\frac{x^{2} \\cdot d x}{\\sqrt{9-x^{2}}}\n$$",
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"content": "<think>\nOkay, so I need to calculate the definite integral of x squared over the square root of (9 minus x squared) from 0 ... | 3,425 | open-r1/OpenR1-Math-220k |
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"content": "Example 1 (Question from the 13th \"Hope Cup\" Invitational Competition) The real roots of the equations $x^{5}+x+1=0$ and $x+\\sqrt[5]{x}+1=0$ are $\\alpha, \\beta$ respectively, then $\\alpha+\\beta$ equals ( ).\nA. -1\nB. $-\\frac{1}{2}$\nC. $\\frac{1}{2}$\nD. 1",
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... | 3,460 | open-r1/OpenR1-Math-220k |
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"content": "Example 5 Given that $x_{1}, x_{2}, \\cdots, x_{10}$ are all positive integers, and $x_{1}+x_{2}+\\cdots+x_{10}=2005$, find the maximum and minimum values of $x_{1}^{2}+x_{2}^{2}+\\cdots+x_{10}^{2}$.",
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"content": "<think>\nOkay, let's see. I need to find the maximum... | 2,700 | open-r1/OpenR1-Math-220k |
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"content": "1. If the set\n$$\nA=\\{1,2, \\cdots, 10\\}, B=\\{1,2,3,4\\},\n$$\n$C$ is a subset of $A$, and $C \\cap B \\neq \\varnothing$, then the number of such subsets $C$ is $(\\quad)$.\n(A) 256\n(B) 959\n(C) 960\n(D) 961",
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"content": "<think>\nOkay, so I need to figure out... | 2,364 | open-r1/OpenR1-Math-220k |
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"content": "Augusto has a wire that is $10 \\mathrm{~m}$ long. He makes a cut at a point on the wire, obtaining two pieces. One piece has a length of $x$ and the other has a length of $10-x$ as shown in the figure below:\n\n![](https://cdn.mathpix.com/cropped/2024_05_01_d02c2755ad3373bde08ag-05.jpg?height=645... | 3,165 | open-r1/OpenR1-Math-220k |
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"content": "29. Choose any three numbers from $a, b, c, d, e$ and find their sum, exactly obtaining the ten different numbers $7,11,13,14,19,21,22,25,26,28$. Then $a+b+c+d+e=$ ( i). MATHEMATICE YoUTH CLUE A. 25\nB. 31\nC. 37\nD. 43",
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"content": "<think>\nOkay, so I need to figu... | 3,220 | open-r1/OpenR1-Math-220k |
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"content": "Problem 3. In the school, there are 50 teachers, of whom 29 drink coffee, 28 drink tea, and 16 do not drink either coffee or tea. How many teachers drink only coffee, and how many drink only tea?",
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"content": "<think>\nOkay, let's see. There's a problem about teache... | 1,327 | open-r1/OpenR1-Math-220k |
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"content": "12.180. A side of the triangle is equal to 15, the sum of the other two sides is 27. Find the cosine of the angle opposite the given side, if the radius of the inscribed circle in the triangle is 4.",
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"content": "<think>\nOkay, let's see. The problem says that one s... | 2,612 | open-r1/OpenR1-Math-220k |
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"content": "## Problem Statement\n\nCalculate the limit of the numerical sequence:\n\n$\\lim _{n \\rightarrow \\infty} \\frac{(n+1)^{4}-(n-1)^{4}}{(n+1)^{3}+(n-1)^{3}}$",
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"content": "<think>\nOkay, so I need to find the limit as n approaches infinity of the expression [(n+1)^4 ... | 3,640 | open-r1/OpenR1-Math-220k |
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"content": "\\section*{Problem 5 - 071225}\n\nAll ordered pairs of real numbers \\((x, y)\\) are to be determined for which the system of equations\n\n\\[\n\\begin{aligned}\nx \\cdot\\left(a x^{2}+b y^{2}-a\\right) & =0 \\\\\ny \\cdot\\left(a x^{2}+b y^{2}-b\\right) & =0\n\\end{aligned}\n\\]\n\nis satisfied. ... | 3,647 | open-r1/OpenR1-Math-220k |
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"content": "40. The sum of three consecutive odd numbers is equal to the fourth power of a single-digit number. Find all such triples of numbers.",
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"content": "<think>\nOkay, let's see. The problem says that the sum of three consecutive odd numbers is equal to the fourth power ... | 2,732 | open-r1/OpenR1-Math-220k |
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"content": "Two is $10 \\%$ of $x$ and $20 \\%$ of $y$. What is $x - y$?\n$(\\mathrm {A}) \\ 1 \\qquad (\\mathrm {B}) \\ 2 \\qquad (\\mathrm {C})\\ 5 \\qquad (\\mathrm {D}) \\ 10 \\qquad (\\mathrm {E})\\ 20$",
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"content": "<think>\nOkay, let's see here. The problem says that two... | 1,217 | open-r1/OpenR1-Math-220k |
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"content": "1. (6 points) Today is January 31, 2015, welcome to the 2015 \"Spring Cup\" Final. The calculation result of the expression $\\frac{\\frac{2015}{1}+\\frac{2015}{0.31}}{1+0.31}$ is",
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"content": "<think>\nOkay, so I need to calculate this expression: (2015/1 + 2015/0.... | 2,430 | open-r1/OpenR1-Math-220k |
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"content": "Consider a regular hexagon with an incircle. What is the ratio of the area inside the incircle to the area of the hexagon?\n",
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"content": "<think>\nOkay, so I need to find the ratio of the area inside the incircle of a regular hexagon to the area of the hexagon itse... | 2,554 | open-r1/OpenR1-Math-220k |
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"content": "30. Find the remainder when the 2018-digit number $\\underbrace{\\overline{55 \\cdots}}_{2018 \\text { 555 }}$ is divided by 13.",
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"content": "<think>\nOkay, so I need to find the remainder when this huge 2018-digit number made up entirely of 5s is divided by 13. Hm... | 2,879 | open-r1/OpenR1-Math-220k |
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"content": "1. A line $l$ intersects a hyperbola $c$, then the maximum number of intersection points is ( ).\nA. 1\nB. 2\nC. 3\nD. 4",
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"content": "<think>\nOkay, so I need to figure out the maximum number of points where a line can intersect a hyperbola. The options are 1, 2, 3... | 2,663 | open-r1/OpenR1-Math-220k |
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"content": "1. Let the universal set be the set of real numbers. If $A=\\{x \\mid \\sqrt{x-2} \\leqslant 0\\}, B=\\left\\{x \\mid 10^{x^{2}-2}=10^{x}\\right\\}$, then $A \\cap \\bar{B}$ is\nA. $\\{2\\}$\nB. $\\{-1\\}$\nC. $\\{x \\mid x \\leqslant 2\\}$\nD. $\\varnothing$",
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"con... | 1,805 | open-r1/OpenR1-Math-220k |
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"content": "7.242. $\\left(16 \\cdot 5^{2 x-1}-2 \\cdot 5^{x-1}-0.048\\right) \\lg \\left(x^{3}+2 x+1\\right)=0$.",
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"content": "<think>\nOkay, let's see. I need to solve the equation: \n\n\\[16 \\cdot 5^{2x-1} - 2 \\cdot 5^{x-1} - 0.048 = 0\\]\nmultiplied by \n\\[\\lg(x^3 + 2x ... | 3,499 | open-r1/OpenR1-Math-220k |
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"content": "In order for Mateen to walk a kilometer (1000m) in his rectangular backyard, he must walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen's backyard in square meters?\n$\\text{(A)}\\ 40 \\qquad \\text{(B)}\\ 200 \\qquad \\text{(C)}\\ 400 \\qquad \\text{(D)}\\ 500 \\q... | 1,849 | open-r1/OpenR1-Math-220k |
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"content": "The knights in a certain kingdom come in two colors. $\\frac{2}{7}$ of them are red, and the rest are blue. Furthermore, $\\frac{1}{6}$ of the knights are magical, and the fraction of red knights who are magical is $2$ times the fraction of blue knights who are magical. What fraction of red knight... | 1,711 | open-r1/OpenR1-Math-220k |
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"content": "A father wants to divide his property among his children: first, he gives 1000 yuan and one-tenth of the remaining property to the eldest child, then 2000 yuan and one-tenth of the remaining property to the second child, then 3000 yuan and one-tenth of the remaining property to the third child, an... | 3,805 | open-r1/OpenR1-Math-220k |
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