data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
t01_math | [
{
"role": "user",
"content": "수열 \\( x_n = \\frac{1}{(2n+1)^2} + \\frac{1}{(2n+2)^2} + \\ldots + \\frac{1}{(2n+2n)^2} \\)이 0으로 수렴하는지 판별하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 항의 개수가 2n개이므로 각 항의 범위를 2n배하여 전체 합을 추정하는 부등식을 작성하세요."
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::cc8171ef09bdbad604a42a6f",
"index": "kd::cc8171ef09bdbad604a42a6f",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 10 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Kevin wants to buy a new coat for $80. He has $15 saved up and receives an allowance of $5 every week. How many months will it take to save enough money to buy the coat?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Convert the ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::de721177ec68937a32b872dd",
"index": "kd::de721177ec68937a32b872dd",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 13 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "23. As shown in Figure 3, a white square with a side length of 8 has four black isosceles right triangles with leg lengths of 2 placed at its four corners. A black square with a side length of \\(2 \\sqrt{2}\\) is placed at the center of the square. A circular coin with a diame... | math | {
"ground_truth": "68",
"style": "rule"
} | {
"uid": "kd::1383fee523a8cc4cb85932d3",
"index": "kd::1383fee523a8cc4cb85932d3",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 24.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Determine all polynomials $P(x)$ such that $P(1) = 210$ and for every real number $x$, the following equation holds:\n\n$$(x + 10)P(2x) = (8x - 32)P(x + 6)$$\n\nFind the general form of $P(x)$ and provide a condition for the constant term.\n\nSolve the problem. Show your reason... | math | {
"ground_truth": "P(x) = 2x^3 - 16x^2 - 32x + 256",
"style": "rule"
} | {
"uid": "kd::149ab3422b61f9218e0b7174",
"index": "kd::149ab3422b61f9218e0b7174",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 -1152 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "During the 2017 campaign, Ideological Party's candidate \"Annie\" polled 60 percent of vote in Conroe County while \"Billy\" polled 30 percent and \"Joe\" received 10 percent. If total votes are 10,000, how many more votes did Annie receive in Worth County compared to Joe?\n\nS... | math | {
"ground_truth": "5000",
"style": "rule"
} | {
"uid": "kd::dd06b230b4a6759f7d2d692e",
"index": "kd::dd06b230b4a6759f7d2d692e",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 10000 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Calculate the area of a symmetrical lens made from two circles with a radius of 20 cm, placed 40 cm apart.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Recognize that the center-to-center distance equals exactly twice the radiu... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::9725344b6daa08aeb375dd74",
"index": "kd::9725344b6daa08aeb375dd74",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 837.7576 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Tamara and Katherine plan to students how to go to the park together with their friends. Tamara has 25 students and Katherine has 3 times as many third grade friends. If there are 160 students going to the park in a bus, how many students will not be on the bus?\n\nSolve the ... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"uid": "kd::58f0617e324f6d545107c4e2",
"index": "kd::58f0617e324f6d545107c4e2",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 75 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "John's dog eats 4 times as much food on weekends as on weekdays. If John's dog eats 50 pounds of food on weekdays, how many pounds of food does it eat in 3 full weekends, assuming he is without work for the 3 weekends?\n\nSolve the problem. Show your reasoning, then put the fin... | math | {
"ground_truth": "1200",
"style": "rule"
} | {
"uid": "kd::1eb0f5c142e6a8ef9a63dfba",
"index": "kd::1eb0f5c142e6a8ef9a63dfba",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 200 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Calculate the value of the following summation: \\[ \\sum_{k=0}^{13} \\binom{26}{2k}\\frac{(2k)!}{k!2^k} \\]\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Apply the recurrence relation I_n = I_{n-1} + (n-1)I_{n-2} iteratively st... | math | {
"ground_truth": "532985208200576",
"style": "rule"
} | {
"uid": "kd::91fd426d1a03bda2e55c3ff4",
"index": "kd::91fd426d1a03bda2e55c3ff4",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 12177 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "If we have 10 bottles of red soda and 8 bottles of blue soda, what is the min number that an extra neckerchief must match the number of blue bottles of soda if we take each bottle and put it in a bag?\n\nSolve the problem. Show your reasoning, then put the final answer inside \... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"uid": "kd::b76e0efbde7747badc504a87",
"index": "kd::b76e0efbde7747badc504a87",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 18 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "a) In Mexico City, there are regulations that restrict private cars from driving on city streets on two specified days of the week. A family needs to have at least ten cars available every day. What is the minimum number of cars the family needs if they can choose the restricte... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"uid": "kd::9eac218542b739d9d19e1b86",
"index": "kd::9eac218542b739d9d19e1b86",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 14 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Let real numbers $a$, $b$, $c$ satisfy $a^2+b^2+c^2=1$.\n(1) If $a+b+c=0$, find the value of $ab+bc+ca$;\n(2) Find the maximum value of $(a+b+c)^2$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Apply the Cauchy-Schwarz inequali... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"uid": "kd::bbe6c9501df41e1cf1224fcc",
"index": "kd::bbe6c9501df41e1cf1224fcc",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\sqrt{3} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Jade bought her five chickens less than twice the number of guinea pigs she bought. If she bought 3 guinea pigs, how many animals does she have in total?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Add the number of guinea pig... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::dc546c587966279a90d065f4",
"index": "kd::dc546c587966279a90d065f4",
"lang": "en",
"rubrics": [
{
"criterion": "Translate the verbal description of the chicken count into a mathematical expression using the given number of guinea pigs.",
"points": 2,
"tags": {
"judge":... |
t01_math | [
{
"role": "user",
"content": "Construct a polynomial over the finite field \\( \\mathbb{Z}_p \\) with a degree less than \\( p^3(p-1) \\) that evaluates to 0 at the origin and 1 at all other points.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Subtract the ... | math | {
"ground_truth": "1 - (1 - x^{p-1})(1 - y^{p-1})(1 - z^{p-1})",
"style": "rule"
} | {
"uid": "kd::67632f46d35183d98bb28f9d",
"index": "kd::67632f46d35183d98bb28f9d",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 27 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Inference 2 If $x_{i}>0, q_{i}>0, i=1,2, \\cdots, n$, and $\\sum_{i=1}^{n} q_{i}=1, \\forall p>1$, then we have\n$$\\sum_{i=1}^{n} q_{i} x_{i} \\frac{1}{\\rho} \\leqslant\\left(\\sum_{i=1}^{n} q_{i} x_{i}\\right)^{\\frac{1}{p}}$$\n\nSolve the problem. Show your reasoning, then ... | math | {
"ground_truth": "\\sum_{i=1}^{n} q_{i} x_{i}^{\\frac{1}{p}} \\leqslant (\\sum_{i=1}^{n} q_{i} x_{i})^{\\frac{1}{p}}",
"style": "rule"
} | {
"uid": "kd::b48e6ead2504cebcfa8f9bc9",
"index": "kd::b48e6ead2504cebcfa8f9bc9",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{x_{i}}{x_{i}^{\\alpha}} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kin... |
t01_math | [
{
"role": "user",
"content": "Elizabeth is getting twice as many silver cashmere sweaters as her 5 friends in her H&M store. If Elizabeth was considering the purchase of 3 of each cashmere sweater, how many cashmere swaters selling price of $400 per sweater would she have spend in all had that been Nathalie... | math | {
"ground_truth": "12000",
"style": "rule"
} | {
"uid": "kd::afe6b7fc831c0f9b923a3fe9",
"index": "kd::afe6b7fc831c0f9b923a3fe9",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 10 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Determine the number of combinations of 10 six-faced dice where exactly one face is missing. For example, if the face with 6 dots is missing, the faces with 1, 2, 3, 4, and 5 dots must all appear at least once.\n\nSolve the problem. Show your reasoning, then put the final answe... | math | {
"ground_truth": "30 618 000",
"style": "rule"
} | {
"uid": "kd::1923ab880625617d0d33d0a1",
"index": "kd::1923ab880625617d0d33d0a1",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 59 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Viet counts the same number of squirrels and flies on a tree. If the number of squirrels on the tree is double the number of flies as the number of squirrels plus 20, what is the total number of squirrels and flies on the tree if there are 100 squirrels on the tree?\n\nSolve th... | math | {
"ground_truth": "140",
"style": "rule"
} | {
"uid": "kd::0cd4c57b33d6abf151e34393",
"index": "kd::0cd4c57b33d6abf151e34393",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 60 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Christine decides to start a club for her highschooler, Spiral Arts. It makes her happy for weeks that she raised the amount of money she had to begin, which is $50! However, all of a sudden, her house payment was due and that needy house costs $25! If Christine received news ... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"uid": "kd::87c6e4c4b16a185ab6e45259",
"index": "kd::87c6e4c4b16a185ab6e45259",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 55 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Arrange the positive odd numbers in three columns as shown below: \n1 \n3 5 \n7 9 11 \n13 15 17 19 \n… … … \nThen, the number 2013 is in the $\\underline{\\hspace{1cm}}$ row and the $\\underline{\\hspace{1cm}}$ column.\n\nSolve the problem. Show your re... | math | {
"ground_truth": "17\\text{th}",
"style": "rule"
} | {
"uid": "kd::9c2ff3efd272b596ea4159e0",
"index": "kd::9c2ff3efd272b596ea4159e0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{44\\cdot45}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "gene... |
t01_math | [
{
"role": "user",
"content": "What is the coefficient of $\\left(9\\left(x+1\\right)\\left(x+2\\right)-7\\left(x+4\\right)+5\\right)+2$?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Identify the numerical factor multiplying the x term in the final simplifie... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"uid": "kd::324bdbbe810845b8f8aa7ec0",
"index": "kd::324bdbbe810845b8f8aa7ec0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 -10 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Michael can do five times more activities than Cyrus, but he bored of already after 10 activities. What's the maximum number of activities Cyrus can do in a day if Michael can do at least twice as many activities as Cyrus?\n\nSolve the problem. Show your reasoning, then put the... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::ff5aee53c9041b6c29cca805",
"index": "kd::ff5aee53c9041b6c29cca805",
"lang": "en",
"rubrics": [
{
"criterion": "Define variables for the number of activities each person performs and translate the given conditions into mathematical inequalities.",
"points": 2,
"tags": {
... |
t01_math | [
{
"role": "user",
"content": "Consider the set \\( S = \\{1, 2, 3, \\ldots, 24, 25\\} \\). Four distinct numbers are chosen from set \\( S \\). What is the probability that these four numbers can represent the side lengths of a convex quadrilateral?\n\nSolve the problem. Show your reasoning, then put the fi... | math | {
"ground_truth": "\\frac{5368}{6325}",
"style": "rule"
} | {
"uid": "kd::175a0ece118b0b1d8e6739ae",
"index": "kd::175a0ece118b0b1d8e6739ae",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 45 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Alyssa is counting the number of students in each grade. She first counts the number of kindergartners and then doubles this number for the number of first-graders. Finally, she performs one less multiplication than the number of kindergartner in her number of second-graders.\n... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"uid": "kd::5ec1885bd1f786489dfc2bbc",
"index": "kd::5ec1885bd1f786489dfc2bbc",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 2.7913 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"... |
t01_math | [
{
"role": "user",
"content": "A colony of ants doubles in size every 5 minutes. The colony started out with 27 ants that multiply according to this rule. In how many minutes will the colony first exceed 2200 ants?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHin... | math | {
"ground_truth": "35",
"style": "rule"
} | {
"uid": "kd::8ff9f41d69cb5a5809d2ad0f",
"index": "kd::8ff9f41d69cb5a5809d2ad0f",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 64 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Joshua's cousin drinks 2 bottles of water that each have 500 ml per bottle every week. If he wants to calculate how much water his cousin drinks in months, how much water does he get?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::e92747fad4232505c1634990",
"index": "kd::e92747fad4232505c1634990",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1000 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Imagine that my laptop is in overflow every round day and every day that it is late it costs $40. First, you give it a one year grace period that costs an additional 10%. How much will it cost to receive full reimbursement?\n\nSolve the problem. Show your reasoning, then put ... | math | {
"ground_truth": "16060",
"style": "rule"
} | {
"uid": "kd::710ee148e1de7a52fd36ff1a",
"index": "kd::710ee148e1de7a52fd36ff1a",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 14600 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Find the quotient when the base-5 number $43_{5}$ is divided by the base-5 number $2_{5}$. Express your answer in base-10.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Verify your result by multiplying the divisor by the quoti... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"uid": "kd::a6ae1d7c77d30d1471e99453",
"index": "kd::a6ae1d7c77d30d1471e99453",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 12 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "What is the sum of all odd integers between 13 and 37?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Apply the arithmetic series sum formula by multiplying the count of terms by the average of the first and last terms."
}
] | math | {
"ground_truth": "325",
"style": "rule"
} | {
"uid": "kd::63449ffe6de41d5075306fbd",
"index": "kd::63449ffe6de41d5075306fbd",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{24}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Example 18 (1985 Poland-Austria Joint Competition Problem) Let $x, y, z, w$ be four real numbers, not all zero, find the maximum value of $S=$ $\\frac{x y+2 y z+z w}{x^{2}+y^{2}+z^{2}+w^{2}}$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}... | math | {
"ground_truth": "\\frac{\\sqrt{2}+1}{2}",
"style": "rule"
} | {
"uid": "kd::1a78d5f470ad8ef13f9615df",
"index": "kd::1a78d5f470ad8ef13f9615df",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 12 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "What is the product of 2 and the result of multiplying four and a number by 4?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Multiply the final intermediate value by two to obtain the complete simplified expression."
}
] | math | {
"ground_truth": "32x",
"style": "rule"
} | {
"uid": "kd::501cef43a2bdea5e96bb6b3a",
"index": "kd::501cef43a2bdea5e96bb6b3a",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 16 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Tim paints the side of a building measuring 315 ft by 60 ft. If one gallon of paint can cover 1500 sq ft of surface, how many gallons of paint did he need?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Round the calculated amoun... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"uid": "kd::3bd8d4a6476c54c3c31d59da",
"index": "kd::3bd8d4a6476c54c3c31d59da",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 18900 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Find the value of the integral \\(\\int^{2\\pi}_{0}\\frac{\\sin^2(x)}{a-b\\cos x}dx\\) without using contour integration, where \\(a > b > 0\\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Apply the standard integral formula f... | math | {
"ground_truth": "\\frac{2\\pi}{a+\\sqrt{a^2-b^2}}",
"style": "rule"
} | {
"uid": "kd::632fb3a0ef077dbb964d3b46",
"index": "kd::632fb3a0ef077dbb964d3b46",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{\\cosx}{b} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic"... |
t01_math | [
{
"role": "user",
"content": "Find \\( k > 0 \\) and \\( m \\in \\mathbb{N} \\) such that \\( n^3 - 7n \\ge kn \\) for all integers \\( n \\ge m \\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Test consecutive integer values for n starting from 1 to find ... | math | {
"ground_truth": "k = 2, m = 3",
"style": "rule"
} | {
"uid": "kd::76bdfc76c78727106cf4b92d",
"index": "kd::76bdfc76c78727106cf4b92d",
"lang": "en",
"rubrics": [
{
"criterion": "Divide the inequality by n to isolate the quadratic expression and analyze its behavior for large n.",
"points": 2,
"tags": {
"judge": false,
"inject... |
t01_math | [
{
"role": "user",
"content": "Seventy-eight students took the bus. Two-thirds of them are from town. The rest came from outside town. The bus couldn't carry 40 students because they occupied too much space. The rest of the passengers got off near the bus station to switch to a smaller, less crowded bus. How... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"uid": "kd::9119a453c6932c5b9976c693",
"index": "kd::9119a453c6932c5b9976c693",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 38 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "8-25 Let $p_{0}>2$ be a given prime number, and the sequence $a_{0}, a_{1}, a_{2}, \\cdots$ satisfies $a_{0}=0$, $a_{1}=1$, and\n$$\na_{n+1}=2 a_{n}+(a-1) a_{n-1}, n=1,2, \\cdots\n$$\n\nwhere the natural number $a$ is a parameter. Find the smallest value of $a$ that satisfies t... | math | {
"ground_truth": "\\prod_{3\\leqp\\leqp_{0}}p",
"style": "rule"
} | {
"uid": "kd::6785954c4e10c2004c3ee9c8",
"index": "kd::6785954c4e10c2004c3ee9c8",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 24160 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Example 7 When is $x$ a rational number such that the algebraic expression $9 x^{2}$ $+23 x-2$ is exactly the product of two consecutive positive even numbers?\n\n\n\nTranslate the above text into English, please keep the original text's line breaks and format, and output the t... | math | {
"ground_truth": "x=2, -\\frac{41}{9}, -17, \\frac{130}{9}",
"style": "rule"
} | {
"uid": "kd::fcc85c68a7c5c2976a92cc16",
"index": "kd::fcc85c68a7c5c2976a92cc16",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 2990 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Solve the partial differential equation \\( \\frac{\\partial u}{\\partial x} - 3x \\frac{\\partial u}{\\partial y} = 0 \\) with the initial condition \\( u(x,0) = \\cos(2x) \\). Determine the function \\( F \\) such that \\( u(x,y) = F(y + 3x) \\).\n\nSolve the problem. Show yo... | math | {
"ground_truth": "u(x,y) = \\cos(\\frac23 (y+3x))",
"style": "rule"
} | {
"uid": "kd::8978799b9a3bccced6ec7312",
"index": "kd::8978799b9a3bccced6ec7312",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{-3}{1} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "커피 머그 $d$개와 커피 $m$잔의 총 비용 $C$를 나타내는 대수식 $C = 4 + 1.3m$이 주어졌을 때, 올바른 연산 순서에 따라 식 $13(-1.1)C$를 어떻게 단순화할 수 있는지를 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: C에 대입한 후 분배법칙을 적용하여 괄호 안의 각 항에 -14.3을 곱하여 최종 식을 완성하라."
}
] | math | {
"ground_truth": "-57.2 - 18.59m",
"style": "rule"
} | {
"uid": "kd::d70f073559082421a386f730",
"index": "kd::d70f073559082421a386f730",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 1859 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "It can take 8 hours to make a submarine worth $2880,000. Submarine Asorry, an upgrade to an older design, can make twice that value in 3/4 as long as the original time. Without working together, how long will it take for two people to make the upgraded submarine?\n\nSolve the p... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"uid": "kd::9ea95b27395315deb3e01071",
"index": "kd::9ea95b27395315deb3e01071",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 720000 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"... |
t01_math | [
{
"role": "user",
"content": "Tom's bicycle had a recent Craigslist sales. He sold it for $120. He also bought a new one and accepted trade-ins. He accepted 18 payments of $6, 12 payments of $9, and any remaining payments of 3 times the amount of the previous total. In the end, how much was the new bicy... | math | {
"ground_truth": "984",
"style": "rule"
} | {
"uid": "kd::438821559a0ded558dd1aa38",
"index": "kd::438821559a0ded558dd1aa38",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 164 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Find all functions \\( f: \\mathbb{Z} \\to \\mathbb{Z} \\) such that \n\\[ f(x+y)((f(x) - f(y))^2 + f(xy)) = f(x^3) + f(y^3) \\]\nfor all integers \\( x, y \\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Substitute y equals z... | math | {
"ground_truth": "f(x) = x \\), \\( f(x) = 0 \\), \\( f(x) = 2 \\), \\( f(x) = \\begin{cases} 1 & \\text{if } x \\text{ is odd} \\ 2 & \\text{if } x \\text{ is even} \\end{cases}",
"style": "rule"
} | {
"uid": "kd::12f533b2cf1f45453d052b6b",
"index": "kd::12f533b2cf1f45453d052b6b",
"lang": "en",
"rubrics": [
{
"criterion": "Test small integer values like zero and one to derive basic properties of the function.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
... |
t01_math | [
{
"role": "user",
"content": "Given a sample of $n$ observations from a discrete uniform distribution with parameter $N$, find the uniformly minimum variance unbiased estimator (UMVUE) of $N$. It is known that the sample maximum $M$ is a complete and sufficient statistic for $N$. Determine a function $g(M)$... | math | {
"ground_truth": "\\widehat N_{\\text{UMVUE}} =g(M) =\\frac{M^{ n+1}-(M-1)^{ n+1}} {M^{ n}-(M-1)^{ n}}",
"style": "rule"
} | {
"uid": "kd::1400ded4f301277c86c1fb7a",
"index": "kd::1400ded4f301277c86c1fb7a",
"lang": "en",
"rubrics": [
{
"criterion": "Set up the expectation equation for the function g(M) using the probability mass function of the sample maximum M.",
"points": 2,
"tags": {
"judge": false,
... |
t01_math | [
{
"role": "user",
"content": "Determine the convergence or divergence of the series $\\sum\\limits_{n=1}^\\infty \\dfrac{(2-3i)^n}{4^n\\,\\sqrt[1000]{n}}$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Simplify the expression by separating the geometric rati... | math | {
"ground_truth": "Converges absolutely",
"style": "rule"
} | {
"uid": "kd::e212824743aec572af5663e9",
"index": "kd::e212824743aec572af5663e9",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.9014 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"... |
t01_math | [
{
"role": "user",
"content": "Donny spends $1 on transport and food for breakfast each day. overs 31 days, he spent a total of $1230. How much does he spend for food and/or newspaper when he buys either of them?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: ... | math | {
"ground_truth": "1199",
"style": "rule"
} | {
"uid": "kd::acd5e132e457ad8dfd2d9d16",
"index": "kd::acd5e132e457ad8dfd2d9d16",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 39 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Find the sum of terms in the nth bracket of the sequence: (1), (4,10,20), (35,56,84,120,165,220), (284, ..., 10 terms), (..., 15 terms), ...\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Recognize that the terms are tetrahedral ... | math | {
"ground_truth": "S_n =\\binom{\\binom{n+2}{3}+3}{4} -\\binom{\\binom{n+1}{3}+3}{4}",
"style": "rule"
} | {
"uid": "kd::7a353b3d60dc43bb27c3cc72",
"index": "kd::7a353b3d60dc43bb27c3cc72",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 12 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "In a population where 12.6% of people are age 65 and over, approximately what percent of the population are of working age adults (above age 17 to age 65)?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Subtract the sum of the un... | math | {
"ground_truth": "62.4%",
"style": "rule"
} | {
"uid": "kd::c9a1e7e1d07978e82b2c6701",
"index": "kd::c9a1e7e1d07978e82b2c6701",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the total population percentage and subtract the known non-working age groups to find the remaining portion.",
"points": 2,
"tags": {
"judge": false... |
t01_math | [
{
"role": "user",
"content": "In Vívás, the one who reaches 15 hits first wins the bout. Suppose in the competition between $A$ and $B$ (at any point within the bout), $A$ scores the next hit with probability $p$, and $B$ with probability $q=1-p$. (They never score a hit simultaneously.)\n\nAssume that in a... | math | {
"ground_truth": "\\binom{k+\\ell}{k}p^{k}q^{\\ell+1}",
"style": "rule"
} | {
"uid": "kd::b3efd0b30e4b653dba8e9155",
"index": "kd::b3efd0b30e4b653dba8e9155",
"lang": "en",
"rubrics": [
{
"criterion": "Model the problem using a recursive probability function that depends on the number of hits each player still needs to win.",
"points": 2,
"tags": {
"judge":... |
t01_math | [
{
"role": "user",
"content": "Three coins are thrown all at once. All of them are either tails (T) only or heads (H) only. Find the number of possible outcomes that are possible, considering every coin has a 50% chance of landing heads and a 50% chance of landing tails.\n\nSolve the problem. Show your reaso... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"uid": "kd::b8021db1e178da3f8fdac7a3",
"index": "kd::b8021db1e178da3f8fdac7a3",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the number of distinct outcomes for a single coin toss to establish the base possibilities.",
"points": 2,
"tags": {
"judge": false,
"inject... |
t01_math | [
{
"role": "user",
"content": "측정 가능 함수 $g:[0,+\\infty) \\to \\mathbb{R}$가 거의 모든 $x \\in [0,+\\infty)$에 대해 $g(x) \\geq 0$이고 $\\int_0^{+\\infty} g(x) \\, dx < +\\infty$를 만족시킨다고 하자. $\\liminf_{x \\to +\\infty} g(x) = 0$이 성립하는지 판별하고, 그 답에 대한 근거를 제시하시오.\n\nSolve the problem. Show your reasoning, then put the fin... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::d7dae270bd5b998fa500cfec",
"index": "kd::d7dae270bd5b998fa500cfec",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 \\pi 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Solve for $x$ if $10<10x<90.$ With the aid of a graph, explain why only $x=1$ is applicable to the inequality while $x=0$ and 2 are not.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Plot the exponential curve and the horizontal... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"uid": "kd::b07dff976266441ce1596720",
"index": "kd::b07dff976266441ce1596720",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 100 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "A piece of string is $24$ inches long. The midpoints of the string are marked, then it is folded at those points. How long, in inches, is each segment of the string now?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Recognize th... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"uid": "kd::65e53909355ce41f83b194e7",
"index": "kd::65e53909355ce41f83b194e7",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 18 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "A power plant needs to send 1000analyst. The plant can send electricity up to 150 pancakes. How many trips will it need to make to bring the canoe 3 miles?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Round the calculated quoti... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"uid": "kd::b3e0d50ba80b61b275bfe9db",
"index": "kd::b3e0d50ba80b61b275bfe9db",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1050 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Given the matrix $dists$ as defined in the original question, find an expression for $X^TX$ in terms of the matrix $dists$. Assume that the matrix $X$ is centered, i.e., the sum of its rows is zero.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\b... | math | {
"ground_truth": "-\\frac12(I-\\frac1n\\mathbf{1}\\mathbf{1}^T)\\text{dists}(I-\\frac1n\\mathbf{1}\\mathbf{1}^T)",
"style": "rule"
} | {
"uid": "kd::26a43d63a2884d5db1c96ec5",
"index": "kd::26a43d63a2884d5db1c96ec5",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 -0.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "In the context of a proof involving a field \\( R \\), condition (iii) is replaced by condition (iv). If \\( R \\) is a field, explain why condition (iii) implies condition (i), leading to the conclusion that \\( \\det(xI - C) = 0 \\) when \\( x \\) is an eigenvalue of \\( C \\... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::aaca4e58e74652f6bcd80bdf",
"index": "kd::aaca4e58e74652f6bcd80bdf",
"lang": "en",
"rubrics": [
{
"criterion": "Use the definition of an eigenvalue to construct a non-zero vector that lies in the kernel of the matrix xI minus C.",
"points": 2,
"tags": {
"judge": false,... |
t01_math | [
{
"role": "user",
"content": "How long did it take Tom to paint a bedroom, if it took him twice as long as the last exercise to paint a tub if it took him 40 minutes to paint the tub (with no breaks in between sections) and he spent 10 minutes planning how to paint it and no time painting his own bathroom?\... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"uid": "kd::2f46bccd9cbf801549e07379",
"index": "kd::2f46bccd9cbf801549e07379",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 80 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Prove the trigonometric identity: \n\\[ \\cos x - \\cos(3x) = 4 \\sin^2 x \\cos x \\]\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Substitute the double-angle identity for sine into the expression to reveal the target factor o... | math | {
"ground_truth": "\\cos x - \\cos(3x) = 4 \\sin^2 x \\cos x",
"style": "rule"
} | {
"uid": "kd::5f858f9399f7390b799eef67",
"index": "kd::5f858f9399f7390b799eef67",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{\\pi}{6} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "An electrician paid $100 a day to His father to fix some electric issues at his house. He fixed 4 pantry lights each day. How manyhungry-fish are there in each pantry, if he worked for 10 days and each fish needed 4 power CONS?\n\nSolve the problem. Show your reasoning, then pu... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"uid": "kd::afa640ab573ada6869ce36c6",
"index": "kd::afa640ab573ada6869ce36c6",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 40 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "$(0,1)$-행렬 $B$가 $n$개의 열과 $n^3$개의 행을 가지며, 각 행에는 정확히 네 개의 $1$이 포함되어 있다고 하자. 각 행에 포함된 $1$의 개수가 네 개보다 적어지도록 해야 할 때, 삭제해야 하는 열의 최소 개수를 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 가능한 모든 4개 열 조합이 $n^3$개 이하일 때, 최대 3개의 열만 남길 수 있음을... | math | {
"ground_truth": "n - 3",
"style": "rule"
} | {
"uid": "kd::483d5a8a78ed79aa15b49a1d",
"index": "kd::483d5a8a78ed79aa15b49a1d",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 27000 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Sally has 32 toys and 4 times as many puzzles as toys. Sean has 58 arcade cards and 3 times as many toys as Sean. How many more toys do Sean and Sally have together than puzzles that Sally has?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxe... | math | {
"ground_truth": "78",
"style": "rule"
} | {
"uid": "kd::0fc7a98ad9996fee168a1c1f",
"index": "kd::0fc7a98ad9996fee168a1c1f",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 128 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "A client wants to drink water for 500 ml and milk twice a day. A bottle of water is 600 ml. How many bottles of water should the client buy?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Round the division result up to the next ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::80fa0c4c92b7a40b1519adc7",
"index": "kd::80fa0c4c92b7a40b1519adc7",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1000 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Linklet is making clay pots for a sale. He makes five clay pots every hour. For the last hour of Saturday, he took a 20-minute break. How many clay pots did Linklet make on Saturday?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint:... | math | {
"ground_truth": "118",
"style": "rule"
} | {
"uid": "kd::b93e32c6c726914eb22e76d3",
"index": "kd::b93e32c6c726914eb22e76d3",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 36 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "A man buys an article for $100, but he got a 10% discount on the initial purchase. After buying, he pays a 5% sales tax on the discounted price. Later, he sells the article for $130 including a 15% sales tax. Find the actual gain percent.\n\nSolve the problem. Show your reasoni... | math | {
"ground_truth": "19.62\\%",
"style": "rule"
} | {
"uid": "kd::b6b31fdf7b5582c42088b607",
"index": "kd::b6b31fdf7b5582c42088b607",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{130}{1.15} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic"... |
t01_math | [
{
"role": "user",
"content": "The segment \\( PQ \\) is divided into several smaller segments. On each of them, a square is constructed (see illustration).\n\nWhat is the length of the path along the arrows if the length of the segment \\( PQ \\) is 73? If necessary, round your answer to 0.01 or write the a... | math | {
"ground_truth": "219",
"style": "rule"
} | {
"uid": "kd::13b5c4c3683b23f29433205c",
"index": "kd::13b5c4c3683b23f29433205c",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 146 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "It took Donna weeks to complete her tax return. Roberta took 3 times as long as Donna to complete his return. Carrie took twice the time Donna and Roberta took together. How many weeks did it take Carrie to complete her return?\n\nSolve the problem. Show your reasoning, then pu... | math | {
"ground_truth": "8D",
"style": "rule"
} | {
"uid": "kd::48ec63e792238253ecd076e4",
"index": "kd::48ec63e792238253ecd076e4",
"lang": "en",
"rubrics": [
{
"criterion": "Assign a variable to represent Donna's unknown time in weeks to express all other durations algebraically.",
"points": 2,
"tags": {
"judge": false,
"... |
t01_math | [
{
"role": "user",
"content": "Anna's instant base pay is $18 per hour. She is paid back pay on every day she works in excess of 6 hours. What does she have to make today, in dollars, if she works 11 hours today?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: ... | math | {
"ground_truth": "198",
"style": "rule"
} | {
"uid": "kd::2857c4e0b9771c4f87446702",
"index": "kd::2857c4e0b9771c4f87446702",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 108 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Given the digits 0 and 9, form the smallest positive number that is a multiple of a given integer \\( n \\). For example, if \\( n = 7 \\), the smallest number is 9009. Determine this number for a given \\( n \\).\n\nSolve the problem. Show your reasoning, then put the final an... | math | {
"ground_truth": "9009",
"style": "rule"
} | {
"uid": "kd::8889bee4296241dce13876b1",
"index": "kd::8889bee4296241dce13876b1",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 90000 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Find the maximum value of \\(|\\ln(x) - f(x)|\\) for \\(0.3 \\le x \\le 1.7\\), where \\(f(x)\\) is the sum of the first three nonzero terms of the Taylor series for \\(\\ln(x)\\) centered at \\(x=1\\).\n\nSolve the problem. Show your reasoning, then put the final answer inside... | math | {
"ground_truth": "0.1446",
"style": "rule"
} | {
"uid": "kd::ae1172c4c490454278fdf403",
"index": "kd::ae1172c4c490454278fdf403",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.14247765 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "A group of college students were surveyed about whether they were taking a mathematics course and whether they were taking an English course. The results are displayed in the following table:\n\n| | M | T | W | Th | F |\n|--------|---|---|---|----|---|\n| 9 A.M. | X | X ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"uid": "kd::1d71fe45f6caa98d6af849c0",
"index": "kd::1d71fe45f6caa98d6af849c0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 13 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "The base of the pyramid \\( T ABCD \\) is a trapezoid \\( ABCD \\) with the length of the shorter base \\( BC \\) equal to \\( 4 \\sqrt{11} \\). The diagonals of the trapezoid \\( AC \\) and \\( BD \\) intersect at point \\( O \\). The ratio of the areas of triangles \\( AOB \\... | math | {
"ground_truth": "105.875",
"style": "rule"
} | {
"uid": "kd::4f34b30da36cb3e3236ced04",
"index": "kd::4f34b30da36cb3e3236ced04",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{28435}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",... |
t01_math | [
{
"role": "user",
"content": "Find the total number of ways to color a regular pentagon using exactly 5 colors, where each vertex must be a different color.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Fix the position of one specific color to eliminate rot... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"uid": "kd::1619f74c24c9673c974343d5",
"index": "kd::1619f74c24c9673c974343d5",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 120 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Evaluate the following trigonometric functions, correct to 4 significant figures: \n(a) \\(\\sin(1.481)\\) (where \\(1.481\\) is in radians) \n(b) \\(\\cos\\left(\\frac{3\\pi}{5}\\right)\\) \n(c) \\(\\tan(2.93)\\) (where \\(2.93\\) is in radians)\n\nSolve the problem. Show y... | math | {
"ground_truth": "0.9960, -0.3090, -0.2148",
"style": "rule"
} | {
"uid": "kd::8bbf616735b21cb364b17f9d",
"index": "kd::8bbf616735b21cb364b17f9d",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.003157770 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Amanda's current bank balance is a total of $4000. She makes a withdrawal of $100, then puts a $15 into savings. The day after, she makes a withdrawal of $300, but then lends $50 to her sister. How much is Amanda's current bank account balance?\n\nSolve the problem. Show you... | math | {
"ground_truth": "3535",
"style": "rule"
} | {
"uid": "kd::1bc91382cc50310ff9b69355",
"index": "kd::1bc91382cc50310ff9b69355",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 -100 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Jamie decides to walk to school from where she lives and calculate how far she has been walking, in miles. The first day of school she walks one mile, the second day she walks two miles, the third day she walks three miles and continues until she walks ten miles the last day. H... | math | {
"ground_truth": "55",
"style": "rule"
} | {
"uid": "kd::461bf277bf650057b3c1a6d3",
"index": "kd::461bf277bf650057b3c1a6d3",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 28 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "The range of 6 flips of a balance coin is which among the following options?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Express the complete set of possible outcomes using interval notation for discrete values."
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"uid": "kd::a1b6c322f7ff6db5788377af",
"index": "kd::a1b6c322f7ff6db5788377af",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the minimum and maximum possible counts of heads in six coin flips.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
"scaffo... |
t01_math | [
{
"role": "user",
"content": "Let $f : S^n \\to \\mathbb{R}^n$ be a function such that $f(-x) = -f(x)$ for all $x \\in S^n$. Prove that there exists a point $y \\in S^n$ such that $f(y) = 0$. Use the Borsuk-Ulam theorem to justify your answer.\n\nSolve the problem. Show your reasoning, then put the final an... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::1236da8921f7b1293164d418",
"index": "kd::1236da8921f7b1293164d418",
"lang": "en",
"rubrics": [
{
"criterion": "Apply the Borsuk-Ulam theorem to the given function to find a point where the function values at antipodal points are equal.",
"points": 2,
"tags": {
"judge"... |
t01_math | [
{
"role": "user",
"content": "The owner of an apartment insured it for 3,750,000 rubles (the actual cost of the apartment is 7,500,000 rubles). The actual damage amounted to 2,750,000 rubles. The insurance compensation under the proportional liability system was 1,350,000 rubles. Determine the amount of the... | math | {
"ground_truth": "50000",
"style": "rule"
} | {
"uid": "kd::b864c40eef86f713ac01275c",
"index": "kd::b864c40eef86f713ac01275c",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 240 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "6/15 of Hansra's plants die. Out of the remaining plants, 40% are perennial and the remaining 60% are annual. What is the probability that Hansra picks an annual plant?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Recognize tha... | math | {
"ground_truth": "\\frac{3}{5}",
"style": "rule"
} | {
"uid": "kd::77e678db89ad0d9fcc706159",
"index": "kd::77e678db89ad0d9fcc706159",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 5.4 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Determine the number of distinct ways to color the faces of a cube using 6 distinct colors, ensuring that no two adjacent faces share the same color.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Recognize that using six distinc... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"uid": "kd::1f1bdac793bd5ea15a0d9bad",
"index": "kd::1f1bdac793bd5ea15a0d9bad",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 720 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Let \\(ABC\\) be a triangle with \\( \\angle A = 60^\\circ \\). Suppose that there exists a point \\(P\\) inside the triangle such that \\(PA = 1\\), \\(PB = 2\\), and \\(PC = 3\\). Find the maximum possible area of triangle \\(ABC\\).\n\nSolve the problem. Show your reasoning,... | math | {
"ground_truth": "\\frac{\\sqrt3 (13+\\sqrt{73})}{8}",
"style": "rule"
} | {
"uid": "kd::a9991a34f84bb2555c85e1e7",
"index": "kd::a9991a34f84bb2555c85e1e7",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{\\sqrt{3}}{4} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "gener... |
t01_math | [
{
"role": "user",
"content": "Each sheet of letter size notebook paper accommodates 200 pages. Whether the one sheet of notebook paper torn out of it has remained separate into two sheets of notebook paper as well, how many pages of text is on each sheet of torn-out notebook paper if the original sheet of ... | math | {
"ground_truth": "85",
"style": "rule"
} | {
"uid": "kd::173b8b2bdeed163f151e6432",
"index": "kd::173b8b2bdeed163f151e6432",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 100 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "How many whole numbers less than 100 have a common factor of 5 with the number 35?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: List the multiples of 5 starting from 5 up to the largest multiple below 100."
}
] | math | {
"ground_truth": "19",
"style": "rule"
} | {
"uid": "kd::0f30ee014bca0fd2af0bf6bd",
"index": "kd::0f30ee014bca0fd2af0bf6bd",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the prime factors of 35 to determine the condition for sharing a common factor.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
... |
t01_math | [
{
"role": "user",
"content": "3 apartments have the same amount and balance with 7 gallons of gas. Each apartment has a goal to cut down their gas use to 5 gallons once they reach their goal this month. How many gallons of gas will be spent on gas by they all reach their goal this month?\n\nSolve the proble... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"uid": "kd::80a4c004d54356f963f063a7",
"index": "kd::80a4c004d54356f963f063a7",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the number of apartments and the target gas consumption per apartment to determine the total usage.",
"points": 2,
"tags": {
"judge": false,
... |
t01_math | [
{
"role": "user",
"content": "유한군 \\(G\\)의 부분군 \\(H\\)가 \\(|H| = 3\\)일 때, \\(|N_{G}(H) : C_{G}(H)|\\)의 값을 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: H의 비자명한 자기동형사상이 존재하는지 확인하여 몫군의 크기가 1 이 아닌 2 임을 유도하라"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::31b28335252e7484c0a9241a",
"index": "kd::31b28335252e7484c0a9241a",
"lang": "ko",
"rubrics": [
{
"criterion": "N/C 정리를 적용하여 정규화자의 몫군을 H의 자기동형사상군으로 연결하는 구조를 확인하라",
"points": 2,
"tags": {
"judge": false,
"inject": true,
"scaffold_rank": 1,
"scaff... |
t01_math | [
{
"role": "user",
"content": "What will be the ratio between the area of a rectangle with length L and width W, and the area of a triangle formed with one of the sides of the rectangle as base B, a vertex on the opposite side of the rectangle, and an angle θ between the base B and the height h from the vert... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::6ae827e61f28e0dca3f1111c",
"index": "kd::6ae827e61f28e0dca3f1111c",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{L\\W}{\\frac{1}{2}\\L\\W} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_k... |
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