data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
t01_math | [
{
"role": "user",
"content": "For the system of linear equations\n\\[4x + y = 72\\]and $$(3a - 1) y + 49x = 0,$$find all possible values of $a.$\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Set the calculated determinant equal to zero and solve the resultin... | math | {
"ground_truth": "\\frac{53}{12}",
"style": "rule"
} | {
"uid": "kd::50b30b38d01bc0e3d581179e",
"index": "kd::50b30b38d01bc0e3d581179e",
"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": "On a complete graph, consider the following four processes: \n- **IP dynamics (Imitation Process)**: Individuals imitate a neighbor's strategy proportional to fitness. \n- **BD-D process (Birth-Death with Death proportional to fitness)**: A birth event selects an individual p... | math | {
"ground_truth": "1 - 1/r",
"style": "rule"
} | {
"uid": "kd::976927a11deeb3cb7ea4e686",
"index": "kd::976927a11deeb3cb7ea4e686",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{ir+N-i-1}{r[(i-1)r+N-i]} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_ki... |
t01_math | [
{
"role": "user",
"content": "If Haleigh has 4 dogs and 3 cats and needs to buy leggings for all of them, how many pairs of leggings does she need in total?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Add the number of dogs to the number of cats to determi... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"uid": "kd::3e95966376afff58ef97193c",
"index": "kd::3e95966376afff58ef97193c",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the total number of individual animals that require a pair of leggings each.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
... |
t01_math | [
{
"role": "user",
"content": "There are five dogs at the beach. To capture them, there are 8 puppies on land. How many dogs, in total, are at the beach now?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Exclude the puppies from the total because the problem ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"uid": "kd::ff335b76ef5fbe52e4d23b6b",
"index": "kd::ff335b76ef5fbe52e4d23b6b",
"lang": "en",
"rubrics": [
{
"criterion": "Identify which animals are physically located at the specific destination mentioned in the question.",
"points": 2,
"tags": {
"judge": false,
"inject... |
t01_math | [
{
"role": "user",
"content": "Calculate:<br/>$(1)(-\\frac{3}{4}-\\frac{5}{8}+\\frac{9}{12})×(-24)$;<br/>$(2)-1^{6}+|\\left(-2\\right)^{3}-10|-\\left(-3\\right)\\div \\left(-1\\right)^{2023}$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Carefully distinguis... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"uid": "kd::a139adb86069d91abf0b1d4b",
"index": "kd::a139adb86069d91abf0b1d4b",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{5\\cdot3}{1} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generi... |
t01_math | [
{
"role": "user",
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nIn $\\triangle{ABC}$ with side lengths $AB = 13$, $AC = 12$, and $BC = 5$, let $O$ and $I$ denote ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"uid": "kd::05e3f61757d2e773d1dfe26f",
"index": "kd::05e3f61757d2e773d1dfe26f",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "When y=1, b=y and for the expression b-2/2, the value is 3. What is the value of b when y=3?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Ignore the contradictory numerical example and rely solely on the explicit rule that b eq... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"uid": "kd::04dbc3bde8c420a14e9b6b62",
"index": "kd::04dbc3bde8c420a14e9b6b62",
"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": "How many hands are in a score?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Verify the result by multiplying the number of hands by the items per hand to ensure it equals a score."
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::0bfb75d7dda2fe6a1b84ac67",
"index": "kd::0bfb75d7dda2fe6a1b84ac67",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 87 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Five items of fruit cost 90p while six items of fruit cost //5 more than that amount. How much would nine items of fruit cost?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Multiply the verified unit price by nine to find the to... | math | {
"ground_truth": "162",
"style": "rule"
} | {
"uid": "kd::52896a46ad14bd2b77713b05",
"index": "kd::52896a46ad14bd2b77713b05",
"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": "Evaluate the following expressions for \\( x = 2 \\):\na) \\( x[x(x+3)+4]+1 \\)\nb) \\( x(x[x(x-7)-5]+8)-3 \\)\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Carefully track negative signs and perform multiplication before additi... | math | {
"ground_truth": "29, -47",
"style": "rule"
} | {
"uid": "kd::e82db9a9e0a7e56d9860aed4",
"index": "kd::e82db9a9e0a7e56d9860aed4",
"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": "A vinegar bottle holds twice the volume of a gallon bottle. A gallon bottle holds 1000ml and fills a liter bottle to the brim. If an'){\nYou are a helpful assistant.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Convert the resu... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::592887c89f86fb964c1755bc",
"index": "kd::592887c89f86fb964c1755bc",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 2000 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "The sum of three positive integers is less than 30, their product is 28 and 2 is the greatest of the three. What are the three integers?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Compare the calculated maximum product agains... | math | {
"ground_truth": "2, 7, 2",
"style": "rule"
} | {
"uid": "kd::3b636550a292675320fc5b17",
"index": "kd::3b636550a292675320fc5b17",
"lang": "en",
"rubrics": [
{
"criterion": "Analyze the constraints on the integers by testing possible values for the greatest integer.",
"points": 2,
"tags": {
"judge": false,
"inject": true,... |
t01_math | [
{
"role": "user",
"content": "The researchers weighed 200 individualmeteorites at recent comma shower. On average thereby, they found 3 Family kangaroosFinderRead and transferred to family kangaroosFinder Read. If there were 225 family kangaroosFinderWrite, how many stayed, from the same collection, on the ... | math | {
"ground_truth": "222",
"style": "rule"
} | {
"uid": "kd::d456ca88434ee0ef0118c262",
"index": "kd::d456ca88434ee0ef0118c262",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 600 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "\\((3x^2 + 2x + c)^{12} = \\sum_{r=0}^{24} A_r x^r\\) 이고, \\(\\frac{A_{19}}{A_5} = \\frac{1}{2^7}\\) 일 때, \\(c\\)의 값을 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 계수 식을 정리할 때 공통된 상수 인수를 약분하여 c의 거듭제곱만 남는 단순한 형태를 유도하라."
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"uid": "kd::9f8fbe47850ec7b833555677",
"index": "kd::9f8fbe47850ec7b833555677",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 139968 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"... |
t01_math | [
{
"role": "user",
"content": "Let \\( x * y = \\frac{xy}{3} - x - y + 6 \\). Find \\( x \\neq 3 \\) such that\n\\[ (x * (x + x' - 3)) + (x * (2x - 3)) = 42 \\]\nwhere \\( x' \\) is symmetric to \\( x \\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Substit... | math | {
"ground_truth": "3 \\pm \\sqrt{33}",
"style": "rule"
} | {
"uid": "kd::8f5d9f6e1a8750931b2cc2ac",
"index": "kd::8f5d9f6e1a8750931b2cc2ac",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{x^{3}-3x^{2}+9x}{3(x-3)} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_ki... |
t01_math | [
{
"role": "user",
"content": "$\\beta$가 다항식 $x^3 - 2$의 근일 때, 갈루아 군 $\\text{Gal}(\\mathbb{Q}[\\beta]/\\mathbb{Q})$을 구하시오. 답은 군의 구조를 이용하여 제시하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 실수 근인 베타를 다른 복소수 근으로 보내는 사상이 정의역에 존재하지 않음을 논리적으로 서술하시오."
}
] | math | {
"ground_truth": "\\{e\\}",
"style": "rule"
} | {
"uid": "kd::5f9965c5a8505875d5327a08",
"index": "kd::5f9965c5a8505875d5327a08",
"lang": "ko",
"rubrics": [
{
"criterion": "다항식이 유리수 위에서 기약인지 확인하고, 생성된 확장이 분해체인지 판별하여 정규 확장이 아님을 보이시오.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
"scaffold_rank": 1,
... |
t01_math | [
{
"role": "user",
"content": "Find the set of values of $k$ so that the function $f:\\mathbb{R^{+}}\\mapsto [2,\\infty]$ given by $f(x)=x^2+kx+k$ is surjective.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Set the calculated minimum value equal to 2 and sol... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::66db3d03399350f1ca13a717",
"index": "kd::66db3d03399350f1ca13a717",
"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": "Tevina dollars is exchanging wash,dry and fold for starbux. She uses the promotion code starbux5 and needs to buy an equal number of each. How many dollars will Teiana only need to pay to exchange for starbux if each is 5 starbux for $1?\n\nSolve the problem. Show your reasonin... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"uid": "kd::0fdde4d189bec52c626bfc64",
"index": "kd::0fdde4d189bec52c626bfc64",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 15 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "A cake weighing one kilogram is cut into two pieces, and each piece is weighed separately, with the measured weights denoted by \\( x \\) and \\( y \\). Assume that the errors in obtaining \\( x \\) and \\( y \\) are independent and normally distributed with mean zero and the s... | math | {
"ground_truth": "T=\\frac{x-y}{x+y-1}",
"style": "rule"
} | {
"uid": "kd::561b8c9cd6d2eee8508fbed1",
"index": "kd::561b8c9cd6d2eee8508fbed1",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{D}{S} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Find numbers $H, J, K$ such that $H! = J \\cdot (J+1) \\cdot \\ldots \\cdot (J+K)$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Test small integer values for H starting from 3 to find a case where H factorial equals a product ... | math | {
"ground_truth": "H=5, J=4, K=2",
"style": "rule"
} | {
"uid": "kd::243cf5f061c6e4a8e7559e9b",
"index": "kd::243cf5f061c6e4a8e7559e9b",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{(J+K)!}{(J-1)!} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "gen... |
t01_math | [
{
"role": "user",
"content": "Let $f: \\mathbb{R} \\to \\mathbb{R}$ be a function such that $f(0) = 0$ and $|f'(x)| \\leq |f(x)|$ for all real numbers $x$. Does this imply that $f(x) = 0$ for all $x$? Justify your answer.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::a6fc5f29536e3543d069a01a",
"index": "kd::a6fc5f29536e3543d069a01a",
"lang": "en",
"rubrics": [
{
"criterion": "Define a non-negative auxiliary function representing the absolute value of f and analyze its derivative behavior.",
"points": 2,
"tags": {
"judge": false,
... |
t01_math | [
{
"role": "user",
"content": "Given a set of points that may not perfectly fit a function, develop a simple algorithm to estimate the second derivative at both endpoints of the set. For example, consider the points (0,0), (1,1), (3,27), and (6,216). The expected second derivatives at the endpoints are 0 and... | math | {
"ground_truth": "f''(0)=0, f''(6)=36",
"style": "rule"
} | {
"uid": "kd::0e32110d3ee85ccb9b868168",
"index": "kd::0e32110d3ee85ccb9b868168",
"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": "Let \\( f \\) be a continuously differentiable and decreasing function towards \\( 0 \\). Define \\( g_x = \\sum_{n>0} (-1)^n f(nx) \\). Find \\( \\lim_{x \\to 0^+} g_x \\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Apply th... | math | {
"ground_truth": "\\lim_{x\\to0^{+}}g(x)=-\\frac12 f(0)",
"style": "rule"
} | {
"uid": "kd::c467b1acb1bc6e899daa55fc",
"index": "kd::c467b1acb1bc6e899daa55fc",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{A}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "As shown in the figure, find the sum of the angles \\( \\angle 1 + \\angle 2 + \\angle 3 + \\angle 4 + \\angle 5 + \\angle 6 + \\angle 7 \\). Express your answer in degrees (\\( ^\\circ \\)) as a whole number.\n\nSolve the problem. Show your reasoning, then put the final answer... | math | {
"ground_truth": "540",
"style": "rule"
} | {
"uid": "kd::585e8b9ad2385bb38196e36a",
"index": "kd::585e8b9ad2385bb38196e36a",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1080 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Mastercard Express offers a continuous discount of 20%. If Leon received a 50% discount on the regular price of $50, calculate the total amount of money he paid when he purchased the item for 3 months.\n\nSolve the problem. Show your reasoning, then put the final answer inside ... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"uid": "kd::86b62695dfb79f7a8e6eb96d",
"index": "kd::86b62695dfb79f7a8e6eb96d",
"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": "John files his report usingetric sheets. Each page can fit 2 pages on a different side of a piece of paper. If angles are 5 per page and can be ordered in blocks of 3. If 200 sheets are used what is the total number of pages read by him?\n\nSolve the problem. Show your reasonin... | math | {
"ground_truth": "400",
"style": "rule"
} | {
"uid": "kd::aea5ad920c0ebb22887af7c0",
"index": "kd::aea5ad920c0ebb22887af7c0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 666 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "In a bipartite graph $G$ with $K$ left nodes and $M$ right nodes, each of the $KM$ potential edges is present independently with probability $p$. As $K$ and $M$ approach infinity, what is the expected number of left nodes connected to exactly one right node?\n\nSolve the proble... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::03764142cd1fc1c394e61605",
"index": "kd::03764142cd1fc1c394e61605",
"lang": "en",
"rubrics": [
{
"criterion": "Apply the linearity of expectation by summing the probabilities for each individual left node.",
"points": 2,
"tags": {
"judge": false,
"inject": tru... |
t01_math | [
{
"role": "user",
"content": "Carson has a savings goal of $70 per week. Tracy has a goal of $55 per week. If Carson saves for 2 months and Tracy saves for 3 months, how much more money does Carson have saved than Tracy?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"uid": "kd::9133ed99b120306b3195167b",
"index": "kd::9133ed99b120306b3195167b",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 4.2857 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"... |
t01_math | [
{
"role": "user",
"content": "Find the surface area of a right cone with base radius \\( r \\) and altitude \\( h \\) by applying Pappus's Centroid Theorem.\n\nPappus's Centroid Theorem states that the surface area \\( S_u \\) of a surface of revolution generated by rotating a plane curve \\( C \\) about an... | math | {
"ground_truth": "\\pi r \\sqrt{r^2 + h^2} + \\pi r^2",
"style": "rule"
} | {
"uid": "kd::eb3df5b5b934363c7958b235",
"index": "kd::eb3df5b5b934363c7958b235",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1}{s_{C}} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",... |
t01_math | [
{
"role": "user",
"content": "Determine the eigenvalues of the following $4 \\times 4$ matrix:\n$$J(\\epsilon)=\\begin{bmatrix} -\\mu & 0 & 0 & -\\frac{\\beta b}{\\mu}\\\\ 0 & -\\sigma & 0 & \\frac{\\beta b}{\\mu}\\\\ 0 & \\sigma & -(\\phi + d) & 0\\\\ 0 & 0 & \\alpha & -(\\phi + \\epsilon) \\end{bmatrix}$$... | math | {
"ground_truth": "-\\mu",
"style": "rule"
} | {
"uid": "kd::56f7e71774cbef50f9c40c60",
"index": "kd::56f7e71774cbef50f9c40c60",
"lang": "en",
"rubrics": [
{
"criterion": "Compute the determinant of the matrix minus lambda times the identity matrix to form the characteristic equation.",
"points": 2,
"tags": {
"judge": false,
... |
t01_math | [
{
"role": "user",
"content": "12 identically priced cellphones are priced at $x each. Ten of them are priced at $410. How much, in dollars, does three phones cost?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Multiply the calculated price of a single phone ... | math | {
"ground_truth": "123",
"style": "rule"
} | {
"uid": "kd::14eafb0f03f1496993d517c0",
"index": "kd::14eafb0f03f1496993d517c0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 41 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Given the fractional equation about $x$: $\\frac{{x+a}}{{x-2}}-\\frac{5}{x}=1$.$(1)$ If the root of the fractional equation is $x=5$, find the value of $a$;$(2)$ If the fractional equation has no solution, find the value of $a$.\n\nSolve the problem. Show your reasoning, then p... | math | {
"ground_truth": "3 \\text{ or } -2",
"style": "rule"
} | {
"uid": "kd::48b50b9fef74091799fb5a90",
"index": "kd::48b50b9fef74091799fb5a90",
"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": "Calculate:<br/>$(1)\\frac{{{x^2}-2x+1}}{{{x^2}-x}}÷({\\frac{1}{x}-1})$;<br/>$(2)-\\sqrt[3]{{27}}+{(3.14-π)^0}+{({-\\frac{1}{2}})^{-1}}$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Recognize that any non-zero number raised to ... | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"uid": "kd::bfaf2872139d44383e506601",
"index": "kd::bfaf2872139d44383e506601",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{x-1}{x} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "David was holding a political rally for Young Liberals. In the first week he raised 8640 potential votes. There were 9 times more people then him in the end of the rally than in the beginning. How many total people attended the rally?\n\nSolve the problem. Show your reasoning, ... | math | {
"ground_truth": "86400",
"style": "rule"
} | {
"uid": "kd::1b370338f09c9f2196b4b378",
"index": "kd::1b370338f09c9f2196b4b378",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 77760 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Toby wants to cut the fence of his yard into five sections, and gave each section 3 meters of fence, so he had 12 meters of steel fence remaining unused. He started by wiring the same length of fence at regular intervals. If he measured 300 centimeters between each wire, how ma... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"uid": "kd::1cd56256bbd38b554596f0b1",
"index": "kd::1cd56256bbd38b554596f0b1",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 15 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "P Rico can earn $3,000.00 for every 10 hours he works. On this month, his+(\\ Melco)+ hack is $10,000.00 a-way-and he works 150 hours wind records. How much would he earn?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Multiply t... | math | {
"ground_truth": "55000",
"style": "rule"
} | {
"uid": "kd::f69c98866f84955dcf7b5f79",
"index": "kd::f69c98866f84955dcf7b5f79",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 15 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Find the first non-zero digit (counting from left to right) of \\( n! \\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Multiply the reduced product by the remaining excess factors of 2 and extract the leading digit using logar... | math | {
"ground_truth": "\\text{First non‑zero digit of }n! =\\Big\\lfloor10^{ \\bigl\\{\\sum_{k=1}^{n}\\log_{10}k\\bigr\\}}\\Big\\rfloor =\\Big\\lfloor10^{ \\bigl\\{ n\\log_{10}\\frac{n}{e} +\\frac12\\log_{1",
"style": "rule"
} | {
"uid": "kd::88aaf3dda939c49a37833e32",
"index": "kd::88aaf3dda939c49a37833e32",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 10.1717 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "실수 $x$에 대해 $\\lfloor x \\rfloor$를 $x$ 이하의 최대 정수로 정의한다. 양의 정수 $n$에 대해 $S(n)$을 다음 식으로 정의한다.\n\\[\n S(n) \n = \\left\\lfloor \\frac{n}{10^{\\lfloor \\log n \\rfloor}} \\right\\rfloor\n + 10 \\left( n - 10^{\\lfloor \\log n \\rfloor} \n \\cdot \\left\\lfloo... | math | {
"ground_truth": "108",
"style": "rule"
} | {
"uid": "kd::d9f4340dc2788f7ef5af2444",
"index": "kd::d9f4340dc2788f7ef5af2444",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 110 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "From identical isosceles triangles, each having an angle opposite the base equal to $45^{\\circ}$ and a lateral side of length 1, a shape is formed as shown in the figure. Find the distance between points $A$ and $B$.\n\nSolve the problem. Show your reasoning, then put the fina... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::121cc3fb59a579d1466a7b6c",
"index": "kd::121cc3fb59a579d1466a7b6c",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\sqrt{\\2-\\sqrt{2}} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "gene... |
t01_math | [
{
"role": "user",
"content": "In the parallelogram \\(ABCD\\), the bisector of angle \\(A\\) divides the opposite side into parts with a ratio of lengths \\(2:1\\). Find the perimeter of the parallelogram if \\(AB=6\\). (Consider all options).\n\nSolve the problem. Show your reasoning, then put the final an... | math | {
"ground_truth": "P=16 \\text{or} P=20",
"style": "rule"
} | {
"uid": "kd::5c123003b955df710672b857",
"index": "kd::5c123003b955df710672b857",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{2}{1} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "The expressions $x^2-k^2$ and $x^2-5k$ are equal to zero when $x = 4$. Find all possible values of $k$, such that $k$ is a positive integer.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Compare the calculated values of k from b... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::de4a6fb1b360c3c1cf6f0c20",
"index": "kd::de4a6fb1b360c3c1cf6f0c20",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{16}{5} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Lakers scored 30 tubs of their own to their contest. The other teams were scored 6 tubs by the last game. If NBA put 2 more tubs than 4 for every tub or other teams did, how many tubs are in the box?\n\nSolve the problem. Show your reasoning, then put the final answer inside ... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"uid": "kd::b3dd76765a1943cf67f3805b",
"index": "kd::b3dd76765a1943cf67f3805b",
"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": "rented out a product from Demonstr';\nthis change madebastar aits production. In total, basitar painter 157 units of produced a minute for the day with an allowance of 43 minutes. basitar received an fight of $6000 each product upon the completion of the production. What is t... | math | {
"ground_truth": "202530",
"style": "rule"
} | {
"uid": "kd::a421b090dcb9ce89727d06d6",
"index": "kd::a421b090dcb9ce89727d06d6",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 6280 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Five cards are drawn from a well-shuffled deck of 52 cards, one by one without replacement. Find the probability of getting exactly three consecutive aces.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Subtract the count of arra... | math | {
"ground_truth": "\\frac{143}{270725}",
"style": "rule"
} | {
"uid": "kd::f73afdd42fed48db3e9ff5fc",
"index": "kd::f73afdd42fed48db3e9ff5fc",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 2256 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "11. In a \" $9 \\times 9$ \" grid paper, each cell can be filled with any one of the four natural numbers 1, 4. After filling, for each \" $2 \\times 2$ \" square, the sum of the four natural numbers is calculated. Among these sums, the same sum appears at least $\\qquad$ times... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"uid": "kd::312a12fc8e51aa74bc678a5f",
"index": "kd::312a12fc8e51aa74bc678a5f",
"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": "Rosella is considering joining both the female basketball league and the male basketball league for next semester. The basketball fee for the female league is $240 and the fee for the male league is $400. Rosella was also asked to contribute a $6 per-participation fee for both ... | math | {
"ground_truth": "880",
"style": "rule"
} | {
"uid": "kd::835195c3b9c760598aa52640",
"index": "kd::835195c3b9c760598aa52640",
"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": "A study-old person drinking juice found that a cup of juice is made up of 100 calories and each serving contains 20 grams of sugar. After doing some research, a doctor recommended that a person should drink no more than 800 calories as sugar/day. Calculate the number of cups of... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"uid": "kd::55012c135e1b9dbbe599dd58",
"index": "kd::55012c135e1b9dbbe599dd58",
"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": "TLP 80 is a pipe that can hold 80 arete pitches. An arete pitch is an arbitrary unit of storage space for sports equipment, usually laundry. If there are 10 80 arete pitch pipes, how many people can it hold who want a place to store, assuming each of them also stores their age... | math | {
"ground_truth": "600",
"style": "rule"
} | {
"uid": "kd::87dd3749710ebb59d6d74660",
"index": "kd::87dd3749710ebb59d6d74660",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 800 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "I bought 3 mangoes and 5 oranges for Rs. 67. After eating 1 mango, I sold the remaining fruits to Raj for Rs. 67. Raj then ate 1 mango and 1 orange and sold the remaining fruits to Ram for Rs. 67. If Raj had an effective profit of 35%, what was my percentage profit?\n\nSolve th... | math | {
"ground_truth": "9.88%",
"style": "rule"
} | {
"uid": "kd::2a04ed34c380a058f6ae52e0",
"index": "kd::2a04ed34c380a058f6ae52e0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{871}{81} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Carol makes vaccuuming the house her chore in an effort to make more money outside the bus. She makes 2$/hr vacuuming and needs to work 20 hours a week for each room she vacuumes. She lives in a house with 8 rooms. She is paid a minimum of 1/4th of her weekly earning. How much ... | math | {
"ground_truth": "80",
"style": "rule"
} | {
"uid": "kd::5919558ac8292b821ff009e1",
"index": "kd::5919558ac8292b821ff009e1",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 160 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Find the maximum possible value of the sum \\(\\sum_{1 \\leq i < j \\leq n} |x_i-x_j|\\), where \\(x_1,...,x_n\\) are integers in the interval \\([1,35]\\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Calculate the final sum b... | math | {
"ground_truth": "10404",
"style": "rule"
} | {
"uid": "kd::3c4c1a1421a3449504469e20",
"index": "kd::3c4c1a1421a3449504469e20",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 306 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "직각삼각형 \\(ABC\\)에서 내접원이 빗변 \\(AB\\) 위의 \\(P\\), \\(BC\\) 위의 \\(R\\), \\(AC\\) 위의 \\(Q\\)에서 각각 접한다고 하자. \\(C_1\\)과 \\(C_2\\)를 각각 \\(C\\)를 \\(PQ\\)와 \\(PR\\)에 대해 대칭시킨 점이라고 할 때, \\(I\\)가 \\(\\triangle ABC\\)의 내심일 때 각 \\(C_1IC_2\\)를 구하시오.\n\nSolve the problem. Show your reasoning, t... | math | {
"ground_truth": "135^\\circ",
"style": "rule"
} | {
"uid": "kd::0cfc3dca560e808b1ff65836",
"index": "kd::0cfc3dca560e808b1ff65836",
"lang": "ko",
"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": "Mr. saferdy isotonic to her dog in her garage. Mr. saferdy needs to make sure the dog drinks a gallon of water total each day. Starting at 4pm, Mr. saferdy will fill the dish with 40 ounces of water at a time. Mrs. saferdy has to go outside to get her chair. When she comes back... | math | {
"ground_truth": "108",
"style": "rule"
} | {
"uid": "kd::598f6bf74e416b1ee4ef085e",
"index": "kd::598f6bf74e416b1ee4ef085e",
"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": "Determine the number of ways to parenthesize the product of \\( n+1 \\) numbers \\( x_0 \\cdot x_1 \\cdot x_2 \\cdot \\ldots \\cdot x_n \\) to specify the order of multiplication. Develop a recurrence relation for \\( C_n \\), the number of ways to parenthesize the product of \... | math | {
"ground_truth": "C_n=\\frac{1}{ n+1 }\\binom{2n}{n}",
"style": "rule"
} | {
"uid": "kd::1b604bdb952251136ff6bffc",
"index": "kd::1b604bdb952251136ff6bffc",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1}{\\n+1} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",... |
t01_math | [
{
"role": "user",
"content": "Matthew has 40 beads in a bracelet. Jason has 50% more beads on a bracelet than Matthew has. If Matthew throws away 10 beads, how many more beads does Matthew would have in his bracelet than Jason has?\n\nSolve the problem. Show your reasoning, then put the final answer inside ... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"uid": "kd::22f15737adc01fd8da4d49b2",
"index": "kd::22f15737adc01fd8da4d49b2",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "(a) Given the air temperature is \\(28^{\\circ} \\mathrm{F}\\), express the wind chill temperature \\(W\\) as a function of the wind speed \\(V\\) using the National Weather Service formula: \n\\[ W = 35.74 + 0.6215 T_a - 35.75 V^{0.16} + 0.4275 T_a V^{0.16} \\] \nwhere \\(T_... | math | {
"ground_truth": "152.29",
"style": "rule"
} | {
"uid": "kd::4a96478c0a62bfbcbf76c4fd",
"index": "kd::4a96478c0a62bfbcbf76c4fd",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 14.73 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Jackson dinner had a value of $80 and he gives 25% as tips. However, 5% of the tip he was supposed to give was Zachary's tip. How much would Jackson have to pay for the dinner, including his tip and Zachary's tip?\n\nSolve the problem. Show your reasoning, then put the final an... | math | {
"ground_truth": "101",
"style": "rule"
} | {
"uid": "kd::144f14ec6d30da9f8fe69cdb",
"index": "kd::144f14ec6d30da9f8fe69cdb",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.05 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Sally and Clara made soccer boquets for a party. Sally made 8 large soccer boquets that contained 2 balls in each boquet, and Clara made 6 smal soccer boquets that contained 9 balls in each boquet. In addition, Sally had 4 big soccer balls and 2 small soccer balls. How many bal... | math | {
"ground_truth": "76",
"style": "rule"
} | {
"uid": "kd::a340d70205f8cf1b0e8acf3c",
"index": "kd::a340d70205f8cf1b0e8acf3c",
"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": "2개의 작은 이등변 삼각형으로 나눌 수 있는 이등변 삼각형의 모든 서로 다른 각의 합을 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 각 경우에서 구해진 꼭지각에 대응하는 밑각을 계산한 후, 중복되지 않는 모든 각의 값을 모아 합산하는 과정을 수행하세요."
}
] | math | {
"ground_truth": "\\frac{3177}{7}",
"style": "rule"
} | {
"uid": "kd::615fdbfaa6c1170745e67210",
"index": "kd::615fdbfaa6c1170745e67210",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 128.571 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Find natural numbers \\(a\\) and \\(x\\) such that \\(a^2 = 2x^4 + 1\\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Set up a system of equations from the factor pairs and solve for integer solutions."
}
] | math | {
"ground_truth": "a=1, x=0",
"style": "rule"
} | {
"uid": "kd::c52c45770337803cdc516bf2",
"index": "kd::c52c45770337803cdc516bf2",
"lang": "en",
"rubrics": [
{
"criterion": "Rewrite the equation as a difference of squares to factor the left side into two integers.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
... |
t01_math | [
{
"role": "user",
"content": "Counting sheep is a common activity. The goats in Andrew's farm count 40 more sheep than cows. The cows count 30 more sheep than pigs. If pigs in Andrew's farm count 30 sheep, calculate the total number of sheep in all the animals on the farm.\n\nSolve the problem. Show your re... | math | {
"ground_truth": "190",
"style": "rule"
} | {
"uid": "kd::6d77d19e41d21060f2c8932a",
"index": "kd::6d77d19e41d21060f2c8932a",
"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": "[ Plane, divided by lines ]\n\nHow many maximum parts can 5 segments divide a plane into?\n\n#\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Ensure each new segment intersects all previous segments at distinct points to maximize... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"uid": "kd::7df54ec9ff2656822010eb35",
"index": "kd::7df54ec9ff2656822010eb35",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 32 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "The initial speed of a golf ball is 56 mph and it is two the size of the golf club. It travels 50 yards per minute over a distance of 200 yards. How long did it take (in seconds) in minutes?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::05ba66310d926a0fcdfc47d4",
"index": "kd::05ba66310d926a0fcdfc47d4",
"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": "비자명한 군 $A$와 $B$에서 $a \\in A$, $b \\in B$가 항등원이 아닌 원소일 때, 자유곱 $A \\ast B$에서 부분군 $A \\ast (ba)B(ba)^{-1}$의 지수를 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 부분군의 생성원인 A의 원소와 (ba)B(ba)^-1의 원소가 준동형사상에서 각각 어떤 값으로 대응되는지 계산하라"
}
... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::ded237a852b6d90dbfae819b",
"index": "kd::ded237a852b6d90dbfae819b",
"lang": "ko",
"rubrics": [
{
"criterion": "A와 B의 원소를 각각 0과 1로 보내는 군 준동형사상을 정의하여 자유곱의 구조를 분석하라",
"points": 2,
"tags": {
"judge": false,
"inject": true,
"scaffold_rank": 1,
"scaf... |
t01_math | [
{
"role": "user",
"content": "Given $a$, $b$, $c$, $d$, and $p$ where $even(a)$, $even(b)$, $odd(c)$, $odd(d)$, $odd(p)$, and $prime(p)$, determine the parity of $modinv_p(c)$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Substitute the known odd parity of ... | math | {
"ground_truth": "\\text{odd}",
"style": "rule"
} | {
"uid": "kd::8de5f9d92a7c45636c99dd11",
"index": "kd::8de5f9d92a7c45636c99dd11",
"lang": "en",
"rubrics": [
{
"criterion": "Reduce the defining congruence modulo 2 to analyze the parity of the unknown inverse.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
... |
t01_math | [
{
"role": "user",
"content": "In a math competition, Grace answered all 18 problems incorrectly except for $N$ problems she answered correctly. For how many values of $N$ did Grace have a positive score?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Count th... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"uid": "kd::aeed38dd0711426fc54a3655",
"index": "kd::aeed38dd0711426fc54a3655",
"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": "There are 15 bouquets of flowers. Each bouquet has 4 roses and 3 tulips. The remaining bouquets have 6 roses and 5 tulips each and there are 5 bouquets of that type. How many flowers are there?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{... | math | {
"ground_truth": "160",
"style": "rule"
} | {
"uid": "kd::063dc775779e260af6a080f0",
"index": "kd::063dc775779e260af6a080f0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 11 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "At a particular temper alto, the owner of a business shook hands with 9 complete times more people than depending on the known amountDuring this time he gained a prescription from some sources. He then went to a plain market and bought 5 pairs of pants complete at 10 dollars ea... | math | {
"ground_truth": "75",
"style": "rule"
} | {
"uid": "kd::78064d6f7d848ba89bce0fbe",
"index": "kd::78064d6f7d848ba89bce0fbe",
"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": "Determine the number of positive divisors of the following integers:\n(a) \\(145546856 = 2^{3} \\cdot 7^{2} \\cdot 13^{5}\\)\n(b) \\(5384464553 = 13^{2} \\cdot 17 \\cdot 37^{4}\\)\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Ad... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"uid": "kd::e66396957faaecdab953b29e",
"index": "kd::e66396957faaecdab953b29e",
"lang": "en",
"rubrics": [
{
"criterion": "Apply the divisor counting formula by multiplying one more than each prime exponent",
"points": 2,
"tags": {
"judge": false,
"inject": true,
... |
t01_math | [
{
"role": "user",
"content": "Prove that for all positive real numbers $x$, $y$, and $z$, the following inequality holds: $$\\frac{x}{y}+\\frac{y}{z+x}+\\frac{z}{x}\\ge 2.$$\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Substitute the critical value back int... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::69230d329bc06ca41c5961e8",
"index": "kd::69230d329bc06ca41c5961e8",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 2.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Problem 7.4. Consider seven-digit natural numbers, in the decimal representation of which each of the digits $1,2,3,4,5,6,7$ appears exactly once.\n\n(a) (1 point) How many of them have the digits from the first to the sixth in ascending order, and from the sixth to the seventh... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"uid": "kd::754fbe2340ce5880b6d87754",
"index": "kd::754fbe2340ce5880b6d87754",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 56 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Compare the smallest positive roots of the equations \\( \\cos(\\sin x) = x \\) and \\( \\sin(\\cos x) = x \\) within the interval \\([0, \\frac{\\pi}{2}]\\). Let \\(x_1\\) be the root of \\(\\sin(\\cos x) = x\\) and \\(x_2\\) be the root of \\(\\cos(\\sin x) = x\\). Determine ... | math | {
"ground_truth": "x_2",
"style": "rule"
} | {
"uid": "kd::40a48df566c63eb57259c9e2",
"index": "kd::40a48df566c63eb57259c9e2",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.76 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "A cone has a volume of 353 cubic centimeters. If the cone is a right circular cone, what is the volume of a cylinder having the same base and height as the cone? Express your answer in terms of $\\pi$.\n\nSolve the problem. Show your reasoning, then put the final answer inside ... | math | {
"ground_truth": "1059",
"style": "rule"
} | {
"uid": "kd::6f86b60f8b7803d9f9a27dd0",
"index": "kd::6f86b60f8b7803d9f9a27dd0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1059\\pi 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Given the linear transformation \\( f: M_{2 \\times 3}(\\mathbb{R}) \\rightarrow \\mathbb{R}^4 \\) defined by \\( f\\begin{pmatrix} a & b & c \\\\ i & j & k \\end{pmatrix} = (a+b+c, a+i+k, b+j-k, c-i-j) \\), and the subspace \\( F \\subseteq \\mathbb{R}^4 \\) spanned by the vec... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"uid": "kd::f9c7896e0d82f5d7ff8e4633",
"index": "kd::f9c7896e0d82f5d7ff8e4633",
"lang": "en",
"rubrics": [
{
"criterion": "Apply the dimension formula relating the preimage dimension to the kernel dimension and the intersection of the target subspace with the image.",
"points": 2,
"tags"... |
t01_math | [
{
"role": "user",
"content": "Given that $x_n$ converges to a positive value $a$ and there exists $0 < M < a$ such that $x_n$ is eventually lower-bounded by $M$, can it be concluded that $\\sqrt{x_n}$ is eventually lower-bounded by $\\sqrt{M}$? If so, explain how this fact can be used to prove that $\\lim_{... | math | {
"ground_truth": "\\sqrt{a}",
"style": "rule"
} | {
"uid": "kd::f598f3d845620a08c58393f8",
"index": "kd::f598f3d845620a08c58393f8",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\sqrt{\\limx_{n}} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic... |
t01_math | [
{
"role": "user",
"content": "6명의 아이로 이루어진 집단에서, 임의의 2명의 아이의 평균 체중은 서로 다른 자연수이다. 아이 중 가장 가벼운 아이의 체중은 11kg이다. 이 집단에서 가장 무거운 아이와 두 번째로 무거운 아이의 체중 합계의 최솟값을 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 15개의 서로 다른 쌍별 합을 만들 수 있는 최소 범위를 고려하여 두 가장 큰 원소의 합이 19 이... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"uid": "kd::d2bbca650fb74abba3b2f11e",
"index": "kd::d2bbca650fb74abba3b2f11e",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 114 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Two players, A and B, take turns rolling a single die. The first player to roll a total of 7 with their last two rolls wins the game. If player A starts, what is the probability that player B wins?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\bo... | math | {
"ground_truth": "5/11",
"style": "rule"
} | {
"uid": "kd::358329520faf522c6d137680",
"index": "kd::358329520faf522c6d137680",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{6}{36} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "If \\(a, b, c\\) are non-zero real numbers and satisfy the equations \\(b^2 + bc = 2ac\\) and \\(9a^2 = 6ab + 7c\\), calculate the ratio \\(a:b:c\\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Factor the resulting cubic polyn... | math | {
"ground_truth": "14:12:9",
"style": "rule"
} | {
"uid": "kd::9b8e8fc366e4bc79506693dd",
"index": "kd::9b8e8fc366e4bc79506693dd",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 -48 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Enumerate all the non-negative, non-unique, non-normalised, numbers in the floating-point system defined by parameters $\\beta=4, s=2, m=-1, M=1$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Compare the set of numbers generate... | math | {
"ground_truth": "\\{0, \\frac14, \\frac12, \\frac34, 1, 2, 3\\}",
"style": "rule"
} | {
"uid": "kd::816bf1ca937ba84a87e862b9",
"index": "kd::816bf1ca937ba84a87e862b9",
"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": "The couple decides to take $3p\\%$ of their profits and share the remaining profits between themselves. If thus share is $33\\%$, what is $p$?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Set up an equation where half of the re... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"uid": "kd::479de0c9fe8d6a0776559da1",
"index": "kd::479de0c9fe8d6a0776559da1",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 66 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "The scores for the players on the basketball team are below. How many more points did{-3} Terrence add than{-2} Terrence did?{-1} Terrence added{-2} points and{-1} Terrence added{-1} point.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"uid": "kd::95891d13a9e0bcf952ffea58",
"index": "kd::95891d13a9e0bcf952ffea58",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the two specific point values mentioned in the problem statement to determine what quantities need comparison.",
"points": 2,
"tags": {
"judge": fal... |
t01_math | [
{
"role": "user",
"content": "Squares $JKLM$ and $NOPQ$ are congruent, $JM=20$, and $P$ is the midpoint of side $JM$ of square $JKLM$. Calculate the area of the region covered by these two squares in the plane.\nA) $500$\nB) $600$\nC) $700$\nD) $800$\nE) $900$\n\nSolve the problem. Show your reasoning, then... | math | {
"ground_truth": "600",
"style": "rule"
} | {
"uid": "kd::2cb479af2b319d244baf939d",
"index": "kd::2cb479af2b319d244baf939d",
"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": "If $f$ is a function such that $f(3) = 5$ and $f(x) = \\frac{x + 4}{2}$, then what is the value of $f^{-1}(5)$?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Set the expression for f(x) equal to 5 and solve the resulting linear ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"uid": "kd::531f5973d875710360e96cb7",
"index": "kd::531f5973d875710360e96cb7",
"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": "쌍곡선 \\( C: \\frac{x^2}{2} - y^2 = 1 \\)이 주어졌을 때, \\( P \\)는 이 쌍곡선의 오른쪽 가지 위의 점이라고 하자. 직선 \\( l \\)은 쌍곡선의 점근선이고, \\( Q \\)는 \\( P \\)에서 \\( l \\)에 내린 수선의 발이다. \\( F_1 \\)은 쌍곡선의 왼쪽 초점이라고 할 때, \\( |PF_1| + |PQ| \\)의 최솟값을 구하시오.\n\nSolve the problem. Show your reasoning, then put th... | math | {
"ground_truth": "1 + 2\\sqrt{2}",
"style": "rule"
} | {
"uid": "kd::7833a732cc70278e81d99930",
"index": "kd::7833a732cc70278e81d99930",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "8. The solution set of the inequality $\\log _{5}\\left(5 x^{2}+2 x\\right) \\cdot \\log _{5}\\left(5+\\frac{2}{x}\\right)>\\log _{5} 5 x^{2}$ is $\\qquad$ .\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Apply the identity for t... | math | {
"ground_truth": "(\\frac{-1-\\sqrt{2}}{5},-\\frac{2}{5})\\cup(\\frac{\\sqrt{2}-1}{5},+\\infty)",
"style": "rule"
} | {
"uid": "kd::d0cfdbb2b7d93c81394bca40",
"index": "kd::d0cfdbb2b7d93c81394bca40",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 -0.49 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "$ABCD$를 대각선 $AC = 10$인 평행사변형이라고 하자. 점 $A$에서 직선 $CD$까지의 거리는 $6$이고, 점 $A$에서 직선 $BC$까지의 거리는 $7$이다. 이 조건을 만족하는 $ABCD$의 서로 닮지 않은 두 가지 구성이 존재한다. 이 두 평행사변형의 넓이의 합은 $\\frac{m}{n}$ ($m, n$은 서로소인 양의 정수)이다. $m + n$을 구하시오.\n\nAnswer: 10\n\nSolve the problem. Show your reasoning, then put t... | math | {
"ground_truth": "4717",
"style": "rule"
} | {
"uid": "kd::cb52bffdd0d71e2c20efc5e5",
"index": "kd::cb52bffdd0d71e2c20efc5e5",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 42.489 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"... |
t01_math | [
{
"role": "user",
"content": "Given the function \\( f(x) = x^2 + 3x + 2 \\) on the interval \\([1, 4]\\), find the mean value using Lagrange's Mean Value Theorem (LMVT).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Set the derivative of the function equal ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"uid": "kd::e39e967cfece7a4256c491ae",
"index": "kd::e39e967cfece7a4256c491ae",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 30 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Evaluate the function \\( f(x) = \\frac{1}{2} \\int_0^x (x-t)^2 g(t) \\, dt \\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Differentiate the resulting integral from the second derivative using the Fundamental Theorem of Calc... | math | {
"ground_truth": "f'''(x) = g(x)",
"style": "rule"
} | {
"uid": "kd::3302b0a2144cc928b29d1383",
"index": "kd::3302b0a2144cc928b29d1383",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "If \\$2000 is invested in an account offering 7.125% annual interest compounded monthly, how much is in the account after 5 years?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Approximate the power term using logarithmic and ex... | math | {
"ground_truth": "$2852.92",
"style": "rule"
} | {
"uid": "kd::63f335ccf205a7e8c16d7c7b",
"index": "kd::63f335ccf205a7e8c16d7c7b",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{i}{12} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Given a mapping f: {1, 2, 3} → {1, 2, 3} that satisfies f(1) < f(2) < f(3) and f(f(x)) = 3x, find the value of f(1). Express your answer as a single integer.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Use the strictly increas... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::d36cf3cd1fd23f90f6342808",
"index": "kd::d36cf3cd1fd23f90f6342808",
"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": "Let $e$ be one of the edges of a cube. How many lines are there in space that intersect exactly those 12 edges of the cube which are skew to $e$?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Observe that a line intersecting two... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"uid": "kd::4591b2e3814ae517eae18bd1",
"index": "kd::4591b2e3814ae517eae18bd1",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.2 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "S ant multiples of 3 in the following list.\n\n897,313,599,797,201\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Verify your selected candidates by performing direct division by three to confirm they yield integers."
}
] | math | {
"ground_truth": "897, 201",
"style": "rule"
} | {
"uid": "kd::fdc4e51f05349daec47f30f7",
"index": "kd::fdc4e51f05349daec47f30f7",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 23 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "공간에서 모든 직선과 동일한 각을 이루는 평면이 존재할 수 있는 직선의 최대 개수를 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 세 직선은 항상 조건을 만족하지만 네 직선에서는 모순이 발생함을 보이기 위해 정사면체의 꼭짓점 방향 벡터를 대입해 보세요."
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"uid": "kd::89b51f5da97c020218045609",
"index": "kd::89b51f5da97c020218045609",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 90 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 half of $30$ and one competent! What does \"competent\" mean?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Look up the standard dictionary definition of the adjective competent to explain its meaning in the ... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"uid": "kd::ff3e3c7342ddab9034f1aad8",
"index": "kd::ff3e3c7342ddab9034f1aad8",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 15 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Find the optimal semi-orthogonal matrix \\( X \\) that minimizes the norm of \\( XQX^T \\), where \\( Q \\) is a diagonal matrix with non-negative entries less than 1, and \\( X \\) has fewer rows than columns.\n\nSolve the problem. Show your reasoning, then put the final answe... | math | {
"ground_truth": "X",
"style": "rule"
} | {
"uid": "kd::173c72e4fd12ac7fb5c044cc",
"index": "kd::173c72e4fd12ac7fb5c044cc",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.25 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Suppose we break a burst of 28 words into 4 equal pieces and the first two pieces are each 3 words short of the target.\n\nHow many words are in the fourth of those 4 pieces?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Divide ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"uid": "kd::682798fc463284c44f013186",
"index": "kd::682798fc463284c44f013186",
"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": "부등식 $\\ln(x^2 - 1) - \\ln(x - 1) > 0$을 풀고, 그 해를 그래프로 검증하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 약분 과정에서 분모가 0 이 되는 점을 제외하고 정의역과 일치하는 구간에서만 식을 단순화하여 해를 구하라."
}
] | math | {
"ground_truth": "(1, \\infty)",
"style": "rule"
} | {
"uid": "kd::8e389591651487df70cadb68",
"index": "kd::8e389591651487df70cadb68",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 1.1 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Let \\( n \\) be a positive integer. There is a board of \\((n + 1) \\times (n + 1)\\) whose squares are numbered in a diagonal pattern. Chepito starts from the lower left square and moves only up or to the right until he reaches the upper right square. During his tour, Chepito... | math | {
"ground_truth": "\\frac{4n^{3}+3n^{2}+5n-3}{3}",
"style": "rule"
} | {
"uid": "kd::27b3c72c4ca2e2158ed683f6",
"index": "kd::27b3c72c4ca2e2158ed683f6",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{(i+j)(i+j+1)}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "ge... |
t01_math | [
{
"role": "user",
"content": "Prove Lemma 4.4.4: Suppose that \\( x \\) is a fixed real number. Then, \\( \\lim_{n \\to \\infty} |x|^n = 0 \\) if \\( |x| < 1 \\), and \\( \\lim_{n \\to \\infty} \\frac{|x|^n}{n!} = 0 \\) regardless of the size of \\( |x| \\).\n\nSolve the problem. Show your reasoning, then p... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::867130c952e2f5077ec062ed",
"index": "kd::867130c952e2f5077ec062ed",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{|x|}{n+1} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",... |
t01_math | [
{
"role": "user",
"content": "14 is X% of 20\nIn this question, what would X be if it were to be solved into a decimal?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Perform the division of 14 by 20 to determine the decimal value of X."
}
] | math | {
"ground_truth": "70",
"style": "rule"
} | {
"uid": "kd::429103f334bd8c05f17555a3",
"index": "kd::429103f334bd8c05f17555a3",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{70}{100} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
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