source stringclasses 10 values | domain listlengths 1 3 | llama8b_solve_rate float64 0 0.09 ⌀ | data_source stringclasses 1 value | prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | extra_info dict |
|---|---|---|---|---|---|---|---|
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the sequence $\\sqrt{2}, \\sqrt{5}, 2... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"answer": "23",
"index": 19000,
"question": "Given the sequence $\\sqrt{2}, \\sqrt{5}, 2\\sqrt{2}, \\sqrt{11}, \\ldots$, then $2\\sqrt{17}$ is its $\\boxed{\\text{nth}}$ term.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are 150 'zeroes' and some 'ones' writ... | math | {
"ground_truth": "78",
"style": "rule"
} | {
"answer": "78",
"index": 19001,
"question": "There are 150 'zeroes' and some 'ones' written on a blackboard. A step involves choosing 3 digits and replacing them with a single digit. If all the 3 digits are identical, they are replaced with the same digit. Otherwise, the digit that appears twice replaces the 3 chosen digits. The minimum number of steps after which there will be no zero written on the blackboard is 76. How many 'ones' are initially written on the blackboard?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n At the supermarket, the price paid for oran... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 19002,
"question": "At the supermarket, the price paid for oranges is proportional to the mass purchased. Annie paid $6 for 2 kg of oranges. How much will Annie pay for a certain mass of oranges if she paid $36 for 12 kg?",
"split": "train"
} |
aops_forum | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The distance between two cells of an infini... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 19003,
"question": "The distance between two cells of an infinite chessboard is defined as the minimum nuber to moves needed for a king for move from one to the other.One the board are chosen three cells on a pairwise distances equal to $ 100$ . How many cells are there that are on the distance $ 50$ from each of the three cells?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n a work which could be finished in 11 days w... | math | {
"ground_truth": "27",
"style": "rule"
} | {
"answer": "27",
"index": 19004,
"question": "a work which could be finished in 11 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the maximum number of 1x1 squares t... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 19005,
"question": "What is the maximum number of 1x1 squares that can be attached to a given unit square \\( K \\) so that no two of them overlap?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A meeting has to be conducted with 4 manage... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 19006,
"question": "A meeting has to be conducted with 4 managers. There are 8 managers to choose from, but a certain number of managers refuse to attend the meeting together. There are 55 ways to select the managers for the meeting. How many managers refuse to attend the meeting together?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n John is trying to save money by buying chea... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"answer": "120",
"index": 19007,
"question": "John is trying to save money by buying cheap calorie-dense food. He can buy 10 burritos for $6 that have a certain number of calories each. He could also buy 5 burgers that are 400 calories each for $8. He gets 50 more calories per dollar from the burgers. How many calories does each burrito have?",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Differential Geometry -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let \\( P \\) be an arbitrary point on the ... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"answer": "25",
"index": 19008,
"question": "Let \\( P \\) be an arbitrary point on the ellipse \\(\\frac{x^{2}}{16}+\\frac{y^{2}}{9}=1\\) other than the endpoints of the major axis. \\( F_{1} \\) and \\( F_{2} \\) are its left and right foci respectively, and \\( O \\) is the center. Find the value of \\( \\left|P F_{1}\\right| \\cdot \\left|P F_{2}\\right| + |O P|^{2} \\).",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that $\\alpha, \\beta \\in \\{1, 2, 3... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"answer": "13",
"index": 19009,
"question": "Given that $\\alpha, \\beta \\in \\{1, 2, 3, 4, 5\\}$, find the total number of pairs $(\\alpha, \\beta)$ such that $\\sin(\\alpha) \\cdot \\cos(\\beta) < 0$. Express your answer as a single integer.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The numbers 7, 8, 9, 10, and 11 are arrange... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 19010,
"question": "The numbers 7, 8, 9, 10, and 11 are arranged in a row in some order. It turns out that the sum of the first three of them is 26, and the sum of the last three is 30. Determine the number that is in the middle.",
"split": "train"
} |
big_math | [
"Mathematics -> Number Theory -> Congruences"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that \\( n \\) is a two-digit natural... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 19011,
"question": "Given that \\( n \\) is a two-digit natural number, when \\( n \\) is divided by 9, the remainder is 1, and when \\( n \\) is divided by 10, the remainder is 3. Calculate the remainder when \\( n \\) is divided by 11. Express your answer as a single integer.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Complex Numbers -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If $(1-mi)(m+i) < 0$, where $i$ is the imag... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 19012,
"question": "If $(1-mi)(m+i) < 0$, where $i$ is the imaginary unit, then find the value of $m$ as a real number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The watchman detained a trespasser and want... | math | {
"ground_truth": "199",
"style": "rule"
} | {
"answer": "199",
"index": 19013,
"question": "The watchman detained a trespasser and wants to chase him away. However, the trespasser said that he made a bet with friends for 100 coins that the watchman wouldn't chase him away (if he gets chased away, he pays friends 100 coins; otherwise, they pay him). To get rid of the watchman, the trespasser offered to name a price. What is the maximum number of coins the watchman can demand so that the trespasser, guided solely by his own benefit, will definitely pay the watchman?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Polynomial Operations -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The polynomial 2x^4 - 3x^3 + ax^2 + 7x + b ... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"answer": "-2",
"index": 19014,
"question": "The polynomial 2x^4 - 3x^3 + ax^2 + 7x + b can be divided by x^2 + x - 2. Find the value of a/b. Express your answer as a single number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given real numbers \\(a_{1}, a_{2}, \\cdots... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 19015,
"question": "Given real numbers \\(a_{1}, a_{2}, \\cdots, a_{5}\\) such that \n\\[\n\\sum_{i=1}^{5} a_{i}^{2} = 1,\n\\]\nfind the maximum value of \n\\[\nT = \\sum_{i=1}^{5} \\left|a_{i} - a_{i+1}\\right| \\quad \\text{where} \\quad a_{6} = a_{1}.\n\\]",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a circle $x^2 + y^2 = 1$, draw a tang... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 19016,
"question": "Given a circle $x^2 + y^2 = 1$, draw a tangent line through a point on the circle that intersects the positive $x$-axis at point $A$ and the positive $y$-axis at point $B$. Find the minimum value of the length $|AB|$.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A team of athletes, one-third of which are ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 19017,
"question": "A team of athletes, one-third of which are snowboarders, descended from the mountain. Some of them took a cable car that holds no more than 10 people, while the rest descended on their own. The number of people who descended on their own was more than 45% but less than 50% of the total number. Determine the number of snowboarders (if the total number of snowboarders is ambiguous based on the problem's conditions, provide the sum of all possible values).",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n How many integer values of m satisfy the tr... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 19018,
"question": "How many integer values of m satisfy the triangle inequality theorem such that the three expressions 2m-1, 4m+5, and 20-m can form the sides of a triangle? Express your answer as a single integer.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Ajay and Balu together can do a piece of wo... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 19019,
"question": "Ajay and Balu together can do a piece of work in some days. Balu and Charan together can do the same work in 16 days. After Ajay has been working at it for 5 days and Balu for 7 days, Charan finishes it in 13 days. In how many days will Charan alone be able to do the work if Ajay and Balu together can do the work in 12 days?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If 7 parallel lines in a plane are intersec... | math | {
"ground_truth": "99",
"style": "rule"
} | {
"answer": "99",
"index": 19020,
"question": "If 7 parallel lines in a plane are intersected by a family of another set of parallel lines, there are 588 parallelograms in the network thus formed. How many parallel lines are in the second set?",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the experimental range is $[628, 774]... | math | {
"ground_truth": "684",
"style": "rule"
} | {
"answer": "684",
"index": 19021,
"question": "Given the experimental range is $[628, 774]$ and the good point is 718, use the 0.618 method to find the addition point value to be tested at this time. Express your answer as a single numerical value.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Statistics -> Mathematical Statistics"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a certain survey, a stratified random sa... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 19022,
"question": "In a certain survey, a stratified random sampling with sample size proportion allocation was used. Some of the data are shown in the table below:\n\n| Sample Category | Sample Size | Mean | Variance |\n|-----------------|-------------|------|----------|\n| $A$ | $10$ | $3.5$| $2$ |\n| $B$ | $30$ | $5.5$| $1$ |\n\nBased on this data, the variance of the total sample is ______.",
"split": "train"
} |
orca_math | [
"Mathematics -> Number Theory -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n What is the smallest number which when incr... | math | {
"ground_truth": "113393",
"style": "rule"
} | {
"answer": "113393",
"index": 19023,
"question": "What is the smallest number which when increased by 7 is divisible by 24, 36, 50, 56, and 81?",
"split": "train"
} |
big_math | [
"Applied Mathematics -> Probability -> Counting Methods -> Permutations"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Xiao Li plans to travel with other friends ... | math | {
"ground_truth": "144",
"style": "rule"
} | {
"answer": "144",
"index": 19024,
"question": "Xiao Li plans to travel with other friends after the 2017 college entrance examination. There are 3 natural scenic spots A, B, C, and 3 cultural and historical scenic spots a, b, c to choose from. Due to time and distance constraints, only 4 scenic spots can be selected for a visit, among which scenic spot A cannot be visited first, and the last visited must be a cultural and historical scenic spot. Calculate the total number of different travel sequences.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Sequences and Series -> Other"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the sequence \\(\\{a_n\\}\\), where \... | math | {
"ground_truth": "-5",
"style": "rule"
} | {
"answer": "-5",
"index": 19025,
"question": "Given the sequence \\(\\{a_n\\}\\), where \\(a_1 = 3\\), \\(a_2 = 5\\), and for \\(n > 2\\), \\(a_n = a_{n-1} - a_{n-2}\\), find the value of \\(a_{2003}\\). Express your answer as a single integer.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Calculus -> Integral Calculus -> Applications of Integrals"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n An object moves at a velocity of $v(t) = t^... | math | {
"ground_truth": "263",
"style": "rule"
} | {
"answer": "263",
"index": 19026,
"question": "An object moves at a velocity of $v(t) = t^2 - 3t + 8$ (m/s). What is its average velocity in the first 30 seconds?",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Polygons"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Cyclic pentagon \\( A B C D E \\) has a rig... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 19027,
"question": "Cyclic pentagon \\( A B C D E \\) has a right angle \\( \\angle A B C = 90^\\circ \\) and side lengths \\( A B = 15 \\) and \\( B C = 20 \\). Supposing that \\( A B = D E = E A \\), find \\( C D \\).",
"split": "train"
} |
omnimath | [
"Mathematics -> Applied Mathematics -> Probability",
"Mathematics -> Geometry -> Solid Geometry -> 3D Shapes"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Jarris is a weighted tetrahedral die with f... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 19028,
"question": "Jarris is a weighted tetrahedral die with faces $F_{1}, F_{2}, F_{3}, F_{4}$. He tosses himself onto a table, so that the probability he lands on a given face is proportional to the area of that face. Let $k$ be the maximum distance any part of Jarris is from the table after he rolls himself. Given that Jarris has an inscribed sphere of radius 3 and circumscribed sphere of radius 10, find the minimum possible value of the expected value of $k$.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n An airline company operates passenger trans... | math | {
"ground_truth": "1500",
"style": "rule"
} | {
"answer": "1500",
"index": 19029,
"question": "An airline company operates passenger transportation between four cities A, B, C, and D. The prices for some of the direct flights between these cities are as follows: AB is 2000 yuan; AC is 1600 yuan; AD is 2500 yuan; CD is 900 yuan; BC is 1200 yuan. If the company's pricing for flights is directly proportional to the straight-line distance between the cities (assuming all four cities are on the same plane), calculate the price for the straight-line distance between B and D. Express your answer in yuan as a whole number.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In triangle $ABC$ , $AB=3$ , $AC=5$ , an... | math | {
"ground_truth": "55",
"style": "rule"
} | {
"answer": "55",
"index": 19030,
"question": "In triangle $ABC$ , $AB=3$ , $AC=5$ , and $BC=7$ . Let $E$ be the reflection of $A$ over $\\overline{BC}$ , and let line $BE$ meet the circumcircle of $ABC$ again at $D$ . Let $I$ be the incenter of $\\triangle ABD$ . Given that $\\cos ^2 \\angle AEI = \\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers, determine $m+n$ .",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A population consists of 20 individuals num... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 19031,
"question": "A population consists of 20 individuals numbered 01, 02,..., 19, 20. 6 individuals are selected using the following random number table. The selection method is to start from the numbers in the 5th and 6th columns of the 1st row of the random number table and select two numbers from left to right as the individual numbers.\n\n| 7816 | 6572 | 0802 | 6314 | 0702 | 4311 |\n|------|------|------|------|------|------|\n| 3204 | 9234 | 4935 | 8200 | 3623 | 4869 |\n\nDetermine the number of the 5th selected individual. Express your answer as a two-digit number (e.g., 07, 11, etc.).",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A rectangle is inscribed in a square with a... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"answer": "18",
"index": 19032,
"question": "A rectangle is inscribed in a square with an area of 24 such that one vertex of the rectangle lies on each side of the square. The sides of the rectangle are in the ratio $1:3$.\n\nFind the area of the rectangle.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Number Theory -> Prime Numbers"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given three prime numbers $a$, $b$, and $c$... | math | {
"ground_truth": "34",
"style": "rule"
} | {
"answer": "34",
"index": 19033,
"question": "Given three prime numbers $a$, $b$, and $c$ satisfy $a+b+c+abc=99$, find the value of $|a-b|+|b-c|+|c-a|$.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Circles"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given \\( a, b \\in \\mathbf{R} \\), the ci... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 19034,
"question": "Given \\( a, b \\in \\mathbf{R} \\), the circle \\( C_{1}: x^{2}+y^{2}-2 x+4 y-b^{2}+5=0 \\) and the circle \\( C_{2}: x^{2}+y^{2}-2(a-6) x-2 a y +2 a^{2}-12 a+27=0 \\) intersect at two distinct points \\( A\\left(x_{1}, y_{1}\\right) \\) and \\( B\\left(x_{2}, y_{2}\\right) \\), and \\( \\frac{y_{1}+y_{2}}{x_{1}+x_{2}}+\\frac{x_{1}-x_{2}}{y_{1}-y_{2}} = 0 \\). Find the value of \\( a \\).",
"split": "train"
} |
orca_math | [
"Mathematics -> Algebra -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Yoongi wants to add two-digit to three-digi... | math | {
"ground_truth": "49",
"style": "rule"
} | {
"answer": "49",
"index": 19035,
"question": "Yoongi wants to add two-digit to three-digit numbers. Yoongi confused the 9 in the ones place of a two-digit number with 6, and switched the digits in the hundreds and ones place of a three-digit number and saw it as 253. If the sum obtained by Yoongi is 299, find the two-digit number.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A group of 6 fruit baskets contains 9 apple... | math | {
"ground_truth": "174",
"style": "rule"
} | {
"answer": "174",
"index": 19036,
"question": "A group of 6 fruit baskets contains 9 apples, 15 oranges, 14 bananas, and 12 grapes in the first three baskets, while the fourth basket has 2 less of each fruit, the fifth basket has 3 more apples and 5 less oranges than the first basket, and the sixth basket contains twice as many bananas and half as many grapes as the third basket. How many fruits are there in total?",
"split": "train"
} |
omnimath | [
"Mathematics -> Algebra -> Intermediate Algebra -> Complex Numbers"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Suppose that $x$ and $y$ are complex number... | math | {
"ground_truth": "-90",
"style": "rule"
} | {
"answer": "-90",
"index": 19037,
"question": "Suppose that $x$ and $y$ are complex numbers such that $x+y=1$ and that $x^{20}+y^{20}=20$. Find the sum of all possible values of $x^{2}+y^{2}$.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A net of a cube is shown with one integer o... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"answer": "90",
"index": 19038,
"question": "A net of a cube is shown with one integer on each face. A larger cube is constructed using 27 copies of this cube. What is the minimum possible sum of all of the integers showing on the six faces of the larger cube?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Polygons"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A regular hexagonal paper with a side lengt... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 19039,
"question": "A regular hexagonal paper with a side length of 1 is joined with a regular triangular paper with a side length of 1. The pieces must be aligned edge-to-edge without overlapping. Find the number of edges in the resulting new shape.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that the domain of the function $y=f(... | math | {
"ground_truth": "-14",
"style": "rule"
} | {
"answer": "-14",
"index": 19040,
"question": "Given that the domain of the function $y=f(x)$ is $\\mathbb{R}$, and the function $g(x)=f(x+5)+f(1-x)$. If the equation $g(x)=0$ has exactly 7 different real solutions, then the sum of these 7 real solutions is \\_\\_\\_\\_\\_\\_.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the sequence $\\{a_n\\}$ that satisfi... | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"answer": "-4",
"index": 19041,
"question": "Given the sequence $\\{a_n\\}$ that satisfies the recursive relation $a_{n+1} = 3a_n + 3^n - 8$ (where $n \\in \\mathbb{N}^+$), and the sequence $\\left\\{ \\frac {a_{n}+\\lambda}{3^{n}} \\right\\}$ forms an arithmetic sequence, find the value of $\\lambda$.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Starting with 5, add 60, then subtract 100,... | math | {
"ground_truth": "33",
"style": "rule"
} | {
"answer": "33",
"index": 19042,
"question": "Starting with 5, add 60, then subtract 100, then add 120, then subtract 100, and continue this sequence. Each addition or subtraction is considered one operation. What is the minimum number of operations required to obtain a result of exactly 500? Express your answer as a whole number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A total area of \\( 2500 \\, \\mathrm{m}^2 ... | math | {
"ground_truth": "156",
"style": "rule"
} | {
"answer": "156",
"index": 19043,
"question": "A total area of \\( 2500 \\, \\mathrm{m}^2 \\) will be used to build identical houses. The construction cost for a house with an area \\( a \\, \\mathrm{m}^2 \\) is the sum of the material cost \\( 100 p_{1} a^{\\frac{3}{2}} \\) yuan, labor cost \\( 100 p_{2} a \\) yuan, and other costs \\( 100 p_{3} a^{\\frac{1}{2}} \\) yuan, where \\( p_{1} \\), \\( p_{2} \\), and \\( p_{3} \\) are consecutive terms of a geometric sequence. The sum of these terms is 21 and their product is 64. Given that building 63 of these houses would result in the material cost being less than the sum of the labor cost and the other costs, find the maximum number of houses that can be built to minimize the total construction cost.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Ramesh purchased a refrigerator for Rs. 155... | math | {
"ground_truth": "4000",
"style": "rule"
} | {
"answer": "4000",
"index": 19044,
"question": "Ramesh purchased a refrigerator for Rs. 15500 after getting a discount of 20% on the labelled price. He spent some amount on transport and Rs. 250 on installation. To earn a 10% profit if no discount was offered, it should be sold for Rs. 21725. How much did Ramesh spend on transport?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given point A (1, 1), and points B, C on th... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 19045,
"question": "Given point A (1, 1), and points B, C on the parabola $y^2 = x$, if $\\angle ABC = 90^\\circ$, then the minimum value of AC is ______.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A train 110 m long is running with a speed ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 19046,
"question": "A train 110 m long is running with a speed of 84 km/hr. In 4.399648028157747 seconds, it will pass a man who is running at a certain speed in the direction opposite to that in which the train is going. What is the speed of the man in km/hr?",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Simplify the expression: \\(6 \\cdot 37 \\q... | math | {
"ground_truth": "1110",
"style": "rule"
} | {
"answer": "1110",
"index": 19047,
"question": "Simplify the expression: \\(6 \\cdot 37 \\quad(\\sqrt{3}+\\sqrt{2})^{2 \\log _{(\\sqrt{3}-\\sqrt{2})}^{\\sqrt{5}}}\\). Express your answer as a single number.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Plane Geometry -> Angles"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that the elevation angle of point B i... | math | {
"ground_truth": "130",
"style": "rule"
} | {
"answer": "130",
"index": 19048,
"question": "Given that the elevation angle of point B in the same direction as observed from point A is 60°, and the depression angle of point C is 70°, find the measure of angle ∠BAC. Express your answer in degrees as a whole number.",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are \\( n \\) distinct lines in the p... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 19049,
"question": "There are \\( n \\) distinct lines in the plane. One of these lines intersects exactly 5 of the \\( n \\) lines, another one intersects exactly 9 of the \\( n \\) lines, and yet another one intersects exactly 11 of them. Find the smallest possible value of \\( n \\). Express your answer as a whole number.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Number Theory -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Paul starts at $1$ and counts by threes: ... | math | {
"ground_truth": "2017",
"style": "rule"
} | {
"answer": "2017",
"index": 19050,
"question": "Paul starts at $1$ and counts by threes: $1, 4, 7, 10, ... $ . At the same time and at the same speed, Penny counts backwards from $2017$ by fi\fves: $2017, 2012, 2007, 2002,...$ . Find the one number that both Paul and Penny count at the same time.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given $x=1999$, then $|4x^2-5x+1|-4|x^2+2x+... | math | {
"ground_truth": "-19990",
"style": "rule"
} | {
"answer": "-19990",
"index": 19051,
"question": "Given $x=1999$, then $|4x^2-5x+1|-4|x^2+2x+2|+3x+7=$ .",
"split": "train"
} |
olympiads | [
"Mathematics -> Calculus -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given \\(x, y, z \\in (0, 2]\\), find the m... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 19052,
"question": "Given \\(x, y, z \\in (0, 2]\\), find the maximum value of the expression\n\n\\[ \nA = \\frac{\\left(x^{3} - 6\\right) \\sqrt[3]{x + 6} + \\left(y^{3} - 6\\right) \\sqrt[3]{y + 6} + \\left(z^{3} - 6\\right) \\sqrt[3]{z + 6}}{x^{2} + y^{2} + z^{2}}\n\\]",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the polar equation of a line is $3\\r... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 19053,
"question": "Given the polar equation of a line is $3\\rho\\cos \\theta-4\\rho\\sin \\theta=3$, find the distance from point $P(2, \\frac {3\\pi}{2})$ to this line.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In Fifi's closet, she hangs all her clothes... | math | {
"ground_truth": "65",
"style": "rule"
} | {
"answer": "65",
"index": 19054,
"question": "In Fifi's closet, she hangs all her clothes on colored plastic hangers. She has clothes hanging on:\n\n- 7 pink hangers\n- 4 green hangers\n- One less blue hanger than there are green hangers\n- One less yellow hanger than there are blue hangers\n- Twice the number of orange hangers as the sum of pink and green hangers\n- Three more purple hangers than the difference between blue and yellow hangers\n- The arithmetic mean of pink, green, and blue hangers as the number of red hangers\n- One more brown hanger than triple the number of red hangers\n- 3 gray hangers for every 5 purple hangers\n\nWhat is the total number of colored hangers in Fifi's closet?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n At the polar bear club, nine friends, inclu... | math | {
"ground_truth": "29",
"style": "rule"
} | {
"answer": "29",
"index": 19055,
"question": "At the polar bear club, nine friends, including Jerry, Elaine, George, Kramer, Newman, Susan, Puddy, Frank, and Estelle, took turns jumping into a swimming pool filled with freezing-cold water. Jerry was in the pool for 3 minutes before becoming too cold to remain in the cold water. Elaine stayed in the pool for twice as long as Jerry. George could only stay in the pool for one-third as long as Elaine. Kramer, who accidentally locked himself in the bathroom, could not find the pool. Newman stayed in the pool for exactly the average amount of time spent by the other friends who went into the pool. Susan managed to last 150 seconds in the pool. Puddy and Frank swam for the same amount of time, which was half of the time Elaine spent in the pool. Estelle left the pool after 0.1 hours. \n\nCalculate the combined total of minutes that Jerry and his friends spent in the cold water (ignoring Kramer since he didn't make it to the pool).",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Graph Theory"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a certain country, any two cities are di... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 19056,
"question": "In a certain country, any two cities are directly connected to each other by one of the following modes of transportation: bus, train, or airplane. It is known that no city is serviced by all three types of transportation, and at the same time, there are no three cities such that any two are connected by the same mode of transportation. Find the maximum possible number of cities in this country.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Gerard cuts a large rectangle into four sma... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 19057,
"question": "Gerard cuts a large rectangle into four smaller rectangles. The perimeters of three of these smaller rectangles are 16, 18, and 24. Find the perimeter of the fourth small rectangle. Express your answer as a whole number.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Micah bought envelopes to send, and dependi... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 19058,
"question": "Micah bought envelopes to send, and depending on the weight of the envelope he will need more stamps. If an envelope weighs more than a certain weight, he will need 5 stamps. If it weighs less than that, it will only need 2 stamps. He bought 52 stamps with 6 envelopes that weigh less than that weight. Micah needed to buy 14 envelopes in total. What is the weight limit for an envelope to need only 2 stamps?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a positive geometric sequence $\\{a_{n}\... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 19059,
"question": "In a positive geometric sequence $\\{a_{n}\\}$, it is known that $a_{1}a_{2}a_{3}=4$, $a_{4}a_{5}a_{6}=8$, and $a_{n}a_{n+1}a_{n+2}=128$. Find the value of $n$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The sum of the first 4 terms of an arithmet... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 19060,
"question": "The sum of the first 4 terms of an arithmetic sequence is 26, the sum of the last 4 terms is 110, and the sum of all terms is 187. The number of terms in this sequence is __________.",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There is a product $a_{1} \\cdot a_{2} \\cd... | math | {
"ground_truth": "33",
"style": "rule"
} | {
"answer": "33",
"index": 19061,
"question": "There is a product $a_{1} \\cdot a_{2} \\cdot \\cdots \\cdot a_{100}$ written on the blackboard, where $a_{1}, a_{2}, \\cdots, a_{100}$ are positive integers. If one of the multiplication symbols is changed to an addition symbol (while keeping the rest multiplication symbols), it is found that 32 out of the 99 resultant sums are even. How many even numbers can there be at most among $a_{1}, a_{2}, \\cdots, a_{100}$?",
"split": "train"
} |
omnimath | [
"Mathematics -> Algebra -> Equations and Inequalities -> Quadratic Functions"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n There are functions $f(x)$ with the followi... | math | {
"ground_truth": "71",
"style": "rule"
} | {
"answer": "71",
"index": 19062,
"question": "There are functions $f(x)$ with the following properties: $f(x)=ax^{2}+bx+c$ for some integers $a, b$ and $c$ with $a>0$, and $f(p)=f(q)=17$ and $f(p+q)=47$ for some prime numbers $p$ and $q$ with $p<q$. For each such function, the value of $f(pq)$ is calculated. The sum of all possible values of $f(pq)$ is $S$. What are the rightmost two digits of $S$?",
"split": "train"
} |
orca_math | [
"Mathematics -> Algebra -> Equations and Inequalities -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n We have the expression 632-A9B=41. Find out... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 19063,
"question": "We have the expression 632-A9B=41. Find out the number that must go into A.",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find the largest possible subset of {1, 2, ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 19064,
"question": "Find the largest possible subset of {1, 2, ... , 15} such that the product of any three distinct elements of the subset is not a square.",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Area"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given a triangle with sides 6, 8, and 10. F... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 19065,
"question": "Given a triangle with sides 6, 8, and 10. Find the length of the shortest segment connecting points on the sides of the triangle and dividing it into two equal-area parts.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given points P(1,3) and Q(-1,2), let point ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 19066,
"question": "Given points P(1,3) and Q(-1,2), let point M be a variable point on the line x-y+1=0. Find the minimum value of |PM|+|QM|.",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A merchant buys n radios for d dollars, whe... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 19067,
"question": "A merchant buys n radios for d dollars, where d is a positive integer. The merchant sells two radios at half the cost price to a charity sale, and the remaining radios at a profit of 8 dollars each. If the total profit is 72 dollars, what is the smallest possible value of n? Express your answer as a single integer.",
"split": "train"
} |
big_math | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the sets $A=\\{-1,0,1,2,3\\}$ and $B=... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"answer": "7",
"index": 19068,
"question": "Given the sets $A=\\{-1,0,1,2,3\\}$ and $B=\\{-1,0,1\\}$, let $f(x)$ be a function from $A$ to $B$. Find the number of possible value sets for the function $f(x)$. Express your answer as a single integer.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Equations and Inequalities -> Quadratic Functions"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $m$ and $n$ be the two real roots of th... | math | {
"ground_truth": "2020",
"style": "rule"
} | {
"answer": "2020",
"index": 19069,
"question": "Let $m$ and $n$ be the two real roots of the quadratic equation $x^{2}+2x-2022=0$. Find the value of $m^{2}+3m+n$.",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given an arithmetic sequence $\\{a_n\\}$ wi... | math | {
"ground_truth": "1007",
"style": "rule"
} | {
"answer": "1007",
"index": 19070,
"question": "Given an arithmetic sequence $\\{a_n\\}$ with the first term being a positive number and the sum of the first $n$ terms denoted as $S_n$, if $a_{1006}$ and $a_{1007}$ are the two roots of the equation $x^2 - 2012x - 2011 = 0$, find the maximum value of the positive integer $n$ for which $S_n > 0$ holds. Express your answer as a positive integer.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Sequences and Series"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If the arithmetic sequence $\\{a_n\\}$ sati... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 19071,
"question": "If the arithmetic sequence $\\{a_n\\}$ satisfies $a_{7}+a_{8}+a_{9} > 0$ and $a_{7}+a_{10} < 0$, then when $n=$ ______, the sum of the first $n$ terms of $\\{a_n\\}$ is maximized.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a Cartesian coordinate system, the param... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 19072,
"question": "In a Cartesian coordinate system, the parametric equation of line $l$ is $\\begin{cases} x=t \\\\ y= \\sqrt{3}t+2\\end{cases}$ (where $t$ is the parameter), and the parametric equation of circle $C$ is $\\begin{cases} x=a\\cos \\theta \\\\ y=a\\sin \\theta \\end{cases}$ (where $a > 0$ and $\\theta$ is the parameter). Let point $P$ be any point on circle $C$. If the maximum distance from point $P$ to line $l$ is $3$, find the value of $a$.",
"split": "train"
} |
omnimath | [
"Mathematics -> Geometry -> Plane Geometry -> Polygons"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $A B C D E F G H$ be an equilateral oct... | math | {
"ground_truth": "405",
"style": "rule"
} | {
"answer": "405",
"index": 19073,
"question": "Let $A B C D E F G H$ be an equilateral octagon with $\\angle A \\cong \\angle C \\cong \\angle E \\cong \\angle G$ and $\\angle B \\cong \\angle D \\cong \\angle F \\cong$ $\\angle H$. If the area of $A B C D E F G H$ is three times the area of $A C E G$, then $\\sin B$ can be written as $\\frac{m}{n}$, where $m, n$ are positive integers and $\\operatorname{gcd}(m, n)=1$. Find $100 m+n$.",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Greatest Common Divisors (GCD)"
] | 0.09375 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n For positive integers \\( m \\) and \\( n \... | math | {
"ground_truth": "325",
"style": "rule"
} | {
"answer": "325",
"index": 19074,
"question": "For positive integers \\( m \\) and \\( n \\), let \\( \\operatorname{gcd}(m, n) \\) denote the largest positive integer that is a factor of both \\( m \\) and \\( n \\). Compute\n\\[ \n\\sum_{n=1}^{91} \\operatorname{gcd}(n, 91) \n\\]",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Algebraic Expressions -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given that $(\\sqrt{2} - x)^{10} = a_0 + a_... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 19075,
"question": "Given that $(\\sqrt{2} - x)^{10} = a_0 + a_1 x + a_2 x^2 +... + a_{10} x^{10}$, calculate the value of $(a_0 + a_2 +... + a_{10})^2 - (a_1 + a_3 +... + a_9)^2$. Express your answer as a single integer.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Vinny weighed 300 pounds then lost some pou... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"answer": "40",
"index": 19076,
"question": "Vinny weighed 300 pounds then lost some pounds in the first month of his diet. He continued his diet but each month, he lost half as much weight as he had lost in the previous month. At the start of the fifth month of his diet, he worked harder to lose extra weight then decided to end his diet. Vinny weighed 250.5 pounds at the end of his diet and lost 12 pounds in the fifth month. How many pounds did he lose in the first month?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Statistics -> Probability -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A cafeteria serves ham and cheese sandwiche... | math | {
"ground_truth": "230",
"style": "rule"
} | {
"answer": "230",
"index": 19077,
"question": "A cafeteria serves ham and cheese sandwiches, ham and tomato sandwiches, and tomato and cheese sandwiches. On a certain day, 80 customers had meals containing both ham and cheese; 90 had meals containing both ham and tomatoes; 100 had meals containing both tomatoes and cheese; and 20 customers had meals that included all three ingredients. How many customers were there?",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Non-Euclidean Geometry -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Given the hyperbola $C$: $\\frac{x^2}{a^2} ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 19078,
"question": "Given the hyperbola $C$: $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$ ($a > 0, b > 0$), its left vertex is $A$, and point $B\\left( 0,\\frac{\\sqrt{15}}{3}b \\right)$. If the perpendicular bisector of segment $AB$ passes through the right focus $F$, find the eccentricity of the hyperbola $C$. Express your answer as a single number.",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Find a four-digit number that is a perfect ... | math | {
"ground_truth": "7744",
"style": "rule"
} | {
"answer": "7744",
"index": 19079,
"question": "Find a four-digit number that is a perfect square, in which its digits can be grouped into two pairs of equal digits.",
"split": "train"
} |
math | [
"Mathematics -> Algebra -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n For real numbers $x,$ $y,$ and $z,$ find th... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 19080,
"question": "For real numbers $x,$ $y,$ and $z,$ find the minimum value of\n\\[2x^2 + 5y^2 + 2z^2 + 4xy - 4yz - 2z - 2x.\\]",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Probability -> Counting Methods -> Combinations"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Distribute 9 identical balls into 3 differe... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"answer": "18",
"index": 19081,
"question": "Distribute 9 identical balls into 3 different boxes with each box containing at least one ball and the number of balls in each box being distinct. How many different distributions are there?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Algebraic Expressions -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n If the constant term of the binomial $({\\s... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 19082,
"question": "If the constant term of the binomial $({\\sqrt{x}-\\frac{2}{{\\sqrt[3]{x}}}})^n$ is $-80$, then $n=\\_\\_\\_\\_\\_\\_$.",
"split": "train"
} |
big_math | [
"Mathematics -> Geometry -> Solid Geometry -> 3D Shapes"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Consider two solid spherical balls, one cen... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"answer": "13",
"index": 19083,
"question": "Consider two solid spherical balls, one centered at $(0, 0, \\frac{21}{2})$ with radius $6$, and the other centered at $(0, 0, 1)$ with radius $\\frac{9}{2}$. Find the number of points $(x, y, z)$ with only integer coordinates (lattice points) that lie within the intersection of the two spheres.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A seller of used cars has 18 cars to sell, ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 19084,
"question": "A seller of used cars has 18 cars to sell, with various prices ranging from $4,000 to $25,000. Each of his clients selects 3 cars that they liked most, influenced by both their preferences and the car prices. If each car was selected at least once and some cars were selected more than once due to overlapping preferences and shared budget ranges, how many clients visited the garage, given that the car with the highest demand was selected 6 times?",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Algebra -> Other"
] | 0.078125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the geometric sequence $\\{a\\_n\\}$, $a... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"answer": "10",
"index": 19085,
"question": "In the geometric sequence $\\{a\\_n\\}$, $a\\_n > 0$, and $a\\_3a\\_5 + a\\_2a\\_10 + 2a\\_4a\\_6 = 100$, find the value of $a\\_4 + a\\_6$.",
"split": "train"
} |
olympiads | [
"Mathematics -> Number Theory -> Other"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let \\( a, b, c \\) be positive integers su... | math | {
"ground_truth": "1936",
"style": "rule"
} | {
"answer": "1936",
"index": 19086,
"question": "Let \\( a, b, c \\) be positive integers such that \\( \\frac{1}{a} + \\frac{1}{b} = \\frac{1}{c} \\) and \\( \\operatorname{gcd}(a, b, c) = 1 \\). Suppose \\( a + b \\leq 2011 \\). Determine the largest possible value of \\( a + b \\).",
"split": "train"
} |
olympiads | [
"Mathematics -> Discrete Mathematics -> Sequences and Series"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In a sequence of natural numbers, each numb... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 19087,
"question": "In a sequence of natural numbers, each number, except for the first one, is obtained by adding to the previous one its largest digit.\n\nWhat is the maximum number of consecutive odd members that can appear in the sequence?",
"split": "train"
} |
olympiads | [
"Mathematics -> Geometry -> Plane Geometry -> Polygons"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n How many triangles are shown in Figure 4? S... | math | {
"ground_truth": "28",
"style": "rule"
} | {
"answer": "28",
"index": 19088,
"question": "How many triangles are shown in Figure 4?",
"split": "train"
} |
omnimath | [
"Mathematics -> Geometry -> Plane Geometry -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In triangle $A B C$ with $A B=8$ and $A C=1... | math | {
"ground_truth": "84",
"style": "rule"
} | {
"answer": "84",
"index": 19089,
"question": "In triangle $A B C$ with $A B=8$ and $A C=10$, the incenter $I$ is reflected across side $A B$ to point $X$ and across side $A C$ to point $Y$. Given that segment $X Y$ bisects $A I$, compute $B C^{2}$.",
"split": "train"
} |
omnimath | [
"Mathematics -> Discrete Mathematics -> Combinatorics"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Compute the number of nonempty subsets $S \... | math | {
"ground_truth": "335",
"style": "rule"
} | {
"answer": "335",
"index": 19090,
"question": "Compute the number of nonempty subsets $S \\subseteq\\{-10,-9,-8, \\ldots, 8,9,10\\}$ that satisfy $|S|+\\min (S)$. $\\max (S)=0$.",
"split": "train"
} |
cn_k12 | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.03125 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A class has a total of 54 students. Using t... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 19091,
"question": "A class has a total of 54 students. Using the systematic sampling method to draw a sample of size 4, given that students with numbers 2, 28, and 41 have been included in the sample, find the student number of the fourth student in the sample.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Tom has 12 coins in quarters and nickels. H... | math | {
"ground_truth": "140",
"style": "rule"
} | {
"answer": "140",
"index": 19092,
"question": "Tom has 12 coins in quarters and nickels. He has 4 quarters and 8 nickels. What is the total value of his coins?",
"split": "train"
} |
olympiads | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n In the first pile, there were 7 nuts, and i... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 19093,
"question": "In the first pile, there were 7 nuts, and in the rest, there were 12 nuts each. How many piles were there in total?",
"split": "train"
} |
math | [
"Mathematics -> Geometry -> Other"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n A lattice point is a point whose coordinate... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"answer": "19",
"index": 19094,
"question": "A lattice point is a point whose coordinates are both integers. How many lattice points are on the boundary or inside the region bounded by $y=|x|$ and $y=-x^2+6$?",
"split": "train"
} |
big_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.0625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The Environmental Protection Bureau of a ci... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 19095,
"question": "The Environmental Protection Bureau of a city proposes two investment plans to increase the city's green space area: Plan A involves a one-time investment of 1 million yuan; Plan B involves an investment of 100,000 yuan in the first year, with an increase of 100,000 yuan each subsequent year. Calculate the number of years it will take for the total investment under Plan B to be no less than the investment under Plan A. Express your answer as a whole number.",
"split": "train"
} |
aops_forum | [
"Mathematics -> Calculus -> Integral Calculus -> Applications of Integrals"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Let $f(x)=\\int_0^{x} e^{t} (\\cos t+\\sin... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 19096,
"question": "Let $f(x)=\\int_0^{x} e^{t} (\\cos t+\\sin t)\\ dt,\\ g(x)=\\int_0^{x} e^{t} (\\cos t-\\sin t)\\ dt.$ \n\nFor a real number $a$ , find $\\sum_{n=1}^{\\infty} \\frac{e^{2a}}{\\{f^{(n)}(a)\\}^2+\\{g^{(n)}(a)\\}^2}.$ ",
"split": "train"
} |
big_math | [
"Mathematics -> Algebra -> Algebraic Expressions -> Other"
] | 0.015625 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n For any real numbers $x, y$, define the ope... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 19097,
"question": "For any real numbers $x, y$, define the operation $x*y = ax + by + cxy$, where $a, b, c$ are constants. It is known that $1*2 = 4$ and $2*3 = 6$. Find the non-zero real number $m$ such that for any real number $x$, $x*m = x$. Express your answer as a single real number.",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n The school principal decided that she wante... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"answer": "14",
"index": 19098,
"question": "The school principal decided that she wanted every class to have an equal number of boys and girls in each first-grade classroom. There are 7 classrooms. There are 68 boys and 53 girls. How many total students can be in each classroom while maintaining an equal distribution of boys and girls in each room?",
"split": "train"
} |
orca_math | [
"Mathematics -> Applied Mathematics -> Math Word Problems"
] | 0.046875 | xinpeng/Big-Math-RL-Verified-Combined-digit-hard-int-only | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer. You should try to truely solve the question by yourself without cheating. <|im_end|>\n<|im_start|>user\n Adam can paint a house in 5 hours. Audrey c... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 19099,
"question": "Adam can paint a house in 5 hours. Audrey can paint the same house in some hours. If they work together, it will take them 2.72727272727 hours to paint the house. How long does it take for Audrey to paint the house alone?",
"split": "train"
} |
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