data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "From the given number $123456789101112 \\cdots 9899100$, remove 100 digits such that the remaining number is the largest possible.",
"role": "user"
}
] | math | {
"ground_truth": "999997859606162 \\cdots 9899100",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the number obtained from the last two nonzero digits of $80!$.",
"role": "user"
}
] | math | {
"ground_truth": "21",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a square with side length determined by the sum of the numbers rolled from a standard 6-sided dice, calculate the probability that the area of the square is less than its p... | math | {
"ground_truth": "\\frac{1}{12}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many triangles with positive area have all their vertices at points $(i,j)$ on the coordinate plane, where $i$ and $j$ are integers between 1 and 6, inclusive?",
"role": ... | math | {
"ground_truth": "6796",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "From the right angle $C$ of triangle $A B C$, a median $C M$ is drawn. The circle inscribed in triangle $A C M$ touches side $C M$ at its midpoint. Find the angles of triangle $A... | math | {
"ground_truth": "30^\\circ, 60^\\circ, 90^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many quadratic residues are there $\\bmod pq$? And $\\bmod p^n$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{(p-1)(q-1)}{4} \\text{ et } \\frac{(p-1)p^{k-1}}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation \\((x+c\\cdot m)^2 - (x+c\\cdot n)^2 = (m-n)^2\\), where \\(m\\) and \\(n\\) are unequal non-zero constants, and \\(c\\) is a constant, find the value of \\(x\... | math | {
"ground_truth": "-11",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the universal set \\\\(U=\\mathbb{R}\\\\), and the sets \\\\(A=\\{-1,0,1,2,3\\}\\\\) and \\\\(B=\\{x|x\\geqslant 2\\}\\\\). Then, \\\\(A\\cap \\complement_{U}B=\\\\) \\_\\_\\... | math | {
"ground_truth": "\\{-1,0,1\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the value of $25$ quarters and $20$ dimes is equal to the value of $15$ quarters, $10$ dimes, and $n$ half-dollars, calculate the value of $n$.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A bookstore raised the original price of a book by a certain percent and subsequently reduced the new price by the same percentage. The final price came out to be 90% of the orig... | math | {
"ground_truth": "B) 32%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The positive integer solutions to the inequality $-3 \\leq 5 - 2x < 3$ are ____.",
"role": "user"
}
] | math | {
"ground_truth": "2, 3, 4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The domain of the function $f(x) = \\log_2{x}$ is $[2, 8]$. Find the domain of the inverse function $f^{-1}(x)$.",
"role": "user"
}
] | math | {
"ground_truth": "[1, 3]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x_0=x_1=1$ , and for $n\\geq1$ $x_{n+1}=\\frac{x_n^2}{x_{n-1}+2x_n}$ ,\n\nfind a formula for $x_n$ as a function of $n$ .",
"role": "user"
}
] | math | {
"ground_truth": "x_n = \\frac{1}{(2n-1)!!}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Lucy needs to save 36 files, each disk has a total capacity of 2 MB, and 5 of the files require 1.2 MB, 16 of the files require 0.6 MB, and the remaining files require... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many values of \\( x \\), where \\(-19 < x < 98\\), satisfy\n\\[ \n\\cos^2 x + 2 \\sin^2 x = 1 ? \n\\]",
"role": "user"
}
] | math | {
"ground_truth": "38",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many integers between 100 and 999 have an odd ones digit, an even tens digit, and an even hundreds digit?",
"role": "user"
}
] | math | {
"ground_truth": "100",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all pairs of integers \\((x, y)\\) satisfying \\(x^{2} = y^{2}\\left(x + y^{4} + 2y^{2}\\right)\\).",
"role": "user"
}
] | math | {
"ground_truth": "(0, 0), (12, 2), (-8, 2)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The probability of an event occurring in each of 625 independent trials is 0.8. Find the probability that the relative frequency of the occurrence of the event deviates from its ... | math | {
"ground_truth": "0.9876",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "It is between 10:00 and 11:00 o'clock, and six minutes from now, the minute hand of a watch will be exactly opposite the place where the hour hand was three minutes ago. What is ... | math | {
"ground_truth": "10:15",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Give methods to find all pairs of positive integers where both the sum and the product are perfect squares. In particular, identify all such pairs that are less than 100.",
"... | math | {
"ground_truth": "(2, 2), (5, 20), (8, 8), (10, 90), (18, 18), (20, 80), (9, 16), (32, 32), (50, 50), (72, 72), (2, 98), (98, 98), (36, 64)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a kite $ABCD$ with $AB = AD$ and $CB = CD$, where side $AB$ is extended beyond $B$ to point $E$. If $\\angle BAD = 94^\\circ$ and diagonal $AC$ bisects $\\angle BAD$, find ... | math | {
"ground_truth": "94^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "It takes 18 minutes for Mark to walk one mile. At that rate, how far in miles will he walk in 15 minutes? Express your answer as a decimal to the nearest tenth.",
"role": "us... | math | {
"ground_truth": "0.8 \\text{ miles}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "4.3535… is a decimal, which can be abbreviated as , and the repeating cycle is .",
"role": "user"
}
] | math | {
"ground_truth": "35",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ordered pairs of integers $(a,b)$ satisfy all of the following inequalities?\n\\[ \\begin{aligned} \na^2 + b^2 &< 25 \\\\ \na^2 + b^2 &< 9a \\\\ \na^2 + b^2 &< 9b \\\\ \... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The transformation corresponding to the second-order matrix $M$ maps the points $(1, -1)$ and $(-2, 1)$ to $(-1, -1)$ and $(0, -2)$, respectively. \n(Ⅰ) Find the inverse matrix ... | math | {
"ground_truth": "x + 4 = 0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a function $y = g(x)$ with the property that if it is shifted $24$ units to the right, then the resulting graph is identical to the original graph of $y = g(x)$. Determi... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$ , let $J$ be the center of the excircle tangent to side $BC$ at $A_{1}$ and to the extensions of the sides $AC$ and $AB$ at $B_{1}$ and $C_{1}$ r... | math | {
"ground_truth": "\\angle BEA_1 = \\angle AEB_1 = 90^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the largest positive integer $n$ such that, when filling the 400 squares of a $20 \\times 20$ grid with any arrangement of the integers from 1 to 400, there is always at lea... | math | {
"ground_truth": "209",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The line $2x-2y-1=0$ intersects the parabola $C:y^{2}=2px\\left(p \\gt 0\\right)$ at points $M$ and $N$. The distance $|MN|$ is 4 units. The projections of $M$ and $N$ onto the d... | math | {
"ground_truth": "9\\sqrt{2}\\pi",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest prime number $p$ for which the number $p^3+2p^2+p$ has exactly $42$ divisors.",
"role": "user"
}
] | math | {
"ground_truth": "23",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If two people, A and B, work together on a project, they can complete it in a certain number of days. If person A works alone to complete half of the project, it takes them 10 da... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the sum of $2\\sqrt[5]{32} + 3\\sqrt[3]{27}$.\nA) 10\nB) 12\nC) 13\nD) 15",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(C) } 13",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "This year February $29$ fell on a Sunday. In what year will February $29$ next fall on a Sunday?",
"role": "user"
}
] | math | {
"ground_truth": "2032",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\mathcal{A}$ be the set of finite sequences of positive integers $a_1,a_2,\\dots,a_k$ such that $|a_n-a_{n-1}|=a_{n-2}$ for all $3\\leqslant n\\leqslant k$ . If $a_... | math | {
"ground_truth": "1597",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The bases of an isosceles trapezoid are $a$ and $b (a > b)$, and the acute angle is $45^{\\circ}$. Find the area of the trapezoid.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{a^2 - b^2}{4}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the measure of $\\angle MON$ given that $O$ is the coordinate origin, the line $y=2$ intersects with $x^{2}+y^{2}+Dx-4y=0$ at two points $M$ and $N$.",
"role": "use... | math | {
"ground_truth": "90^{\\circ}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a math contest, 15% of the participants scored 65 points, 20% scored 85 points, 40% scored 95 points, and the rest scored 110 points. What is the difference between the mean a... | math | {
"ground_truth": "B) 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given: The line $y=2x-4$ intersects the $x$-axis and the $y$-axis at points $A(m,0)$ and $B(0,n)$, respectively. Find the value of $m-n$.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The expression \\( x^4 + 1 \\) is to be divided by the trinomial \\( x^2 + px + q \\). What values should \\( p \\) and \\( q \\) be chosen so that the division is exact (without... | math | {
"ground_truth": "\\begin{array}{ll}\n(p, q) & \\text{Values}\\\\\n(0, \\pm i) & \\\\\n(\\sqrt{2}, 1) & \\\\\n(-\\sqrt{2}, 1) & \\\\\n\\end{array}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a $300^{\\circ}$ sector of a circle of radius 10, determine the dimensions of the cone that can be formed by aligning the two straight sides.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S$ be the set $\\{1, 2, ..., 10\\}$ . Let $A$ be a subset of $S$ .\nWe arrange the elements of $A$ in increasing order, that is, $A = \\{a_1, a_2, ...., a_k\\}$ wi... | math | {
"ground_truth": "2^{n-3} (5n^2 + 5n + 2)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the remainder when the product $1234 \\cdot 1567 \\cdot 1912$ is divided by 5.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For some constant $k$ the polynomial $p(x) = 3x^2 + kx + 117$ has the property that $p(1) = p(10)$ . Evaluate $p(20)$ .",
"role": "user"
}
] | math | {
"ground_truth": "657",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the greatest positive integer $A{}$ with the following property: however we place the numbers $1,2,\\ldots, 100$ on a $10\\times 10$ board, each number appearing ... | math | {
"ground_truth": "54",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Observe the following equations: $2^2=1+3$, $2^3=3+5$, $2^4=7+9$, ..., $3^2=1+3+5$, $3^3=7+9+11$, $3^4=25+27+29$, ..., $4^2=1+3+5+7$, $4^3=13+15+17+19$, $4^4=61+63+65+67$, ... Ac... | math | {
"ground_truth": "p^{q-1}-p+1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two cars, Car A and Car B, are traveling from city A to city B at a speed of 55 km/hour. At 10 AM, the distance traveled by Car A is 5 times the distance traveled by Car B. At 12... | math | {
"ground_truth": "8 \\text{ hours}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $x$ such that $2x+1$ is a perfect square but none of the integers $2x+2, 2x+3, \\ldots, 3x+2$ are perfect squares.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The only prime factors of an integer $n$ are 2 and 3. If the sum of the divisors of $n$ (including itself) is $1815$ , find $n$ .",
"role": "user"
}
] | math | {
"ground_truth": "648",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Six people are sitting at a round table. Let $f\\geq 0$ be the number of people sitting next to at least one female and $m\\geq0$ be the number of people sitting next to at least... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an ellipse $C$: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 (a > b > 0)$ with eccentricity $e = \\frac{\\sqrt{6}}{3}$, and points $A$, $B$ on the ellipse $C$, where $N(3,1)$ i... | math | {
"ground_truth": "12\\ \\text{points}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For \\( y = \\frac{3x + 1}{4x - 9} \\), find the \\( x \\)-value where there is a vertical asymptote.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the arithmetic sequence {a_n} starts with 3 and has a common difference of 1, and the geometric sequence {b_n} starts with 1 and has a common ratio of 2, find the valu... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $$f(x)= \\begin{cases} f(x-5), & x>0 \\\\ 2^{x}+ \\int_{ 0 }^{ \\frac {\\pi}{6} } \\cos3tdt, & x\\leq 0 \\end{cases}$$, evaluate $f(2017)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{11}{24}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( n = x - 3\\log_y(x) \\). Find \\( n \\) when \\( x = 8 \\) and \\( y = 2\\).",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all positive real $M$ such that for any positive reals $a,b,c$ , at least one of $a + \\dfrac{M}{ab}, b + \\dfrac{M}{bc}, c + \\dfrac{M}{ca}$ is greater than or eq... | math | {
"ground_truth": "M = \\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the solution set of the inequality \\(\\left(\\frac{\\pi}{2}\\right)^{(x-1)^{2}} \\leq\\left(\\frac{2}{\\pi}\\right)^{x^{2}-5 x-5}\\).\n(a) \\([-1, 4]\\)\n(b) \\((-\\infty, ... | math | {
"ground_truth": "\\text{(c) } [-\\frac{1}{2}, 4]",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an ellipse centered at the origin with its axes of symmetry being the coordinate axes, and passing through the point (4, 0) with an eccentricity of $\\frac{\\sqrt{3}}{2}$, ... | math | {
"ground_truth": "\\frac{y^2}{64} + \\frac{x^2}{16} = 1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence of length 20 containing zeros and ones, determine the number of arrangements such that all the zeros are consecutive, or all the ones are consecutive, or both.",... | math | {
"ground_truth": "380",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The test this year was held on Monday, 22 August 2022 on 09.10-11.40 (GMT+7) for the essay section and was held on 12.05-13.30 (GMT+7) for the short answers section, which was to... | math | {
"ground_truth": "381",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A stone is dropped into a well, and the sound of the stone hitting the bottom is heard 7.7 seconds later. If the distance fallen by the stone in \\( t \\) seconds is \\( 16t^2 \\... | math | {
"ground_truth": "784",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the smallest solution for the equation \\[\\frac{3x}{x-3} + \\frac{3x^2 - 36}{x} = 14.\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5 - \\sqrt{241}}{6}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A company ordered a large souvenir. During delivery, two members were absent, so those present paid 18 Ft more per person than initially planned. Soon, one of the absent members ... | math | {
"ground_truth": "\\text{10 members and 720 Ft}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a polynomial \\( P(x) \\) with integer coefficients and degree greater than or equal to 5, where it has distinct integer roots, one of which is 0, express the set of intege... | math | {
"ground_truth": "\\{ \\alpha \\mid P(P(\\alpha)) = 0, \\alpha \\in \\mathbb{Z} \\} = \\{ \\alpha \\mid P(\\alpha) = 0, \\alpha \\in \\mathbb{Z} \\}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $m>1$ be a natural number and $N=m^{2017}+1$ . On a blackboard, left to right, are written the following numbers:\n\\[N, N-m, N-2m,\\dots, 2m+1,m+1, 1.\\]\nOn each move, w... | math | {
"ground_truth": "X = \\frac{m^{2017} + 1}{m + 1} + m",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the number of significant digits in the measurement of the side of a square whose computed area is $3.2400$ square inches to the nearest ten-thousandth of a square inch... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the limit\n\n$$\n\\lim _{n \\rightarrow \\infty} \\frac{n \\sqrt[6]{n}+\\sqrt[5]{32 n^{10}+1}}{(n+\\sqrt[4]{n}) \\sqrt[3]{n^{3}-1}}\n$$",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given \\( 4x - 5y - z = 0 \\) and \\( x + 5y - 18z = 0 \\), with \\( z \\neq 0 \\), find the numerical value of \\( \\frac{x^2 + 4xy}{y^2 + z^2} \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3622}{9256}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all points on the straight line which joins $(4, 11)$ to $(16, 1)$ and whose coordinates are positive integers.",
"role": "user"
}
] | math | {
"ground_truth": "(5, 3)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the function \\( y = g(x) = \\frac{x^2}{Ax^2 + Bx + C} \\), where \\( A, B, \\) and \\( C \\) are integers. The function has vertical asymptotes at \\( x = -1 \\) and \\... | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A school has $100$ students and $5$ teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are $5... | math | {
"ground_truth": "-13.5",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $n$ is a real number, then the simultaneous system \n$2nx + 3y = 2$\n$3ny + 4z = 3$\n$4x + 2nz = 4$\nhas no solution if and only if $n$ is equal to which of the following?\nA)... | math | {
"ground_truth": "-\\sqrt[3]{4}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $\\int_{0}^{1} \\frac{\\sin x}{x} \\, dx$ with an accuracy of 0.01.",
"role": "user"
}
] | math | {
"ground_truth": "0.94",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the set of real numbers $\\alpha$ that can be expressed in the form \\[\\alpha=\\sum_{n=0}^{\\infty}\\frac{x_{n+1}}{x_n^3}\\]\nwhere $x_0,x_1,x_2,\\dots$ is an inc... | math | {
"ground_truth": "\\alpha \\ge \\frac{3\\sqrt{3}}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of \n\\[\n\\frac{(.5)^4}{(.05)^3}\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "500",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence of 0s and 1s of length 23 that begins with a 0, ends with a 0, contains no two consecutive 0s, and contains no four consecutive 1s, determine the number of such ... | math | {
"ground_truth": "200",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a triangle \\( \\triangle ABC \\) with vertices at \\( (x_1, y_1), (x_2, y_2), (x_3, y_3) \\), find the coordinates of point \\( P \\) on the plane such that the sum of the... | math | {
"ground_truth": "P \\left(\\frac{x_1 + x_2 + x_3}{3}, \\frac{y_1 + y_2 + y_3}{3} \\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCD$ be a trapezoid with the measure of base $AB$ twice that of base $DC$, and let $E$ be the point of intersection of the diagonals. If the measure of diagonal $AC$ is $11... | math | {
"ground_truth": "\\frac{11}{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A=\\{1,a-1\\}$, $B=\\{-1,2a-3,1-2a\\}$. If $A\\subseteq B$, then solve for the value of $a$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let's draw a circle around the triangle \\(ABC\\) and rotate it around the tangent drawn to the circle at point \\(A\\). What is the surface area described by side \\(BC\\) and w... | math | {
"ground_truth": "\\frac{4 S^2 \\pi}{3abc} (b^2 + c^2)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the greatest value of $x$ such that \\[\\frac{x^2 - x - 30}{x-6} = \\frac{2}{x+4}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$ABCDE$ is a regular pentagon. $AP$, $AQ$, and $AR$ are the perpendiculars dropped from $A$ onto $CD$, $BC$ extended, and $DE$ extended, respectively. Let $O$ be the center of th... | math | {
"ground_truth": "AO + AQ + AR = 8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider:\n\\begin{eqnarray*}\n&(1)& x\\text{ and }y\\text{ are both integers between 100 and 999, inclusive;}\\qquad \\qquad \\qquad \\qquad \\qquad \\\\\n&(2)& y\\text{ is the ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two tangents are drawn from an exterior point $A$ to a circle, touching the circle at points $B$ and $C$, respectively. A third tangent intersects segment $AB$ at $P$ and segment... | math | {
"ground_truth": "\\textbf{(C)}\\ 48",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the distance of the centre of gravity of a uniform $100$ -dimensional solid hemisphere of radius $1$ from the centre of the sphere with $10\\%$ relative error.",
"r... | math | {
"ground_truth": "0.113 \\pm 0.0113",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\(\\sin \\theta - \\cos \\theta = \\frac{\\sqrt{6} - \\sqrt{2}}{2}\\), find the value of \\(24\\left(\\sin ^{3} \\theta - \\cos ^{3} \\theta\\right)^{2}\\).",
"role": "us... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a differentiable function $f(x)$ with its derivative denoted as $f'(x)$, and it satisfies $f(x) = 3x^2 + 2xf'(2)$, then $f'(5) = \\_\\_\\_\\_\\_\\_$.",
"role": "user"
... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the addition shown below where $A$, $B$, $C$, and $D$ are distinct digits, and there exists a carry into the last column, determine the number of different values possible ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the mass of a hemisphere if at each point its surface density is numerically equal to the distance of this point from the radius, which is perpendicular to the base of the h... | math | {
"ground_truth": "\\frac{\\pi^2 R^3}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the value of \\( b \\) such that the graph of the equation \\[ x^2 + 9y^2 - 6x + 27y = b \\] is a non-degenerate ellipse.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{145}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For positive integers $n$, let $D(n)$ denote the number of pairs of different adjacent digits in the binary (base two) representation of $n$. Consider $n$ such that $14 \\leq n \... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $PQR$, lines $QR$, $RP$, and $PQ$ are tangents to circle $O$ at points $R$, $Q$, and $P$ respectively, and $\\angle QPR = 25^\\circ$. Find $\\angle QOR$.",
"role"... | math | {
"ground_truth": "25^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a 24-inch by 30-inch pan of chocolate cake, determine the number of pieces the pan contains if each piece measures 3 inches by 2 inches.",
"role": "user"
}
] | math | {
"ground_truth": "120",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "1. \\([x]\\) is the integer part of the number \\(x\\) (the greatest integer that does not exceed \\(x\\)), and \\(\\{x\\} = x - [x]\\) is the fractional part of the number \\(x\... | math | {
"ground_truth": "1) \\text{For } a = 1, x = 5 ; 2) \\text{For } a = \\frac{3}{2}, x = \\frac{13}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the equation \\(xyz = x + y\\) in natural numbers \\(x, y, z\\).",
"role": "user"
}
] | math | {
"ground_truth": "(2, 2, 1), (1, 1, 2)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $2^a + 2^b + 5^e = 3^c + 3^d + 5^f$, find the number of integers $a, b, c, d, e, f$ that can possibly be negative.\nA) 6\nB) 5\nC) 4\nD) 3\nE) 0",
"role": "user"
}
] | math | {
"ground_truth": "E) 0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Triangle $ABC$ has side $AB = 10$ inches. A line $DEF$ is drawn parallel to line $AB$, where point $D$ is on segment $AC$ and point $E$ is on segment $BC$. Line $AE$ extended bis... | math | {
"ground_truth": "\\frac{20}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle ABC, the sides opposite to angles A, B, and C are a, b, and c respectively. Given that b=6, a=2c, and B= $$\\frac {π}{3}$$, find the area of triangle ABC.",
"role... | math | {
"ground_truth": "6 \\sqrt {3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A straight line connects City A at $(0, 0)$ to City B, 300 meters away at $(300, 0)$ . At time $t=0$ , a bullet train instantaneously sets out from City A to City B while ano... | math | {
"ground_truth": "180",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate \\[\\frac{3}{\\log_8{5000^4}} + \\frac{2}{\\log_9{5000^4}},\\] giving your answer as a fraction in lowest terms.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two workers are working on producing identical workpieces and both are just meeting the standard rate. By applying an innovation, one completes a workpiece 5 minutes faster, and ... | math | {
"ground_truth": "15 \\text{ minutes}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
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