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": "Define a $\\textit{good word}$ as a sequence of letters that consists only of the letters $A$, $B$, $C$, and $D$ — some of these letters may not appear in the sequence — and in w... | math | {
"ground_truth": "2441",
"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": "Find all natural numbers that are 36 times the sum of their digits.",
"role": "user"
}
] | math | {
"ground_truth": "324 \\, ; \\, 648",
"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": "Alice is making a batch of cookies and needs $\\frac{5}{2}$ cups of sugar. Her measuring cup holds $\\frac{1}{4}$ cup of sugar. How many times must she fill that cup to get the c... | math | {
"ground_truth": "10",
"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 the area of the large square is 36, find the area of the smaller square inscribed in the circle.",
"role": "user"
}
] | math | {
"ground_truth": "18",
"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": "A box contains $6$ chips, numbered $1$, $2$, $3$, $4$, $5$, and $6$. Chips are drawn randomly one at a time without replacement until the sum of the values drawn exceeds $9$. Wha... | math | {
"ground_truth": "C) \\frac{2}{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": "The maximum value of $\\frac{(3^t - 4t)t}{9^t}$ for real values of $t$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{16}",
"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 $M$ be the second smallest positive integer that is divisible by every positive integer less than $8$. Find the sum of the digits of $M$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Two angles of an isosceles triangle measure $50^\\circ$ and $x^\\circ$. What is the sum of the three possible values of $x$?\nA) 165°\nB) 195°\nC) 180°\nD) 210°",
"role": "us... | math | {
"ground_truth": "\\textbf{(B)}\\ 195",
"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 pyramid is constructed using twenty cubical blocks: the first layer has 10 blocks arranged in a square, the second layer contains 6 blocks arranged in a larger square centered ... | math | {
"ground_truth": "54",
"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": "Five tiles are marked X and three other tiles are marked O. The eight tiles are randomly arranged in a row. What is the probability that the arrangement reads XXXOOXOX?",
"ro... | math | {
"ground_truth": "\\frac{1}{56}",
"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 daily records of the material entering and leaving a certain warehouse are shown in the table below (positive numbers represent incoming material, negative numbers represent ... | math | {
"ground_truth": "\\text{Option 2 is more appropriate.}",
"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 solid box measures 20 cm by 15 cm by 10 cm. A new solid is formed by removing a cube 4 cm on a side from each of four corners on one face and each of two corners on the opposit... | math | {
"ground_truth": "12.8\\%",
"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": "Determine the smallest integer n such that $(x^2+y^2+z^2+w^2)^2\\le n(x^4+y^4+z^4+w^4)$ for all real numbers $x, y, z, w$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Given that $33 \\cdot 32$ is less than or equal to $x$, find the sum of the largest integer less than or equal to $x$ and the smallest integer greater than or equal to $x$.",
... | math | {
"ground_truth": "\\{ x \\mid 2 < x < 3 \\}",
"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 that $r$ and $s$ are relatively prime positive integers such that $\\dfrac{r}{s}=\\dfrac{2(\\sqrt{2}+\\sqrt{10})}{5\\left(\\sqrt{3+\\sqrt{5}}\\right)}$ , find $r$ an... | math | {
"ground_truth": "(r, s) = (4, 5)",
"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 ratio of $a$ to $b$ is $5:2$, the ratio of $c$ to $d$ is $4:1$, and the ratio of $d$ to $b$ is $1:4$. Determine the ratio of $a$ to $c$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{2}",
"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": "Point \\( D \\) lies on the extension of side \\( AC \\) of triangle \\( ABC \\), whose area is \\( S \\); point \\( A \\) is between \\( D \\) and \\( C \\). Let \\( O \\) be th... | math | {
"ground_truth": "2S_l - \\frac{S}{3}",
"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 $\\sin \\left(x- \\frac {\\pi}{4}\\right)= \\frac {3}{5}$, calculate the value of $\\cos \\left(x+ \\frac {\\pi}{4}\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{3}{5}",
"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": "Jacob jogs at a constant rate of 4 miles per hour. He jogs for 2 hours, then stops to take a rest for 30 minutes. After the break, he continues jogging for another 1 hour. How ma... | math | {
"ground_truth": "12.0",
"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": "If $\\sin 2\\theta= \\frac {2}{3}$, calculate the value of $\\tan \\theta + \\frac {1}{\\tan \\theta}$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Let rectangle \\(ABCD\\) be defined with vertices \\(A = (0,0)\\), \\(B = (0,5)\\), \\(C = (8,5)\\), and \\(D = (8,0)\\). Draw lines from \\(A\\) at \\(45^\\circ\\) and from \\(B... | math | {
"ground_truth": "B) Area = 40, Intersection Point = (2.5, 2.5)",
"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": "Let $ ABC$ be a triangle with circumradius $ R$ , perimeter $ P$ and area $ K$ . Determine the maximum value of: $ \\frac{KP}{R^3}$ .",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{27}{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": "Find the number of integers \\( n \\) such that \\[1+\\left\\lfloor\\dfrac{200n}{201}\\right\\rfloor=\\left\\lceil\\dfrac{198n}{200}\\right\\ceil.\\]",
"role": "user"
}
] | math | {
"ground_truth": "40200",
"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 the quadratic equation x^2 + px - q = 0, where p and q are positive numbers. If the absolute difference between the roots of this equation is 2, find the value of p.",
... | math | {
"ground_truth": "\\sqrt{4 - 4q}",
"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 triangle has vertices at $(0,0)$, $(4,4)$, and $(12,0)$. A line defined by the equation $y = mx$ divides this triangle into two regions of equal area. Determine the sum of all ... | math | {
"ground_truth": "\\textbf{(A)} \\ \\frac{1}{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: $-5 + 2 \\times (-3) + (-12) \\div (-2)$.",
"role": "user"
}
] | math | {
"ground_truth": "-5",
"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 that $f(x)=ax^{2}+bx+3a+b$ is an even function with a domain of $[a-1,2a]$, find the value of $a+b$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{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": "Let $\\alpha$, $\\beta$, $\\gamma$ represent three different planes, and $a$, $b$, $c$ represent three different lines. Consider the following five propositions: \n(1) If $a \\p... | math | {
"ground_truth": "(2)",
"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 value of \\( x = \\frac{1}{\\log_{\\frac{1}{2}} \\frac{1}{3}} + \\frac{1}{\\log_{\\frac{1}{5}} \\frac{1}{3}} \\) belongs to which interval.",
"role": "user"
}
] | math | {
"ground_truth": "(2, 3)",
"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 7-digit palindromes can be formed using the digits 1, 1, 2, 2, 2, 4, 4?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"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 complex number \\( z \\) satisfy the equation\n\\[\n\\frac{2017z - 25}{z - 2017} = 3 + 4i,\n\\]\nwhere \\( i \\) is the imaginary unit. Determine the modulus \\( |z| \\) ... | math | {
"ground_truth": "5",
"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 $81^{\\frac{1}{4}} - 16^{\\frac{1}{2}}$.",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"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 the rectangular coordinate system xOy, a polar coordinate system is established with the origin O of the rectangular coordinate system as the pole and the positive semi-axis o... | math | {
"ground_truth": "\\frac{8}{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": "Triangle $DEF$ has a perimeter of 3010 units. The sides have lengths that are all integer values with $DE < EF \\leq FD$. What is the smallest possible value of $EF - DE$?",
... | math | {
"ground_truth": "1",
"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 game involves rolling a die. If a 1, 2, or 3 is rolled, the player earns 1 point. If a 4 or 5 is rolled, the player earns 2 points. If a 6 is rolled, the player earns 3 points.... | math | {
"ground_truth": "\\frac{7}{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": "If there are 150 seats in a row, calculate the fewest number of seats that must be occupied so the next person to be seated must sit next to someone.",
"role": "user"
}
] | math | {
"ground_truth": "37",
"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 that the graph of the function $y=f(x)$ is symmetric to the graph of $g(x)=\\log\\_ax$ ($a>0$ and $a\\neq 1$) about the $x$-axis, and the graph of $g(x)$ passes through the... | 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": "There are $n$ $(n \\ge 3)$ players in a table tennis tournament, in which any two players have a match. Player $A$ is called not out-performed by player $B$ , if at least ... | math | {
"ground_truth": "n \\geq 5",
"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 the parabola $E$: $y^{2}=2px (p > 0)$ with focus $F$, and a point $(3,m)$ on $E$ with a distance of $4$ to the focus.\n\n(I) Find the equation of the parabola $E$;\n\n(II) ... | math | {
"ground_truth": "2x+y-2=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": "Given the equation $\\left(a-1\\right)x^{2}+\\sqrt {a+1}x+2=0$, determine the range of values for $a$.",
"role": "user"
}
] | math | {
"ground_truth": "B: a\\geqslant -1 \\text{ and } a\\neq 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": "Three young brother-sister pairs from different families need to take a trip in a van. There are six children in total who will occupy the second and third rows, each of which ha... | math | {
"ground_truth": "96",
"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": "Evaluate the expression: $[x - (2y + z)] - [(x + 2y) - 3z]$",
"role": "user"
}
] | math | {
"ground_truth": "-4y + 2z",
"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 between the midpoints of two skew edges of a cube, whose total surface area is $36 \\mathrm{~cm}^{2}$.",
"role": "user"
}
] | math | {
"ground_truth": "3 \\, \\text{cm}",
"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 $n$ be a given positive integer. Alice and Bob play a game. In the beginning, Alice determines an integer polynomial $P(x)$ with degree no more than $n$ . Bob doesn’t kn... | math | {
"ground_truth": "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": "Each of 3000 boxes in a line contains a single red marble, and for $1 \\le k \\le 3000$, the box in the $k\\text{th}$ position also contains $k$ white marbles. Isabella begins at... | math | {
"ground_truth": "55",
"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 $a > 0, b > 0$. If $\\sqrt{3}$ is the geometric mean of $3^{a}$ and $3^{b}$, then the minimum value of $\\frac{1}{a} + \\frac{1}{b}$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Find the equation of the line that passes through the point \\((1, 3)\\) and has a tangent line with a slope equal to \\(2x - 3\\).",
"role": "user"
}
] | math | {
"ground_truth": "y = x^2 - 3x + 5",
"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 $r$ is positive and the line whose equation is $x + y = r + 1$ is tangent to the circle whose equation is $x^2 + y^2 = r^2$, then find the value of $r$.\nA) $1 + \\sqrt{2}$\nB... | math | {
"ground_truth": "1 + \\sqrt{2}",
"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 real number $a$ denote by $[a]$ the greatest integer not exceeding $a$ .\nHow many positive integers $n\\leq 10000$ are there which is $[\\sqrt{n}]$ is a divisor of ... | math | {
"ground_truth": "300",
"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 right-angled triangle has an area of \\( 36 \\mathrm{~m}^2 \\). A square is placed inside the triangle such that two sides of the square are on two sides of the triangle, and o... | math | {
"ground_truth": "16 \\, \\text{m}^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": "Marisa has two identical cubical dice labeled with the numbers $\\{1, 2, 3, 4, 5, 6\\}$ . However, the two dice are not fair, meaning that they can land on each face with differ... | math | {
"ground_truth": "16",
"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 regular pyramid has a rectangular base with sides of lengths 2 and 3 and has lateral faces that are isosceles triangles. A cube is placed within the pyramid so that one face is... | math | {
"ground_truth": "\\frac{39\\sqrt{39}}{27}",
"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": "Points $ K$ , $ L$ , $ M$ , and $ N$ lie in the plane of the square $ ABCD$ so that $ AKB$ , $ BLC$ , $ CMD$ , and $ DNA$ are equilateral triangles. If $ ABCD$ has ... | math | {
"ground_truth": "32 + 16\\sqrt{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 $T$ be the set of complex numbers of the form $x + yi$, where $x$ and $y$ are real numbers, such that\n\\[\n\\frac{1}{2} \\leq x \\leq \\frac{\\sqrt{3}}{2} \\quad \\text{and}... | math | {
"ground_truth": "m = 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": "An interstellar hotel has $100$ rooms with capacities $101,102,\\ldots, 200$ people. These rooms are occupied by $n$ people in total. Now a VIP guest is about to arrive and... | math | {
"ground_truth": "8824",
"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": "Two parabolas are represented by the equations \\(y = 2x^2 + 5x - 3\\) and \\(y = x^2 + 2\\). Determine all points where these two parabolas intersect. List the points in order o... | math | {
"ground_truth": "(-5, 27); (1, 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": "Given that the area ratios of red, yellow, blue, and black are 6:2:1:4, calculate the probability that a pointer will stop on either the red or blue area.",
"role": "user"
... | math | {
"ground_truth": "\\frac{8}{13}",
"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 general formulas for sequences $\\{a_n\\}$ and $\\{b_n\\}$ are $a_n = an + 2$ and $b_n = bn + 1$ (where $a$ and $b$ are constants), and $a > b$, determine the number of... | 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": "The equation $x^2 - (m+1)x + m = 0$ has roots $r$ and $s$. Find the value of $|r+s - 2rs|$.",
"role": "user"
}
] | math | {
"ground_truth": "|1 - m|",
"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": "We will say that two positive integers $a$ and $b$ form a *suitable pair* if $a+b$ divides $ab$ (its sum divides its multiplication). Find $24$ positive integers that c... | math | {
"ground_truth": "\\{(3, 6), (4, 12), (5, 20), (6, 30), (7, 42), (8, 56), (9, 72), (10, 90), (11, 110), (12, 132), (13, 156), (14, 168)\\}",
"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": "Quadrilateral $F$ under the mapping $f:(x, y) \\rightarrow (x-1, y+2)$ results in quadrilateral $F'$. The area of quadrilateral $F$ is 6. What is the area of quadrilateral $F'$?"... | math | {
"ground_truth": "6",
"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": "A cube with an edge length of $3$ inches is iced on all faces. It is cut into four vertical pieces as shown in a top view, where $N$ is a point one-third of the way along a top e... | math | {
"ground_truth": "C) 36",
"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 ordered pair \\((x, y)\\) if:\n\\[\nx + y + 1 = (6 - x) + (6 - y)\n\\]\n\\[\nx - y + 2 = (x - 2) + (y - 2)\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\left(\\frac{5}{2}, 3\\right)",
"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 smallest four two-digit primes are written in different squares of a \\(2 \\times 2\\) table. The sums of the numbers in each row and column are calculated. Two of these sums... | math | {
"ground_truth": "412",
"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 one third of Mars' surface is not covered by ice, and only two thirds of that exposed area is suitable for human colonies due to rocky terrain and atmospheric conditions, what... | math | {
"ground_truth": "\\frac{2}{9}",
"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 the progression $12^{\\dfrac{1}{13}}, 12^{\\dfrac{2}{13}}, 12^{\\dfrac{3}{13}}, \\dots, 12^{\\dfrac{n}{13}}$. \nFind the smallest positive integer $n$ such that the product... | math | {
"ground_truth": "B) 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": "Marcus has two numbers, $x$ and $y$. When he divides $x$ by 60, he gets a remainder of 47. When he divides $y$ by 45, he gets a remainder of 26. What remainder does he get when h... | math | {
"ground_truth": "13",
"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 sum of the first $n$ terms of a sequence $\\{a_{n}\\}$ is $S_{n}$, $a_{1}=4$, and ${S}_{n+1}=2{S}_{n}+{a}_{1}$ for $n\\in\\mathbb{N}^{*}$. \n$(1)$ Find the genera... | math | {
"ground_truth": "n = 5",
"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 paper triangle with vertices at $(0,0), (30,0),$ and $(15,20).$ The vertices of its midpoint triangle are the midpoints of its sides. A triangular pyramid is formed by... | math | {
"ground_truth": "1125 \\text{ cubic units}",
"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": "Which grows faster: \\( x \\) or \\( x^2 \\) (for \\( x > 0 \\))? Provide a graphical representation.",
"role": "user"
}
] | math | {
"ground_truth": "\\begin{cases}\n x \\quad & \\text{increases faster for} \\quad 0 < x < \\frac{1}{2} \\\\\n x^2 \\quad & \\text{increases faster for} \\quad x > \\frac{1}{2}\n \\end{cases}",
"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": "Consider a set $X$ with $|X| = n\\geq 1$ elements. A family $\\mathcal{F}$ of distinct subsets of $X$ is said to have property $\\mathcal{P}$ if there exist $A,B \\in ... | math | {
"ground_truth": "2^{n-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": "If $x=-3$ is a root of the quadratic equation $x^{2}+3x+k=0$, determine the other root of the equation and the value of $k$.",
"role": "user"
}
] | math | {
"ground_truth": "0,0",
"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": "How many ways are there to arrange the numbers $1$ through $8$ into a $2$ by $4$ grid such that the sum of the numbers in each of the two rows are all multiples of $6,$ ... | math | {
"ground_truth": "288",
"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": "Alexio now has 200 cards numbered 1-200, inclusive, and places them in a box. Alexio then chooses a card from the box at random. What is the probability that the number on the ca... | math | {
"ground_truth": "\\frac{162}{200}",
"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": "Thirty of King Arthur's knights are seated at their customary round table. Four of them are chosen - all choices being equally likely - and are sent off to slay a troublesome dra... | math | {
"ground_truth": "16",
"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 sides $AB,~ BC$, and $CD$ of quadrilateral $ABCD$ have lengths $4,~ 5$, and $20$, respectively, and vertex angles $B$ and $C$ are obtuse with $\\sin C = - \\cos B =\\f... | math | {
"ground_truth": "\\sqrt{674}",
"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": "Let $x$ be a complex number such that $x^7=1$ and $x\\neq 1$. Compute the sum\n\\[\n\\frac{x^2}{x-1} + \\frac{x^4}{x^2-1} + \\frac{x^6}{x^3-1}.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "1",
"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 $b > 0$, and let $Q(x)$ be a polynomial with integer coefficients such that\n\\[Q(2) = Q(4) = Q(6) = Q(8) = b\\]and\n\\[Q(1) = Q(3) = Q(5) = Q(7) = -b.\\]\nWhat is the smalle... | math | {
"ground_truth": "315",
"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": "**p17.** Let the roots of the polynomial $f(x) = 3x^3 + 2x^2 + x + 8 = 0$ be $p, q$ , and $r$ . What is the sum $\\frac{1}{p} +\\frac{1}{q} +\\frac{1}{r}$ ?**p18.** Two stu... | math | {
"ground_truth": "-\\frac{1}{8}",
"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 $S$ be the set of positive integers less than $10^6$ that can be written as the sum of two perfect squares. Compute the number of elements in $S$ . Your score will be gi... | math | {
"ground_truth": "215907",
"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": "Two distinct squares of the $8\\times8$ chessboard $C$ are said to be adjacent if they have a vertex or side in common.\nAlso, $g$ is called a $C$ -gap if for every number... | math | {
"ground_truth": "9",
"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": "Two points $A(x_1, y_1)$ and $B(x_2, y_2)$ are selected on the graph of $f(x) = \\ln x$ with $0 < x_1 < x_2$. The points $C$ and $D$ trisect the segment $\\overline{AB}$, with $A... | math | {
"ground_truth": "2 \\pm \\sqrt{\\ln 2}",
"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 \\(\\omega = -\\frac{1}{2} + \\frac{1}{2}i\\sqrt3\\). Define \\(T\\) as the set of all points in the complex plane of the form \\(a + b\\omega + c\\omega^2\\), where \\(0 \\l... | math | {
"ground_truth": "C)\\ 8\\sqrt{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": "Find all natural numbers $n> 1$ for which the following applies:\nThe sum of the number $n$ and its second largest divisor is $2013$ .\n\n(R. Henner, Vienna)",
"role": "... | math | {
"ground_truth": "n = 1342",
"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": "Sasha wrote on the board all two-digit numbers divisible by 6 and then erased those that do not end in 4. What is the largest number that remained on the board?",
"role": "us... | math | {
"ground_truth": "84",
"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 that the four digits of 2012 are used, determine the number of 4-digit numbers greater than 1000.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"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": "Given the ellipse: $\\dfrac{x^2}{10-m} + \\dfrac{y^2}{m-2} = 1$ has a focal length of $4$, then $m$ equals \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "m=4 \\text{ or } 8",
"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 $p$ be a prime number and let $k$ be a positive integer. Suppose that the numbers $a_i=i^k+i$ for $i=0,1, \\ldots,p-1$ form a complete residue system modulo $p$ . Wh... | math | {
"ground_truth": "\\{0, 1, 2, \\ldots, p-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": "What is the slope of the line represented by the equation $4x + 5y = 20$?",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{4}{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 a complex number $z$ satisfying the equation $z + 3i = 3 - i$, calculate the modulus $|z|$.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"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 new proposal for letter postage rates includes a base rate of $25$ cents for the first ounce and $18$ cents for each additional ounce or fraction thereof. Additionally, there i... | math | {
"ground_truth": "1.25",
"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 definite integral:\n\n$$\n\\int_{0}^{\\frac{2 \\pi}{3}} \\frac{1+\\sin x}{1+\\cos x+\\sin x} \\, dx\n$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\pi}{3} + \\ln 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": "How many of the first $1000$ numbers in the sequence $101, 1001, 10001, 100001, \\dots$ are divisible by $13$?\nA) 165\nB) 166\nC) 167\nD) 168\nE) 169",
"role": "user"
}
] | math | {
"ground_truth": "A) 165",
"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 number of 4-digit integers where all digits are different, the first digit is not zero, the integer is a multiple of 5, the last digit is 5, and 6 is the largest di... | math | {
"ground_truth": "100",
"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": "On a straight road, there are an odd number of warehouses. The distance between adjacent warehouses is 1 kilometer, and each warehouse contains 8 tons of goods. A truck with a lo... | math | {
"ground_truth": "25",
"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 measures of angles $A$ and $B$ are both positive, integer numbers of degrees. The measure of angle $A$ is a multiple of the measure of angle $B$, and angles $A$ and $B$ are s... | math | {
"ground_truth": "17",
"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 $x$ is a real number and $|x-5| + |x-7| < b$ where $b > 0$, determine the range of values that $b$ must fall into for the inequality to hold for some $x$.",
"role": "us... | math | {
"ground_truth": "b > 2",
"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": "You have a length of string and 7 beads in the 7 colors of the rainbow. You place the beads on the string as follows - you randomly pick a bead that you haven't used yet, then ra... | math | {
"ground_truth": "\\frac{1}{5040}",
"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": "Consider two sets of consecutive integers. Let $A$ be the least common multiple (LCM) of the integers from $15$ to $25$ inclusive. Let $B$ be the least common multiple of $A$ and... | math | {
"ground_truth": "3 \\cdot 37 \\cdot 41 \\cdot 43",
"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 $S$ be a real number. It is known that however we choose several numbers from the interval $(0, 1]$ with sum equal to $S$ , these numbers can be separated into two subse... | math | {
"ground_truth": "5.5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
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