data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "From a group of 5 people, including A and B, we need to select 3 people and arrange them in a row. Calculate the number of arrangements where A is not at the head.",
"role": ... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 ellipse $\\frac{x^{2}}{4}+ \\frac{y^{2}}{3}=1$, a moving line $l$ intersects the ellipse at points $B$ and $C$ ($B$ is in the first quadrant).\n(1) If the coordinates o... | math | {
"ground_truth": "2 \\sqrt {3}x-2y- \\sqrt {30}=0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 N be a positive multiple of 5. One red ball and N green balls are arranged in a line in random order. Let P(N) be the probability that at least 3/5 of the green balls are o... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"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 that $\\log_{b} 1024$ is a positive integer, how many positive integers $b$ satisfy this condition.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Real numbers $x,y,z$ are chosen such that $$ \\frac{1}{|x^2+2yz|} ,\\frac{1}{|y^2+2zx|} ,\\frac{1}{|x^2+2xy|} $$ \nare lengths of a non-degenerate triangle .\nFind all po... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a four-digit positive integer $N$, where the digits in each place are all different and not equal to zero, if the sum of the digits in the thousands and tens places is equal ... | math | {
"ground_truth": "8514 \\text{ or } 3168",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 map below shows an east/west road connecting the towns of Acorn, Centerville, and Midland, and a north/south road from Centerville to Drake. The distances from Acorn to Cente... | math | {
"ground_truth": "65",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 integers \\( m \\) and \\( n \\) such that \\( n^2 \\) is a multiple of \\( m \\), \\( m^3 \\) is a multiple of \\( n^2 \\), \\( n^4 \\) is a multiple of \\( m^3 \\), \\( m^... | math | {
"ground_truth": "m = 32 \\text{ and } n = 16",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that triangle $ABC$ has $b=c$ and $a^{2}=2b^{2}(1-\\sin A)$, determine the measure of angle $A$.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac {\\pi}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 the random variable $\\xi$ follows a normal distribution $N(0, \\sigma^2)$, and $P(\\xi > 2) = 0.023$, calculate $P(-2 \\leq \\xi \\leq 2)$.",
"role": "user"
}
] | math | {
"ground_truth": "0.954",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate: $(2014 \\times 2014 + 2012) - 2013 \\times 2013$.",
"role": "user"
}
] | math | {
"ground_truth": "6039",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a triangle with a base of length $b$ and an altitude of length $3h$, and a rectangle inscribed in this triangle with a height of $x$ and a base positioned along the base of... | math | {
"ground_truth": "\\frac{bx}{3h}(3h-x)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 a 4x4x4 cube made out of 64 normal dice, where each die's opposite sides still sum to 7. Find the smallest possible sum of all of the values visible on the 6 faces of th... | math | {
"ground_truth": "144",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 a certain triangle all of its altitudes are integers whose sum is less than 20. If its Inradius is also an integer Find all possible values of area of the triangle.",
"ro... | math | {
"ground_truth": "6 \\text{ and } 12",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 is a triangle $ABC$ with $\\angle BAC=45$ ; $AD, BE, CF$ are altitudes and $EF \\cap BC=X$ . If $AX \\parallel DE$ , find the angles of the triangle.",
"role": "... | math | {
"ground_truth": "\\angle B = 75^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Estimate the time it takes to send $100$ blocks of data over a communications channel if each block consists of $800$ \"chunks\" and the channel can transmit $200$ chunks per sec... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 height of a cylinder is $1$, and the circumferences of its two bases are on the surface of the same sphere with a diameter of $2$, calculate the volume of the cylinder.... | math | {
"ground_truth": "\\dfrac{3\\pi}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Utilize systematic sampling to select a sample of size 50 from a population of 8000 individuals (numbered 0000, 0001, ..., 7999). Given that the last sampled number is 7900, find... | math | {
"ground_truth": "0060, 0220",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 how many integers $N$ between 1 and 2000 is the fraction $\\frac{N^2+7}{N+5}$ not in lowest terms?\nA) 85 \nB) 256 \nC) 385 \nD) 486 \nE) 512",
"role": "user"
}
] | math | {
"ground_truth": "C) 385",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 equation $3x^2 - 4x + k = 0$ with real roots. Find the value of $k$ for which the product of the roots of the equation is a maximum.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{4}{3}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a mathematics competition with 1000 participating students, each student is assigned a number: 0001, 0002, 0003, ..., 1000. By using systematic sampling to draw a sample of 50... | math | {
"ground_truth": "0415",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Parallelogram $ABCD$ has vertices $A(1,3)$, $B(3,8)$, $C(7, 6)$, and $D(5, 1)$. It is first reflected over the $y$-axis, producing parallelogram $A'B'C'D'$, and then $A'B'C'D'$ i... | math | {
"ground_truth": "(-1, 5)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three people, A, B, and C, arrive at the shore of a reservoir. A swims to the opposite shore at a speed of \\( v \\) km/h. Meanwhile, B and C take a motorboat moving at a speed o... | math | {
"ground_truth": "\\frac{31b}{130v}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Maria and John shared a pizza with 10 equally-sized slices. Maria wanted a plain pizza, but John wanted olives on one-third of the pizza. The cost of a plain pizza was $10$ dolla... | math | {
"ground_truth": "2.6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Parabola C is defined by the equation y²=2px (p>0). A line l with slope k passes through point P(-4,0) and intersects with parabola C at points A and B. When k=$\\frac{1}{2}$, po... | math | {
"ground_truth": "2\\sqrt{11}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 the lines \\(2y + x + 3 = 0\\) and \\(3y + cx + 2 = 0\\) are perpendicular, find the value of \\(c\\).",
"role": "user"
}
] | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $a > 0$, the constant term in the expansion of $({a \\over \\sqrt{x}} - x)^6$ is $15$. Find the value of $\\int_{-a}^{a} (\\sqrt{1 - x^2} + \\sin 2x) dx$.",
"role"... | math | {
"ground_truth": "{\\pi \\over 2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 \\( x_{i} (i=1, 2, 3, 4) \\) be real numbers such that \\( \\sum_{i=1}^{4} x_{i} = \\sum_{i=1}^{4} x_{i}^{7} = 0 \\). Find the value of the following expression: \n\\[ u = x_... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the constant $k$ such that the sum of all $x \\ge 0$ satisfying $\\sqrt{x}(x+12)=17x-k$ is $256.$ *Proposed by Michael Tang*",
"role": "user"
}
] | math | {
"ground_truth": "90",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $XYZ$, medians $\\overline{XU}$ and $\\overline{YV}$ are perpendicular. If $XU = 10$ and $YV = 24$, and the altitude from vertex $Z$ to $\\overline{XY}$ is $16$, calc... | math | {
"ground_truth": "160",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 the graph of the function $f(x)=\\sin (\\omega x+\\varphi)$ (where $\\omega > 0$, $|\\varphi| < \\frac{\\pi}{2}$) is transformed by shrinking all the x-coordinates to half of ... | math | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle, given that a small bottle can hold 35 milliliters of shampoo and a large bot... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate:\n\n1) \\(x^{4} - 2x^{3} + 3x^{2} - 2x + 2\\) given that \\(x^{2} - x = 3\\)\n\n2) \\(2x^{4} + 3x^{2}y^{2} + y^{4} + y^{2}\\) given that \\(x^{2} + y^{2} = 1\\)",
"... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfy $|\\overrightarrow{a}|=2|\\overrightarrow{b}|=2$, and the angle between $\\overrightarrow{a}$ and $\\overrighta... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 different scenario: My friend Lisa is peculiar about numbers. She only likes numbers that are divisible by both 5 and 2. How many different last digits are possible in... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 1 to 100, take a pair of integers (repetitions allowed) so that their sum is greater than 100. How many ways are there to pick such pairs?",
"role": "user"
}
] | math | {
"ground_truth": "5050",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are five balls numbered 1, 2, 3, 4, 5, and five boxes also numbered 1, 2, 3, 4, 5. Now, these five balls are to be placed into the five boxes with only one box left empty. ... | math | {
"ground_truth": "1200",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An equilateral triangle of side length $10$ is completely filled in by non-overlapping equilateral triangles of side length $1$. Calculate the number of small triangles required.... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle with a radius of 3 is centered at point $A$. A square, also centered at $A$, has its sides equal to the circle's diameter. Calculate the difference between the area of t... | math | {
"ground_truth": "36 - 9\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 integers $(x, y)$ such that $2x^3 + xy - 7 = 0$.",
"role": "user"
}
] | math | {
"ground_truth": "(-7, -99),(-1, -9),(1, 5),(7, -97)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $2^x$ be the greatest power of $2$ that is a factor of $900$, and let $5^y$ be the greatest power of $5$ that is a factor of $900$. Evaluate the following expression: $$\\lef... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose a number is chosen at random from the set of all five-digit numbers where the sum of the digits equals 40. What is the probability that this number will be divisible by 7... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Bhairav runs a 15-mile race at 28 miles per hour, while Daniel runs at 15 miles per hour and Tristan runs at 10 miles per hour. What is the greatest length of time, in *minutes*,... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$N$ coins are placed on a table, $N - 1$ are genuine and have the same weight, and one is fake, with a different weight. Using a two pan balance, the goal is to determine with... | math | {
"ground_truth": "N = 2n + 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$$\n\\text{Consider the system of inequalities:}\n\\begin{cases}\nx + 2y \\leq 6 \\\\\n3x + y \\geq 3 \\\\\nx \\leq 4 \\\\\ny \\geq 0\n\\end{cases}\n$$\nDetermine the number of u... | math | {
"ground_truth": "2\\sqrt{5}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all functions \\( f: \\mathbf{Q}_{+} \\rightarrow \\mathbf{Q}_{+} \\) such that for all \\( x, y \\in \\mathbf{Q}_{+} \\), the following equation holds:\n$$\nf\\left(x^{2} f... | math | {
"ground_truth": "f(x) = 1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For each positive integer \\( n \\), let \\( S_n \\) be the set that contains the integers from 1 to \\( n \\), inclusive; that is, \\( S_n = \\{1, 2, 3, \\ldots, n\\} \\).\n\nFo... | math | {
"ground_truth": "n=1348 \\text{ and } n=1350",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the least positive integer $n$ satisfying the following statement: for eash pair of positive integers $a$ and $b$ such that $36$ divides $a+b$ and $n$ divides ... | math | {
"ground_truth": "1296",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 the length to the width of a rectangle is $5$ : $2$. If the rectangle has a diagonal of length $d$, find the area of the rectangle in terms of $d$.",
"role": "us... | math | {
"ground_truth": "\\frac{10}{29}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 statements $p:$ For any $x\\in R$, $ax^{2}+ax-1 < 0$, and $q:\\frac{3}{a\\-1}+1 < 0.$, if the statement \"p or q\" is false, then the range of values for the real numbe... | math | {
"ground_truth": "(-\\infty,-4]\\cup[1,\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 Ace jogs at a constant speed and Flash jogs at twice Ace's speed but starts jogging $t$ minutes after Ace, who has been given a head start of $y$ meters, determine the... | math | {
"ground_truth": "2(y + 60vt)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 sequence $\\{a_n\\}$ is an arithmetic sequence, and $S_n$ is the sum of its first $n$ terms. If $a_1=6$ and $a_3+a_5=0$, then $S_6=$ ______.",
"role": "user"
... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 a plane intersects a geometric solid and the cross-section is a triangle, then the possible geometric solids are: ① cube; ② cylinder; ③ cone; ④ regular triangular prism____ (W... | math | {
"ground_truth": "①③④",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 solution set of the inequality $x-1\\leqslant \\frac{{1+x}}{3}$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "x \\leqslant 2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 integers between $1000$ and $5000$ contain both the digits $3$ and $4$?",
"role": "user"
}
] | math | {
"ground_truth": "720",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 the least positive integer $k$ such that when $\\frac{k}{2023}$ is written in simplest form, the sum of the numerator and denominator is divisible by $7$ .\n\n*Proposed... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Square \\(PQRS\\) has an area of 144. Point \\(T\\) lies on side \\(\\overline{RS}\\). Points \\(U\\) and \\(V\\) are the midpoints of \\(\\overline{PT}\\) and \\(\\overline{QT}\... | math | {
"ground_truth": "34",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose \\(\\log _{x} t=6\\), \\(\\log _{y} t=10\\) and \\(\\log _{z} t=15\\). If \\(\\log _{x y z} t=d\\), find the value of \\(d\\).",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of the first $n$ terms of a geometric sequence $\\{a_n\\}$ is $S_n$, and $S_n = 3 \\cdot 2^n + k$. Calculate the value of $k$.",
"role": "user"
}
] | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 call a number \"remarkable\" if it has exactly 4 distinct natural divisors, among which there are two such that neither is a multiple of the other. How many \"remarkable\" ... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$ we have $|AB| \\ne |AC|$ . The bisectors of $\\angle ABC$ and $\\angle ACB$ meet $AC$ and $AB$ at $E$ and $F$ , respectively, and intersect at I.... | math | {
"ground_truth": "60^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many 4-digit numbers greater than 1000 can be formed using the digits of 2033?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 $500,000,000,000 - 3 \\times 111,111,111,111$.",
"role": "user"
}
] | math | {
"ground_truth": "166,666,666,667",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 points \\\\(A\\\\), \\\\(B\\\\), and \\\\(C\\\\) are on the surface of a sphere \\\\(O\\\\), with \\\\(AB=BC=CA=3\\\\), and the distance from the center \\\\(O\\\\) of the ... | math | {
"ground_truth": "\\frac{27}{2}\\pi",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 circle is situated inside the parabola described by the equation $y = \\frac{x^2}{4}$. The circle is tangent to the parabola at exactly two points. Determine the vertical dista... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "At Maplewood Youth League, $75\\%$ of the adolescents play basketball, $45\\%$ of the adolescents go cycling, and $60\\%$ of the basketball players also go cycling. To the neares... | math | {
"ground_truth": "C) 55%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "All the roots of the polynomial $z^6-10z^5+Az^4+Bz^3+Cz^2+Dz+16$ are positive integers, possibly repeated. Express $B$ in terms of $A$.",
"role": "user"
}
] | math | {
"ground_truth": "-88",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A square of perimeter 20 is inscribed in a square of perimeter 28. What is the greatest distance between a vertex of the inner square and a vertex of the outer square?",
"rol... | math | {
"ground_truth": "\\sqrt{65}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For real numbers $a,\\ b$ , define a point $P_n(x_n,\\ y_n)$ by \n\\[(x_0,\\ y_0)=(1,\\ 0)\\]\n\n\\[(x_{n+1},\\ y_{n+1})=(ax_n-by_n,\\ bx_n+ay_n)\\ \\ (n=0,\\ 1,\\ 2,\\ \\cdot... | math | {
"ground_truth": "\\left( \\frac{1}{2}, \\frac{\\sqrt{3}}{2} \\right)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 journey from $A$ to $B$ consists of 3 km uphill, 6 km downhill, and 12 km on flat ground. The motorcyclist completed this journey in 1 hour and 7 minutes and the reverse jour... | math | {
"ground_truth": "12 \\text{ km/h, 30 km/h}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x$ cows give $x+1$ cans of milk in $x+2$ days, determine how many days will it take $x+3$ cows to give $x+5$ cans of milk.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{x(x+2)(x+5)}{(x+1)(x+3)}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a modified card game, a player is dealt a hand of $15$ cards from a deck of $60$ unique cards. The number of distinct (unordered) hands that can be dealt to the player can be ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 an $18 \\times 8$ grid (as shown), the digits $1$, $9$, $9$, and $8$ are drawn. Determine the fraction of the shaded area relative to the total area of the grid.",
"role":... | math | {
"ground_truth": "\\frac{37}{72}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each face of a cube is given a single narrow stripe painted from the center of one edge to the center of the opposite edge. The choice of the edge pairing is made at random and i... | math | {
"ground_truth": "\\frac{3}{16}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"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 table showing the relationship between $x$ and $y$, derive an expression for $y$ in terms of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "y = x^3 - 3x^2 + 5x + 9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 circle with area \\(A_1\\) is inscribed within a larger circle whose total area is \\(A_1 + A_2\\). If the radius of the larger circle is \\(8\\), and \\(A_1, A_2,\\) and \\(A_... | math | {
"ground_truth": "\\frac{8\\sqrt{3}}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 sets $A=\\{x|x^{2}-7x+6\\leqslant 0\\}$ and $B=\\{x|x^{2}-2x+1-m^{2}\\leqslant 0, m \\gt 0\\}$. \n$(1)$ If $m=1$, find $A\\cap B$; \n$(2)$ If $x\\in A$ is a sufficient an... | math | {
"ground_truth": "[5,+\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 units digit of $7^{8^5}$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 points $A(1, 0, 1)$, $B(-2, 2, 1)$, $C(2, 0, 3)$, and $D(0, 4, -2)$, find the angle between the line $AB$ and the plane $BCD$.",
"role": "user"
}
] | math | {
"ground_truth": "\\alpha = \\arcsin\\left(\\frac{\\sqrt{13}}{\\sqrt{101}}\\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"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 $(n,p)$ of positive integers such that \n- $p$ is a prime, $n>1$ ,\n- $(p-1)^{n} + 1$ is divisible by $n^{p-1}$ .",
"role": "user"
}
] | math | {
"ground_truth": "(2, 2), (3, 3)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 $\\triangle DEF$ have side lengths $DE=12$, $DF=15$, and $EF=17$. Inside $\\angle D$ are located two circles: one tangent to rays $\\overline{DE}$ and $\\overline{DF}$, and t... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 distinct similar rhombi share a diagonal. The smaller rhombus has an area of 1, and the larger rhombus has an area of 9. Compute the side length of the larger rhombus.",
... | math | {
"ground_truth": "\\sqrt{15}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A square piece of paper has sides of length $120$. From each corner, a wedge is cut where each of the two cuts for the wedge starts at a distance $\\sqrt{20}$ from the corner, me... | math | {
"ground_truth": "\\sqrt{10}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 natural numbers $p$ and $q$ do not end in zero and the product of any pair, $p$ and $q$, is a power of 10. If $p > q$, determine the last digit of $p - q$.",
"role": "use... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 ratio of boys to girls is $3:4$ and there are $42$ students in the class, calculate the difference between the number of girls and the number of boys.",
"role": "us... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 sequence $1990-1980+1970-1960+\\cdots -20+10$, calculate the sum.",
"role": "user"
}
] | math | {
"ground_truth": "1000",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$ P(x)$ is a quadratic trinomial. What maximum number of terms equal to the sum of the two preceding terms can occur in the sequence $ P(1)$ , $ P(2)$ , $ P(3)$ , $ \\dots?$... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 $x \\diamondsuit y = 4x + 2y + xy$ for all $x$ and $y$, what is the value of $3 \\diamondsuit 5$?",
"role": "user"
}
] | math | {
"ground_truth": "37",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 function $f(x)=(\\sin x+\\cos x)^{2}+\\cos 2x$.\n\n(1) Find the smallest positive period of $f(x)$;\n\n(2) Find the maximum and minimum values of $f(x)$ on the interval... | math | {
"ground_truth": "1+ \\sqrt {2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 the distance light travels in one year is approximately $6,000,000,000,000$ miles, calculate the distance light travels in $50$ years.",
"role": "user"
}
] | math | {
"ground_truth": "3 \\times 10^{14} \\text{ miles}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 positive real numbers $ a,\\ b$ , two graphs of the function : $ x^a$ and $ \\ln bx$ have a tangency of point.\r\n\r\n(1) Let $ (s,\\ t)$ be the tangency of point, exp... | math | {
"ground_truth": "\\frac{a^{-\\frac{a-1}{a}}}{a+1}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 25 ml of a 70% solution of acetic acid and 500 ml of a 5% solution of acetic acid. Find the maximum volume of a 9% solution of acetic acid that can be obtained from the... | math | {
"ground_truth": "406.25 \\text{ ml}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a moving circle is tangent to the circle \\\\(C:\\\\) \\\\({(x+4)}^{2}+{{y}^{2}}=100\\\\) and passes through the point \\\\(A(4,0)\\\\), the equation of the trajectory of t... | math | {
"ground_truth": "\\dfrac{{x}^{2}}{25}+ \\dfrac{{y}^{2}}{9}=1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 $6$ -digit positive integers have their digits in nondecreasing order from left to right? Note that $0$ cannot be a leading digit.",
"role": "user"
}
] | math | {
"ground_truth": "3003",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 $\\mathbf{c}$ and $\\mathbf{d}$ are vectors such that $\\|\\mathbf{c}\\| = 5$ and $\\|\\mathbf{d}\\| = 13$, and the angle $\\phi$ between $\\mathbf{c}$ and $\\mathbf{d}$ is co... | math | {
"ground_truth": "[32.5,65]",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 sides of an equilateral triangle with sides of length $n$ have been divided into equal parts, each of length $1$ , and lines have been drawn through the points of division... | math | {
"ground_truth": "\\frac{n^2 - n}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 b men take c days to lay f bricks, calculate the number of days it will take c men working at the same rate to lay b bricks.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{b^2}{f}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"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 that the sequence $\\{a_n\\}$ is an arithmetic sequence, if $a_4+2a_6+a_8=12$, calculate the sum of the first $11$ terms of this sequence.",
"role": "user"
}
] | math | {
"ground_truth": "33",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 month with $30$ days has the same number of Tuesdays and Thursdays. Determine the number of possible days of the week which could be the first day of this month.",
"role": ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 space, there are $n$ segments, none of which are parallel to the same plane. For any two segments, the line connecting their midpoints is perpendicular to both segments. What ... | math | {
"ground_truth": "n = 2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
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