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": "Number $a$ is such that $\\forall a_1, a_2, a_3, a_4 \\in \\mathbb{R}$ , there are integers $k_1, k_2, k_3, k_4$ such that $\\sum_{1 \\leq i < j \\leq 4} ((a_i - k_i) - (a_... | math | {
"ground_truth": "1.75",
"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": "Palindromes are numbers that read the same forwards and backwards, like 5775. What is the least possible four-digit palindrome that is divisible by 5?",
"role": "user"
}
] | math | {
"ground_truth": "5005",
"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 $\\ell$ be a line and $P$ be a point in $\\mathbb{R}^3$ . Let $S$ be the set of points $X$ such that the distance from $X$ to $\\ell$ is greater than or equal to... | math | {
"ground_truth": "\\frac{16 \\pi d^3}{27\\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 $P$ be an interior point of triangle $ABC$ . Let $a,b,c$ be the sidelengths of triangle $ABC$ and let $p$ be it's semiperimeter. Find the maximum possible value of ... | math | {
"ground_truth": "\\frac{2}{\\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": "$\\frac{2+3+4}{3}=\\frac{1990+1991+1992}{N}$, calculate the value of $N$.",
"role": "user"
}
] | math | {
"ground_truth": "1991",
"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": "What is the greatest possible value of $x+y$ if $x^2 + y^2 = 100$ and $xy = 40$?",
"role": "user"
}
] | math | {
"ground_truth": "6\\sqrt{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": "What is the maximum possible value of the sine of a $2^{n}$ degree angle, where $n$ is a positive integer?",
"role": "user"
}
] | math | {
"ground_truth": "0.8988",
"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 the function $f(x) = 5x - 7$. For what value of $b$ is $f(b) = 0$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{7}{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": "Solve the equation $\\frac{n!}{2} = k! + l!$ in natural numbers, where $n! = 1 \\cdot 2 \\cdot \\ldots n$. In your answer, indicate 0 if there are no solutions, $n$ if there is o... | math | {
"ground_truth": "10",
"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": "What quantities of 5% and 20% salt solutions in water are needed to prepare 90 kg of a 7% salt solution?",
"role": "user"
}
] | math | {
"ground_truth": "78 \\, \\text{kg of the 5\\% solution and 12 \\, kg of the 20\\% solution}",
"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 quadrilateral is inscribed in a circle. Find the sum of the four angles inscribed into the segments outside the quadrilateral, expressed in degrees.",
"role": "user"
}
] | math | {
"ground_truth": "540",
"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": "Paul ran 4 laps around a 600-meter track at his local park. For each lap, he ran the first 200 meters at an average speed of 3 meters per second and the remaining 400 meters at a... | math | {
"ground_truth": "8 \\text{ minutes and 53 seconds}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an $n$ -by- $m$ grid, $1$ row and $1$ column are colored blue, the rest of the cells are white. If precisely $\\frac{1}{2010}$ of the cells in the grid are blue, how m... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a, b, c$ be integers in the set $\\{1, 2, 3, 4, 5, 6\\}$ satisfying the conditions:\n\\[\nabc \\equiv 1 \\pmod{7},\n\\]\n\\[\n2c \\equiv 5 \\pmod{7},\n\\]\n\\[\n3b \\equiv 4... | math | {
"ground_truth": "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": "Suppose that $\\sec x + \\tan x = \\frac{19}{6}$, and that $\\csc x + \\cot x = \\frac{p}{q}$, where $\\frac{p}{q}$ is in lowest terms. Find $p+q$.",
"role": "user"
}
] | math | {
"ground_truth": "47",
"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 diagram shows two intersecting line segments that form some of the sides of two squares with side lengths $3$ and $6$ . Two line segments join vertices of these squares. F... | math | {
"ground_truth": "63",
"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 function $f(x)= \\frac {1}{3^{x}-1}+ \\frac {1}{2}$, find:\n$(1)$ the domain of $f(x)$;\n$(2)$ discuss the odd or even symmetry of $f(x)$.",
"role": "user"
}
] | math | {
"ground_truth": "f(x) \\text{ is an odd function on the domain } (-\\infty,0)\\cup(0,+\\infty)",
"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": "Koschei the Immortal poses three two-digit numbers: \\(a, b, c\\). Ivan Tsarevich must provide him with three numbers: \\(X, Y, Z\\), after which Koschei will tell him the sum \\... | math | {
"ground_truth": "X = 1, Y = 100, Z = 10000",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = kx^2 + (2k-1)x + k$, $g(x) = \\log_2(x+k)$ ($k \\in \\mathbb{R}$) \n(1) If $f(0) = 7$, find the minimum value $m$ of the function $g(x)$ on the interv... | math | {
"ground_truth": "\\frac{2}{3} \\leq k \\leq 31",
"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 Henry's three brothers have ages that are distinct single-digit positive integers, one brother is twice as old as another, and the square of the youngest brother's age... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence $\\{a_n\\}$ where $a_1=3$, $a_2=7$, and for $n\\geq1$ and $n\\in\\mathbb{N}^*$, $a_{n+2}$ is equal to the units digit of $a_n\\cdot a_{n+1}$. Find the value of t... | math | {
"ground_truth": "9",
"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 how many 3-digit whole numbers, whose digit-sum is $25$, are even.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A sequence is defined by \\( a_0 = \\frac{1}{3} \\) and \\( a_n = 1 + (a_{n - 1} - 1)^2 \\). Compute\n\\[\na_0 a_1 a_2 \\dotsm.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{1 + b_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": "A shape was cut out from a regular hexagon as shown in the picture. The marked points on both the perimeter and inside the hexagon divide the respective line segments into quarte... | math | {
"ground_truth": "4:1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The volume of the parallelepiped generated by the vectors $\\begin{pmatrix} 3 \\\\ 4 \\\\ 5 \\end{pmatrix}$, $\\begin{pmatrix} 2 \\\\ m \\\\ 3 \\end{pmatrix}$, and $\\begin{pmatr... | math | {
"ground_truth": "3 + \\frac{2\\sqrt{15}}{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 $m \\in \\mathbb{R}$, a moving line passing through a fixed point A is described by $x + my = 0$, and another moving line passing through a fixed point B is described by $m... | math | {
"ground_truth": "\\frac{5}{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": "In triangle \\( \\triangle ABC \\), given that \\( \\cos A + \\sin B = 1 \\) and \\( \\sin A + \\cos B = \\sqrt{3} \\), find the value of \\( \\cos (A - C) \\).",
"role": "us... | math | {
"ground_truth": "\\frac{\\sqrt{3}}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the result of the subtraction $888,888,888,888 - 111,111,111,111$.",
"role": "user"
}
] | math | {
"ground_truth": "777,777,777,777",
"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": "Sam has 4 red lava lamps and 4 blue lava lamps. He arranges them in a row on a shelf randomly, and then randomly turns 4 of them on. What is the probability that the leftmost lam... | math | {
"ground_truth": "\\frac{4}{49}",
"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": "During a math test, Oleg was supposed to divide a given number by 2, and then add 6 to the result. However, he hurried and instead multiplied the given number by 2, and then subt... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the domain of the function $y=f(x)$ is $[-2,4]$, determine the domain of the function $g(x)=f(x+1)+f(-x)$.",
"role": "user"
}
] | math | {
"ground_truth": "[-3,2]",
"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": "Let $S$ be a set of positive integers, such that $n \\in S$ if and only if $$ \\sum_{d|n,d<n,d \\in S} d \\le n $$ Find all positive integers $n=2^k \\cdot p$ where $k$... | math | {
"ground_truth": "k = x(a+1) - 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $ \\{a_n\\}$ is a sequence in which all the terms are integers, and $ a_2$ is odd. For any natural number $ n$ , $ n(a_{n \\plus{} 1} \\minus{} a_n \\plus{} 3) \... | math | {
"ground_truth": "66",
"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 probability of a sudden event occurring without any preventive measures is 0.3, and it will cause a loss of 4 million yuan if it happens. There are two independent prev... | math | {
"ground_truth": "85\\text{ (in ten thousand yuan)}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all real numbers $a$ such that $3 < a < 4$ and $a(a-3\\{a\\})$ is an integer.\n\n(Here $\\{a\\}$ denotes the fractional part of $a$ .)",
"role": "user"
}
] | math | {
"ground_truth": "a = 3 + \\frac{\\sqrt{17} - 3}{4}, \\frac{7}{2}, 3 + \\frac{\\sqrt{33} - 3}{4}, 3 + \\frac{\\sqrt{41} - 3}{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": "In the geometric sequence $\\{a\\_n\\}$, $a\\_3a\\_7=8$, then $a\\_5=$ _____ .",
"role": "user"
}
] | math | {
"ground_truth": "±2 \\sqrt {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": "If $a^5 +5a^4 +10a^3 +3a^2 -9a-6 = 0$ where $a$ is a real number other than $-1$ , what is $(a + 1)^3$ ? $ \n\\textbf{a)}\\ 1\n\\qquad\\textbf{b)}\\ 3\\sqrt 3\n\\qquad\\tex... | math | {
"ground_truth": "7",
"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": "On the planet Mars there are $100$ states that are in dispute. To achieve a peace situation, blocs must be formed that meet the following two conditions:\n(1) Each block must h... | math | {
"ground_truth": "6",
"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": "In a lottery with 5 cash prizes and 20 merchandise prizes for every 1000 tickets, what is the probability of winning with a single ticket?",
"role": "user"
}
] | math | {
"ground_truth": "0.025",
"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 whole numbers lie in the interval between $\\frac{7}{3}$ and $3\\pi$?",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that $n$ people $A_1$ , $A_2$ , $\\ldots$ , $A_n$ , ( $n \\geq 3$ ) are seated in a circle and that $A_i$ has $a_i$ objects such that \r\n\\[ a_1 + a_2 + \\cdot... | math | {
"ground_truth": "x_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": "Find all angles \\( \\theta,\\) \\( 0 \\le \\theta \\le 2\\pi,\\) such that for all real numbers \\( x,\\) \\( 0 \\le x \\le 1,\\)\n\\[\nx^2 \\cos \\theta - x(1 - x) + (1 - x)^2 ... | math | {
"ground_truth": "\\left( \\frac{\\pi}{2}, \\frac{3\\pi}{2} \\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 sum of eight consecutive positive integers is 3652, find the largest of these eight integers.",
"role": "user"
}
] | math | {
"ground_truth": "460",
"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 parabolic arch has a height of $25$ inches and a span of $50$ inches. Calculate the height, in inches, of the arch at the point $10$ inches from the center $M$.",
"role": "... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCDEF$ be a regular hexagon with side length $2$ . A circle with radius $3$ and center at $A$ is drawn. Find the area inside quadrilateral $BCDE$ but outside the c... | math | {
"ground_truth": "4\\sqrt{3} - 9\\pi",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a ticket to a school play cost $x$ dollars, where $x$ is a whole number, determine the number of possible values for $x$ where $9x = 48$ and $10x = 64$.",
"role": ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a certain city, a bus route has six stops, named A<sub>0</sub>, A<sub>1</sub>, A<sub>2</sub>, A<sub>3</sub>, A<sub>4</sub>, and A<sub>5</sub>. Two passengers, A and B, board t... | math | {
"ground_truth": "\\frac{4}{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": "How many four-digit whole numbers are there such that the leftmost digit is a prime number, the second digit is even, and all four digits are different?\nA) 1020 \nB) 1064 \nC)... | math | {
"ground_truth": "B) 1064",
"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": "Ali Baba and a thief are sharing a treasure consisting of 100 gold coins, divided into 10 piles of 10 coins each. Ali Baba selects 4 piles, places a cup near each of them, and pu... | math | {
"ground_truth": "72",
"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 $\\frac{1}{3}$ of all the ninth graders are paired with $\\frac{2}{5}$ of all the sixth graders, calculate the fraction of the total number of sixth and ninth graders ... | math | {
"ground_truth": "\\frac{4}{11}",
"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": "Alfred, Bruno, Christophe, and Damien are playing cards with a deck of 32 cards. Damien deals all the cards to the players. When it is pointed out that the number of cards among ... | math | {
"ground_truth": "A = 7, B = 7, C = 13, D = 8",
"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": "Amy, Becky, and Chloe went shopping. Becky spent only 15% of what Chloe spent. However, Amy spent 60% more than Chloe. Together they spent £55. How much did Amy spend?\nA £3\nB £... | math | {
"ground_truth": "\\pounds 32",
"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 $\\textit{composite number}$ is a number that has more than one prime factor. Find the minimum positive difference between two composite numbers whose sum is 93.",
"role": ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a + 3 = (b-1)^2$ and $b + 3 = (a-1)^2$. Assuming $a \\neq b$, determine the value of $a^2 + b^2$.\nA) 5\nB) 10\nC) 15\nD) 20\nE) 25",
"role": "user"
}
] | math | {
"ground_truth": "10",
"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 area of rectangle A B C D is given by the product of its length and width.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"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 $a, b, c$ be the roots of $x^3-12x^2+14x-1=0$, and let $s = \\sqrt{a} + \\sqrt{b} + \\sqrt{c}$. Find $s^4-24s^2-10s$.",
"role": "user"
}
] | math | {
"ground_truth": "-144",
"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": "Experts and Viewers play \"What? Where? When?\" until one side wins six rounds. The probability of Experts winning a single round is 0.6, and there are no ties. Currently, the Ex... | math | {
"ground_truth": "0.4752",
"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": "When Amy walks to school, she averages 80 steps per minute, and each of her steps is 70 cm long. It takes her 20 minutes to get to school. Her friend, Ben, also going to the same... | math | {
"ground_truth": "\\text{It takes Ben }18\\frac{2}{3}\\text{ minutes to walk to school.}",
"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": "At the 4 PM show, all the seats in the theater were taken, and 65 percent of the audience was children. At the 6 PM show, again, all the seats were taken, but this time only 50 p... | math | {
"ground_truth": "520",
"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": "Solve the equation $\\arcsin \\frac{2 x}{\\sqrt{15}}+\\arcsin \\frac{3 x}{\\sqrt{15}}=\\arcsin \\frac{4 x}{\\sqrt{15}}$.",
"role": "user"
}
] | math | {
"ground_truth": "0, \\pm \\frac{15}{16}",
"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": "In the diagram, $D$ and $E$ are the midpoints of $\\overline{AC}$ and $\\overline{BC}$ respectively, where $A(0,8)$, $B(0,0)$, and $C(10,0)$. Find the sum of the slope and $y$-in... | math | {
"ground_truth": "\\frac{36}{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": "In the coordinate plane \\(xOy\\), given points \\(A(1,3)\\), \\(B\\left(8 \\frac{1}{3}, 1 \\frac{2}{3}\\right)\\), and \\(C\\left(7 \\frac{1}{3}, 4 \\frac{2}{3}\\right)\\), the ... | math | {
"ground_truth": "\\frac{5 \\sqrt{10}}{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": "The area between two concentric circles is $18\\pi$ square inches. Calculate the length of a chord of the larger circle that is tangent to the smaller circle.\nA) \\( 3\\sqrt{2} ... | math | {
"ground_truth": "C) \\( 6\\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": "The angles of a pentagon are in arithmetic progression. Find the value of one of the angles in degrees.",
"role": "user"
}
] | math | {
"ground_truth": "108",
"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 inequality in terms of $x$, $ax-b > 0$, has a solution set of $(-\\infty,-1)$, solve the inequality $(x-2)(ax+b) < 0$.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty,1)\\cup(2,+\\infty)",
"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": "What is the coefficient of $a^3b^3$ in $(a+b)^6\\left(c + \\dfrac{1}{c}\\right)^8$?",
"role": "user"
}
] | math | {
"ground_truth": "1400",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is known that $\\sqrt{3}b\\sin \\left(B+C\\right)+a\\cos B=c$.... | math | {
"ground_truth": "9\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A point is chosen randomly from within a circular region with radius $r$. A related concentric circle with radius $\\sqrt{r}$ contains points that are closer to the center than t... | math | {
"ground_truth": "\\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": "Each team plays each of the other teams in its own division twice and every team in the other division once. Determine the total number of conference games scheduled.",
"role... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider a polynomial $P(z) = z^4 + 6z^3 + 8z^2 + 12z + 9$. It has four complex roots: $z_1$, $z_2$, $z_3$, and $z_4$. Let $f(z) = -2i\\overline{z}$ be a transformation function.... | math | {
"ground_truth": "C) 176",
"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 particle is projected vertically upward with an initial velocity higher than in the previous scenario. The elevation $s$ in feet after $t$ seconds in the presence of air resist... | math | {
"ground_truth": "368.1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In some cells of a $10 \\times 10$ board, $k$ rooks are placed, and then all the cells that are attacked by at least one rook (the rook also attacks the cell it stands on) are ma... | math | {
"ground_truth": "16",
"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": "What is the largest amount of elements that can be taken from the set $\\{1, 2, ... , 2012, 2013\\}$ , such that within them there are no distinct three, say $a$ , $b$ ,and $... | math | {
"ground_truth": "672",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Rectangle PQRS lies in a plane with PQ = RS = 2 and QR = SP = 6, determine the length of the path traveled by point P after the rectangle is rotated 90^{\\circ} clockw... | math | {
"ground_truth": "\\left(3+\\sqrt{10}\\right)\\pi",
"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 a square with a side of 5 cm. The vertices of a second square are located on the four sides of the first square; the vertices of a third square are located on the four side... | 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": "Find the integer $n,$ $-150 < n < 150,$ such that $\\tan n^\\circ = \\tan 225^\\circ.$",
"role": "user"
}
] | math | {
"ground_truth": "-135, -45, 45, 135",
"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 a terrible storm, $n$ dwarfs are climbing up a rope ladder in a chain. If there is a sudden thunderstorm, each dwarf, independently of the others, may fall with a probability ... | math | {
"ground_truth": "n+1-\\frac{1}{p}+\\frac{(1-p)^{n+1}}{p}",
"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 $\\left(3-\\pi \\right)^{0}=\\_\\_\\_\\_\\_\\_.$",
"role": "user"
}
] | math | {
"ground_truth": "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": "\\( P(x) \\) is a fourth-degree polynomial with integer coefficients, with a leading coefficient that is positive. It is known that \\( P(\\sqrt{3}) = P(\\sqrt{5}) \\). Find the ... | math | {
"ground_truth": "\\pm 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": "Five students are arranged in a row, and students A, B, and C must be together. Determine the number of different possible arrangements.",
"role": "user"
}
] | math | {
"ground_truth": "36",
"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 base angle of an isosceles triangle is $42^\\circ$. Calculate its apex angle.",
"role": "user"
}
] | math | {
"ground_truth": "96^{\\circ}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a shape formed by joining six squares of side length $8$ cm as shown, determine the smallest possible area of a rectangle that can completely contain this shape.",
"rol... | math | {
"ground_truth": "768 \\, \\text{cm}^2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The difference between the largest and smallest of the four numbers is as large as possible, and the average of the four numbers is 4. Determine the average of the other two numb... | math | {
"ground_truth": "2 \\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the domain of the function $f(x) = \\lg \\left( \\frac{2}{x+1} - 1 \\right)$ be set $A$, and the range of the function $g(x) = -x^{2} + 2x + a (0 \\leqslant x \\leqslant 3, a... | math | {
"ground_truth": "(-\\infty, -2] \\cup [4, +\\infty)",
"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 $PQR$ has vertices at $P(-1,3)$, $Q(2,7)$, and $R(4,0)$. Determine the coordinates of point $S$ inside the triangle such that the three smaller triangles $PQS$, $QRS$, a... | math | {
"ground_truth": "\\frac{70}{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": "Carlos and Nina play a game where Carlos picks an integer between 1 and 4500 inclusive. Nina divides 4500 by that integer and checks if the result is an integer. How many integer... | math | {
"ground_truth": "24",
"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 the maximum number $ c$ such that for all $n \\in \\mathbb{N}$ to have \\[ \\{n \\cdot \\sqrt{2}\\} \\geq \\frac{c}{n}\\] where $ \\{n \\cdot \\sqrt{2}\\} \\equal{} n \... | math | {
"ground_truth": "c = \\frac{\\sqrt{2}}{4}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The polynomial $P$ is a quadratic with integer coefficients. For every positive integer $n$ , the integers $P(n)$ and $P(P(n))$ are relatively prime to $n$ . If $P(3) ... | math | {
"ground_truth": "859",
"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 $x_i\\ (i = 1, 2, \\cdots 22)$ be reals such that $x_i \\in [2^{i-1},2^i]$ . Find the maximum possible value of $$ (x_1+x_2+\\cdots +x_{22})(\\frac{1}{x_1}+\\frac{1}{x_2... | math | {
"ground_truth": "2^{24}",
"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": "(1) A competition is held in \\( n \\) (\\(n > 1\\)) rounds, and a total of \\( m \\) medals are awarded. In the first round, 1 medal is awarded along with \\(\\frac{1}{7}\\) of ... | math | {
"ground_truth": "2^n + (-1)^n \\cdot 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": "There is a type of cell, each hour 2 cells die, and the remaining cells each split into 2. If after 5 hours the number of cells is 164, how many cells were there initially?",
... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all triples $(x,y,z)$ which satisfy the equations: $1)$ $x(y^2+z)=z(z+xy)$ $2)$ $y(z^2+x)=x(x+yz)$ $3)$ $z(x^2+y)=y(y+xz)$",
"role": "user"
}
] | math | {
"ground_truth": "(1, 1, 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": "Find the positive value of $t$ that satisfies $ab = t-3i$ given $|a|=3$ and $|b|=5$.",
"role": "user"
}
] | math | {
"ground_truth": "6\\sqrt{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": "At Rawlings Middle School, there are 240 students with a ratio of boys to girls of 3:2. Waverly Middle School has 200 students, where the ratio of boys to girls is 3:5. All stude... | math | {
"ground_truth": "\\frac{221}{440}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $a^2 = b(b + c)$. Find the value of $\\frac{B}{A}$.",
... | math | {
"ground_truth": "\\frac{1}{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": "In a large city, an average of 300 children are born daily, which is 109,500 per year. The probability of giving birth to a boy is 0.51. Find the expected value, variance, and st... | math | {
"ground_truth": "M(X) = 55845, \\ D(X) = 27363.75, \\ \\sigma(X) \\approx 165.42",
"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 $x < 0$, the maximum value of $3x +\\dfrac{4}{x}$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "-4\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify the following expression:\n\\[\n\\left(\\frac{a}{b} \\sqrt[3]{b-\\frac{4 a^{6}}{b^{3}}}-a^{2} \\sqrt[3]{\\frac{b}{a^{6}}-\\frac{4}{b^{3}}}+\\frac{2}{a b} \\sqrt[3]{a^{3}... | math | {
"ground_truth": "(a + b) \\sqrt[3]{ b^2 + 2a^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": "Calculate the value of the product: $\\left(\\frac{1\\cdot5}{3\\cdot3}\\right)\\left(\\frac{3\\cdot7}{5\\cdot5}\\right)\\left(\\frac{5\\cdot9}{7\\cdot7}\\right)\\cdots\\left(\\fr... | math | {
"ground_truth": "\\frac{101}{297}",
"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": "Solve the system of equations in real numbers:\n\n$$\n\\left\\{\\begin{array}{l}\nx_{1} + x_{2} = x_{3}^{2} \\\\\nx_{2} + x_{3} = x_{4}^{2} \\\\\nx_{3} + x_{1} = x_{5}^{2} \\\\\n... | math | {
"ground_truth": "\\{2, 2, 2, 2, 2\\} \\quad \\text{or} \\quad \\{0, 0, 0, 0, 0\\}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
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