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": "If $x < \\alpha$, evaluate the expression $\\left|x - \\sqrt{(x-\\alpha)^2}\\right|$ for a given parameter $\\alpha$.\n**A)** $2x - \\alpha$ \n**B)** $\\alpha - 2x$ \n**C)** $2... | math | {
"ground_truth": "\\alpha - 2x",
"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": "The maximum and minimum values of the function y=x^3-2x^2+1 in the interval [-1, 2] are (2, -1).",
"role": "user"
}
] | 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": "The total in-store price for a blender is $\\$75.99$. A television commercial advertises the same blender for four easy payments of $\\$17.99$ and a one-time shipping fee of $\\$... | math | {
"ground_truth": "497",
"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 the determinant of the following matrix:\n\\[\n\\begin{vmatrix} 3 & 0 & 1 \\\\ -5 & 5 & -4 \\\\ 3 & 3 & 6 \\end{vmatrix}\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "96",
"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": "A plane has a special point $O$ called the origin. Let $P$ be a set of 2021 points in the plane such that\n\n\n- no three points in $P$ lie on a line and\n- no two points i... | math | {
"ground_truth": "\\binom{2021}{3} - 2021 \\times \\binom{1010}{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": "Find the value of $a+b$ if the repeating decimal $0.\\overline{35}$ is expressed as a fraction $\\frac{a}{b}$, with $a$ and $b$ being positive coprime integers.",
"role": "us... | math | {
"ground_truth": "134",
"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 a cone with vertex \\( P \\), a base radius of 2, and a height of 1. On the base of the cone, a point \\( Q \\) is chosen such that the angle between the line \\( PQ \\) an... | math | {
"ground_truth": "3 \\pi",
"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": "With three different digits, all greater than $0$ , six different three-digit numbers are formed. If we add these six numbers together the result is $4.218$ . The sum of the th... | math | {
"ground_truth": "8, 7, 4",
"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 the diagram, $AB$ and $CD$ are diameters of a circle with a radius of 6 that intersect at right angles at point $O$. The points $B$ and $D$ are on the horizontal diameter, and... | math | {
"ground_truth": "36 + 18\\pi",
"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 that $M(m,n)$ is any point on the circle $C$: $x^{2}+y^{2}-4x-14y+45=0$.\n\n(1) Find the maximum value of $m+2n$.\n\n(2) Find the maximum and minimum values of $\\frac{n-3}... | math | {
"ground_truth": "2- \\sqrt{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": "What is the radius of a circle inscribed in a rhombus with diagonals of length $14$ and $30$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{105\\sqrt{274}}{274}",
"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 the area of the region bounded by a function $y=-x^4+16x^3-78x^2+50x-2$ and the tangent line which is tangent to the curve at exactly two distinct points.\n\nProposed by K... | math | {
"ground_truth": "\\frac{1296}{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 two sets of real numbers \\(A=\\{a_{1}, a_{2}, \\cdots, a_{100}\\}\\) and \\(B=\\{b_{1}, b_{2}, \\cdots, b_{10}\\}\\), if a mapping \\(f\\) from \\(A\\) to \\(B\\) exists s... | math | {
"ground_truth": "\\binom{99}{49}",
"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 the function $g(x+2)=2x-3$, find the expression for $g(x)$.",
"role": "user"
}
] | math | {
"ground_truth": "2x - 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": "In the multiplication problem shown in the diagram, the same Chinese character represents the same digit, and different Chinese characters represent different digits. After corre... | math | {
"ground_truth": "1537",
"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 the complex number $\\frac{2+ai}{1+i}$ where $a \\in \\mathbb{R}$, find the value of $a$ such that the complex number is a purely imaginary number.",
"role": "user"
}... | math | {
"ground_truth": "-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 $n$ be positive integer and $S$ = { $0,1,…,n$ }, Define set of point in the plane. $$ A = \\{(x,y) \\in S \\times S \\mid -1 \\leq x-y \\leq 1 \\} $$ , We want to plac... | math | {
"ground_truth": "n+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": "In a trapezoid $ABCD$, $\\overline{AD}$ is perpendicular to $\\overline{DC}$, $AD = 4$, $AB = 4$, and $DC = 8$. Additionally, point $E$ is on $\\overline{DC}$, and $\\overline{BE... | math | {
"ground_truth": "8",
"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 a cube toy has a snapping button on one side and five sides with receptacles, determine the minimum number of such cubes required to assemble them so that none of the ... | math | {
"ground_truth": "5",
"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 a sequence $\\{a_n\\}$ where $a_1=3$, $a_2=6$, and $a_{n+2}=a_{n+1}-a_n$, find the value of $a_{2010}$.",
"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": "Define a sequence by $a_0=2019$ and $a_n=a_{n-1}^{2019}$ for all positive integers $n$ . Compute the remainder when \\[a_0+a_1+a_2+\\dots+a_{51}\\] is divided by $856$ .\n\... | math | {
"ground_truth": "428",
"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 sum of three numbers $a$, $b$, $c$ is 180. When the smallest number $a$ is multiplied by 8, the result is $m$. The value $m$ is obtained by subtracting 10 from the largest nu... | math | {
"ground_truth": "\\frac{369912000}{4913}",
"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": "Point $G$ is taken on side $AB$ of square $WXYZ$. At $Z$, a perpendicular is drawn to $ZG$, meeting $WY$ extended at $H$. The area of square $WXYZ$ is $324$ square inches, and th... | math | {
"ground_truth": "B) 12\\sqrt{11}",
"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": "If the function $y = x^2 + px + q + ax^2$ has a minimum value of zero, and $a$ is a positive constant, what is the value of $q$?\nA) $\\frac{p^2}{4}$ \nB) $\\frac{p^2}{2(1+a)}$ ... | math | {
"ground_truth": "\\frac{p^2}{4(1+a)}",
"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": "The sum of two numbers is $18$ and their product is $80$. What is the smaller number?",
"role": "user"
}
] | math | {
"ground_truth": "8",
"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": "What is the sum of the odd integers from 1 through 49, inclusive?",
"role": "user"
}
] | math | {
"ground_truth": "625",
"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 number of terms n in an arithmetic progression with a first term that is an integer, a common difference of 3, and a sum of 120.",
"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": "Find the area of a polygon with vertices given as \\( (2,1), (4,3), (7,1), (6,6) \\).\nA) 5\nB) 7.5\nC) 10\nD) 12",
"role": "user"
}
] | math | {
"ground_truth": "B) 7.5",
"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": "An arithmetic sequence starts with the term $3$ and has a common difference of $8$. A second sequence begins with $5$ and has a common difference of $9$. In the range of $1$ to $... | math | {
"ground_truth": "59",
"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": "Determine the number of angles $\\theta$ between $0$ and $2 \\pi$ , other than integer multiples of $\\pi /2$ , such that the quantities $\\sin \\theta, \\cos \\theta, $ ... | math | {
"ground_truth": "4",
"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 an acute triangle $\\triangle ABC$ where the internal angles $A$, $B$, and $C$ are opposite to sides $a$, $b$, and $c$ respectively, and $a=3$, $b=\\sqrt{13}$. If $a\\sin 2... | math | {
"ground_truth": "\\frac{2\\sqrt{19}}{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": "Given the function $f(x)$ satisfies $f(a+b)=f(a)f(b)$ and $f(1)=2$, evaluate the expression $$\\frac{f^2(1)+f(2)}{f(1)} + \\frac{f^2(2)+f(4)}{f(3)} + \\frac{f^2(3)+f(6)}{f(5)} + ... | math | {
"ground_truth": "16",
"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 numbers from 1 to 200, inclusive, are placed in a bag and a number is randomly selected. What is the probability that it is not a perfect power (integers that can be expresse... | math | {
"ground_truth": "\\frac{179}{200}",
"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": "A certain type of bacteria divides every 15 minutes (splitting from one into two). The time it takes for this type of bacteria to divide from 1 to 4096 is ____ hours.",
"role... | 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": "If three-fifths of the boys and four-fifths of the girls passed the test, with an equal number of boys and girls passing, determine the minimum possible number of students in Ms.... | 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": "A revised formula $N=5 \\times 10^7 \\times x^{-5/2}$ gives the number of individuals in a different group whose income surpasses $x$ dollars. Find the minimum income, in dollars... | math | {
"ground_truth": "10^2",
"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 \\(\\triangle ABC\\), \\(AC = AB = 25\\) and \\(BC = 40\\). From \\(D\\), perpendiculars are drawn to meet \\(AC\\) at \\(E\\) and \\(AB\\) at \\(F\\), calculate the value of ... | math | {
"ground_truth": "24",
"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 all positive solutions of the equation\n\n$$\nx^{101}+100^{99}=x^{99}+100^{101}\n$$\n\nBe sure to justify your answer.",
"role": "user"
}
] | math | {
"ground_truth": "100",
"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 the direction vectors of the lines $a$ and $b$ are $\\overrightarrow{a}=(1,0,-1)$ and $\\overrightarrow{b}=(1,-1,0)$, and both lines $a$ and $b$ are parallel to the pl... | math | {
"ground_truth": "( \\frac{\\sqrt{3}}{3},\\frac{\\sqrt{3}}{3},\\frac{\\sqrt{3}}{3}) \\text{ or } (-\\frac{\\sqrt{3}}{3},-\\frac{\\sqrt{3}}{3},-\\frac{\\sqrt{3}}{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": "A sequence $a_1, a_2, \\ldots$ satisfies $a_1 = \\dfrac 52$ and $a_{n + 1} = {a_n}^2 - 2$ for all $n \\ge 1.$ Let $M$ be the integer which is closest to $a_{2023}.$ T... | math | {
"ground_truth": "4",
"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": "Suppose the roots of the polynomial $Q(x)=x^3+dx^2+ex+f$ are $\\cos \\frac{\\pi}{9}, \\cos \\frac{4\\pi}{9},$ and $\\cos \\frac{7\\pi}{9}$. Find the value of $def$.",
"role":... | 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": "The polynomial $x^{2n}+1+(x+1)^{2n}$ is not divisible by $x^2+x+1$ if $n$ equals",
"role": "user"
}
] | math | {
"ground_truth": "21",
"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 polynomial $(x+y)^7$ is expanded in decreasing powers of $x$. The third and fourth terms have equal values when evaluated at $x=a$ and $y=b$, where $a$ and $b$ are positive n... | math | {
"ground_truth": "\\frac{5}{8}",
"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 square sheet of paper has an area of $16 \\text{ cm}^2$. The front is white and the back is black. When the sheet is folded so that point $A$ rests on the diagonal, and then ag... | math | {
"ground_truth": "\\frac{8\\sqrt{3}}{3}",
"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 $g(x) = 4x^3 + 5$, find the value of $x$ so that $g^{-1}(x) = 5$.",
"role": "user"
}
] | math | {
"ground_truth": "505",
"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": "A mixture of $40$ liters of paint consists of $20\\%$ red tint, $35\\%$ yellow tint, and $45\\%$ water. Three liters of yellow tint and two liters of red tint are added to the or... | math | {
"ground_truth": "38\\%",
"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 real numbers $x$ and $y$ are chosen independently using a method where a fair coin is flipped twice, find the probability that $|x-y| > \\tfrac{1}{2}$.",
"role": "... | math | {
"ground_truth": "\\textbf{(C)} \\frac{1}{2}",
"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 \n\\[\n\\min_{y \\in \\mathbb{R}} \\max_{0 \\le x \\le 1} |x^3 - xy|.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "0",
"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": "Let $I = \\{2, 4, a^2 - a - 3\\}$ and $A = \\{4, 1 - a\\}$. If the complement of set $A$ relative to $I$, denoted as $\\complement_{I}A$, is $\\{-1\\}$, determine the value of $a... | 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": "In the Cartesian coordinate system, the curve $C$ consists of all points whose product of distances to two fixed points $A(1,0)$ and $B(-1,0)$ equals $2$. For curve $C$, there ar... | math | {
"ground_truth": "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": "Let $(x_1, y_1)$ , $(x_2, y_2)$ , $(x_3, y_3)$ , $(x_4, y_4)$ , and $(x_5, y_5)$ be the vertices of a regular pentagon centered at $(0, 0)$ . Compute the product of all po... | 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": "If $x > 1$, find the minimum value of the function $y = x + \\frac{1}{x} + \\frac{16x}{x^2 + 1}$.",
"role": "user"
}
] | math | {
"ground_truth": "y_{min} = 8",
"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": "Four pirates, Jack, Jimmy, Tom, and Sanji, share a total of 280 gold coins. Jack says: \"I received 11 fewer coins than Jimmy, 15 more than Tom, and 20 fewer than Sanji.\" How ma... | math | {
"ground_truth": "86",
"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 diagram below shows an isosceles triangle with base $21$ and height $28$ . Inscribed in the triangle is a square. Find the area of the shaded region inside the triangle ... | math | {
"ground_truth": "150",
"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 the terminal side of angle $\\theta$ passes through point P(-4t, 3t) (t≠0), then the value of $2\\sin\\theta + \\cos\\theta$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "\\pm \\frac{2}{5}",
"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": "What is the units digit of the product of the first four positive composite numbers?",
"role": "user"
}
] | math | {
"ground_truth": "8",
"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": "Determine the value of $\\frac{16!}{7!9!}$.",
"role": "user"
}
] | math | {
"ground_truth": "1,441,440",
"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": "Let $P(a,b)$ be a moving point on the ellipse $\\frac{{x}^{2}}{{a}^{2}}+ \\frac{{y}^{2}}{{b}^{2}}=1 (a > b > 0)$, and satisfies $|P{F}_{2}|=|{F}_{1}{F}_{2}|$.\n\n(1) Find the ecc... | math | {
"ground_truth": "\\frac{x^2}{16} + \\frac{y^2}{12} = 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": "ABCD is an n x n board. We call a diagonal row of cells a positive diagonal if it is parallel to AC. How many coins must be placed on an n x n board such that every cell either h... | math | {
"ground_truth": "\\lceil \\frac{2n - 1}{3} \\rceil",
"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": "Stack 100 unit cubes to form a polyhedron. List the possible surface areas of the polyhedra in ascending order, and find the first 6 surface areas.",
"role": "user"
}
] | math | {
"ground_truth": "130, 134, 136, 138, 140, 142",
"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 $a$ and $b$ be real numbers such that $2 < a < b$ and no triangle with positive area can have side lengths $2$, $a$, and $b$ or $\\frac{1}{b}$, $\\frac{1}{a}$, and $2$. Deter... | 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": "In the land of Puzzleonia, which uses the standard English alphabet (26 letters, A through Z), every word in their language has 5 letters or less, ensuring that each word contain... | math | {
"ground_truth": "2186085",
"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": "A cube has a side length of 1 unit. A regular octahedron is formed by joining the midpoints of the edges of the cube. Find the ratio of the surface area of the cube to the surfac... | math | {
"ground_truth": "\\sqrt{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 Professor Miller has nine different language books on a bookshelf: two Arabic, three German, and four Spanish, calculate the number of ways to arrange the nine books on the... | math | {
"ground_truth": "4! \\times 3! \\times 4! = 24 \\times 6 \\times 24 = 3456",
"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": "Let the sum of positive numbers $x_1, x_2, ... , x_n$ be $1$ . \nLet $s$ be the greatest of the numbers $\\big\\{\\frac{x_1}{1+x_1}, \\frac{x_2}{1+x_1+x_2}, ..., \\frac{x_n... | math | {
"ground_truth": "\\frac{1}{n+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": "For which natural numbers \\( n \\), for any numbers \\( \\alpha, \\beta, \\gamma \\) that are the angles of an acute-angled triangle, the inequality\n\n$$\n\\sin n \\alpha + \\s... | math | {
"ground_truth": "4",
"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": "Matilda has a set of sticker packs and wants to distribute them into baskets, each containing exactly 7 packs. She currently has 40 sticker packs. What is the minimum number of a... | math | {
"ground_truth": "\\text{B) 2}",
"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 unit cube is sliced along one of its body diagonals to create two identical tetrahedra and the remaining middle portion as a truncated rectangular pyramid. One of these cuts oc... | math | {
"ground_truth": "\\frac{5}{6}",
"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 angles in a triangle are in arithmetic progression, and the side lengths are $3, 7, x$. Find the sum of the possible values of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "45",
"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": "We are given 5040 balls in k different colors, where the number of balls of each color is the same. The balls are put into 2520 bags so that each bag contains two balls of differ... | math | {
"ground_truth": "6",
"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 $ABC$, point $E$ lies on $\\overline{AC}$ such that $AE:EC = 1:3$, and point $F$ lies on $\\overline{AB}$ such that $AF:FB = 1:4$. Let point $P$ be the intersection o... | math | {
"ground_truth": "\\left(\\frac{3}{5}, \\frac{1}{5}, \\frac{1}{5}\\right)",
"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": "Lizzie and Alex are playing a game on the whiteboard. Initially, $n$ twos are written\non the board. On a player’s turn they must either \n 1. change any single positive ... | math | {
"ground_truth": "n \\not\\equiv 0 \\pmod{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": "Given the function $f(x)=\\lg[(m^{2}-3m+2)x^{2}+(m-1)x+1]$, find the range of values for the real number $m$ such that the domain of the function is $\\mathbb{R}$.",
"role": ... | math | {
"ground_truth": "m > \\frac {7}{3} \\text{ or } m \\leqslant 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": "Given a line $l$ passing through the point $(1, 0)$ with an inclination angle of $\\alpha$, in the Cartesian coordinate system $xOy$, with $O$ as the pole and the positive half-a... | math | {
"ground_truth": "\\frac{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": "Given the ellipse $\\dfrac {x^{2}}{6}+ \\dfrac {y^{2}}{2}=1$ and the hyperbola $\\dfrac {x^{2}}{3}-y^{2}=1$ share common foci $F_{1}$ and $F_{2}$, and $P$ is a common point of th... | math | {
"ground_truth": "\\dfrac {1}{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": "In $\\vartriangle ABC, AB=AC=14 \\sqrt2 , D$ is the midpoint of $CA$ and $E$ is the midpoint of $BD$ . Suppose $\\vartriangle CDE$ is similar to $\\vartriangle ABC$ . F... | math | {
"ground_truth": "14",
"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 permutations \\(a, b, c, d, e, f, g, h\\) of \\(1, 2, 3, 4, 5, 6, 7, 8\\) satisfy \\(a < b\\), \\(b > c\\), \\(c < d\\), \\(d > e\\), \\(e < f\\), \\(f > g\\), \\(g < h\... | math | {
"ground_truth": "1385",
"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 the cube root of \\( m \\) be a number of the form \\( n + r \\), where \\( n \\) is a positive integer and \\( r \\) is a positive real number less than \\( \\frac{1}{1000} ... | math | {
"ground_truth": "19",
"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 distance from point P(1, 2, 2) to the origin is to be calculated.",
"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 $h(x)=4x-3$, and let $p(x)=h(h(h(x)))$. If the domain of $p$ is $1\\leq x\\leq 3$, compute the range of $p$.",
"role": "user"
}
] | math | {
"ground_truth": "1 \\leq p(x) \\leq 129",
"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 a family outing to a theme park, the Thomas family, comprising three generations, plans to purchase tickets. The two youngest members, categorized as children, get a 40% disco... | math | {
"ground_truth": "49.27",
"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": "Let $T=\\text{TNFTPP}$ . Let $R$ be the region consisting of the points $(x,y)$ of the cartesian plane satisfying both $|x|-|y|\\leq T-500$ and $|y|\\leq T-500$ . Find ... | math | {
"ground_truth": "1024",
"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 a similar game, Hardy and Ramanujan both pick a complex number again. This time, the product of their numbers is $40 + 24i$, and Hardy selects $3 + 7i$. What number did Ramanu... | math | {
"ground_truth": "4 - \\frac{104}{29}i",
"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": "Let $S_0=0$ and let $S_k$ equal $a_1+2a_2+\\ldots+ka_k$ for $k\\geq 1$ . Define $a_i$ to be $1$ if $S_{i-1}<i$ and $-1$ if $S_{i-1}\\geq i$ . What is the larges... | math | {
"ground_truth": "1092",
"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 last digit of a natural number is 2016 times smaller than the number itself. Find all such numbers.",
"role": "user"
}
] | math | {
"ground_truth": "4032, 8064, 12096, 16128",
"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 analytic function \\( f(z) \\) if\n\n$$\nu(x, y) = \\operatorname{Re} f(z) = x^3 - 3xy^2 + 2y \\quad \\text{and} \\quad f(i) = 2.\n$$",
"role": "user"
}
] | math | {
"ground_truth": "f(z) = z^3 - 2iz + (2 + 3i)",
"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 last non-zero digit of the product of all natural numbers from 1 to 40.",
"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": "Subtract $123.45$ from $678.90.$ Express the result as a decimal to the nearest hundredth.",
"role": "user"
}
] | math | {
"ground_truth": "555.55",
"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 that $59$ is to be written as the sum of two distinct primes, determine the number of distinct ways in which this can be done.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"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": "Tony the gardener planted tulips and daisies in a square flowerbed of side-length $12 \\mathrm{~m}$, arranged as shown. What is the total area, in $\\mathrm{m}^{2}$, of the regio... | math | {
"ground_truth": "48",
"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": "Circles \\(\\omega_{1}, \\omega_{2},\\) and \\(\\omega_{3}\\) are centered at \\(M, N,\\) and \\(O\\), respectively. The points of tangency between \\(\\omega_{2}\\) and \\(\\ome... | math | {
"ground_truth": "2 \\sqrt{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": "How many positive three-digit integers have a remainder of 2 when divided by 6, a remainder of 5 when divided by 9, and a remainder of 7 when divided by 11?",
"role": "user"
... | math | {
"ground_truth": "5",
"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": "We are given a convex quadrilateral $ABCD$ in the plane.\n(*i*) If there exists a point $P$ in the plane such that the areas of $\\triangle ABP, \\triangle BCP, \\triangle C... | math | {
"ground_truth": "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": "Determine if Rolle's theorem applies to the function \\( f(x) = x^2 + 2x + 7 \\) on the interval \\([-6, 4]\\), and if so, find the corresponding value \\( c \\).",
"role": "... | math | {
"ground_truth": "-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": "Let the function $f(x) = -\\frac{1}{3}x^3 + 2ax^2 - 3a^2x + b$ (where constants $a$, $b$ satisfy $0 < a < 1$, $b \\in \\mathbb{R}$). \n$(1)$ Find the intervals of monotonicity a... | math | {
"ground_truth": "\\frac{4}{5} \\leqslant a < 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": "Eight spheres, each of radius $2$, are placed one per octant, and are each tangent to the coordinate planes. Determine the radius of the smallest sphere, centered at the origin, ... | math | {
"ground_truth": "2\\sqrt{3} + 2",
"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": "Wheat costs $72$ cents per pound, and oats cost $36$ cents per pound. If Alex buys 30 total pounds of wheat and oats, and spends a total of $\\$16.20$, how many pounds of wheat d... | math | {
"ground_truth": "15.0\\text{ pounds}",
"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 an odd function $f(x)$ defined on $\\mathbb{R}$, which satisfies $f(x) = f(x + 4)$, and $f(1) = -1$, find the value of $f(1) + f(2) + \\ldots + f(10)$.",
"role": "user"... | 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": "In an increasing list of consecutive integers, the 3rd and 4th numbers in the list add to 11. Calculate the 6th number in the list.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"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": "Evaluate $D(72)$, where $D(n)$ denotes the number of ways of representing the positive integer $n$ as a product \\[n = f_1 \\cdot f_2 \\cdots f_k,\\] with $k \\geq 1$, each $f_i$... | math | {
"ground_truth": "\\textbf{B) 38}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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