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": "If set $A = \\{1, 2, 3\\}$, calculate the number of non-empty sets $B$ that satisfy $A \\cup B = A$.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"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 triangular plot of land is represented in a drawing where 1 cm equals 3 miles. The triangle has a base of 12 cm and a height of 8 cm. How large is the actual plot of land in sq... | math | {
"ground_truth": "1118.88 \\text{ km}^2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\tan \\alpha = 3$, calculate the following expression: $$\\frac {\\sin(\\alpha-\\pi)+\\cos(\\pi-\\alpha)}{\\sin( \\frac {\\pi}{2}-\\alpha )+\\cos( \\frac {\\pi}{2}+\... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given quadrilateral $EFGH$, $EF = 6$, $FG = 18$, $GH = 6$, and $HE = 10$, with angle $EFG$ as a right angle, calculate the length of $EG$.",
"role": "user"
}
] | math | {
"ground_truth": "6\\sqrt{10}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Rationalize the denominator of \\(\\frac{\\sqrt{50}}{\\sqrt{25}-\\sqrt{5}}\\). The answer can be written as \\(\\frac{A\\sqrt{B}+C}{D}\\), where \\(A\\), \\(B\\), \\(C\\), and \\... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $y=ax^{2}+b$, the slope of the tangent line at point $(1,3)$ is $2$. Find $\\frac{a}{b}$____.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{a}{b} = \\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the system of equations. Provide the largest value of $y$ in the solution.\n\n$$\n\\left\\{\\begin{array}{l}\nx^{2}+3 x y-y^{2}=27 \\\\\n3 x^{2}-x y+y^{2}=27\n\\end{array}\... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a fair 8-sided die labeled from 1 to 8, find the probability that every even number (2, 4, 6, 7, 8) appears at least once before the first occurrence of an odd number (1, 3... | math | {
"ground_truth": "\\frac{15625}{32768}",
"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": "Acute-angled $\\triangle ABC$ is inscribed in a circle with center at $O$. The measures of arcs are $\\stackrel \\frown {AB} = 80^\\circ$ and $\\stackrel \\frown {BC} = 100^\\cir... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the base edge length of a regular hexagonal pyramid is $3$, and its side edge length is $5$, what is the volume of the pyramid?",
"role": "user"
}
] | math | {
"ground_truth": "18\\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": "In Box A, there are 2 balls numbered 1 and 2. In Box B, there are 3 balls numbered 1, 2, and 3. If one ball is randomly drawn from each box, what is the probability that the sum ... | math | {
"ground_truth": "B: \\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": "A farmer purchased 800 sheep. He sold 750 of them for the price he paid for all 800 sheep. The remaining 50 sheep were sold at a price 10% higher per head than the other 750 shee... | math | {
"ground_truth": "C) 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": "Let $f(x)=x^2+3x+2$ and let $S$ be the set of integers $\\{0, 1, 2, \\dots , 25 \\}$. Find the number of members $s$ of $S$ such that $f(s)$ has remainder zero when divided by $6... | math | {
"ground_truth": "17",
"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": "Dima saw a strange clock in a museum (see the diagram). Unlike regular clocks, this one has no numbers on its dial, and it is impossible to tell the top of the clock; moreover, t... | math | {
"ground_truth": "4:50",
"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 positive integer $n$ is *magical* if $\\lfloor \\sqrt{\\lceil \\sqrt{n} \\rceil} \\rfloor=\\lceil \\sqrt{\\lfloor \\sqrt{n} \\rfloor} \\rceil$ . Find the number of magical i... | math | {
"ground_truth": "1330",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each of 8 balls is randomly and independently painted either black or white with equal probability. Calculate the probability that every ball is different in color from exactly h... | math | {
"ground_truth": "\\frac{35}{128}",
"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": "If $A=30^\\circ$, $B=40^\\circ$, and $C=5^\\circ$, then calculate the value of $(1+\\tan A)(1+\\tan B)(1+\\tan C)$.",
"role": "user"
}
] | math | {
"ground_truth": "3 + \\sqrt{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A right triangle has an area of 150 square units, and a leg length of 30 units. What is the perimeter of the triangle, in units?",
"role": "user"
}
] | math | {
"ground_truth": "40 + 10\\sqrt{10}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given Lucas has saved some money from his summer job to buy several books for school. He spends one fourth of his money to buy one half of the books he wants. What fraction of hi... | math | {
"ground_truth": "\\frac{1}{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": "In square $ABCD$ with side length $2$ , let $M$ be the midpoint of $AB$ . Let $N$ be a point on $AD$ such that $AN = 2ND$ . Let point $P$ be the intersection of segm... | math | {
"ground_truth": "\\frac{2}{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": "If the function $f(x)=\\sin (ωx+φ)(ω > 0,|φ| < \\dfrac{π }{2})$ is a monotonically decreasing function in the interval $[\\dfrac{π }{6},\\dfrac{2π }{3}]$, and the function value ... | math | {
"ground_truth": "\\dfrac{\\sqrt{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 \\(a, b, c\\) be real numbers such that\n\\[ 3ab + 2 = 6b, \\quad 3bc + 2 = 5c, \\quad 3ca + 2 = 4a. \\]\n\nSuppose the only possible values for the product \\(abc\\) are \\(... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all integer polynomials $P(x)$ , the highest coefficent is 1 such that: there exist infinitely irrational numbers $a$ such that $p(a)$ is a positive integer.",
"rol... | math | {
"ground_truth": "P(x) = x + a_0",
"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 $x$ is a positive integer less than 150, how many solutions does the congruence $x + 17 \\equiv 75 \\pmod{46}$ have?",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Output statement 2a from problem 210.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{The traveler will visit the line } NN \\text{ with probability } 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": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. Given that $a = 2$, $3b\\sin C - 5c\\sin B\\cos A = 0$, the maximum area of $\\tri... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function\n$$\nf(x) = \\log_a \\left(ax^2 - x + \\frac{1}{2}\\right)\n$$\nis always positive in the interval $[1,2]$, find the range of the real number $a$.",
"role"... | math | {
"ground_truth": "\\left(\\frac{1}{2}, \\frac{5}{8}\\right) \\cup \\left(\\frac{3}{2}, +\\infty\\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Philena and Nathan are playing a game. First, Nathan secretly chooses an ordered pair $(x, y)$ of positive integers such that $x \\leq 20$ and $y \\leq 23$ . (Philena knows ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given three points A, B, and C on the parabola y^2 = 4x, the slopes of AB, BC, and CA are 3, 6, and -2, respectively. Find the coordinates of the centroid of △ABC.",
"role": ... | math | {
"ground_truth": "(\\frac{14}{27}, 0)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the functions $f(x)=5^{|x|}$ and $g(x)=ax^{2}-x$ $(a \\in \\mathbb{R})$, if $f[g(1)]=1$, then determine the value of $a$.",
"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": "Given a sequence $\\{a_{n}\\}$ with the sum of the first $n$ terms denoted as $S_{n}$, $a_{1}=3$, $\\frac{{S}_{n+1}}{{S}_{n}}=\\frac{{3}^{n+1}-1}{{3}^{n}-1}$, $n\\in N^{*}$. \n$... | math | {
"ground_truth": "\\frac{9}{32}",
"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": "Calculate: $\\log _{2}1+\\log _{3}9=\\_\\_\\_\\_\\_\\_.(Enter the answer as a number)$",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle \\(ABC\\), the angle bisectors at vertices \\(A\\) and \\(C\\) intersect at point \\(D\\). Find the radius of the circumcircle of triangle \\(ABC\\) if the radius of ... | 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": "An infinite geometric series has a common ratio of $\\frac{1}{4}$ and a sum of 80. What is the first term of the series?",
"role": "user"
}
] | math | {
"ground_truth": "60",
"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 $-2$ is a solution (root) of $x^3+hx-12=0$, find the value of $h$.",
"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": "How to cut off a triangle equal to one-fourth of a given triangle by a line parallel to one of its sides? How to cut off a triangle equal to its $n$-th part by such a line? How t... | math | {
"ground_truth": "\\text{height given by }\\frac{h}{\\sqrt{n}} \\text{ and removing an area of }\\frac{n-1}{n} A_{\\text{triangle}}",
"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 surface integral of the second kind\n\n$$\n\\iint_{S} x \\, dy \\, dz + y \\, dz \\, dx + z \\, dx \\, dy\n$$\n\nwhere \\( S \\) is the inner side of the ellipsoid ... | math | {
"ground_truth": "-4 \\pi a b c",
"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 clerts are there in a right angle?",
"role": "user"
}
] | math | {
"ground_truth": "125",
"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": "There are four different taps that can fill a swimming pool. If the first and the second taps are turned on simultaneously, the pool fills up in 2 hours. If the second and the th... | math | {
"ground_truth": "\\frac{12}{5}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the integral equation:\na) \\(y(\\tau)=\\int_{0}^{t} y(\\tau) \\, d\\tau + 1\\);\nb) \\(\\int_{0}^{t} y(\\tau) \\sin(t-\\tau) \\, d\\tau = 1 - \\cos t\\).",
"role": "us... | math | {
"ground_truth": "y(t) = 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": "Consider 2016 points arranged on a circle. We are allowed to jump ahead by 2 or 3 points in clockwise direction.\n\nWhat is the minimum number of jumps required to visit all poin... | math | {
"ground_truth": "2017",
"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 length of the major axis of an ellipse is $12 \\mathrm{~cm}$, and the minor axis is $10 \\mathrm{~cm}$. If we use the major axis as the x-axis and one of its vertices as the ... | math | {
"ground_truth": "31.25 \\text{ cm}^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": "Define a modified Lucas sequence as follows: \\( M_0 = 3, M_1 = 1 \\), and each subsequent term is given by \\( M_n = M_{n-1} + M_{n-2} + 2 \\). Compute the units digit of \\( M_... | 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": "Determine the range of the function $f(x) = \\left(\\frac{1}{2}\\right)^{-x^2 + 4x + 1}$ for $0 \\leq x \\leq 3$.",
"role": "user"
}
] | math | {
"ground_truth": "\\left[\\frac{1}{32}, \\frac{1}{2}\\right]",
"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 knight begins on the lower-left square of a standard chessboard. How many squares could the knight end up at after exactly 2009 legal knight's moves? (A knight's move is 2 squa... | math | {
"ground_truth": "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": "Given the repeating base-$k$ representation of the fraction $\\frac{7}{51}$ is $0.\\overline{23}_k$, find the value of $k$ in the base-$k$ system.",
"role": "user"
}
] | math | {
"ground_truth": "16",
"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 $a^{2}-2a=1$, calculate the value of $3a^{2}-6a-4$.",
"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": "A semicircle of radius 3 cm sits atop a flat base that partly overlaps another semicircle (just its top sits just below) with diameter 8 cm. Find the area of the $\\textit{lune}$... | math | {
"ground_truth": "3.5\\pi \\text{ cm}^2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Nathaniel and Obediah play a game in which they take turns rolling a fair six-sided die and keep a running tally of the sum of the results of all rolls made. A player wins if, af... | math | {
"ground_truth": "\\frac{5}{11}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a regular $n$-sided polygon $A_{1} A_{2} \\cdots A_{n}$ with side length $a$, find its covering radius.",
"role": "user"
}
] | math | {
"ground_truth": "r = \\frac{a}{2 \\sin \\frac{\\pi}{n}}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers \\( n \\) such that every integer formed by \\( n-1 \\) ones and one seven is a prime number.",
"role": "user"
}
] | math | {
"ground_truth": "n = 1 \\text{ and } n = 2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of positive integers $n$ such that the highest power of $7$ dividing $n!$ is $8$ .",
"role": "user"
}
] | 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": "Given polynomials of the form $x^5 + ax^4 + bx^3 + cx^2 + dx + 2020$, where $a$, $b$, $c$, and $d$ are real numbers, how many have the property that whenever $r$ is a root, so is... | math | {
"ground_truth": "2",
"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 rhombus $ABCD$ . A point $M$ is chosen on its side $BC$ . The lines, which pass through $M$ and are perpendicular to $BD$ and $AC$ , meet line $AD$ in points ... | math | {
"ground_truth": "\\frac{BM}{MC} = \\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In order to encourage water conservation, a water supply company has set the following pricing standards for tap water: For each household, the part of the monthly water usage no... | math | {
"ground_truth": "\\text{Household A: 14 yuan, Household B: 6.9 yuan, Household C: 3.15 yuan}",
"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 units digit of $27^3 - 17^3$?",
"role": "user"
}
] | math | {
"ground_truth": "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": "Eight teams play a soccer tournament where each team again plays every other team exactly once. Each game results in a win or a loss, with no ties, and every team has an equal ch... | math | {
"ground_truth": "2841",
"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": "Four friends buy a gift together for $<<84>>. The first friend pays one third of the sum of the amounts paid by the other three friends; the second friend pays one fourth of the ... | math | {
"ground_truth": "\\textdollar 40",
"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": "If $\\alpha \\in \\left(\\pi, \\frac{3}{2}\\pi\\right)$, simplify $\\sqrt{\\frac{1}{2} + \\frac{1}{2}\\sqrt{\\frac{1}{2} + \\frac{1}{2}\\cos 2\\alpha}}$ to \\_\\_\\_\\_\\_\\_.",
... | math | {
"ground_truth": "\\sin \\frac{\\alpha}{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": "Given the complex number $z$ that satisfies $\\bar{z}i = 3 + 4i$ (where $i$ is the imaginary unit), find the value of $|z|$.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A two-digit number is even, and the sum of its digits is subtracted from the number itself. The units digit of the result is $4$. Determine how many two-digit numbers satisfy the... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sequence of nonnegative integers \\(a_1 < a_2 < \\ldots < a_k\\) such that \\(\\frac{2^{225}+1}{2^{15}+1} = 2^{a_1} + 2^{a_2} + \\ldots + 2^{a_k}\\), determine the valu... | math | {
"ground_truth": "113",
"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": "What is the largest quotient that can be obtained using two numbers from the set $\\{ -30, -4, 0, 3, 5, 10 \\}$?",
"role": "user"
}
] | math | {
"ground_truth": "7.5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $(2)_x(3)^4=)_a(_{0}+)_a(_{1}x+)_a(_{2}x^{2}+)_a(_{3}x^{3}+)_a(_{4}x^{4}$, then $(a_{0}+a_{2}+a_{4})^2-(a_{1}+a_{2})^2=$______.",
"role": "user"
}
] | math | {
"ground_truth": "625",
"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 square and a regular pentagon have the same perimeter. Let $C$ be the area of the circle circumscribed about the square, and $D$ the area of the circle circumscribed around the... | math | {
"ground_truth": "\\frac{25(5-2\\sqrt{5})}{128}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all natural numbers that cannot be represented as the sum of three natural numbers whose product is a perfect square.",
"role": "user"
}
] | math | {
"ground_truth": "1, 2, 4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Siva has the following expression, which is missing operations: $$ \\frac12 \\,\\, \\_ \\,\\,\\frac14 \\,\\, \\_ \\,\\, \\frac18 \\,\\, \\_ \\,\\,\\frac{1}{16} \\,\\, \\_ \\,... | math | {
"ground_truth": "39",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangular prism with dimensions $20$ cm by $1$ cm by $7$ cm is made with blue $1$ cm unit cubes. The outside of the rectangular prism is coated in gold paint. If a cu... | math | {
"ground_truth": "\\frac{9}{35}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Rationalize the denominator of the expression:\n$$\\frac{5}{\\sqrt[3]{3}+\\sqrt[3]{27}}$$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5\\sqrt[3]{9}}{12}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that in the convex quadrilateral $PQRS$, $PQ = 24, \\angle P = 45^\\circ$, and $\\overline{PQ} \\parallel \\overline{RS}$, the lengths of the sides, in some order, form a g... | math | {
"ground_truth": "53",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a string of \\(P\\) 's and \\(Q\\) 's, the value is defined to be the product of the positions of the \\(P\\) 's. For example, the string \\(P P Q P Q Q\\) has value \\(1 \\c... | math | {
"ground_truth": "\\frac{2005^{1002}}{2004!}",
"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 $f(x)$ satisfies $f(x+y)-f(y)=(x+2y-2)x$ for all real numbers $x$, $y$, and $f(1)=0$.\n\n$(1)$ Find the expression for the function $f(x)$; \n$(2)$ Let $g(x)=... | math | {
"ground_truth": "k\\geqslant 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": "Consider the 3x3 matrix given by \n\\[\\left[\\begin{matrix} x & 9 & y\\\\ 8 & z & 6\\\\ 3 & 5 & 7\\end{matrix}\\right]\\]\nwhere \\(x\\), \\(y\\), and \\(z\\) are integers. If i... | math | {
"ground_truth": "B) 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify $\\frac{cx(bx^2 + 3a^2y^2 + c^2z^2) + bz(bx^2 + 3c^2x^2 + a^2y^2)}{cx + bz}$.",
"role": "user"
}
] | math | {
"ground_truth": "bx^2 + a^2y^2 + c^2z^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": "How many ways are there to arrange the $6$ permutations of the tuple $(1, 2, 3)$ in a sequence, such that each pair of adjacent permutations contains at least one entry in co... | math | {
"ground_truth": "144",
"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": "Alec needs to buy 20 identical caps and has $\\$200$. The store charges a $\\$5$ entrance fee. Each cap has the same whole-dollar price. Considering an $8\\%$ sales tax on the pr... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The remainder when the polynomial \\( x^{12} - x^{6} + 1 \\) is divided by \\( x^{2} - 1 \\) is calculated.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Consider two solid spherical balls, one centered at $\\left( 0, 0, 5 \\right)$ with a radius 4, and the other centered at $(0,0,0)$ with a radius 3. How many points $(x,y,z)$ wit... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\(x \\cdot (x+y) = x^2 + 12\\), what is the value of \\(xy\\)?",
"role": "user"
}
] | math | {
"ground_truth": "12",
"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": "Optimus Prime and Bumblebee start simultaneously from points \\( A \\) and \\( B \\) respectively, traveling towards each other. As robots, their speed ratio is 4:3. After meetin... | math | {
"ground_truth": "350 \\text{ kilometers}",
"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 functions $f(x)=-x^{2}+6x+m$ and $g(x)=2\\sin(2x+\\frac{π}{3})$. For any $x_{0}∈[0,\\frac{π}{4}]$, there exist $x_{1}$ and $x_{2}\\in \\left[-1,3\\right]$, such that $f... | math | {
"ground_truth": "[-7, 8]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the units digit of $8^{2022}$?",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A palindrome is a natural number that reads the same forwards and backwards in the decimal system (e.g. 1129211 or 7337). Determine all pairs $(m, n)$ of natural numbers so that ... | math | {
"ground_truth": "\\text{Either } m \\leq 9 \\text{ or } n \\leq 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": "An arithmetic sequence with a common difference \\( r \\) is a sequence of numbers \\( s_{0}, s_{1}, s_{2}, \\ldots \\) that satisfies \\( s_{k+1} = s_{k} + r \\) for every index... | math | {
"ground_truth": "s_n = s_0 + nr",
"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 positive integer $n$ is called *Olympic*, if there exists a quadratic trinomial with integer coeffecients $f(x)$ satisfying $f(f(\\sqrt{n}))=0$ . Determine, with proof, th... | math | {
"ground_truth": "2010",
"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 $E$ be a set of $n$ points in the plane $(n \\geq 3)$ whose coordinates are integers such that any three points from $E$ are vertices of a nondegenerate triangle whos... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a right triangle with the right angle at $C$. Let $M$ be the midpoint of $[AB]$ and $H$ be the foot of the altitude from $C$. Given that $CH=1$ and $CM=2$, determine... | math | {
"ground_truth": "15^\\circ \\text{ or } 75^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a line \\( l \\) intersects an ellipse \\( C: \\frac{x^{2}}{2}+y^{2}=1 \\) at points \\( A \\) and \\( B \\), and \\( O \\) is the origin of the coordinates.\n1. Find the m... | math | {
"ground_truth": "2 \\sqrt{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": "Assume the updated table shows the 1990 U.S. population, in millions, for each region by ethnic group. To the nearest percent, what percent of the U.S. Asian population lived in ... | math | {
"ground_truth": "B) 46%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the binomial expansion of $(a+b)^6$, calculate the sum of the numerical coefficients.",
"role": "user"
}
] | math | {
"ground_truth": "64",
"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": "Luciano uses 150 grams of apple juice, 200 grams of sugar, and 300 grams of water to make a fruity drink. There are 50 calories in 100 grams of apple juice and 400 calories in 10... | math | {
"ground_truth": "(B) 404 calories",
"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 $x^4 + 6x^3 + 4px^2 + 2qx + r$ be divisible by $x^3 + 4x^2 + 2x + 1$. Determine the value of $(p + q)r$.\nA) -5\nB) 0\nC) 2.5\nD) 5",
"role": "user"
}
] | math | {
"ground_truth": "B) 0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For all integers $n$ greater than 1, define $a_n = \\dfrac{1}{\\log_n 5000}$. Let $b = a_2 + a_3 + a_5$ and $c = a_{8} + a_{9} + a_{10} + a_{12}$. Find $b - c.$",
"role": "us... | math | {
"ground_truth": "-\\log_{5000} 288",
"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 fruit store received 250 kilograms of peaches, which is 50 kilograms more than twice the amount of pears received. How many kilograms of pears did the store receive?",
"rol... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For what digit $d$ is the six-digit number $56789d$ a multiple of 9?",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In quadrilateral $ABCD$ , $AB \\parallel CD$ and $BC \\perp AB$ . Lines $AC$ and $BD$ intersect at $E$ . If $AB = 20$ , $BC = 2016$ , and $CD = 16$ , find the area of... | math | {
"ground_truth": "8960",
"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 circular face of a clock with radius 20 cm and a circular disk with radius 10 cm externally tangent to the clock face at 12 o'clock, and the disk rolling clockwise arou... | math | {
"ground_truth": "4",
"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": "Determine the value of \\(x\\) that satisfies the equation \\(\\frac{3}{x-2} = \\frac{6}{x-3}\\).\nA) \\(x = 0\\) \nB) \\(x = 1\\) \nC) \\(x = 2\\) \nD) \\(x = 3\\) \nE) No r... | math | {
"ground_truth": "\\text{B) } x = 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 store sells a type of notebook. The retail price for each notebook is 0.30 yuan, a dozen (12 notebooks) is priced at 3.00 yuan, and for purchases of more than 10 dozen, each do... | math | {
"ground_truth": "51.30",
"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 constants $A,$ $B,$ $C,$ and $D$ such that\n\\[\\frac{x^2 - 9}{(x - 2)(x - 3)(x - 5)(x + 1)} = \\frac{A}{x - 2} + \\frac{B}{x - 3} + \\frac{C}{x - 5} + \\frac{D}{x + 1}.\\]"... | math | {
"ground_truth": "\\left(-\\frac{5}{9}, 0, \\frac{4}{9}, -\\frac{1}{9}\\right)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
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