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": "In triangle $ABC$, $BC = 6$, $AC = 3$, and $\\angle C = 30^\\circ$. Altitudes $AD$, $BE$, and $CF$ intersect at the orthocenter $H$. Find the ratio $AH:HD$.",
"role": "user"
... | math | {
"ground_truth": "0.155",
"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 method of pairing is a very important mathematical thinking method, which refers to the method of transforming an expression or a part of an expression into a complete square... | 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 that the ratios $\\dfrac{x}{n}$, $\\dfrac{y}{n+1}$, and $\\dfrac{z}{n+2}$ are equal, where $x+y+z=90$, determine the number of triples of positive integers $(x,y,z)$.",
... | 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": "A passenger left his belongings in an automatic storage locker and forgot the number required to retrieve them. He only remembers that the number contained the digits 23 and 37. ... | math | {
"ground_truth": "356",
"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 function $f(x) = \\sin x - \\cos x + x + 1$ where $0 < x < 2\\pi$. Find the intervals of monotonicity and the extrema of the function $f(x)$.",
"role": "user"
}
... | math | {
"ground_truth": "\\pi + 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": "All of the roots of $x^3+ax^2+bx+c$ are positive integers greater than $2$ , and the coeffi\u000ecients satisfy $a+b+c+1=-2009$ . Find $a$",
"role": "user"
}
] | math | {
"ground_truth": "-58",
"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 hyperbola \\(\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1\\) (\\(a>0, b>0\\)) with left and right foci \\(F_{1}\\) and \\(F_{2}\\), respectively, point \\(A\\) is on the... | math | {
"ground_truth": "\\frac{\\sqrt{6}}{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": "A woman has a total of $7500 invested, part at 5% and the remainder at 7%. If her annual returns from both investments are equal, what average rate of interest does she realize o... | math | {
"ground_truth": "B) 5.8%",
"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 distinct terms are in the expansion of \\[(x+y)(a+b+c)(d+e+f)?\\]",
"role": "user"
}
] | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $V=[(x,y,z)|0\\le x,y,z\\le 2008]$ be a set of points in a 3-D space.\nIf the distance between two points is either $1, \\sqrt{2}, 2$ , we color the two points differently... | 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": "Find all triplets of real numbers $(x,y,z)$ that are solutions to the system of equations $x^2+y^2+25z^2=6xz+8yz$ $ 3x^2+2y^2+z^2=240$",
"role": "user"
}
] | math | {
"ground_truth": "(6, 8, 2) \\text{ or } (-6, -8, -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": "It is known that \\(\\frac{\\sin 3 x}{(2 \\cos 2 x+1) \\sin 2 y}=\\frac{1}{5}+\\cos ^{2}(x-2 y)\\) and \\(\\frac{\\cos 3 x}{(1-2 \\cos 2 x) \\cos 2 y}=\\frac{4}{5}+\\sin ^{2}(x-2... | math | {
"ground_truth": "-\\frac{3}{5} \\text{ and } 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": "Given that $S_{n}$ is the sum of the first $n$ terms of the sequence $\\{a_n\\}$, with $a_{1} < 2$, $a_n > 0$, and $6S_{n}= a_{n}^{2}+3a_{n}+2$ for $n \\in \\mathbb{N^*}$. \n$(1... | math | {
"ground_truth": "T_{2n} = 18n^2-3n",
"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": "Tom’s kitchen clock, which is inaccurate, gains time at a constant rate but changes its rate of gain halfway through the day. In the morning, as he starts to read, both his kitch... | math | {
"ground_truth": "\\textbf{(B) }3:20 \\text{ PM}",
"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 the inequality $(-2)^{n}a-3^{n-1}-(-2)^{n} < 0$ holds for any positive integer $n$, then the range of values for the real number $a$ is ________.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2} < a < \\frac{7}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the sequence \\(\\{a_n\\}\\) be defined as follows:\n\\[ \n\\begin{aligned}\n& a_1 = 1, \\quad a_2 = 3, \\\\\n& a_n = 3a_{n-1} - a_{n-2} \\quad (n \\in \\mathbb{Z}_+, n \\geq... | math | {
"ground_truth": "n = 3 \\cdot 2^{2013}",
"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": "For how many integer values of $n$ is the value of $3200\\cdot \\left(\\tfrac{5}{8}\\right)^n$ an integer?",
"role": "user"
}
] | math | {
"ground_truth": "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 circular track with diameter $500$ is externally tangent at a point A to a second circular track with diameter $1700.$ Two runners start at point A at the same time and ru... | math | {
"ground_truth": "501",
"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 \\\\(2i-3\\\\) is a root of the real-coefficient equation \\\\(2x^{2}+px+q=0\\\\), find \\\\(p-q=\\\\) \\_\\_\\_\\_\\_",
"role": "user"
}
] | math | {
"ground_truth": "-14",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\frac{10+11+12}{3}=\\frac{2024+2025+2026}{M}$, calculate the value of $M$.",
"role": "user"
}
] | math | {
"ground_truth": "552",
"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 smallest number, \\( n \\), which is the product of 3 distinct primes where the mean of all its factors is not an integer?",
"role": "user"
}
] | math | {
"ground_truth": "130",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the function $f(x) = \\frac{3e^{|x|}-x\\cos x}{e^{|x|}}$ has a maximum value of $p$ and a minimum value of $q$ on the interval $x \\in [-\\frac{\\pi}{2}, \\frac{\\pi}{... | math | {
"ground_truth": "p + q = 6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a$ be the sum of the numbers: $99 \\times 0.9$ $999 \\times 0.9$ $9999 \\times 0.9$ $\\vdots$ $999\\cdots 9 \\times 0.9$ where the final number in the list is $0.9$ ... | math | {
"ground_truth": "891",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a group of 8 people consisting of 5 females and 3 males, 3 individuals are selected at random to form a committee. What is the probability that all selected members are female... | math | {
"ground_truth": "\\frac{5}{28}",
"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 $f(x) = x^3 + mx^2 - m^2x + 1$ where $m$ is a constant and $m > 0$, and the function has a maximum value of $9$.\n\n(I) Find the value of $m$ and the monotonic... | math | {
"ground_truth": "y - f(\\frac{-2 + \\sqrt{22}}{3}) = 2(x - \\frac{-2 + \\sqrt{22}}{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": "Compute \\[ \\left\\lfloor \\dfrac {2011^3}{2009 \\cdot 2010} - \\dfrac {2009^3}{2010 \\cdot 2011} \\right\\rfloor,\\] where $\\lfloor x \\rfloor$ denotes the greatest integer le... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When Dave walks to school, he averages 90 steps per minute, and each of his steps is 75 cm long. It takes him 16 minutes to get to school. His brother, Jack, going to the same sc... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the parabola C: y^2 = 4x with focus F, and a point A(x_0, y_0) on the parabola C, if |AF| = (5/4)x_0, determine the value of x_0.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We define the distance between numbers as the absolute value of their difference. It is known that the sum of the distances from eight consecutive natural numbers to some number ... | math | {
"ground_truth": "27 \\text{ and } -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": "Fill in numbers in the boxes below so that the sum of the entries in each three consecutive boxes is $2005$ . What is the number that goes into the leftmost box?\n\n[asy]\nsize(... | math | {
"ground_truth": "118",
"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": "Calculate the following expressions:\n1. $(1)(0.001)\\;^{- \\frac {1}{3}}+27\\;^{\\frac {2}{3}}+( \\frac {1}{4})\\;^{- \\frac {1}{2}}-( \\frac {1}{9})^{-1.5}$\n2. $\\frac {1}{2}\... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$ m$ and $ n$ are positive integers. In a $ 8 \\times 8$ chessboard, $ (m,n)$ denotes the number of grids a Horse can jump in a chessboard ( $ m$ horizontal $ n$ vertic... | math | {
"ground_truth": "t = 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": "A triangular array has a new total number of $2080$ coins arranged similarly, with $1$ coin in the first row, $2$ coins in the second row, and so on up to $N$ coins in the $N$th ... | 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": "Let \\( p \\) and \\( q \\) be distinct prime numbers. Determine the integer solutions \\((a, b)\\) of\n\n\\[ \\frac{1}{a} + \\frac{1}{b} = \\frac{1}{pq} \\]",
"role": "user"... | math | {
"ground_truth": "(1 + pq, p^2 q^2 + pq), (p(q + 1), pq(q + 1)), (q(p + 1), pq(p + 1)), (2pq, 2pq), (p^2 q(p + q), q^2 + pq), (q^2 + pq, p^2 + pq), (pq(p + 1), q(p + 1)), (pq(q + 1), p(q + 1)), (p^2 q^2 + pq, 1 + pq)",
"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 functions \\( f:\\{1,2,3,4,5\\} \\rightarrow \\{1,2,3,4,5\\} \\) have the property that \\( f(\\{1,2,3\\}) \\) and \\( f(f(\\{1,2,3\\})) \\) are disjoint?",
"role": ... | math | {
"ground_truth": "94",
"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": "Two circles have radius 5 and 26. The smaller circle passes through center of the larger one. What is the difference between the lengths of the longest and shortest chords of the... | math | {
"ground_truth": "52 - 2\\sqrt{235}",
"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 at the beginning of the time measurement there was \\( m_{0} \\) grams of substance \\( A \\) and \\( 2 m_{0} \\) grams of substance \\( B \\), then after any number of \\( t ... | math | {
"ground_truth": "10 \\text{ years}, 5 \\text{ years}",
"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 ellipse is drawn with major and minor axes of lengths 12 and 6, respectively. Using one focus as a center, a circle is drawn that is tangent to the ellipse, with no part of th... | math | {
"ground_truth": "3\\sqrt{4 - 2\\sqrt{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": "An odd function $f(x)$ is increasing on the interval $[3,7]$ and has a maximum value of 8 and a minimum value of -1 on the interval $[3,6]$. Calculate $2f(-6) + f(-3)$.",
"ro... | math | {
"ground_truth": "-15",
"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 $x \\geq \\frac{3}{2}$, find the minimum value of $\\frac{2x^2 - 2x + 1}{x - 1}$.",
"role": "user"
}
] | math | {
"ground_truth": "2\\sqrt{2} + 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": "Find the derivative.\n\n$$\ny=\\frac{1}{12} \\cdot \\ln \\frac{x^{4}-x^{2}+1}{\\left(x^{2}+1\\right)^{2}}-\\frac{1}{2 \\sqrt{3}} \\operatorname{arctg} \\frac{\\sqrt{3}}{2 x^{2}-1... | math | {
"ground_truth": "y' = \\frac{x^{3}}{\\left(x^{4} - x^{2} + 1\\right) \\left( x^{2} + 1 \\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": "Consider the data set $[8, 22, 35, 35, 42, 44, 44, 47, 55, 62]$. The median $Q_2 = 43$, the first quartile $Q_1 = 35$, and the third quartile $Q_3 = 47$. An outlier in a data set... | math | {
"ground_truth": "\\textbf{(B)}\\ 1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a tennis tournament, each competitor plays against every other competitor, and there are no draws. Call a group of four tennis players ``ordered'' if there is a clear winner a... | 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 S\\_n be the sum of the first n terms of the sequence {a\\_n}, and S\\_n = $\\frac{3}{2}$(a\\_n - 1) (n ∈ N*),\n(1) Find the general term formula for {a\\_n};\n(2) The sequen... | math | {
"ground_truth": "\\frac{n}{2(n+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": "Find the value of \\( k \\) so that the line \\( 6x - 4y + k = 0 \\) is tangent to the parabola \\( y^2 = 16x \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{32}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the hyperbola $\\frac{x^{2}}{a^{2}} - \\frac{y^{2}}{5} = 1$ with its right focus at $(3, 0)$, find its eccentricity.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{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": "A large rectangle has side lengths of $(2x + 14)$ and $(2x + 10)$. Within this rectangle, there is a rectangular hole with side lengths of $(4x - 6)$ and $(2x - 4)$. Additionally... | math | {
"ground_truth": "-3x^2 + 82x + 125",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $g : \\mathbb{R} \\to \\mathbb{R}$ be a function such that\n\\[g(xg(y) + 2x) = 2xy + g(x)\\] for all $x,$ $y.$\nLet $n$ be the number of possible values of $g(3),$ and let $s... | 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": "Given the cubic polynomial $3x^3 + 6x^2 - 42x + 27 = 0$, find the sum of all the roots.\nA) -6 \nB) -2 \nC) 0 \nD) 2 \nE) 6",
"role": "user"
}
] | math | {
"ground_truth": "B) -2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the three points $A(-1,-2)$, $B(4,8)$, and $C(5,x)$ are on the same line, calculate the value of the real number $x$.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"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 $f(x)= \\sqrt {x-1}+\\lg (3-x)$, determine the domain of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "[1,3)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose \\( x_{1}, x_{2}, \\cdots, x_{n}, y_{1}, y_{2}, \\cdots, y_{n}, z_{1}, z_{2}, \\cdots, z_{n} \\) are all 1 or -1, and \\( x_{1} y_{1}+x_{2} y_{2}+\\cdots+x_{n} y_{n}=0 \\... | math | {
"ground_truth": "n = 4k",
"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 indefinite integral\n\n$$\n\\int \\operatorname{ctg} x \\ln \\sin x \\, dx\n$$",
"role": "user"
}
] | math | {
"ground_truth": "\\int \\operatorname{ctg} x \\ln \\sin x \\, dx = \\frac{\\ln^2 (\\sin x)}{2} + 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": "Given two positive integers $x$ and $y$, where $x$ is divided by $y$ and the quotient is $u$ and the remainder is $v$, determine the remainder when $(x+3uy+4)$ is divided by $y$.... | math | {
"ground_truth": "v + 4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a positive number $x$ and a positive number $y$, and that $x\\%$ of $y$ is $5$ and $y = 2x + 10$, solve for $x$.",
"role": "user"
}
] | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Use the Horner's method to calculate the value of the polynomial \\\\(f(x)=x^{5}+3x^{4}-5x^{3}+7x^{2}-9x+11\\\\) when \\\\(x=4\\\\).",
"role": "user"
}
] | math | {
"ground_truth": "1559",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The weights of four weights form an increasing geometric progression consisting of positive numbers. How can you determine the heaviest weight with no more than two weighings?",
... | math | {
"ground_truth": "aq^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": "Proposition p: \"There exists a real number $m$ such that the equation $x^2+mx+1=0$ has real roots.\" What is the negation of proposition p?",
"role": "user"
}
] | math | {
"ground_truth": "\\text{For all real numbers } m, \\text{ the equation } x^2+mx+1=0 \\text{ does not have real roots.}",
"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 $4251_6 + 2343_6$. Express your answer in base 6.",
"role": "user"
}
] | math | {
"ground_truth": "11004_6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If there exists a real number $x$ in the interval $[0,1]$ such that $2x(3x+a)<1$, then the range of values for $a$ is ___.",
"role": "user"
}
] | math | {
"ground_truth": "a \\in (-\\infty, 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": "Maria buys 5 apples, each priced at $0.75. If she pays with a $10 bill, calculate the amount of change that Maria will receive.",
"role": "user"
}
] | math | {
"ground_truth": "\\textdollar 6.25",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle with center $C$ and radius 10 units, and a point \\(R\\) located 15 units away from $C$, are given. What is the locus of the midpoint of the segment connecting \\(R\\) t... | math | {
"ground_truth": "B) Circle with center (0,10) and radius 3.3 units",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that four complex numbers lie at the vertices of a square in the complex plane, with three of the numbers being $1+2i, -2+i$, and $-1-2i$, determine the fourth number.",
... | math | {
"ground_truth": "2-i",
"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": "A train travels the first part of its journey, covering 150 miles at a speed of 50 mph. After a brief stop of 30 minutes, it continues to travel another 240 miles at a speed of 8... | math | {
"ground_truth": "C) 6.5 hours",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate \\(\\left\\lfloor \\sqrt{2}+\\sqrt[3]{\\frac{3}{2}}+\\sqrt[4]{\\frac{4}{3}}+\\ldots+\\sqrt[2009]{\\frac{2009}{2008}} \\right\\rfloor\\), where \\(\\left\\lfloor x \\rig... | math | {
"ground_truth": "2008",
"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 dart board is a circular disc with a radius of 10 units and contains a central square target. The square has its vertices on the circle. Calculate the probability that a dart t... | math | {
"ground_truth": "\\frac{2}{\\pi}",
"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 ${\\left( \\sqrt[3]{x}+ \\frac{1}{x}\\right)}^{n}$, the sum of the coefficients of all terms is $256$.\n(1) Find $n$.\n(2) Find the constant term in ... | math | {
"ground_truth": "n=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": "Solve the system of equations\n\n$$\n\\begin{aligned}\nx + y & = a \\\\\n\\tan x \\cdot \\tan y & = b\n\\end{aligned}\n$$\n\nwhere \\(a\\) and \\(b\\) are real parameters.",
... | math | {
"ground_truth": "y = \\frac{\\pi}{2} + k\\pi - x",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x) = x^2 + x + 1$ . Determine the ordered pair $(p,q)$ of primes satisfying $f(p) = f(q) + 242$ .\n\n*2016 CCA Math Bonanza #8*",
"role": "user"
}
] | math | {
"ground_truth": "(61, 59)",
"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": "Suppose there are $2017$ spies, each with $\\frac{1}{2017}$ th of a secret code. They communicate by telephone; when two of them talk, they share all information they know wit... | math | {
"ground_truth": "4030",
"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 the function \\( f(x) = \\left\\{\n\\begin{array}{ll}\n\\frac{1}{p} & \\text{if } x = \\frac{q}{p}, \\\\\n0 & \\text{if } x \\neq \\frac{q}{p},\n\\end{array}\n\\right. \\)\nw... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve for $x$ in the equation\n\\[ 4^{(\\sqrt{16^x})} = 16^{(\\sqrt{2^x})}. \\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $S_n$ and $T_n$ respectively be the sums of the first $n$ terms of arithmetic sequences $\\{a_n\\}$ and $\\{b_n\\}$, and $\\frac {S_{n}}{T_{n}} = \\frac {n}{2n+1}$ for $n \... | math | {
"ground_truth": "\\frac {11}{23}",
"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": "Marius is organizing his eight leopards, each a different height, for another wildlife photo. This time, the two shortest leopards still insist on being at the ends of the line-u... | math | {
"ground_truth": "960 \\text{ ways.}",
"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": "It is clear that if we take a random natural number from a sufficiently long segment of the natural number series, the probability that this number will be divisible by 10 will b... | math | {
"ground_truth": "\\frac{1}{19}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that {a<sub>n</sub>} is an arithmetic sequence, S<sub>n</sub> is the sum of its first n terms, and S<sub>11</sub> = \\frac {22π}{3}, find the value of tan(a<sub>6</sub>)."... | math | {
"ground_truth": "-\\frac{1}{\\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": "Let $\\mathbf{M}$ be a matrix and let $\\mathbf{v}$ and $\\mathbf{w}$ be vectors such that\n\\[\\mathbf{M} \\mathbf{v} = \\begin{pmatrix} 5 \\\\ 1 \\end{pmatrix} \\quad \\text{an... | math | {
"ground_truth": "\\begin{pmatrix} 5 \\\\ -7 \\end{pmatrix}",
"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 vectors $\\overrightarrow {OA}$ and $\\overrightarrow {OB}$ satisfy $|\\overrightarrow {OA}|=|\\overrightarrow {OB}|=1$, $\\overrightarrow {OA} \\perp \\overrightarrow {OB}... | math | {
"ground_truth": "1+\\sqrt {2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $$f(x)=\\sin x\\cos x+ \\sqrt {3}\\sin^{2}x- \\frac { \\sqrt {3}}{2}$$.\n(1) Find the range of the function $f(x)$ when $x\\in[0, \\frac {π}{2}]$.\n(2) In tria... | math | {
"ground_truth": "BC=3 \\sqrt {2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given complex numbers $z_{1}$ and $z_{2}$ correspond to points $z_{1}(1,1)$ and $z_{2}(0,1)$ in the complex plane, calculate the imaginary part of $\\frac{{z}_{1}}{{z}_{2}}$.",
... | 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 six unit squares are arranged in a 2x3 rectangle on the coordinate plane, with the lower left corner at the origin. A straight line, extending from (d,0) to (4,3), divides ... | math | {
"ground_truth": "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": "What fraction of the area of the circumscribed circle of an equilateral triangle with side length \\(a\\) is covered by the circles drawn around the vertices with radius \\(\\fra... | math | {
"ground_truth": "0.914",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that there are $n > 15$ students in a class with an average score of 10 and a subgroup of 15 students with an average score of 16, determine the average score of the remain... | math | {
"ground_truth": "\\frac{10n - 240}{n-15}",
"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": "Kolya and Zhenya agreed to meet in the metro in the first hour of the afternoon. Kolya arrives at the meeting place between noon and one o'clock, waits 10 minutes, and leaves. Zh... | math | {
"ground_truth": "\\frac{19}{60}",
"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 total number of positive integers that are divisors of both $35$ and $64.$",
"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": "Find the maximum of $x+y$ given that $x$ and $y$ are positive real numbers that satisfy \\[x^3+y^3+(x+y)^3+36xy=3456.\\]",
"role": "user"
}
] | math | {
"ground_truth": "12",
"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 \\\\(f(x)= \\dfrac{4^{x}}{4^{x}+2}\\\\). By using the method of reverse order addition, the value of \\\\(f\\left( \\dfrac{1}{11} \\right)+f\\left( \\dfrac{2}{11} \\right)+\\... | 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": "Find the number of ordered triples of sets $(T_1, T_2, T_3)$ such that\n1. each of $T_1, T_2$ , and $T_3$ is a subset of $\\{1, 2, 3, 4\\}$ ,\n2. $T_1 \\subseteq T_2 \\cup... | math | {
"ground_truth": "625",
"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 general, if there are $d$ doors in every room (but still only 1 correct door) and $r$ rooms, the last of which leads into Bowser's level, what is the expected number of doors ... | math | {
"ground_truth": "\\frac{d(d^r - 1)}{d - 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": "Let $N$ be a positive integer whose decimal representation contains $11235$ as a contiguous substring, and let $k$ be a positive integer such that $10^k>N$ . Find the min... | math | {
"ground_truth": "89",
"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": "Determine the value of $\\sin 45^{\\circ}\\sin 105^{\\circ}+\\sin 45^{\\circ}\\sin 15^{\\circ}$.",
"role": "user"
}
] | 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": "The integers \\( a, b, c, d, e, f, \\) and \\( g \\), none of which is negative, satisfy the following five simultaneous equations:\n$$\n\\begin{array}{l}\na + b + c = 2, \\\\\nb... | 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": "Given a $100$ dollar coat on sale for 20% off, an additional 5 dollars are taken off the sale price by using a discount coupon, and a sales tax of 8% is paid on the final selling... | math | {
"ground_truth": "81",
"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": "Suppose \\( a \\) and \\( b \\) are positive integers not exceeding 100 such that\n\\[ ab = \\left(\\frac{\\operatorname{lcm}(a, b)}{\\operatorname{gcd}(a, b)}\\right)^2. \\]\n\n... | math | {
"ground_truth": "78",
"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": "It takes Brian 80 seconds to walk down an escalator when it is not operating, and only 30 seconds to walk down the escalator when it is operating. Calculate the time it takes for... | math | {
"ground_truth": "48",
"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": "Seven socks, colored blue, brown, black, red, purple, green, and yellow are in a drawer. In how many different ways can we select three socks from the drawer if the order of the ... | 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": "Solve for $x$: $10 - 2x = 16$.",
"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": "Given a positive integer $k$ , a pigeon and a seagull play a game on an $n\\times n$ board. The pigeon goes first, and they take turns doing the operations. The pigeon will ch... | math | {
"ground_truth": "k \\leq n \\leq 2k - 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the smallest possible natural number $n$ for which the equation $x^2 -nx + 2014 = 0$ has integer roots?",
"role": "user"
}
] | math | {
"ground_truth": "91",
"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 points O(0,0), A(1,1), and line l: x-y+1=0 with point P on line l, find the minimum value of |PA|+|PO|.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
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