data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "In acute triangle $ABC$, $\\sin A=\\frac{2\\sqrt{2}}{3}$. Find the value of $\\sin^{2}\\frac{B+C}{2}+\\cos (3\\pi -2A)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{13}{9}"
} | {
"split": "train",
"index": 24949,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At 11:00 a.m. how many degrees are in the smaller angle formed by the minute hand and the hour hand of the clock? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 24950,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A geometric sequence of positive integers is formed for which the first term is 2 and the fifth term is 162. What is the sixth term of the sequence? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "486"
} | {
"split": "train",
"index": 24951,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Moore's law says that the number of transistors that can be placed inexpensively on a silicon chip doubles every two years. In 1990, a typical CPU contained about $1,\\!000,\\!000$ transistors. According to Moore's law, how many transistors did a typical CPU contain in the year... | math | {
"style": "rule",
"ground_truth": "32,\\!000,\\!000"
} | {
"split": "train",
"index": 24952,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many three-digit numbers are composed of three distinct digits such that one digit is the average of the other two? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "112"
} | {
"split": "train",
"index": 24953,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two tangents are drawn to a circle from an exterior point $A$; they touch the circle at points $B$ and $C$ respectively. A third tangent intersects segment $AB$ in $P$ and $AC$ in $R$, and touches the circle at $Q$. Given that $AB=25$ and $PQ = QR = 2.5$, calculate the perimete... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 24954,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The area of a rhombus with diagonals of 6cm and 8cm is in cm<sup>2</sup>, and its perimeter is in cm. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 24955,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many distinct sequences of five letters can be made from the letters in COMPUTER if each letter can be used only once, each sequence must begin with M, end with R, and the third letter must be a vowel (A, E, I, O, U)? Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 24956,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest base-10 integer that can be represented as $XX_6$ and $YY_8$, where $X$ and $Y$ are valid digits in their respective bases? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "63"
} | {
"split": "train",
"index": 24957,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $y=a^{x+4}+2$ with $a \\gt 0$ and $a \\gt 1$, find the value of $\\sin \\alpha$ if the terminal side of angle $\\alpha$ passes through a point on the graph of the function. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 24958,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the area of quadrilateral ABCD given that $\\angle A = \\angle D = 120^{\\circ}$, $AB = 5$, $BC = 7$, $CD = 3$, and $DA = 4$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{47\\sqrt{3}}{4}"
} | {
"split": "train",
"index": 24959,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\( g(x) = \\frac{x^5 - 1}{4} \\), find \\( g^{-1}(-7/64) \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left(\\frac{9}{16}\\right)^{\\frac{1}{5}}"
} | {
"split": "train",
"index": 24960,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the maximum area that a quadrilateral with side lengths of 1, 4, 7, and 8 can have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 24961,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the function $$f(x)=(2m+3)x^{m^2-3}$$ is a power function, determine the value of $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 24962,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a,$ $b,$ $c$ be distinct complex numbers such that\n\\[\\frac{a}{1 - b} = \\frac{b}{1 - c} = \\frac{c}{1 - a} = k.\\]Find the sum of all possible values of $k.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 24963,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A triangle has sides of length 888, 925, and $x>0$. Find the value of $x$ that minimizes the area of the circle circumscribed about the triangle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "259"
} | {
"split": "train",
"index": 24964,
"solution": "259."
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(x) = 4x - 9$ and $g(f(x)) = 3x^2 + 4x - 2.$ Find $g(-10).$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{-45}{16}"
} | {
"split": "train",
"index": 24965,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the planar vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ that satisfy $\\overrightarrow{a} \\cdot (\\overrightarrow{a} + \\overrightarrow{b}) = 3$, and $|\\overrightarrow{a}| = 2$, $|\\overrightarrow{b}| = 1$, find the angle between the vectors $\\overrightarrow... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\pi}{3}"
} | {
"split": "train",
"index": 24966,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The mean of one set of seven numbers is 15, and the mean of a separate set of eight numbers is 20. What is the mean of the set of all fifteen numbers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17.67"
} | {
"split": "train",
"index": 24967,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $G$ be the centroid of quadrilateral $ABCD$. If $GA^2 + GB^2 + GC^2 + GD^2 = 116$, find the sum $AB^2 + AC^2 + AD^2 + BC^2 + BD^2 + CD^2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "464"
} | {
"split": "train",
"index": 24968,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(x) = Ax + B$ and $g(x) = Bx + A$, where $A \\neq B$. If $f(g(x)) - g(f(x)) = B - A$, what is $A + B$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 24969,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( x_{0} > 0 \\), \\( x_{0} \\neq \\sqrt{3} \\), a point \\( Q\\left( x_{0}, 0 \\right) \\), and a point \\( P(0, 4) \\), the line \\( PQ \\) intersects the hyperbola \\( x^{2} - \\frac{y^{2}}{3} = 1 \\) at points \\( A \\) and \\( B \\). If \\( \\overrightarrow{PQ} = t ... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 24970,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A natural number plus 13 is a multiple of 5, and its difference with 13 is a multiple of 6. What is the smallest natural number that satisfies these conditions? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 24971,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the sequence of positive integers \\(1, 2, 3, 4, \\cdots\\), remove multiples of 3 and 4, but keep all multiples of 5 (for instance, 15 and 120 should not be removed). The remaining numbers form a new sequence: \\(a_{1} = 1, a_{2} = 2, a_{3} = 5, a_{4} = 7, \\cdots\\). Find ... | math | {
"style": "rule",
"ground_truth": "3331"
} | {
"split": "train",
"index": 24972,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate \r\n\r\n\\[T = \\sum \\frac{1}{n_1! \\cdot n_2! \\cdot \\cdots n_{1994}! \\cdot (n_2 + 2 \\cdot n_3 + 3 \\cdot n_4 + \\ldots + 1993 \\cdot n_{1994})!}\\]\r\n\r\nwhere the sum is taken over all 1994-tuples of the numbers $n_1, n_2, \\ldots, n_{1994} \\in \\mathbb{N} \... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{1994!}"
} | {
"split": "train",
"index": 24973,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $∀x∈(0,+\\infty)$, $ln2x-\\frac{ae^{x}}{2}≤lna$, then find the minimum value of $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{e}"
} | {
"split": "train",
"index": 24974,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive, three-digit integers contain at least one $3$ as a digit but do not contain a $5$ as a digit? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "200"
} | {
"split": "train",
"index": 24975,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On graph paper (1 cell = 1 cm), two equal triangles ABC and BDE are depicted. \n\nFind the area of their common part. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.8"
} | {
"split": "train",
"index": 24976,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all positive integers $k<202$ for which there exist a positive integers $n$ such that\n$$\\bigg {\\{}\\frac{n}{202}\\bigg {\\}}+\\bigg {\\{}\\frac{2n}{202}\\bigg {\\}}+\\cdots +\\bigg {\\{}\\frac{kn}{202}\\bigg {\\}}=\\frac{k}{2}$$ Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "1, 100, 101, 201"
} | {
"split": "train",
"index": 24977,
"solution": "\nTo solve the given problem, we need to find all positive integers \\( k < 202 \\) such that there exists a positive integer \\( n \\) satisfying the condition:\n\n\\[\n\\left\\{\\frac{n}{202}\\right\\} + \\left\\{\\frac{2n}{202}\\right\\} + \\cdots + \\left\\{\\f... |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $xOy$, the parametric equation of curve $C_1$ is $\\begin{cases} x=t^{2} \\\\ y=2t \\end{cases}$ (where $t$ is the parameter), and in the polar coordinate system with the origin $O$ as the pole and the positive $x$-axis as the polar axis, the ... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 24978,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any t... | math | {
"style": "rule",
"ground_truth": "76"
} | {
"split": "train",
"index": 24979,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest palindrome that is larger than 2015? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2112"
} | {
"split": "train",
"index": 24980,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Assume that $f$ and $g$ are functions for which $f^{-1}(g(x))=5x+3$. Find $g^{-1}(f(-7))$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 24981,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of three numbers \\(x, y,\\) and \\(z\\) is 120. If we decrease \\(x\\) by 10, we get the value \\(M\\). If we increase \\(y\\) by 10, we also get the value \\(M\\). If we multiply \\(z\\) by 10, we also get the value \\(M\\). What is the value of \\(M\\)? Let's think s... | math | {
"style": "rule",
"ground_truth": "\\frac{400}{7}"
} | {
"split": "train",
"index": 24982,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = x^3 + ax^2 + bx + a^2$ has an extremum of 10 at $x = 1$, find the value of $f(2)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 24983,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given sets $A=\\{1,2,3,4,5\\}$, $B=\\{0,1,2,3,4\\}$, and a point $P$ with coordinates $(m,n)$, where $m\\in A$ and $n\\in B$, find the probability that point $P$ lies below the line $x+y=5$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{2}{5}"
} | {
"split": "train",
"index": 24984,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Tom, Dick, and Harry each flip a fair coin repeatedly until they get their first tail. Calculate the probability that all three flip their coins an even number of times and they all get their first tail on the same flip. Let's think step by step and put only the final answer wi... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{63}"
} | {
"split": "train",
"index": 24985,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let function $G(n)$ denote the number of solutions to the equation $\\cos x = \\sin nx$ on the interval $[0, 2\\pi]$. For each integer $n$ greater than 2, what is the sum $\\sum_{n=3}^{100} G(n)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10094"
} | {
"split": "train",
"index": 24986,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x$ be chosen randomly from the interval $(0,1)$. What is the probability that $\\lfloor\\log_{10}5x\\rfloor - \\lfloor\\log_{10}x\\rfloor = 0$? Here $\\lfloor x\\rfloor$ denotes the greatest integer that is less than or equal to $x$.\nA) $\\frac{1}{9}$\nB) $\\frac{1}{10}$\... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{9}"
} | {
"split": "train",
"index": 24987,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\triangle{PQR}$ be a right triangle with $PQ = 90$, $PR = 120$, and $QR = 150$. Let $C_{1}$ be the inscribed circle. Construct $\\overline{ST}$ with $S$ on $\\overline{PR}$ and $T$ on $\\overline{QR}$, such that $\\overline{ST}$ is perpendicular to $\\overline{PR}$ and ta... | math | {
"style": "rule",
"ground_truth": "725"
} | {
"split": "train",
"index": 24988,
"solution": "[asy] pointpen = black; pathpen = black + linewidth(0.7); pair P = (0,0), Q = (90, 0), R = (0, 120), S=(0, 60), T=(45, 60), U = (60,0), V=(60, 40), O1 = (30,30), O2 = (15, 75), O3 = (70, 10); D(MP(\"P\",P)--MP(\"Q\",Q)--MP(\"R\",R,W)--cycle); D(MP(\"S\",S,W) -- MP(... |
deepscaler | [
{
"role": "user",
"content": "What is the distance, in units, between the points $(3, -2)$ and $(7, 5)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{65}"
} | {
"split": "train",
"index": 24989,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circular spinner for a game has a radius of 10 cm. The probability of winning on one spin of this spinner is $\\frac{2}{5}$. What is the area, in sq cm, of the WIN sector? Express your answer in terms of $\\pi$.\n\n[asy]import graph;\n\ndraw(Circle((0,0),25),black);\n\ndraw((... | math | {
"style": "rule",
"ground_truth": "40\\pi"
} | {
"split": "train",
"index": 24990,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Figure $OPQR$ is a square. Point $O$ is the origin, and point $Q$ has coordinates (2,2). What are the coordinates for $T$ so that the area of triangle $PQT$ equals the area of square $OPQR$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(-2,0)"
} | {
"split": "train",
"index": 24991,
"solution": "1. **Identify the coordinates of points in the square**: Given that $OPQR$ is a square with $O$ at the origin $(0,0)$ and $Q$ at $(2,2)$, we can determine the coordinates of the other points. Since $OQ$ is a diagonal of the square and the length of each side of the... |
deepscaler | [
{
"role": "user",
"content": "Eight distinct integers are picked at random from $\\{1,2,3,\\ldots,15\\}$. What is the probability that, among those selected, the third smallest is $5$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{21}"
} | {
"split": "train",
"index": 24992,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a basketball match, Natasha attempted only three-point shots, two-point shots, and free-throw shots. She was successful on $25\\%$ of her three-point shots and $40\\%$ of her two-point shots. Additionally, she had a free-throw shooting percentage of $50\\%$. Natasha attempte... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 24993,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle with center $O$ has radius $5,$ and has two points $A,B$ on the circle such that $\\angle AOB = 90^{\\circ}.$ Rays $OA$ and $OB$ are extended to points $C$ and $D,$ respectively, such that $AB$ is parallel to $CD,$ and the length of $CD$ is $200\... | math | {
"style": "rule",
"ground_truth": "5 + \\frac{15\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 24994,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Michael writes down all the integers between 1 and $N$ inclusive on a piece of paper and discovers that exactly $40 \\%$ of them have leftmost digit 1 . Given that $N>2017$, find the smallest possible value of $N$. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "1481480"
} | {
"split": "train",
"index": 24995,
"solution": "Let $d$ be the number of digits of $N$. Suppose that $N$ does not itself have leftmost digit 1 . Then the number of integers $1,2, \\ldots, N$ which have leftmost digit 1 is $$1+10+10^{2}+\\ldots+10^{d-1}=\\frac{10^{d}-1}{9}$$ so we must have $\\frac{10^{d}-1}{9}=\... |
deepscaler | [
{
"role": "user",
"content": "Evaluate the argument $\\theta$ of the complex number\n\\[\ne^{11\\pi i/60} + e^{31\\pi i/60} + e^{51 \\pi i/60} + e^{71\\pi i /60} + e^{91 \\pi i /60}\n\\]\nexpressed in the form $r e^{i \\theta}$ with $0 \\leq \\theta < 2\\pi$. Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "\\frac{17\\pi}{20}"
} | {
"split": "train",
"index": 24996,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A point \\( A \\) in the plane with integer coordinates is said to be visible from the origin \\( O \\) if the open segment \\( ] O A[ \\) contains no point with integer coordinates. How many such visible points are there in \\( [0,25]^{2} \\setminus \\{(0,0)\\} \\)? Let's thin... | math | {
"style": "rule",
"ground_truth": "399"
} | {
"split": "train",
"index": 24997,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many integer values of $a$ does the equation $$x^2 + ax + 12a = 0$$ have integer solutions for $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 24998,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the integral $\\int_{2}^{3}{\\frac{x-2}{\\left( x-1 \\right)\\left( x-4 \\right)}dx}=$\n\nA) $-\\frac{1}{3}\\ln 2$\nB) $\\frac{1}{3}\\ln 2$\nC) $-\\ln 2$\nD) $\\ln 2$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{3}\\ln 2"
} | {
"split": "train",
"index": 24999,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( a_{1}, a_{2}, \\cdots, a_{105} \\) be a permutation of \\( 1, 2, \\cdots, 105 \\), satisfying the condition that for any \\( m \\in \\{3, 5, 7\\} \\), for all \\( n \\) such that \\( 1 \\leqslant n < n+m \\leqslant 105 \\), we have \\( m \\mid (a_{n+m}-a_{n}) \\). How m... | math | {
"style": "rule",
"ground_truth": "3628800"
} | {
"split": "train",
"index": 25000,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An electronic clock always displays the date as an eight-digit number. For example, January 1, 2011, is displayed as 20110101. What is the last day of 2011 that can be evenly divided by 101? The date is displayed as $\\overline{2011 \\mathrm{ABCD}}$. What is $\\overline{\\mathr... | math | {
"style": "rule",
"ground_truth": "1221"
} | {
"split": "train",
"index": 25001,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The lengths of the sides of a triangle are consecutive integers, and the largest angle is twice the smallest angle. Find the cosine of the smallest angle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 25002,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the triangle \\( \\triangle ABC \\), the maximum value of \\( \\sin A + \\sin B + 2 \\sqrt{7} \\sin C \\) is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{27}{4}"
} | {
"split": "train",
"index": 25003,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If a die is rolled, event \\( A = \\{1, 2, 3\\} \\) consists of rolling one of the faces 1, 2, or 3. Similarly, event \\( B = \\{1, 2, 4\\} \\) consists of rolling one of the faces 1, 2, or 4.\n\nThe die is rolled 10 times. It is known that event \\( A \\) occurred exactly 6 ti... | math | {
"style": "rule",
"ground_truth": "\\frac{16}{3}"
} | {
"split": "train",
"index": 25004,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, where $C=60 ^{\\circ}$, $AB= \\sqrt {3}$, and the height from $AB$ is $\\frac {4}{3}$, find the value of $AC+BC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt {11}"
} | {
"split": "train",
"index": 25005,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\sqrt{18} < \\sqrt{n^2}$ and $\\sqrt{n^2} < \\sqrt{200}$, determine the number of integers n. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 25006,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow{a}=(1, \\sqrt {3})$ and $\\overrightarrow{b}=(-2,2 \\sqrt {3})$, calculate the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac {\\pi}{3}"
} | {
"split": "train",
"index": 25007,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given triangle $ABC$, $\\overrightarrow{CA}•\\overrightarrow{CB}=1$, the area of the triangle is $S=\\frac{1}{2}$,<br/>$(1)$ Find the value of angle $C$;<br/>$(2)$ If $\\sin A\\cos A=\\frac{{\\sqrt{3}}}{4}$, $a=2$, find $c$. Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{6}}{3}"
} | {
"split": "train",
"index": 25008,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( x + y + z = xy + yz + zx \\), find the minimum value of \\( \\frac{x}{x^2 + 1} + \\frac{y}{y^2 + 1} + \\frac{z}{z^2 + 1} \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1/2"
} | {
"split": "train",
"index": 25009,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many of the numbers from the set $\\{1,\\ 2,\\ 3,\\ldots,\\ 100\\}$ have a perfect square factor other than one? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 25010,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Hawkins, Dustin, and Lucas start playing a game where each begins with $\\$2$. A bell rings every $10$ seconds, and each player with money independently chooses one of the other two players at random to give $\\$1$. If a player has only $\\$1$ left, there is a $\\frac{1}{3}$ pr... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 25011,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Juan rolls a fair regular decagonal die marked with the numbers 1 through 10. Then Amal rolls a fair eight-sided die. What is the probability that the product of the two rolls is a multiple of 4? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{5}"
} | {
"split": "train",
"index": 25012,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( x \\in \\left(-\\frac{3\\pi}{4}, \\frac{\\pi}{4}\\right) \\), and \\( \\cos \\left(\\frac{\\pi}{4} - x\\right) = -\\frac{3}{5} \\). Find the value of \\( \\cos 2x \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{24}{25}"
} | {
"split": "train",
"index": 25013,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $(2,12)$ and $(8,3)$ are the coordinates of two opposite vertices of a rectangle, what is the sum of the $x$-coordinates of the other two vertices? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 25014,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a ten-digit number. From left to right:\n- Its first digit indicates the number of zeros in the ten-digit number.\n- Its second digit indicates the number of ones in the ten-digit number.\n- Its third digit indicates the number of twos in the ten-digit number.\n- ...\n... | math | {
"style": "rule",
"ground_truth": "6210001000"
} | {
"split": "train",
"index": 25015,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The terms of the sequence $(b_i)$ defined by $b_{n + 2} = \\frac {b_n + 2021} {1 + b_{n + 1}}$ for $n \\ge 1$ are positive integers. Find the minimum possible value of $b_1 + b_2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 25016,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sequence \\(\\left\\{a_{n}\\right\\}\\) that satisfies\n\\[ a_{n}=\\left[(2+\\sqrt{5})^{n}+\\frac{1}{2^{n}}\\right] \\quad \\text{for} \\quad n \\in \\mathbf{Z}_{+}, \\]\nwhere \\([x]\\) denotes the greatest integer less than or equal to the real number \\(x\\). Let \... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{5} - 2}{4}"
} | {
"split": "train",
"index": 25017,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate $\\log_3 27\\sqrt3$. Express your answer as an improper fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac72"
} | {
"split": "train",
"index": 25018,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two different natural numbers are selected from the set $\\{1, 2, 3, 4, 5, 6, 7, 8\\}$. What is the probability that the greatest common factor of these two numbers is one? Express your answer as a common fraction. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 25019,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(ABCDEF\\) be a regular hexagon and let point \\(O\\) be the center of the hexagon. How many ways can you color these seven points either red or blue such that there doesn't exist any equilateral triangle with vertices of all the same color? Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 25020,
"solution": "Without loss of generality, let \\(O\\) be blue. Then we can't have any two adjacent blues on the perimeter of \\(ABCDEF\\). However, because of the two larger equilateral triangles \\(ACE\\) and \\(BDF\\), we need at least two blues to keep us from having an all r... |
deepscaler | [
{
"role": "user",
"content": "For an arithmetic sequence $\\{a_n\\}$ with a non-zero common difference, some terms $a_{k_1}$, $a_{k_2}$, $a_{k_3}$, ... form a geometric sequence $\\{a_{k_n}\\}$, and it is given that $k_1 \\neq 1$, $k_2 \\neq 2$, $k_3 \\neq 6$. Find the value of $k_4$. Let's think step by st... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 25021,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest possible value of the expression $$\\frac{(a+b)^2+(b-c)^2+(c-a)^2}{b^2},$$where $b > c > a$ are real numbers, and $b \\neq 0.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{3}"
} | {
"split": "train",
"index": 25022,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $y=f(x)$ has an inverse function $y=f^{-1}(x)$, and $y=f(x+2)$ and $y=f^{-1}(x-1)$ are inverse functions of each other, then $f^{-1}(2007)-f^{-1}(1)=$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4012"
} | {
"split": "train",
"index": 25023,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the definition: $min\\{a,b\\} = \\begin{cases} a,\\quad a\\leqslant b \\\\ b,\\quad a > b \\end{cases}$. If a point $P(x,y)$ is randomly selected within the region defined by $\\begin{cases} 0\\leqslant x\\leqslant 2 \\\\ 0\\leqslant y\\leqslant 6 \\end{cases}$, find the ... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 25024,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Mountain bikes are a popular means of transportation for high school students, with a huge market and fierce competition. The total sales of type $A$ bikes operated by a certain brand dealer last year was $50,000. This year, the selling price per bike is $400 less than last yea... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 25025,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, we have $\\angle A = 90^\\circ$ and $\\sin B = \\frac{4}{7}$. Find $\\cos C$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac47"
} | {
"split": "train",
"index": 25026,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a_n = n(2n+1)$ . Evaluate\n\\[\n \\biggl | \\sum_{1 \\le j < k \\le 36} \\sin\\bigl( \\frac{\\pi}{6}(a_k-a_j) \\bigr) \\biggr |.\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 25027,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Toward the end of a game of Fish, the 2 through 7 of spades, inclusive, remain in the hands of three distinguishable players: \\mathrm{DBR}, \\mathrm{RB}, and DB , such that each player has at least one card. If it is known that DBR either has more than one card or has an even-... | math | {
"style": "rule",
"ground_truth": "450"
} | {
"split": "train",
"index": 25028,
"solution": "First, we count the number of distributions where each player has at least 1 card. The possible distributions are: - Case 1: $4 / 1 / 1$ : There are 3 choices for who gets 4 cards, 6 choices for the card that one of the single-card players holds, and 5 choices for ... |
deepscaler | [
{
"role": "user",
"content": "Given a basketball player made 8 baskets during a game, each worth 1, 2, or 3 points, calculate the total number of different numbers that could represent the total points scored by the player. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 25029,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When $0.76\\overline{204}$ is expressed as a fraction in the form $\\frac{x}{999000}$, what is the value of $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "761280"
} | {
"split": "train",
"index": 25030,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many natural numbers greater than one have a product with their smallest prime divisor that is not greater than 100? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "33"
} | {
"split": "train",
"index": 25031,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the coefficient of the second term in the expansion of $((x+2y)^{n})$ is $8$, find the sum of the coefficients of all terms in the expansion of $((1+x)+(1+x)^{2}+…+(1+x)^{n})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 25032,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four cyclists. Four identical circles represent four tracks. The four cyclists start from the center at noon. Each moves along their track at speeds: the first at 6 km/h, the second at 9 km/h, the third at 12 km/h, and the fourth at 15 km/h. They agreed to ride until they all m... | math | {
"style": "rule",
"ground_truth": "12:26:40"
} | {
"split": "train",
"index": 25033,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many ways are there to list the numbers 1 to 10 in some order such that every number is either greater or smaller than all the numbers before it? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "512"
} | {
"split": "train",
"index": 25034,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The perpendicular to the side $AB$ of the trapezoid $ABCD$, passing through its midpoint $K$, intersects the side $CD$ at point $L$. It is known that the area of quadrilateral $AKLD$ is five times greater than the area of quadrilateral $BKLC$. Given $CL=3$, $DL=15$, and $KC=4$,... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 25035,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We roll five dice, each a different color. In how many ways can the sum of the rolls be 11? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "205"
} | {
"split": "train",
"index": 25036,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rectangular yard contains three flower beds in the shape of congruent isosceles right triangles. The remainder of the yard has a trapezoidal shape, with the parallel sides measuring $10$ meters and $20$ meters. What fraction of the yard is occupied by the flower beds?\nA) $\\... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 25037,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the terminating decimal expansion of $\\frac{11}{125}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.088"
} | {
"split": "train",
"index": 25038,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many integers $m$, with $1 \\leq m \\leq 30$, is it possible to find a value of $n$ so that $n!$ ends with exactly $m$ zeros? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 25039,
"solution": "If $n!$ ends with exactly $m$ zeroes, then $n!$ is divisibe by $10^{m}$ but not divisible by $10^{m+1}$. In this case, we can write $n!=10^{m} \\cdot q$ where $q$ is not divisible by 10. Since $2<5$, when $n \\geq 2$, the product $n!=1 \\cdot 2 \\cdot 3 \\cdots \\c... |
deepscaler | [
{
"role": "user",
"content": "Two 600 mL pitchers contain orange juice. One pitcher is 1/3 full and the other pitcher is 2/5 full. Water is added to fill each pitcher completely, then both pitchers are poured into one large container. What fraction of the mixture in the large container is orange juice? Let'... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{30}"
} | {
"split": "train",
"index": 25040,
"solution": "1. **Calculate the amount of orange juice in each pitcher:**\n - The first pitcher is $\\frac{1}{3}$ full of orange juice. Since the total capacity of the pitcher is $600$ mL, the amount of orange juice in the first pitcher is:\n \\[\n 600 \\times \\frac{... |
deepscaler | [
{
"role": "user",
"content": "What is the value of $\\sqrt[3]{3^5 + 3^5 + 3^5}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 25041,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The figure is constructed from $11$ line segments, each of which has length $2$. The area of pentagon $ABCDE$ can be written as $\\sqrt{m} + \\sqrt{n}$, where $m$ and $n$ are positive integers. What is $m + n ?$ Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 25042,
"solution": "1. **Identify Key Triangles and Midpoint**: \n Let $M$ be the midpoint of $CD$. Given that the figure is constructed from line segments each of length $2$, and considering the symmetry and angles in the figure, we can identify that $\\triangle AED$ and $\\triangl... |
deepscaler | [
{
"role": "user",
"content": "Given that there is a gathering attended by 1982 people, and among any group of 4 people, at least 1 person knows the other 3. How many people, at minimum, must know all the attendees at this gathering? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "1979"
} | {
"split": "train",
"index": 25043,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Person A and Person B decided to go to a restaurant. Due to high demand, Person A arrived first and took a waiting number, while waiting for Person B. After a while, Person B arrived but did not see Person A, so he also took a waiting number. While waiting, Person B saw Person ... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 25044,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ n \\geq 2$ be a positive integer and $ \\lambda$ a positive real number. Initially there are $ n$ fleas on a horizontal line, not all at the same point. We define a move as choosing two fleas at some points $ A$ and $ B$, with $ A$ to the left of $ B$, and letting the fle... | math | {
"style": "rule",
"ground_truth": "\\lambda \\ge \\frac{1}{n-1}"
} | {
"split": "train",
"index": 25045,
"solution": "\nLet \\( n \\geq 2 \\) be a positive integer and \\( \\lambda \\) a positive real number. There are \\( n \\) fleas on a horizontal line, and we need to find the values of \\( \\lambda \\) for which, given any point \\( M \\) and any initial positions of the fleas... |
deepscaler | [
{
"role": "user",
"content": "Jo is thinking of a positive integer less than 100. It is one less than a multiple of 8, and it is three less than a multiple of 7. What is the greatest possible integer Jo could be thinking of? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "95"
} | {
"split": "train",
"index": 25046,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A factory's annual fixed cost for producing a certain product is 2.5 million yuan. For every $x$ thousand units produced, an additional cost $C(x)$ is incurred. When the annual output is less than 80 thousand units, $C(x)=\\frac{1}{3}x^2+10x$ (in million yuan). When the annual ... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 25047,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three boxes each contain an equal number of hockey pucks. Each puck is either black or gold. All 40 of the black pucks and exactly $\\frac{1}{7}$ of the gold pucks are contained in one of the three boxes. Determine the total number of gold hockey pucks. Let's think step by step... | math | {
"style": "rule",
"ground_truth": "140"
} | {
"split": "train",
"index": 25048,
"solution": ""
} |
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