data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $C: \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$ ($a > b > 0$) with an eccentricity of $\\frac{\\sqrt{5}}{5}$, and the equation of the right directrix is $x=5$.\n\n(1) Find the equation of the ellipse; \n(2) A line $l$ with a slope of 1 passes through the right fo... | math | {
"style": "rule",
"ground_truth": "\\frac{16\\sqrt{10}}{9}"
} | {
"split": "train",
"index": 37049,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( P, Q, R, \\) and \\( S \\) be positive real numbers such that\n\\[\n\\log_{10} (PQ) + \\log_{10} (PS) = 2, \\\\\n\\log_{10} (QS) + \\log_{10} (QR) = 3, \\\\\n\\log_{10} (RP) + \\log_{10} (RS) = 5.\n\\]\nCompute the value of the product \\( PQRS \\). Let's think step by ... | math | {
"style": "rule",
"ground_truth": "100000"
} | {
"split": "train",
"index": 37050,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of solutions of $2^{2x}-3^{2y}=55$, in which $x$ and $y$ are integers, is:\n\\[\\textbf{(A)} \\ 0 \\qquad\\textbf{(B)} \\ 1 \\qquad \\textbf{(C)} \\ 2 \\qquad\\textbf{(D)} \\ 3\\qquad \\textbf{(E)} \\ \\text{More than three, but finite}\\]\n Let's think step by step ... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 37051,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a rectangle divided into a 2x4 grid of equally spaced points, calculate the total number of distinct triangles that can be formed using three of these points as vertices. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 37052,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The angle bisectors $\\mathrm{AD}$ and $\\mathrm{BE}$ of the triangle $\\mathrm{ABC}$ intersect at point I. It turns out that the area of triangle $\\mathrm{ABI}$ is equal to the area of quadrilateral $\\mathrm{CDIE}$. Find the maximum possible value of angle $\\mathrm{ACB}$. L... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 37053,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Definition: If the line $l$ is tangent to the graphs of the functions $y=f(x)$ and $y=g(x)$, then the line $l$ is called the common tangent line of the functions $y=f(x)$ and $y=g(x)$. If the functions $f(x)=a\\ln x (a>0)$ and $g(x)=x^{2}$ have exactly one common tangent line, ... | math | {
"style": "rule",
"ground_truth": "2e"
} | {
"split": "train",
"index": 37054,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the set of all positive integers that have four digits in base $2$. What is the sum of all of the elements in $S$, when expressed in base $2$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1011100"
} | {
"split": "train",
"index": 37055,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a sequence of hexagons where each new hexagon adds two layers of dots instead of one. The first hexagon has 1 dot. The second hexagon has 1 central dot, 6 dots in the first layer, and 12 dots in the second layer, making a total of 19 dots. Determine the total number of... | math | {
"style": "rule",
"ground_truth": "61"
} | {
"split": "train",
"index": 37056,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the volume of the region in space defined by\n\\[|x + y + z| + |x + y - z| \\le 8\\]and $x,$ $y,$ $z \\ge 0.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 37057,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Gary purchased a large beverage, but only drank $m/n$ of it, where $m$ and $n$ are relatively prime positive integers. If he had purchased half as much and drunk twice as much, he would have wasted only $2/9$ as much beverage. Find $m+n$. Let's think step by step and put only t... | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 37058,
"solution": "Let $x$ be the fraction consumed, then $(1-x)$ is the fraction wasted. We have $\\frac{1}{2} - 2x =\\frac{2}{9} (1-x)$, or $9 - 36x = 4 - 4x$, or $32x = 5$ or $x = 5/32$. Therefore, $m + n = 5 + 32 = \\boxed{037}$."
} |
deepscaler | [
{
"role": "user",
"content": "Given that a match between two people is played with a best-of-five-games format, where the winner is the first to win three games, and that the probability of person A winning a game is $\\dfrac{2}{3}$, calculate the probability that person A wins with a score of $3:1$. Let's ... | math | {
"style": "rule",
"ground_truth": "\\dfrac{8}{27}"
} | {
"split": "train",
"index": 37059,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Eight semicircles line the inside of a square with side length 2 as shown. What is the radius of the circle tangent to all of these semicircles? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{5}-1}{2}"
} | {
"split": "train",
"index": 37060,
"solution": "1. **Understanding the Configuration**: \n - The square has a side length of 2.\n - Each semicircle inside the square has a diameter of 1 (since 4 semicircles fit along one side of the square, and the side length is 2).\n - Therefore, the radius of each semic... |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\frac{1}{x+1}$, point $O$ is the coordinate origin, point $A_{n}(n,f(n))$ where $n \\in \\mathbb{N}^{*}$, vector $\\overrightarrow{a}=(0,1)$, and $\\theta_{n}$ is the angle between vector $\\overrightarrow{OA}_{n}$ and $\\overrightarrow{a}$. Compute th... | math | {
"style": "rule",
"ground_truth": "\\frac{2016}{2017}"
} | {
"split": "train",
"index": 37061,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\( A = \\frac{0.375 \\times 2.6}{2 \\frac{1}{2} \\times 1 \\frac{1}{5}}+\\frac{0.625 \\times 1.6}{3 \\times 1.2 \\times 4 \\frac{1}{6}}+6 \\frac{2}{3} \\times 0.12+28+\\frac{1 \\div 9}{7}+\\frac{0.2}{9 \\times 22} \\), then when \\( A \\) is expressed as a fraction, the num... | math | {
"style": "rule",
"ground_truth": "1901/3360"
} | {
"split": "train",
"index": 37062,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A pen and its ink refill together cost $\\;\\$1.10$. The pen costs $\\;\\$1$ more than the ink refill. What is the cost of the pen in dollars? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1.05"
} | {
"split": "train",
"index": 37063,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(x)=ax^2+bx+c$, where $a$, $b$, and $c$ are integers. Suppose that $f(1)=0$, $50<f(7)<60$, $70<f(8)<80$, $5000k<f(100)<5000(k+1)$ for some integer $k$. What is $k$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 37064,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Every day, Xiaoming goes to school along a flat road \\(AB\\), an uphill road \\(BC\\), and a downhill road \\(CD\\) (as shown in the diagram). Given that \\(AB : BC : CD = 1 : 2 : 1\\) and that Xiaoming's speeds on flat, uphill, and downhill roads are in the ratio 3 : 2 : 4, r... | math | {
"style": "rule",
"ground_truth": "19:16"
} | {
"split": "train",
"index": 37065,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Homer started peeling a pile of 60 potatoes at a rate of 4 potatoes per minute. Five minutes later, Christen joined him peeling at a rate of 6 potatoes per minute. After working together for 3 minutes, Christen took a 2-minute break, then resumed peeling at a rate of 4 potatoes... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 37066,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Expand $(2t^2 -3t+2)(-3t^2 + t-5)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-6t^4 +11t^3 -19t^2 +17t -10"
} | {
"split": "train",
"index": 37067,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A square $ABCD$ with a side length of $2$ is rotated around $BC$ to form a cylinder. Find the surface area of the cylinder. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16\\pi"
} | {
"split": "train",
"index": 37068,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$A B C D$ is a cyclic quadrilateral with sides $A B=10, B C=8, C D=25$, and $D A=12$. A circle $\\omega$ is tangent to segments $D A, A B$, and $B C$. Find the radius of $\\omega$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{\\frac{1209}{7}} \\text{ OR } \\frac{\\sqrt{8463}}{7}"
} | {
"split": "train",
"index": 37069,
"solution": "Denote $E$ an intersection point of $A D$ and $B C$. Let $x=E A$ and $y=E B$. Because $A B C D$ is a cyclic quadrilateral, $\\triangle E A B$ is similar to $\\triangle E C D$. Therefore, $\\frac{y+8}{x}=\\frac{25}{10}$ and $\\frac{x+12}{y}=\\frac{25}{10}$. We get $... |
deepscaler | [
{
"role": "user",
"content": "The bug Josefína landed in the middle of a square grid composed of 81 smaller squares. She decided not to crawl away directly but to follow a specific pattern: first moving one square south, then one square east, followed by two squares north, then two squares west, and repeati... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 37070,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)= \\frac {1}{3}x^{3}+x^{2}+ax+1$, and the slope of the tangent line to the curve $y=f(x)$ at the point $(0,1)$ is $-3$. \n$(1)$ Find the intervals of monotonicity for $f(x)$; \n$(2)$ Find the extrema of $f(x)$. Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "-\\frac{2}{3}"
} | {
"split": "train",
"index": 37071,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three hexagons of increasing size are shown below. Suppose the dot pattern continues so that each successive hexagon contains one more band of dots. How many dots are in the next hexagon?\n[asy] // diagram by SirCalcsALot, edited by MRENTHUSIASM size(250); path p = scale(0.8)*u... | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 37072,
"solution": "To solve this problem, we need to understand the pattern of how the dots are arranged in each hexagon and how the number of dots increases as the hexagons grow in size.\n\n1. **Observing the pattern:**\n - The first hexagon has 1 dot.\n - The second hexagon has... |
deepscaler | [
{
"role": "user",
"content": "\\(\\log _{\\sqrt{3}} x+\\log _{\\sqrt{3}} x+\\log _{\\sqrt[6]{3}} x+\\ldots+\\log _{\\sqrt{3}} x=36\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 37073,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that Li Ming mistakenly read the units digit of \\(a\\) as 1 instead of 7 and got a product of 255, and Wang Ning mistakenly read the tens digit of \\(a\\) as 6 instead of 5 and got a product of 335, calculate the correct product of \\(a \\cdot b\\). Let's think step by s... | math | {
"style": "rule",
"ground_truth": "285"
} | {
"split": "train",
"index": 37074,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The diagram shows a right-angled triangle \\( ACD \\) with a point \\( B \\) on the side \\( AC \\). The sides of triangle \\( ABD \\) have lengths 3, 7, and 8. What is the area of triangle \\( BCD \\)? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{3}"
} | {
"split": "train",
"index": 37075,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A group of friends are sharing a bag of candy. On the first day, they eat $\frac{1}{2}$ of the candies in the bag. On the second day, they eat $\frac{2}{3}$ of the remaining candies. On the third day, they eat $\frac{3}{4}$ of the remaining candies. On the fourth day, they eat ... | math | {
"style": "rule",
"ground_truth": "720"
} | {
"split": "train",
"index": 37076,
"solution": "We work backwards through the given information. At the end, there is 1 candy remaining. Since $\frac{5}{6}$ of the candies are removed on the fifth day, this 1 candy represents $\frac{1}{6}$ of the candies left at the end of the fourth day. Thus, there were $6 \ti... |
deepscaler | [
{
"role": "user",
"content": "If the eccentricity of the conic section \\(C\\): \\(x^{2}+my^{2}=1\\) is \\(2\\), determine the value of \\(m\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\dfrac {1}{3}"
} | {
"split": "train",
"index": 37077,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a geometric sequence $\\{a_n\\}$ with a common ratio $q$, and the product of its first $n$ terms is $T_n$, where the first term $a_1 > 1$, and $a_{2014}a_{2015} - 1 > 0$, $\\frac{a_{2014} - 1}{a_{2015} - 1} < 0$, find the largest natural number $n$ such that $T_n > 1$. Le... | math | {
"style": "rule",
"ground_truth": "4028"
} | {
"split": "train",
"index": 37078,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We use \\( S_{k} \\) to represent an arithmetic sequence with the first term \\( k \\) and common difference \\( k^{2} \\). For example, \\( S_{3} \\) is \\( 3, 12, 21, \\cdots \\). If 306 is a term in \\( S_{k} \\), the sum of all possible \\( k \\) that satisfy this condition... | math | {
"style": "rule",
"ground_truth": "326"
} | {
"split": "train",
"index": 37079,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. Given that $c\\sin A= \\sqrt {3}a\\cos C$ and $(a-c)(a+c)=b(b-c)$, consider the function $f(x)=2\\sin x\\cos ( \\frac {π}{2}-x)- \\sqrt {3}\\sin (π+x)\\cos x+\\sin ( \\frac ... | math | {
"style": "rule",
"ground_truth": "\\frac {5}{2}"
} | {
"split": "train",
"index": 37080,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the value of $l$ for which\n\\[\\frac{9}{x + y + 1} = \\frac{l}{x + z - 1} = \\frac{13}{z - y + 2}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 37081,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the system \\begin{align*}x + y &= z + u,\\\\2xy & = zu.\\end{align*} Find the greatest value of the real constant $m$ such that $m \\leq x/y$ for any positive integer solution $(x,y,z,u)$ of the system, with $x \\geq y$. Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "3 + 2\\sqrt{2}"
} | {
"split": "train",
"index": 37082,
"solution": "\nTo solve this problem, we need to analyze the given system of equations:\n\n\\[\n\\begin{align*}\n1) \\quad & x + y = z + u,\\\\\n2) \\quad & 2xy = zu.\n\\end{align*}\n\\]\n\nOur goal is to find the greatest value of the real constant \\( m \\) such that \\( m \\... |
deepscaler | [
{
"role": "user",
"content": "Suppose a point $P$ has coordinates $(m, n)$, where $m$ and $n$ are the points obtained by rolling a dice twice consecutively. The probability that point $P$ lies outside the circle $x^{2}+y^{2}=16$ is _______. Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "\\frac {7}{9}"
} | {
"split": "train",
"index": 37083,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an isosceles triangle \\( \\triangle ABC \\) with base angles \\( \\angle ABC = \\angle ACB = 50^\\circ \\), points \\( D \\) and \\( E \\) lie on \\( BC \\) and \\( AC \\) respectively. Lines \\( AD \\) and \\( BE \\) intersect at point \\( P \\). Given \\( \\angle ABE =... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 37084,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a special event, the five Vietnamese famous dishes including Phở, (Vietnamese noodle), Nem (spring roll), Bún Chả (grilled pork noodle), Bánh cuốn (stuffed pancake), and Xôi gà (chicken sticky rice) are the options for the main courses for the dinner of Monday, Tuesday, an... | math | {
"style": "rule",
"ground_truth": "150"
} | {
"split": "train",
"index": 37085,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The chart below gives the air distance in miles between selected world cities. If two different cities from the chart are chosen at random, what is the probability that the distance between them is less than $7000$ miles? Express your answer as a common fraction.\n\n\\begin{tab... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 37086,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x$ and $y$ be real numbers such that $3x + 2y \\le 7$ and $2x + 4y \\le 8.$ Find the largest possible value of $x + y.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{11}{4}"
} | {
"split": "train",
"index": 37087,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The highest temperatures from April 1st to April 6th in a certain region were 28℃, 21℃, 22℃, 26℃, 28℃, and 25℃, respectively. Calculate the variance of the highest temperature data for these six days. Let's think step by step and put only the final answer within \\boxed{}."
}... | math | {
"style": "rule",
"ground_truth": "\\frac{22}{3}"
} | {
"split": "train",
"index": 37088,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a circle of radius 12 with center at point \\( O \\), there are points \\( A \\) and \\( B \\). Lines \\( AC \\) and \\( BC \\) are tangent to this circle. Another circle with center at point \\( M \\) is inscribed in triangle \\( ABC \\) and touches side \\( AC \\) at point... | math | {
"style": "rule",
"ground_truth": "120"
} | {
"split": "train",
"index": 37089,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A wooden cube, whose edges are one centimeter long, rests on a horizontal surface. Illuminated by a point source of light that is $x$ centimeters directly above an upper vertex, the cube casts a shadow on the horizontal surface. The area of the shadow, which does not include th... | math | {
"style": "rule",
"ground_truth": "166"
} | {
"split": "train",
"index": 37090,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the domain of the real-valued function $$f(x)=\\sqrt{-10x^2-11x+6}.$$ Give the endpoints in your answer as common fractions, not mixed numbers or decimals. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left[-\\frac{3}{2}, \\frac{2}{5}\\right]"
} | {
"split": "train",
"index": 37091,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A regular hexagon with side length 1 has an arbitrary interior point that is reflected over the midpoints of its six sides. Calculate the area of the hexagon formed in this way. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 37092,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $x$ in the equation $\\sqrt{\\frac{72}{25}} = \\sqrt[4]{\\frac{x}{25}}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "207.36"
} | {
"split": "train",
"index": 37093,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of the prime factors of $2010$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "77"
} | {
"split": "train",
"index": 37094,
"solution": "1. **Find the prime factorization of $2010$:**\n - Start by checking divisibility by the smallest prime, $2$. Since $2010$ is even, it is divisible by $2$. \n \\[\n 2010 \\div 2 = 1005\n \\]\n - Next, check divisibility by $3$. The sum of the digits... |
deepscaler | [
{
"role": "user",
"content": "Given \\( \\alpha, \\beta \\in (0, \\pi) \\), and \\( \\tan \\alpha, \\tan \\beta \\) are the roots of the equation \\( x^{2} + 3x + 1 = 0 \\), find the value of \\( \\cos(\\alpha - \\beta) \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 37095,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A paper equilateral triangle $ABC$ has side length 12. The paper triangle is folded so that vertex $A$ touches a point on side $\\overline{BC}$ a distance 9 from point $B$. Find the square of the length of the line segment along which the triangle is folded.\n\n[asy]\nimport cs... | math | {
"style": "rule",
"ground_truth": "\\frac{59319}{1225}"
} | {
"split": "train",
"index": 37096,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A$ and $B$ be two opposite vertices of a cube with side length 1. What is the radius of the sphere centered inside the cube, tangent to the three faces that meet at $A$ and to the three edges that meet at $B$? Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "2 - \\sqrt{2}"
} | {
"split": "train",
"index": 37097,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest integer less than $-\\frac{15}4$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4"
} | {
"split": "train",
"index": 37098,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive value of $x$ such that $x + 4321$ results in a palindrome? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 37099,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rectangle \\(ABCD\\) has area 2016. Point \\(Z\\) is inside the rectangle and point \\(H\\) is on \\(AB\\) so that \\(ZH\\) is perpendicular to \\(AB\\). If \\(ZH : CB = 4 : 7\\), what is the area of pentagon \\(ADCZB\\)? Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "1440"
} | {
"split": "train",
"index": 37100,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Matilda has a summer job delivering newspapers. She earns \\$6.00 an hour plus \\$0.25 per newspaper delivered. Matilda delivers 30 newspapers per hour. How much money will she earn during a 3-hour shift? Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "\\$40.50"
} | {
"split": "train",
"index": 37101,
"solution": "During a 3-hour shift, Matilda will deliver \\( 3 \\times 30=90 \\) newspapers. Therefore, she earns a total of \\( 3 \\times \\$6.00+90 \\times \\$0.25=\\$18.00+\\$22.50=\\$40.50 \\) during her 3-hour shift."
} |
deepscaler | [
{
"role": "user",
"content": "In triangle \\(ABC\\), angle \\(C\\) is \\(60^\\circ\\) and the radius of the circumcircle of this triangle is \\(2\\sqrt{3}\\).\n\nA point \\(D\\) is taken on the side \\(AB\\) such that \\(AD = 2DB\\) and \\(CD = 2\\sqrt{2}\\). Find the area of triangle \\(ABC\\). Let's think... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{2}"
} | {
"split": "train",
"index": 37102,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are two positive integers \\( A \\) and \\( B \\). The sum of the digits of \\( A \\) is 19, and the sum of the digits of \\( B \\) is 20. When the two numbers are added together, there are two carries. What is the sum of the digits of \\( (A+B) \\)? Let's think step by s... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 37103,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In \\\\(\\triangle ABC\\\\), the sides opposite to angles \\\\(A\\\\), \\\\(B\\\\), and \\\\(C\\\\) are \\\\(a\\\\), \\\\(b\\\\), and \\\\(c\\\\) respectively. It is given that \\\\(a+b=5\\\\), \\\\(c=\\sqrt{7}\\\\), and \\\\(4{{\\left( \\sin \\frac{A+B}{2} \\right)}^{2}}-\\cos... | math | {
"style": "rule",
"ground_truth": "\\frac {3 \\sqrt {3}}{2}"
} | {
"split": "train",
"index": 37104,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Which number in the array below is both the largest in its column and the smallest in its row? (Columns go up and down, rows go right and left.)\n\\[\\begin{tabular}{ccccc} 10 & 6 & 4 & 3 & 2 \\\\ 11 & 7 & 14 & 10 & 8 \\\\ 8 & 3 & 4 & 5 & 9 \\\\ 13 & 4 & 15 & 12 & 1 \\\\ 8 & 2... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 37105,
"solution": "To solve this problem, we need to identify the number that is both the largest in its column and the smallest in its row from the given array. We will proceed by first finding the largest number in each column and then checking if any of these numbers are also the ... |
deepscaler | [
{
"role": "user",
"content": "The numbers \\( p_1, p_2, p_3, q_1, q_2, q_3, r_1, r_2, r_3 \\) are equal to the numbers \\( 1, 2, 3, \\dots, 9 \\) in some order. Find the smallest possible value of\n\\[\nP = p_1 p_2 p_3 + q_1 q_2 q_3 + r_1 r_2 r_3.\n\\] Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "214"
} | {
"split": "train",
"index": 37106,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive integers less than $1000$ are either a perfect cube or a perfect square? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 37107,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the polynomial function $f(x) = 2x^5 - 5x^4 - 4x^3 + 3x^2 - 6x + 7$, using the Horner's method when $x = 5$, we can obtain $v_2 = \\_$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 37108,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( x \\in \\mathbf{R} \\). Find the minimum value of the algebraic expression \\( (x+1)(x+2)(x+3)(x+4) + 2019 \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2018"
} | {
"split": "train",
"index": 37109,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify:<br/>$(1)(-\\frac{1}{2}+\\frac{2}{3}-\\frac{1}{4})÷(-\\frac{1}{24})$;<br/>$(2)3\\frac{1}{2}×(-\\frac{5}{7})-(-\\frac{5}{7})×2\\frac{1}{2}-\\frac{5}{7}×(-\\frac{1}{2})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{5}{14}"
} | {
"split": "train",
"index": 37110,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ava and Tiffany participate in a knockout tournament consisting of a total of 32 players. In each of 5 rounds, the remaining players are paired uniformly at random. In each pair, both players are equally likely to win, and the loser is knocked out of the tournament. The probabi... | math | {
"style": "rule",
"ground_truth": "116"
} | {
"split": "train",
"index": 37111,
"solution": "Each match eliminates exactly one player, so exactly $32-1=31$ matches are played, each of which consists of a different pair of players. Among the $\\binom{32}{2}=\\frac{32 \\cdot 31}{2}=496$ pairs of players, each pair is equally likely to play each other at some... |
deepscaler | [
{
"role": "user",
"content": "An electronic clock displays time from 00:00:00 to 23:59:59. How much time throughout the day does the clock show a number that reads the same forward and backward? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 37112,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 8 identical balls in a box, consisting of three balls numbered 1, three balls numbered 2, and two balls numbered 3. A ball is randomly drawn from the box, returned, and then another ball is randomly drawn. The product of the numbers on the balls drawn first and second... | math | {
"style": "rule",
"ground_truth": "225/64"
} | {
"split": "train",
"index": 37113,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define the sequence $f_{1}, f_{2}, \\ldots:[0,1) \\rightarrow \\mathbb{R}$ of continuously differentiable functions by the following recurrence: $$ f_{1}=1 ; \\quad f_{n+1}^{\\prime}=f_{n} f_{n+1} \\quad \\text { on }(0,1), \\quad \\text { and } \\quad f_{n+1}(0)=1 $$ Show that... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{1-x}"
} | {
"split": "train",
"index": 37114,
"solution": "First of all, the sequence $f_{n}$ is well defined and it holds that $$ f_{n+1}(x)=e^{\\int_{0}^{x} f_{n}(t) \\mathrm{d} t} \\tag{2} $$ The mapping $\\Phi: C([0,1)) \\rightarrow C([0,1))$ given by $$ \\Phi(g)(x)=e^{\\int_{0}^{x} g(t) \\mathrm{d} t} $$ is monotone, ... |
deepscaler | [
{
"role": "user",
"content": "A circle with area $A_1$ is contained in the interior of a larger circle with area $A_1+A_2$. If the radius of the larger circle is $3$, and if $A_1 , A_2, A_1 + A_2$ is an arithmetic progression, then the radius of the smaller circle is Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 37115,
"solution": "1. **Identify the areas of the circles**: \n Given that the area of the larger circle is $A_1 + A_2$ and its radius is $3$, we can calculate its area using the formula for the area of a circle, $A = \\pi r^2$. Thus, the area of the larger circle is:\n \\[\n A... |
deepscaler | [
{
"role": "user",
"content": "Let $ABCD$ be a cyclic quadrilateral, and $E$ be the intersection of its diagonals. If $m(\\widehat{ADB}) = 22.5^\\circ$ , $|BD|=6$ , and $|AD|\\cdot|CE|=|DC|\\cdot|AE|$ , find the area of the quadrilateral $ABCD$ . Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "9\\sqrt{2}"
} | {
"split": "train",
"index": 37116,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Selina takes a sheet of paper and cuts it into 10 pieces. She then takes one of these pieces and cuts it into 10 smaller pieces. She then takes another piece and cuts it into 10 smaller pieces and finally cuts one of the smaller pieces into 10 tiny pieces. How many pieces of pa... | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 37117,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $0 < \\alpha < \\pi$, $\\tan\\alpha = -2$.\n(1) Find the value of $\\sin\\left(\\alpha + \\frac{\\pi}{6}\\right)$;\n(2) Calculate the value of $$\\frac{2\\cos\\left(\\frac{\\pi}{2} + \\alpha\\right) - \\cos(\\pi - \\alpha)}{\\sin\\left(\\frac{\\pi}{2} - \\alpha\\right) - ... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{5}"
} | {
"split": "train",
"index": 37118,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Add 76.893 to 34.2176 and round to the nearest tenth. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "111.1"
} | {
"split": "train",
"index": 37119,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The International Mathematical Olympiad is being organized in Japan, where a folklore belief is that the number $4$ brings bad luck. The opening ceremony takes place at the Grand Theatre where each row has the capacity of $55$ seats. What is the maximum number of contestants th... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 37120,
"solution": "\nTo address the problem, we need to determine the maximum number of contestants that can be seated in a single row of 55 seats under the restriction that no two contestants are seated 4 seats apart.\n\nLet's denote the seats in the row as positions \\(1, 2, 3, \\l... |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be the integer such that $0 \\le n < 29$ and $4n \\equiv 1 \\pmod{29}$. What is $\\left(3^n\\right)^4 - 3 \\pmod{29}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 37121,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $N = 100^2 + 99^2 - 98^2 - 97^2 + 96^2 + \\cdots + 4^2 + 3^2 - 2^2 - 1^2$, where the additions and subtractions alternate in pairs. Find the remainder when $N$ is divided by $1000$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 37122,
"solution": "Since we want the remainder when $N$ is divided by $1000$, we may ignore the $100^2$ term. Then, applying the difference of squares factorization to consecutive terms,\n\\begin{align*} N &= (99-98)(99+98) - (97-96)(97+96) + (95-94)(95 + 94) + \\cdots + (3-2)(3+2) -... |
deepscaler | [
{
"role": "user",
"content": "Suppose that $x, y$, and $z$ are complex numbers of equal magnitude that satisfy $$x+y+z=-\\frac{\\sqrt{3}}{2}-i \\sqrt{5}$$ and $$x y z=\\sqrt{3}+i \\sqrt{5}.$$ If $x=x_{1}+i x_{2}, y=y_{1}+i y_{2}$, and $z=z_{1}+i z_{2}$ for real $x_{1}, x_{2}, y_{1}, y_{2}, z_{1}$, and $z_{2... | math | {
"style": "rule",
"ground_truth": "1516"
} | {
"split": "train",
"index": 37123,
"solution": "From the conditions, it is clear that $a, b, c$ all have magnitude $\\sqrt{2}$. Conjugating the first equation gives $2\\left(\\frac{a b+b c+c a}{a b c}\\right)=-\\frac{\\sqrt{3}}{2}+i \\sqrt{5}$, which means $a b+b c+c a=\\left(-\\frac{\\sqrt{3}}{4}+i \\frac{\\sqr... |
deepscaler | [
{
"role": "user",
"content": "Find the number of square units in the area of the shaded region. Consider a rectangular plot with vertices at points (0,0), (40,0), (40,20), and (0,20). Within this rectangle, a shaded polygon is formed with vertices at (0,0), (20,0), (40,10), (40,20), and (10,20). Determine t... | math | {
"style": "rule",
"ground_truth": "600"
} | {
"split": "train",
"index": 37124,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\([x]\\) represents the largest integer not exceeding \\( x \\), if \\([x+0.1] + [x+0.2] + \\ldots + [x+0.9] = 104\\), what is the minimum value of \\( x \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11.5"
} | {
"split": "train",
"index": 37125,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the degree measure of the angle\n\n$$\n\\delta=\\arccos \\left(\\left(\\sin 2541^{\\circ}+\\sin 2542^{\\circ}+\\cdots+\\sin 6141^{\\circ}\\right)^{\\cos 2520^{\\circ}}+\\cos 2521^{\\circ}+\\cdots+\\cos 6120^{\\circ}\\right)\n$$ Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "69"
} | {
"split": "train",
"index": 37126,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\( AC = 1.5 \\, \\text{cm} \\) and \\( AD = 4 \\, \\text{cm} \\), what is the relationship between the areas of triangles \\( \\triangle ABC \\) and \\( \\triangle DBC \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3/5"
} | {
"split": "train",
"index": 37127,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the famous book \"Algorithm for Direct Calculation\" by the Chinese mathematician Cheng Dawei of the Ming Dynasty, there is a well-known math problem:\n\n\"One hundred mantou for one hundred monks, three big monks have no dispute, three small monks share one, how many big an... | math | {
"style": "rule",
"ground_truth": "75"
} | {
"split": "train",
"index": 37128,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An urn contains one red ball and one blue ball. A box of extra red and blue balls lies nearby. George performs the following operation four times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns those two matching balls to... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"split": "train",
"index": 37129,
"solution": "To solve this problem, we need to calculate the probability that after four operations, the urn contains exactly three red balls and three blue balls. We start with one red ball and one blue ball in the urn.\n\n#### Step 1: Understanding the possible sequences\nTo ... |
deepscaler | [
{
"role": "user",
"content": "In the isosceles right triangle \\(ABC\\) with \\(\\angle A = 90^\\circ\\) and \\(AB = AC = 1\\), a rectangle \\(EHGF\\) is inscribed such that \\(G\\) and \\(H\\) lie on the side \\(BC\\). Find the maximum area of the rectangle \\(EHGF\\). Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "1/4"
} | {
"split": "train",
"index": 37130,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the spring college entrance examination of Shanghai in 2011, there were 8 universities enrolling students. If exactly 3 students were admitted by 2 of these universities, the number of ways this could happen is ____. Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "168"
} | {
"split": "train",
"index": 37131,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Write $\\mathbf{2012}$ as the sum of $N$ distinct positive integers, where $N$ is at its maximum. What is the maximum value of $N$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "62"
} | {
"split": "train",
"index": 37132,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Real numbers $x$ and $y$ satisfy the equation $x^2 + y^2 = 10x - 6y - 34$. What is $x+y$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 37133,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the line \\( p \\) be the perpendicular bisector of points \\( A = (20, 12) \\) and \\( B = (-4, 3) \\). Determine the point \\( C = (x, y) \\) where line \\( p \\) meets segment \\( AB \\), and calculate \\( 3x - 5y \\). Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "-13.5"
} | {
"split": "train",
"index": 37134,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cube with a side of 10 is divided into 1000 smaller cubes each with an edge of 1. A number is written in each small cube such that the sum of the numbers in each column of 10 cubes (along any of the three directions) equals 0. In one of the cubes (denoted as A), the number 1 ... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 37135,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A gardener plans to enclose a rectangular garden with 480 feet of fencing. However, one side of the garden will be twice as long as another side. What is the maximum area of this garden? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12800"
} | {
"split": "train",
"index": 37136,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\sin \\alpha = 3 \\sin \\left(\\alpha + \\frac{\\pi}{6}\\right)$, find the value of $\\tan \\left(\\alpha + \\frac{\\pi}{12}\\right)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2 \\sqrt{3} - 4"
} | {
"split": "train",
"index": 37137,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The function $f$ is defined on positive integers as follows:\n\\[f(n) = \\left\\{\n\\begin{array}{cl}\nn + 10 & \\text{if $n < 10$}, \\\\\nf(n - 5) & \\text{if $n \\ge 10$}.\n\\end{array}\n\\right.\\]Find the maximum value of the function. Let's think step by step and put only ... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 37138,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the sum of the first $n$ terms of the sequence ${a_n}$ is $S_n$, and the sum of the first $n$ terms of the sequence ${b_n}$ is $T_n$. It is known that $a_1=2$, $3S_n=(n+2)a_n$, and $a_nb_n=\\frac{1}{2}$. If $\\lambda > T_n$ holds true for any $n\\in\\mathbb{N}^*$, fi... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 37139,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the rectangular coordinate system $xOy$, the ordinary equation of curve $C_1$ is $x^2+y^2-2x=0$. Establish a polar coordinate system with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of curve $C_2$ is $\\rho^{2}= \\frac {... | math | {
"style": "rule",
"ground_truth": "\\frac { \\sqrt {30}}{5}-1"
} | {
"split": "train",
"index": 37140,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many different rectangles with sides parallel to the grid can be formed by connecting four of the dots in a $5 \\times 5$ square array of dots? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 37141,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $u=-6$ and $x=\frac{1}{3}(3-4 u)$, 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": "9"
} | {
"split": "train",
"index": 37142,
"solution": "Substituting, $x=\frac{1}{3}(3-4 u)=\frac{1}{3}(3-4(-6))=\frac{1}{3}(3+24)=\frac{1}{3}(27)=9$."
} |
deepscaler | [
{
"role": "user",
"content": "On a dark and stormy night Snoopy suddenly saw a flash of lightning. Ten seconds later he heard the sound of thunder. The speed of sound is 1088 feet per second and one mile is 5280 feet. Estimate, to the nearest half-mile, how far Snoopy was from the flash of lightning. Let's ... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 37143,
"solution": "1. **Calculate the distance the sound traveled**: The problem states that the speed of sound is 1088 feet per second and it took 10 seconds for the sound of thunder to reach Snoopy after the flash of lightning. Therefore, the distance the sound traveled can be calc... |
deepscaler | [
{
"role": "user",
"content": "A bug crawls along a number line, starting at $-2$. It crawls to $-6$, then turns around and crawls to $5$. How many units does the bug crawl altogether? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 37144,
"solution": "1. **Calculate the distance from $-2$ to $-6$:**\n The distance on a number line is the absolute difference between the two points. Thus, the distance from $-2$ to $-6$ is:\n \\[\n |-6 - (-2)| = |-6 + 2| = |-4| = 4 \\text{ units}\n \\]\n\n2. **Calculate the... |
deepscaler | [
{
"role": "user",
"content": "Starting with the number 100, Shaffiq repeatedly divides his number by two and then takes the greatest integer less than or equal to that number. How many times must he do this before he reaches the number 1? Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 37145,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve for $x$: $x+2x = 400-(3x+4x)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 37146,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\alpha$ and $\\beta$ are the roots of the equation $x^2 - 3x - 2 = 0,$ find the value of $5 \\alpha^4 + 12 \\beta^3.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "672.5 + 31.5\\sqrt{17}"
} | {
"split": "train",
"index": 37147,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In parallelogram $ABCD$, let $O$ be the intersection of diagonals $\\overline{AC}$ and $\\overline{BD}$. Angles $CAB$ and $DBC$ are each twice as large as angle $DBA$, and angle $ACB$ is $r$ times as large as angle $AOB$. Find $\\lfloor 1000r \\rfloor$. Let's think step by step... | math | {
"style": "rule",
"ground_truth": "777"
} | {
"split": "train",
"index": 37148,
"solution": "[asy]size(180); pathpen = black+linewidth(0.7); pair B=(0,0), A=expi(pi/4), C=IP(A--A + 2*expi(17*pi/12), B--(3,0)), D=A+C, O=IP(A--C,B--D); D(MP(\"A\",A,N)--MP(\"B\",B)--MP(\"C\",C)--MP(\"D\",D,N)--cycle); D(B--D); D(A--C); D(MP(\"O\",O,SE)); D(anglemark(D,B,A,4))... |
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