data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Find the number of permutations of $1, 2, 3, 4, 5, 6$ such that for each $k$ with $1$ $\\leq$ $k$ $\\leq$ $5$, at least one of the first $k$ terms of the permutation is greater than $k$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "461"
} | {
"split": "train",
"index": 28049,
"solution": "If $6$ is the first number, then there are no restrictions. There are $5!$, or $120$ ways to place the other $5$ numbers.\n If $6$ is the second number, then the first number can be $2, 3, 4,$ or $5$, and there are $4!$ ways to place the other $4$ numbers. $4 \\cdo... |
deepscaler | [
{
"role": "user",
"content": "Given $O$ as the circumcenter of $\\triangle ABC$ and $D$ as the midpoint of $BC$. If $\\overrightarrow{AO} \\cdot \\overrightarrow{AD}=4$ and $BC=2 \\sqrt{6}$, then find the length of $AD$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 28050,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a regular triangular prism $ABC-A_1B_1C_1$ with side edges equal to the edges of the base, the sine of the angle formed by $AB_1$ and the lateral face $ACCA_1$ is equal to _______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{6}}{4}"
} | {
"split": "train",
"index": 28051,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $a \\in \\{0,1,2\\}$ and $b \\in \\{-1,1,3,5\\}$, the probability that the function $f(x) = ax^2 - 2bx$ is an increasing function in the interval $(1, +\\infty)$ is $(\\quad\\quad)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 28052,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $α$ is an angle in the fourth quadrant and $\\cos α= \\frac {3}{5}$.\n(1) Find the value of $\\tan α$;\n(2) Find the value of $\\frac {\\sin ( \\frac {3}{2}π-α)+2\\cos (α+ \\frac {π}{2})}{\\sin (α-π)-3\\cos (2π-α)}$. Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 28053,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider all angles measured in degrees. Calculate the product $\\prod_{k=1}^{22} \\csc^2(4k-3)^\\circ = m^n$, where $m$ and $n$ are integers greater than 1. Find the value of $m+n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 28054,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $A=\\{-3,-2,-1,0,1,2,3\\}$, $a$ and $b$ are elements of $A$. How many cases are there where $|a| \\lt |b|$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 28055,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the units digit of $7 \\cdot 17 \\cdot 1977 - 7^3$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 28056,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a right triangular prism $\\mathrm{ABC}-\\mathrm{A}_{1} \\mathrm{~B}_{1} \\mathrm{C}_{1}$, the lengths of the base edges and the lateral edges are all 2. If $\\mathrm{E}$ is the midpoint of $\\mathrm{CC}_{1}$, what is the distance from $\\mathrm{C}_{1}$ to the plane $\\mathr... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 28057,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $L,E,T,M,$ and $O$ be digits that satisfy $LEET+LMT=TOOL.$ Given that $O$ has the value of $0,$ digits may be repeated, and $L\\neq0,$ what is the value of the $4$ -digit integer $ELMO?$ Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "1880"
} | {
"split": "train",
"index": 28058,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The expression $\\frac{x^2-3x+2}{x^2-5x+6} \\div \\frac{x^2-5x+4}{x^2-7x+12}$, when simplified is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 28059,
"solution": "1. **Factorize each quadratic expression** in the given complex fraction:\n - Numerator of the first fraction: $x^2 - 3x + 2 = (x-2)(x-1)$.\n - Denominator of the first fraction: $x^2 - 5x + 6 = (x-3)(x-2)$.\n - Numerator of the second fraction: $x^2 - 5x + 4... |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, it is given that $BD:DC = 3:2$ and $AE:EC = 3:4$. Point $M$ is the intersection of $AD$ and $BE$. If the area of $\\triangle ABC$ is 1, what is the area of $\\triangle BMD$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{15}"
} | {
"split": "train",
"index": 28060,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Today is December 19, 2010. What is the integer part of the sum $\\frac{2010}{1000}+\\frac{1219}{100}+\\frac{27}{10}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 28061,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$, respectively. It is given that $\\frac{b}{c} = \\frac{2\\sqrt{3}}{3}$ and $A + 3C = \\pi$.\n\n$(1)$ Find the value of $\\cos C$;\n\n$(2)$ Find the value of $\\sin B$;\n\n$(3)$ ... | math | {
"style": "rule",
"ground_truth": "\\frac{9\\sqrt{2}}{4}"
} | {
"split": "train",
"index": 28062,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sports league has 20 teams split into four divisions of 5 teams each. How many games are there in a complete season if each team plays every other team in its own division three times and every team in the other divisions once? Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "270"
} | {
"split": "train",
"index": 28063,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the geometric sequence $\\{a_n\\}$ with a common ratio greater than $1$, $a_3a_7=72$, $a_2+a_8=27$, calculate $a_{12}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 28064,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For what value of $x$ does $10^{x} \\cdot 100^{2x}=1000^{5}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 28065,
"solution": "1. **Rewrite the equation using properties of exponents:**\n Given the equation \\(10^x \\cdot 100^{2x} = 1000^5\\), we start by expressing all terms with base 10:\n \\[\n 100 = 10^2 \\quad \\text{and} \\quad 1000 = 10^3\n \\]\n Therefore, the equation be... |
deepscaler | [
{
"role": "user",
"content": "Alice and Bob are playing the Smallest Positive Integer Game. Alice says, \"My number is 24.\" Bob says, \"What kind of silly smallest number is that? Every prime factor of your number is also a prime factor of my number.\"\n\nWhat is the smallest possible number that Bob could... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 28066,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the ancient Chinese mathematical text \"The Mathematical Classic of Sunzi\", there is a problem stated as follows: \"Today, a hundred deer enter the city. Each family takes one deer, but not all are taken. Then, three families together take one deer, and all deer are taken. ... | math | {
"style": "rule",
"ground_truth": "75"
} | {
"split": "train",
"index": 28067,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nGiven real numbers \\(a_{1}, a_{2}, \\cdots, a_{n}\\) which are all greater than 0 (where \\(n\\) is a natural number no less than 4) and satisfy the equation \\(a_{1} + a_{2} + \\cdots + a_{n} = 1\\), find the maximum value of the sum \\(S = \\sum_{k=1}^{n} \\frac{a_{k}^{2}}... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 28068,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $xOy$, a polar coordinate system is established with the origin $O$ as the pole and the positive half-axis of the x-axis as the polar axis. It is known that the point $P(\\sqrt {2}, \\frac {7\\pi}{4})$ lies on the line $l: \\rho\\cos\\theta +2... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{5}}{10}"
} | {
"split": "train",
"index": 28069,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The left and right foci of the hyperbola $C$ are respectively $F_1$ and $F_2$, and $F_2$ coincides with the focus of the parabola $y^2=4x$. Let the point $A$ be an intersection of the hyperbola $C$ with the parabola, and suppose that $\\triangle AF_{1}F_{2}$ is an isosceles tri... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2} + 1"
} | {
"split": "train",
"index": 28070,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When $n$ is divided by 6, a remainder of 1 is given. What is the remainder when $n+2010$ is divided by 6? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 28071,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Of the following sets, the one that includes all values of $x$ which will satisfy $2x - 3 > 7 - x$ is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x >\\frac{10}{3}"
} | {
"split": "train",
"index": 28072,
"solution": "To find the set of all values of $x$ that satisfy the inequality $2x - 3 > 7 - x$, we start by simplifying the inequality:\n\n1. **Combine like terms**: \n \\[\n 2x - 3 > 7 - x\n \\]\n Add $x$ to both sides to get all $x$ terms on one side:\n \\[\n 2x +... |
deepscaler | [
{
"role": "user",
"content": "The sum of the numerical coefficients in the complete expansion of $(x^2 - 2xy + y^2)^7$ is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 28073,
"solution": "1. **Identify the Expression**: The given expression is $(x^2 - 2xy + y^2)^7$. \n\n2. **Recognize the Binomial Expansion**: Observe that $x^2 - 2xy + y^2$ can be rewritten as $(x-y)^2$. Therefore, the expression becomes $((x-y)^2)^7 = (x-y)^{14}$.\n\n3. **Apply the... |
deepscaler | [
{
"role": "user",
"content": "A quarry wants to sell a large pile of gravel. At full price, the gravel would sell for $3200$ dollars. But during the first week the quarry only sells $60\\%$ of the gravel at full price. The following week the quarry drops the price by $10\\%$ , and, again, it sells $60... | math | {
"style": "rule",
"ground_truth": "3000"
} | {
"split": "train",
"index": 28074,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Class 2-5 planted 142 trees. Class 2-3 planted 18 fewer trees than Class 2-5. How many trees did Class 2-3 plant? How many trees did the two classes plant in total? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "266"
} | {
"split": "train",
"index": 28075,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "As a result of five measurements of the rod's length with one device (without systematic errors), the following results (in mm) were obtained: $92, 94, 103, 105, 106$. Find: a) the sample mean length of the rod; b) the sample variance and the unbiased corrected variance of the ... | math | {
"style": "rule",
"ground_truth": "42.5"
} | {
"split": "train",
"index": 28076,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\cos \\theta = \\frac{1}{4},$ then find $\\cos 3 \\theta.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{11}{16}"
} | {
"split": "train",
"index": 28077,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many natural numbers between 150 and 300 are divisible by 9? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 28078,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathbf{A} = \\begin{pmatrix} a & 1 \\\\ -2 & d \\end{pmatrix}$ for some real numbers $a$ and $d.$ If\n\\[\\mathbf{A} + \\mathbf{A}^{-1} = \\mathbf{0},\\]then find $\\det \\mathbf{A}.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 28079,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of all two-digit positive integers whose squares end with the digits 25? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "644"
} | {
"split": "train",
"index": 28080,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An arbitrary point \\( E \\) inside the square \\( ABCD \\) with side length 1 is connected by line segments to its vertices. Points \\( P, Q, F, \\) and \\( T \\) are the points of intersection of the medians of triangles \\( BCE, CDE, DAE, \\) and \\( ABE \\) respectively. Fi... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{9}"
} | {
"split": "train",
"index": 28081,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the convex pentagon $ABCDE$, $\\angle A = \\angle B = 120^{\\circ}$, $EA = AB = BC = 2$, and $CD = DE = 4$. The area of $ABCDE$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7 \\sqrt{3}"
} | {
"split": "train",
"index": 28082,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A hotel packed breakfast for each of three guests. Each breakfast should have consisted of three types of rolls, one each of nut, cheese, and fruit rolls. The preparer wrapped each of the nine rolls and once wrapped, the rolls were indistinguishable from one another. She then r... | math | {
"style": "rule",
"ground_truth": "79"
} | {
"split": "train",
"index": 28083,
"solution": "Call the three different types of rolls as A, B, and C. We need to arrange 3As, 3Bs, and 3Cs in a string such that A, B, and C appear in the first three, second three, and the third three like ABCABCABC or BCABACCAB. This can occur in $\\left(\\frac{3!}{1!1!1!}\\ri... |
deepscaler | [
{
"role": "user",
"content": "Two distinct numbers are selected simultaneously and at random from the set $\\{1, 2, 3, 6, 9\\}$. What is the probability that the smaller one divides the larger one? Express your answer as a common fraction. Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 28084,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If for any positive integer \\( m \\), the set\n$$\n\\{m, m+1, m+2, \\cdots, m+99\\}\n$$\nin any \\( n \\)-element subset with \\( n \\geq 3 \\), there are always three elements that are pairwise coprime, find the smallest value of \\( n \\). Let's think step by step and put on... | math | {
"style": "rule",
"ground_truth": "68"
} | {
"split": "train",
"index": 28085,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the polar coordinate system, the equation of curve C is $\\rho^2\\cos2\\theta=9$. Point P is $(2\\sqrt{3}, \\frac{\\pi}{6})$. Establish a Cartesian coordinate system with the pole O as the origin and the positive half-axis of the x-axis as the polar axis. \n(1) Find the par... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 28086,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x,$ $y,$ and $z$ be positive real numbers such that $xyz = 1.$ Find the minimum value of\n\\[(x + 2y)(y + 2z)(xz + 1).\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 28087,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For what value(s) of $k$ does the pair of equations $y=x^2$ and $y=3x+k$ have two identical solutions? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{9}{4}"
} | {
"split": "train",
"index": 28088,
"solution": "1. **Identify the condition for identical solutions**: The problem states that the equations $y = x^2$ and $y = 3x + k$ should have two identical solutions. This means that the quadratic equation formed by equating these two expressions should have exactly one uniq... |
deepscaler | [
{
"role": "user",
"content": "What is the sum of all four-digit integers from 1000 to 5000, where each number increases by 4 from the previous one? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3003000"
} | {
"split": "train",
"index": 28089,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define $n!!$ to be $n(n-2)(n-4)\\cdots 3\\cdot 1$ for $n$ odd and $n(n-2)(n-4)\\cdots 4\\cdot 2$ for $n$ even. When $\\sum_{i=1}^{2009} \\frac{(2i-1)!!}{(2i)!!}$ is expressed as a fraction in lowest terms, its denominator is $2^ab$ with $b$ odd. Find $\\dfrac{ab}{10}$.\n Let's ... | math | {
"style": "rule",
"ground_truth": "401"
} | {
"split": "train",
"index": 28090,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The picture shows the same die in three different positions. When the die is rolled, what is the probability of rolling a 'YES'?\n\nA) \\(\\frac{1}{3}\\)\nB) \\(\\frac{1}{2}\\)\nC) \\(\\frac{5}{9}\\)\nD) \\(\\frac{2}{3}\\)\nE) \\(\\frac{5}{6}\\) Let's think step by step and put... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 28091,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, angle $C$ is a right angle and the altitude from $C$ meets $\\overline{AB}$ at $D$. The lengths of the sides of $\\triangle ABC$ are integers, $BD = 17^3$, and $\\cos B = m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Let's think ... | math | {
"style": "rule",
"ground_truth": "162"
} | {
"split": "train",
"index": 28092,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define a domino to be an ordered pair of distinct positive integers. A proper sequence of dominos is a list of distinct dominos in which the first coordinate of each pair after the first equals the second coordinate of the immediately preceding pair, and in which $(i,j)$ and $(... | math | {
"style": "rule",
"ground_truth": "761"
} | {
"split": "train",
"index": 28093,
"solution": "We can draw a comparison between the domino a set of 40 points (labeled 1 through 40) in which every point is connected with every other point. The connections represent the dominoes.\n You need to have all even number of segments coming from each point except 0 or... |
deepscaler | [
{
"role": "user",
"content": "Given the quadratic function $f(x)=x^{2}-x+k$, where $k\\in\\mathbb{Z}$, if the function $g(x)=f(x)-2$ has two distinct zeros in the interval $(-1, \\frac{3}{2})$, find the minimum value of $\\frac{[f(x)]^{2}+2}{f(x)}$. Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "\\frac{81}{28}"
} | {
"split": "train",
"index": 28094,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the minimum value of\n\\[\n\\sqrt{x^2 + (2 - x)^2} + \\sqrt{(2 - x)^2 + (2 + x)^2}\n\\]\nover all real numbers \\( x \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{5}"
} | {
"split": "train",
"index": 28095,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, we have $\\angle C = 90^\\circ$, $AB = 13$, and $BC = 5$. What is $\\tan A$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{12}"
} | {
"split": "train",
"index": 28096,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two distinct positive integers from 1 to 50 inclusive are chosen. Let the sum of the integers equal $S$ and the product equal $P$. What is the probability that $P+S$ is one less than a multiple of 5? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "\\frac{89}{245}"
} | {
"split": "train",
"index": 28097,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The teacher of the summer math camp brought with him several shirts, several pairs of pants, several pairs of shoes, and two jackets for the entire summer. On each lesson, he wore pants, a shirt, and shoes, and wore a jacket for some lessons. On any two lessons, at least one el... | math | {
"style": "rule",
"ground_truth": "216"
} | {
"split": "train",
"index": 28098,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Express $(5-4i)-2(3+6i)$ as a complex number. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1-16i"
} | {
"split": "train",
"index": 28099,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the sum: $\\dfrac{2}{100} + \\dfrac{5}{1000} + \\dfrac{8}{10000} + \\dfrac{6}{100000}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.02586"
} | {
"split": "train",
"index": 28100,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given points $A(-1, 2, 0)$, $B(5, 2, -1)$, $C(2, -1, 4)$, and $D(-2, 2, -1)$ in space, find:\n\na) the distance from vertex $D$ of tetrahedron $ABCD$ to the intersection point of the medians of the base $ABC$;\n\nb) the equation of the plane $ABC$;\n\nc) the height of the tetra... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 28101,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are $13$ positive integers greater than $\\sqrt{15}$ and less than $\\sqrt[3]{B}$ . What is the smallest integer value of $B$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4097"
} | {
"split": "train",
"index": 28102,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the 43rd digit after the decimal point in the decimal representation of $\\frac{1}{13}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 28103,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The circles $C_1$ and $C_2$ are defined by the equations $x^2 + y^2 = 1$ and $(x - 2)^2 + y^2 = 16,$ respectively. Find the locus of the centers $(a,b)$ of all circles externally tangent to $C_1$ and internally tangent to $C_2.$ Enter your answer in the form\n\\[Pa^2 + Qb^2 +... | math | {
"style": "rule",
"ground_truth": "84a^2 + 100b^2 - 168a - 441 = 0"
} | {
"split": "train",
"index": 28104,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On November 15, a dodgeball tournament took place. In each game, two teams competed. A win was awarded 15 points, a tie 11 points, and a loss 0 points. Each team played against every other team once. At the end of the tournament, the total number of points accumulated was 1151.... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 28105,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On his birthday, the last guest to arrive was Yana, who gave Andrey a ball, and the second last was Eduard, who gave him a calculator. While using the calculator, Andrey noticed that the product of the total number of gifts he received and the number of gifts he had before Edua... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 28106,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the value of $12 \\times 24 + 36 \\times 12$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "720"
} | {
"split": "train",
"index": 28107,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle \\( \\triangle ABC \\), \\( AB = 6 \\), \\( BC = 4 \\), and the length of the median to side \\( AC \\) is \\( \\sqrt{10} \\). Find the value of \\( \\sin^6 \\left( \\frac{A}{2} \\right) + \\cos^6 \\left( \\frac{A}{2} \\right) \\). Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "\\frac{211}{256}"
} | {
"split": "train",
"index": 28108,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$ABCD$ is a square that is made up of two identical rectangles and two squares of area $4 \\mathrm{~cm}^{2}$ and $16 \\mathrm{cm}^{2}$. What is the area, in $\\mathrm{cm}^{2}$, of the square $ABCD$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 28109,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the number of ways to arrange the letters of the word MAMMAAD. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "140"
} | {
"split": "train",
"index": 28110,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A,B,C$ be angles of a triangle, where angle $B$ is obtuse, and \\begin{align*}\n\\cos^2 A + \\cos^2 B + 2 \\sin A \\sin B \\cos C &= \\frac{15}{8} \\text{ and} \\\\\n\\cos^2 B + \\cos^2 C + 2 \\sin B \\sin C \\cos A &= \\frac{14}{9}.\n\\end{align*}There are positive intege... | math | {
"style": "rule",
"ground_truth": "222"
} | {
"split": "train",
"index": 28111,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(x)=2 x^{3}-2 x$. For what positive values of $a$ do there exist distinct $b, c, d$ such that $(a, f(a))$, $(b, f(b)),(c, f(c)),(d, f(d))$ is a rectangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left[\\frac{\\sqrt{3}}{3}, 1\\right]"
} | {
"split": "train",
"index": 28112,
"solution": "Say we have four points $(a, f(a)),(b, f(b)),(c, f(c)),(d, f(d))$ on the curve which form a rectangle. If we interpolate a cubic through these points, that cubic will be symmetric around the center of the rectangle. But the unique cubic through the four points is $... |
deepscaler | [
{
"role": "user",
"content": "Find $\\frac{7}{17} - \\frac{4}{51}$. Reduce your answer to simplest form. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 28113,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From the natural numbers 1 to 100, each time we take out two different numbers so that their sum is greater than 100, how many different ways are there to do this? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2500"
} | {
"split": "train",
"index": 28114,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the function $f(x)=\\frac{1}{3}x^{3}-\\frac{3}{2}x^{2}+ax+4$ is strictly decreasing on the interval $[-1,4]$, then the value of the real number $a$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4"
} | {
"split": "train",
"index": 28115,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $[x]$ denote the greatest integer less than or equal to $x$. When $0 \\leqslant x \\leqslant 10$, find the number of distinct integers represented by the function $f(x) = [x] + [2x] + [3x] + [4x]$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "61"
} | {
"split": "train",
"index": 28116,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If Greg rolls six fair six-sided dice, what is the probability that he rolls more 2's than 5's? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{16710}{46656}"
} | {
"split": "train",
"index": 28117,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two nonhorizontal, non vertical lines in the $xy$-coordinate plane intersect to form a $45^{\\circ}$ angle. One line has slope equal to $6$ times the slope of the other line. What is the greatest possible value of the product of the slopes of the two lines? Let's think step by ... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"split": "train",
"index": 28118,
"solution": "1. **Identify the relationship between the slopes and the angle**: Given that two lines intersect at a $45^\\circ$ angle, we can use the tangent addition formula to relate the slopes of the lines. Let the slope of one line be $m_1$ and the other be $m_2$. The tange... |
deepscaler | [
{
"role": "user",
"content": "At the end of which year did Steve have more money than Wayne for the first time? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2004"
} | {
"split": "train",
"index": 28119,
"solution": "Steve's and Wayne's amounts of money double and halve each year, respectively. By 2004, Steve has more money than Wayne."
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(x) = x^2 - x + 2010$. What is the greatest common divisor of $f(100)$ and $f(101)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 28120,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle is divided into two segments by a chord equal to the side of a regular inscribed triangle. Determine the ratio of the areas of these segments. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4\\pi - 3\\sqrt{3}}{8\\pi + 3\\sqrt{3}}"
} | {
"split": "train",
"index": 28121,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a matrix $A = \\begin{pmatrix} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\end{pmatrix}$ where $a_{11}, a_{12}, a_{21}, a_{22} \\in \\{0, 1\\}$, and the determinant of $A$ is 0. Determine the number of distinct matrices $A$. Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 28122,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that all terms are positive in the geometric sequence $\\{a_n\\}$, and the sum of the first $n$ terms is $S_n$, if $S_1 + 2S_5 = 3S_3$, then the common ratio of $\\{a_n\\}$ equals \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 28123,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From time $t=0$ to time $t=1$ a population increased by $i\\%$, and from time $t=1$ to time $t=2$ the population increased by $j\\%$. Therefore, from time $t=0$ to time $t=2$ the population increased by Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "\\left(i+j+\\frac{ij}{100}\\right)\\%"
} | {
"split": "train",
"index": 28124,
"solution": "1. **Identify the scale factors for each time period:**\n - From $t=0$ to $t=1$, the population increases by $i\\%$. The scale factor for this increase is $1 + \\frac{i}{100}$.\n - From $t=1$ to $t=2$, the population increases by $j\\%$. The scale factor for th... |
deepscaler | [
{
"role": "user",
"content": "Palindromic primes are two-digit prime numbers such that the number formed when the digits are reversed is also prime. What is the sum of all palindromic primes less than 50? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "109"
} | {
"split": "train",
"index": 28125,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(x_{1}, x_{2}\\) be the roots of the quadratic equation \\(ax^{2} + bx + c = 0\\) with real coefficients. If \\(x_{1}\\) is an imaginary number and \\(\\frac{x_{1}^{2}}{x_{2}}\\) is a real number, determine the value of \\(S = 1 + \\frac{x_{1}}{x_{2}} + \\left(\\frac{x_{1... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 28126,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\frac{1}{1-x-x^{2}-x^{3}}=\\sum_{i=0}^{\\infty} a_{n} x^{n}$, for what positive integers $n$ does $a_{n-1}=n^{2}$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1, 9"
} | {
"split": "train",
"index": 28127,
"solution": "Multiplying both sides by $1-x-x^{2}-x^{3}$ the right hand side becomes $a_{0}+\\left(a_{1}-a_{0}\\right) x+\\left(a_{2}-a_{1}-a_{0}\\right) x^{2}+\\ldots$, and setting coefficients of $x^{n}$ equal to each other we find that $a_{0}=1, a_{1}=1, a_{2}=2$, and $a_{n}... |
deepscaler | [
{
"role": "user",
"content": "Vasya wrote a note on a piece of paper, folded it in four, and labeled the top with \"MAME\". Then he unfolded the note, added something else, folded it along the creases in a random manner (not necessarily the same as before), and left it on the table with a random side up. Fi... | math | {
"style": "rule",
"ground_truth": "1/8"
} | {
"split": "train",
"index": 28128,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nA two-digit integer between 10 and 99, inclusive, is chosen at random. Each possible integer is equally likely to be chosen. What is the probability that its tens digit is a multiple of its units (ones) digit? Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "23/90"
} | {
"split": "train",
"index": 28129,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Distinct points $A, B, C, D$ are given such that triangles $A B C$ and $A B D$ are equilateral and both are of side length 10 . Point $E$ lies inside triangle $A B C$ such that $E A=8$ and $E B=3$, and point $F$ lies inside triangle $A B D$ such that $F D=8$ and $F B=3$. What i... | math | {
"style": "rule",
"ground_truth": "\\frac{91 \\sqrt{3}}{4}"
} | {
"split": "train",
"index": 28130,
"solution": "$\\angle F B D+\\angle A B F=\\angle A B D=60^{\\circ}$. Since $E B=B F=3$, this means that $E B F$ is an equilateral triangle of side length 3. Now we have $[A E F D]=[A E B D]-[E B F]-[F B D]=[A E B]+[A B D]-[E B F]-$ $[F B D]=[A B D]-[E B F]=\\frac{\\sqrt{3}}{4}... |
deepscaler | [
{
"role": "user",
"content": "How many ways are there to arrange the letters of the word $\\text{BA}_1\\text{N}_1\\text{A}_2\\text{N}_2\\text{A}_3$, in which the three A's and the two N's are considered different? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "720"
} | {
"split": "train",
"index": 28131,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a set of data: $2$, $x$, $4$, $6$, $10$, with an average value of $5$, find the standard deviation of this data set. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}"
} | {
"split": "train",
"index": 28132,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x$ and $y$ be real numbers such that\n\\[\\frac{\\sin x}{\\cos y} + \\frac{\\sin y}{\\cos x} = 1 \\quad \\text{and} \\quad \\frac{\\cos x}{\\sin y} + \\frac{\\cos y}{\\sin x} = 6.\\]Compute\n\\[\\frac{\\tan x}{\\tan y} + \\frac{\\tan y}{\\tan x}.\\] Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "\\frac{124}{13}"
} | {
"split": "train",
"index": 28133,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\triangle ABC$ is an isosceles right triangle with one leg length of $1$, determine the volume of the resulting geometric solid when $\\triangle ABC$ is rotated around one of its sides Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}\\pi}{6}"
} | {
"split": "train",
"index": 28134,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A district in a city is laid out in an $11 \\times 11$ grid. Every day, a sprinkler truck departs from the bottom-left corner $A(0,0)$ and travels along the streets to reach the top-right corner $B(10,10)$. At each intersection, the driver randomly chooses a direction, as long ... | math | {
"style": "rule",
"ground_truth": "1 - \\frac{\\binom{18}{9}}{\\binom{20}{10}}"
} | {
"split": "train",
"index": 28135,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose $x$ is a real number such that $\\sin \\left(1+\\cos ^{2} x+\\sin ^{4} x\\right)=\\frac{13}{14}$. Compute $\\cos \\left(1+\\sin ^{2} x+\\cos ^{4} x\\right)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{3 \\sqrt{3}}{14}"
} | {
"split": "train",
"index": 28136,
"solution": "We first claim that $\\alpha:=1+\\cos ^{2} x+\\sin ^{4} x=1+\\sin ^{2} x+\\cos ^{4} x$. Indeed, note that $$\\sin ^{4} x-\\cos ^{4} x=\\left(\\sin ^{2} x+\\cos ^{2} x\\right)\\left(\\sin ^{2} x-\\cos ^{2} x\\right)=\\sin ^{2} x-\\cos ^{2} x$$ which is the desired a... |
deepscaler | [
{
"role": "user",
"content": "How many integers are greater than $\\sqrt{15}$ and less than $\\sqrt{50}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 28137,
"solution": "Using a calculator, $\\sqrt{15} \\approx 3.87$ and $\\sqrt{50} \\approx 7.07$. The integers between these real numbers are $4,5,6,7$, of which there are 4 . Alternatively, we could note that integers between $\\sqrt{15}$ and $\\sqrt{50}$ correspond to values of $\\... |
deepscaler | [
{
"role": "user",
"content": "The remainder when \\( 104^{2006} \\) is divided by 29 is ( ) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 28138,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Coins are arranged in a row from left to right. It is known that two of them are fake, they lie next to each other, the left one weighs 9 grams, the right one weighs 11 grams, and all the remaining are genuine and each weighs 10 grams. The coins are weighed on a balance scale, ... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 28139,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A hexagon inscribed in a circle has three consecutive sides, each of length 3, and three consecutive sides, each of length 5. The chord of the circle that divides the hexagon into two trapezoids, one with three sides, each of length 3, and the other with three sides, each of le... | math | {
"style": "rule",
"ground_truth": "409"
} | {
"split": "train",
"index": 28140,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a sequence $\\{x_n\\}$ that satisfies $x_{n+2}=|x_{n+2}-x_n|$ (where $n \\in \\mathbb{N}^*$), if $x_1=1$, $x_2=a$ (where $a \\leqslant 1$ and $a \\neq 0$), and $x_{n+3}=x_n$ for any positive integer $n$, then the sum of the first 2017 terms of the sequence $\\{x_n\\}$ is ... | math | {
"style": "rule",
"ground_truth": "1345"
} | {
"split": "train",
"index": 28141,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Gauss family has three boys aged $7,$ a girl aged $14,$ and a boy aged $15.$ What is the mean (average) of the ages of the children? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 28142,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABCD$ be a quadrilateral with side lengths $AB=2, BC=3, CD=5$, and $DA=4$. What is the maximum possible radius of a circle inscribed in quadrilateral $ABCD$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{30}}{7}"
} | {
"split": "train",
"index": 28143,
"solution": "Let the tangent lengths be $a, b, c, d$ so that $a+b=2, b+c=3, c+d=5, d+a=4$. Then $b=2-a$ and $c=1+a$ and $d=4-a$. The radius of the inscribed circle of quadrilateral $ABCD$ is given by $\\sqrt{\\frac{abc+abd+acd+bcd}{a+b+c+d}}=\\sqrt{\\frac{-7a^{2}+16a+8}{7}}$. T... |
deepscaler | [
{
"role": "user",
"content": "A square is drawn inside a rectangle. The ratio of the width of the rectangle to a side of the square is $2:1$. The ratio of the rectangle's length to its width is $2:1$. What percent of the rectangle's area is inside the square? Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "12.5"
} | {
"split": "train",
"index": 28144,
"solution": "1. **Assigning Dimensions Based on Given Ratios:**\n - Let the side length of the square be $s$.\n - According to the problem, the width of the rectangle is twice the side of the square. Therefore, the width of the rectangle is $2s$.\n - The ratio of the rect... |
deepscaler | [
{
"role": "user",
"content": "For a positive integer \\( n \\), consider the function\n\n\\[ \nf(n)=\\frac{4n+\\sqrt{4n^2-1}}{\\sqrt{2n+1}+\\sqrt{2n-1}} \n\\]\n\nCalculate the value of\n\n\\[ \nf(1)+f(2)+f(3)+\\cdots+f(40) \n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "364"
} | {
"split": "train",
"index": 28145,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively. Given that $\\cos(B-C) - 2\\sin B\\sin C = -\\frac{1}{2}$.\n1. Find the measure of angle $A$.\n2. When $a = 5$ and $b = 4$, find the area of $\\triangle ABC$. Let's think ste... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{3} + \\sqrt{39}"
} | {
"split": "train",
"index": 28146,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( n = 2^{31} \\times 3^{19} \\times 5^7 \\). How many positive integer divisors of \\( n^2 \\) are less than \\( n \\) but do not divide \\( n \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13307"
} | {
"split": "train",
"index": 28147,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\displaystyle\\frac{m}{n} = 15$, $\\displaystyle\\frac{p}{n} = 3$, and $\\displaystyle \\frac{p}{q} = \\frac{1}{10}$, then what is $\\displaystyle\\frac{m}{q}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 28148,
"solution": ""
} |
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