data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "How much money does Roman give Dale if Roman wins a contest with a prize of $\\$ 200$, gives $30 \\%$ of the prize to Jackie, and then splits $15 \\%$ of what remains equally between Dale and Natalia? Let's think step by step and put only the final answer within \\boxed{}."
}... | math | {
"style": "rule",
"ground_truth": "\\$ 10.50"
} | {
"split": "train",
"index": 35349,
"solution": "To determine $30 \\%$ of Roman's $\\$ 200$ prize, we calculate $\\$ 200 \\times 30 \\%=\\$ 200 \\times \\frac{30}{100}=\\$ 2 \\times 30=\\$ 60$. After Roman gives $\\$ 60$ to Jackie, he has $\\$ 200-\\$ 60=\\$ 140$ remaining. He splits $15 \\%$ of this between Dale... |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $xOy$, point $F$ is a focus of the ellipse $C$: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 (a > b > 0)$, and point $B_1(0, -\\sqrt{3})$ is a vertex of $C$, $\\angle OFB_1 = \\frac{\\pi}{3}$.\n\n$(1)$ Find the standard equation of $C$;\n\n$(2)$ I... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 35350,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "11 people were standing in line under the rain, each holding an umbrella. They stood so close together that the umbrellas touched each other. Once the rain stopped, people closed their umbrellas and maintained a distance of 50 cm between each other. By how many times did the le... | math | {
"style": "rule",
"ground_truth": "2.2"
} | {
"split": "train",
"index": 35351,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $P$ is a moving point on the parabola $y^{2}=4x$, and $Q$ is a moving point on the circle $x^{2}+(y-4)^{2}=1$, find the minimum value of the sum of the distance between points $P$ and $Q$ and the distance between point $P$ and the axis of symmetry of the parabola. Le... | math | {
"style": "rule",
"ground_truth": "\\sqrt{17}-1"
} | {
"split": "train",
"index": 35352,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive integer \\( n \\) such that\n\\[\n\\sqrt{5 n}-\\sqrt{5 n-4}<0.01\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8001"
} | {
"split": "train",
"index": 35353,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathbf{a},$ $\\mathbf{b},$ and $\\mathbf{c}$ be three vectors such that $\\mathbf{a}$ is a unit vector, $\\mathbf{b}$ and $\\mathbf{c}$ have magnitudes of 2, and $\\mathbf{a} \\cdot \\mathbf{b} = 0$, $\\mathbf{b} \\cdot \\mathbf{c} = 4$. Given that\n\\[\n\\mathbf{a} = p(... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 35354,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let three non-identical complex numbers \\( z_1, z_2, z_3 \\) satisfy the equation \\( 4z_1^2 + 5z_2^2 + 5z_3^2 = 4z_1z_2 + 6z_2z_3 + 4z_3z_1 \\). Denote the lengths of the sides of the triangle in the complex plane, with vertices at \\( z_1, z_2, z_3 \\), from smallest to larg... | math | {
"style": "rule",
"ground_truth": "2:\\sqrt{5}:\\sqrt{5}"
} | {
"split": "train",
"index": 35355,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given four real numbers that form an arithmetic sequence: -9, $a_1$, $a_2$, -1, and five real numbers that form a geometric sequence: -9, $b_1$, $b_2$, $b_3$, -1, find the value of $b_2(a_2-a_1)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-8"
} | {
"split": "train",
"index": 35356,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of geese in a flock increases so that the difference between the populations in year $n+2$ and year $n$ is directly proportional to the population in year $n+1$. If the populations in the years $1994$, $1995$, and $1997$ were $39$, $60$, and $123$, respectively, then... | math | {
"style": "rule",
"ground_truth": "84"
} | {
"split": "train",
"index": 35357,
"solution": "1. **Define Variables:**\n Let $x$ be the population in $1996$, and let $k$ be the constant of proportionality.\n\n2. **Set Up Equations Based on Given Information:**\n - For $n = 1994$, the population difference between $1996$ and $1994$ is directly proportion... |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer that is a multiple of each of 3, 5, 7, and 9? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "315"
} | {
"split": "train",
"index": 35358,
"solution": "Since 9 is a multiple of 3, every positive integer that is a multiple of 9 is also a multiple of 3. The smallest positive integer that is a multiple of each of 7 and 9 is 63. The smallest multiple of 63 that is also a multiple of 5 is 315."
} |
deepscaler | [
{
"role": "user",
"content": "If $b$ and $c$ are constants and $(x + 2)(x + b) = x^2 + cx + 6$, then $c$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 35359,
"solution": "1. **Expand the left-hand side of the equation**: \n \\[\n (x + 2)(x + b) = x^2 + bx + 2x + 2b = x^2 + (b+2)x + 2b\n \\]\n\n2. **Compare with the right-hand side of the equation**:\n \\[\n x^2 + cx + 6\n \\]\n By comparing coefficients, we equate the ... |
deepscaler | [
{
"role": "user",
"content": "Point \\( A \\) lies on the line \\( y = \\frac{5}{12} x - 11 \\), and point \\( B \\) lies on the parabola \\( y = x^{2} \\). What is the minimum length of segment \\( AB \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6311/624"
} | {
"split": "train",
"index": 35360,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $M$ be a subset of $\\{1,2,3... 2011\\}$ satisfying the following condition: \nFor any three elements in $M$ , there exist two of them $a$ and $b$ such that $a|b$ or $b|a$ .\nDetermine the maximum value of $|M|$ where $|M|$ denotes the number of elements in ... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 35361,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A proper divisor of a number is one that is not equal to the number itself. What is the sum of the proper divisors of \\( 450 \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "759"
} | {
"split": "train",
"index": 35362,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given set \\( A = \\{0, 1, 2, 3, 4, 5, 9\\} \\), and \\( a, b \\in A \\) where \\( a \\neq b \\). The number of functions of the form \\( y = -a x^2 + (4 - b)x \\) whose vertex lies in the first quadrant is ___.\n Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 35363,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In trapezoid $PQRS$, leg $\\overline{QR}$ is perpendicular to bases $\\overline{PQ}$ and $\\overline{RS}$, and diagonals $\\overline{PR}$ and $\\overline{QS}$ are perpendicular. Given that $PQ=\\sqrt{23}$ and $PS=\\sqrt{2023}$, find $QR^2$. Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "100\\sqrt{46}"
} | {
"split": "train",
"index": 35364,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify $\\sqrt{288}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12\\sqrt{2}"
} | {
"split": "train",
"index": 35365,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The value of $x$ that satisfies $\\log_{2^x} 3^{20} = \\log_{2^{x+3}} 3^{2020}$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "103"
} | {
"split": "train",
"index": 35366,
"solution": "Recall the identity $\\log_{a^n} b^{m} = \\frac{m}{n}\\log_{a} b$ (which is easily proven using exponents or change of base). Then this problem turns into \\[\\frac{20}{x}\\log_{2} 3 = \\frac{2020}{x+3}\\log_{2} 3\\] Divide $\\log_{2} 3$ from both sides. And we are... |
deepscaler | [
{
"role": "user",
"content": "Compute $\\dbinom{16}{15}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 35367,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a regular tetrahedron ABCD with an edge length of 2, G is the centroid of triangle BCD, and M is the midpoint of line segment AG. The surface area of the circumscribed sphere of the tetrahedron M-BCD is __________. Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "6\\pi"
} | {
"split": "train",
"index": 35368,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The function $f(x)$ satisfies $f(1) = 1$ and\n\\[f(x + y) = 3^y f(x) + 2^x f(y)\\]for all real numbers $x$ and $y.$ Find the function $f(x).$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3^x - 2^x"
} | {
"split": "train",
"index": 35369,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $f(\\alpha)= \\dfrac {\\sin (\\pi-\\alpha)\\cos (2\\pi-\\alpha)\\cos (-\\alpha+ \\dfrac {3}{2}\\pi)}{\\cos ( \\dfrac {\\pi}{2}-\\alpha)\\sin (-\\pi-\\alpha)}$ \n$(1)$ Simplify $f(\\alpha)$; \n$(2)$ If $\\alpha$ is an angle in the third quadrant, and $\\cos (\\alpha- \\d... | math | {
"style": "rule",
"ground_truth": "-\\dfrac {1}{2}"
} | {
"split": "train",
"index": 35370,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given triangle $ABC$ with angles $A$, $B$, $C$ and their respective opposite sides $a$, $b$, $c$, if $\\cos B= \\frac{1}{4}, b=3$, and $\\sin C=2\\sin A$, find the area of triangle $ABC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9\\sqrt{15}}{16}"
} | {
"split": "train",
"index": 35371,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a plane, four circles with radii $1,3,5,$ and $7$ are tangent to line $\\ell$ at the same point $A,$ but they may be on either side of $\\ell$. Region $S$ consists of all the points that lie inside exactly one of the four circles. What is the maximum possible area of region ... | math | {
"style": "rule",
"ground_truth": "65\\pi"
} | {
"split": "train",
"index": 35372,
"solution": "1. **Understanding the Problem**: We are given four circles with radii $1, 3, 5,$ and $7$ that are tangent to a line $\\ell$ at the same point $A$. The circles can be on either side of $\\ell$. We need to find the maximum possible area of region $S$, which consists... |
deepscaler | [
{
"role": "user",
"content": "Express the quotient $1021_3 \\div 11_3$ in base $3$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22_3"
} | {
"split": "train",
"index": 35373,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sequence $(a_n)$ is defined recursively by $a_0=1$, $a_1=\\sqrt[17]{3}$, and $a_n=a_{n-1}a_{n-2}^2$ for $n\\geq 2$. What is the smallest positive integer $k$ such that the product $a_1a_2\\cdots a_k$ is an integer? Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 35374,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Dima and Sergey were picking raspberries from a bush that had 900 berries. Dima alternated his actions while picking: he put one berry in the basket, and then he ate the next one. Sergey also alternated: he put two berries in the basket, and then he ate the next one. It is know... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 35375,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A nickel is placed on a table. The number of nickels which can be placed around it, each tangent to it and to two others is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 35376,
"solution": "To solve this problem, we need to determine how many nickels can be placed around a central nickel such that each is tangent to the central nickel and to its two neighboring nickels.\n\n1. **Understanding the Problem:**\n - Each nickel is a circle, and we are ask... |
deepscaler | [
{
"role": "user",
"content": "A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token in the discard pile. The game ends when some player runs out of tokens. Players $A$, $B$, and $... | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 35377,
"solution": "\nWe will analyze the game by observing the token distribution and the net change in tokens over a set of rounds. We will use the first solution approach as it provides a clear and concise method to determine the number of rounds.\n\n#### Step 1: Understanding the ... |
deepscaler | [
{
"role": "user",
"content": "Find the value of \\(\\tan \\left(\\tan^{-1} \\frac{1}{2} + \\tan^{-1} \\frac{1}{2 \\times 2^2} + \\tan^{-1} \\frac{1}{2 \\times 3^2} + \\cdots + \\tan^{-1} \\frac{1}{2 \\times 2009^2}\\right)\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2009}{2010}"
} | {
"split": "train",
"index": 35378,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the lines $l_1: ax+2y-1=0$ and $l_2: 8x+ay+2-a=0$, if $l_1 \\parallel l_2$, find the value of the real number $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4"
} | {
"split": "train",
"index": 35379,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What are the solutions for \\(5x^2 + 6 = 2x - 15\\)? Express your solutions in the form \\(x = a \\pm b i,\\) and compute \\(a + b^2\\) presented as a fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{109}{25}"
} | {
"split": "train",
"index": 35380,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two circles with equal radii intersect as shown. The area of the shaded region equals the sum of the areas of the two unshaded regions. If the area of the shaded region is $216\\pi$, what is the circumference of each circle? Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "36\\pi"
} | {
"split": "train",
"index": 35381,
"solution": "Suppose that the radius of each of the circles is $r$. Since the two circles are identical, then the two circles have equal area. Since the shaded area is common to the two circles, then the unshaded pieces of each circle have equal areas. Since the combined area o... |
deepscaler | [
{
"role": "user",
"content": "In Pascal's Triangle, each entry is the sum of the two entries above it. In which row of Pascal's Triangle do three consecutive entries occur that are in the ratio $3: 4: 5$?\n\n(The top row of Pascal's Triangle has only a single $1$ and is the $0$th row.) Let's think step by s... | math | {
"style": "rule",
"ground_truth": "62"
} | {
"split": "train",
"index": 35382,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each of the $25$ balls is tossed independently and at random into one of $5$ bins. Let $r$ be the probability that one bin ends up with $6$ balls, another with $7$ balls, and the other three with $4$ balls each. Let $s$ be the probability that one bin ends up with $5$ balls and... | math | {
"style": "rule",
"ground_truth": "\\frac{10 \\cdot \\binom{25}{6}\\binom{19}{7}\\binom{12}{4}\\binom{8}{4}\\binom{4}{4}}{\\binom{25}{5}\\binom{20}{5}\\binom{15}{5}\\binom{10}{5}\\binom{5}{5}}"
} | {
"split": "train",
"index": 35383,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( 0<a<b<c<d<300 \\) and the equations:\n\\[ a + d = b + c \\]\n\\[ bc - ad = 91 \\]\n\nFind the number of ordered quadruples of positive integers \\((a, b, c, d)\\) that satisfy the above conditions. Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "486"
} | {
"split": "train",
"index": 35384,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A right isosceles triangle is inscribed in a triangle with a base of 30 and a height of 10 such that its hypotenuse is parallel to the base of the given triangle, and the vertex of the right angle lies on this base. Find the hypotenuse. Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 35385,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Due to a snow and ice disaster, a citrus orchard suffered severe damage. To address this, experts proposed a rescue plan for the fruit trees, which needs to be implemented over two years and is independent each year. The plan estimates that in the first year, the probability of... | math | {
"style": "rule",
"ground_truth": "0.2"
} | {
"split": "train",
"index": 35386,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find a monic quartic polynomial, in $x,$ with rational coefficients such that $2+\\sqrt{2}$ and $1-\\sqrt{3}$ are roots of the polynomial. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x^4-6x^3+8x^2+4x-4"
} | {
"split": "train",
"index": 35387,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a set $T = \\{a, b, c, d, e, f\\}$, determine the number of ways to choose two subsets of $T$ such that their union is $T$ and their intersection contains exactly three elements. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "80"
} | {
"split": "train",
"index": 35388,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A traffic light at an intersection has a red light that stays on for $40$ seconds, a yellow light that stays on for $5$ seconds, and a green light that stays on for $50$ seconds (no two lights are on simultaneously). What is the probability of encountering each of the following... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{19}"
} | {
"split": "train",
"index": 35389,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Tom, Dick and Harry started out on a $100$-mile journey. Tom and Harry went by automobile at the rate of $25$ mph, while Dick walked at the rate of $5$ mph. After a certain distance, Harry got off and walked on at $5$ mph, while Tom went back for Dick and got him to the destina... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 35390,
"solution": "1. **Define Variables:**\n Let $d_1$ be the distance Harry traveled by car, and $d_2$ be the distance Tom backtracked to pick up Dick. Let $T$ be the total time for the trip.\n\n2. **Set Up Equations:**\n - **Harry's journey:** He travels $d_1$ miles by car and... |
deepscaler | [
{
"role": "user",
"content": "Find the smallest possible area of an ellipse passing through $(2,0),(0,3),(0,7)$, and $(6,0)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{56 \\pi \\sqrt{3}}{9}"
} | {
"split": "train",
"index": 35391,
"solution": "Let $\\Gamma$ be an ellipse passing through $A=(2,0), B=(0,3), C=(0,7), D=(6,0)$, and let $P=(0,0)$ be the intersection of $A D$ and $B C$. $\\frac{\\text { Area of } \\Gamma}{\\text { Area of } A B C D}$ is unchanged under an affine transformation, so we just have... |
deepscaler | [
{
"role": "user",
"content": "What is the sum of all positive integer values of $n$ such that $\\frac{n+18}{n}$ is an integer? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 35392,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of all digits used in the numbers 1, 2, 3, ..., 999 is . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13500"
} | {
"split": "train",
"index": 35393,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the least integer value of $x$ such that $\\lvert2x+ 7\\rvert\\le 16$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-11"
} | {
"split": "train",
"index": 35394,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $$f(x)= \\begin{cases} \\overset{2^{x},x\\geq 3,}{f(x+1),x<3}\\end{cases}$$, find the value of $f(\\log_2 6)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 35395,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given non-zero vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfying $\\overrightarrow{a}^{2}=(5 \\overrightarrow{a}-4 \\overrightarrow{b})\\cdot \\overrightarrow{b}$, find the minimum value of $\\cos < \\overrightarrow{a}, \\overrightarrow{b} >$. Let's think step ... | math | {
"style": "rule",
"ground_truth": "\\frac {4}{5}"
} | {
"split": "train",
"index": 35396,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the length of side $PQ$ in the right-angled triangle $PQR$, where $PR = 15$ units and $\\angle PQR = 45^\\circ$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 35397,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For $\\pi \\le \\theta < 2\\pi$, let\n\\begin{align*} P &= \\frac12\\cos\\theta - \\frac14\\sin 2\\theta - \\frac18\\cos 3\\theta + \\frac{1}{16}\\sin 4\\theta + \\frac{1}{32} \\cos 5\\theta - \\frac{1}{64} \\sin 6\\theta - \\frac{1}{128} \\cos 7\\theta + \\cdots \\end{align*}\... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 35398,
"solution": "Use sum to product formulas to rewrite $P$ and $Q$\n\\[P \\sin\\theta\\ + Q \\cos\\theta\\ = \\cos \\theta\\ - \\frac{1}{4}\\cos \\theta + \\frac{1}{8}\\sin 2\\theta + \\frac{1}{16}\\cos 3\\theta - \\frac{1}{32}\\sin 4\\theta + ...\\]\n Therefore, \\[P \\sin \\thet... |
deepscaler | [
{
"role": "user",
"content": "What is the area enclosed by the graph of $|x| + |2y|$ = 10 shown here?\n\n[asy]\ndraw((0,-10)--(0,10),Arrows);\ndraw((-15,0)--(15,0),Arrows);\nlabel(\"$y$\",(0,10),NE);\nlabel(\"$x$\",(15,0),SE);\ndraw((10,0)--(0,5)--(-10,0)--(0,-5)--cycle);\n[/asy] Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 35399,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Convert the binary number $101110_2$ to an octal number. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "56_8"
} | {
"split": "train",
"index": 35400,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A reflection takes $\\begin{pmatrix} -1 \\\\ 7 \\end{pmatrix}$ to $\\begin{pmatrix} 5 \\\\ -5 \\end{pmatrix}.$ Which vector does the reflection take $\\begin{pmatrix} -4 \\\\ 3 \\end{pmatrix}$ to? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\begin{pmatrix} 0 \\\\ -5 \\end{pmatrix}"
} | {
"split": "train",
"index": 35401,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given distinct natural numbers \\( k, l, m, n \\), it is known that there exist three natural numbers \\( a, b, c \\) such that each of the numbers \\( k, l, m, n \\) is a root of either the equation \\( a x^{2} - b x + c = 0 \\) or the equation \\( c x^{2} - 16 b x + 256 a = 0... | math | {
"style": "rule",
"ground_truth": "325"
} | {
"split": "train",
"index": 35402,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $N$ is represented as $11000_2$ in binary, what is the binary representation of the integer that comes immediately before $N$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10111_2"
} | {
"split": "train",
"index": 35403,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The coefficient of $x^2$ in the expansion of $(1+2x)^5$ is __________. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 35404,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If each of the four numbers $3, 4, 6,$ and $7$ replaces a $\\square$, what is the largest possible sum of the fractions shown? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{23}{6}"
} | {
"split": "train",
"index": 35405,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\\[ y = x + \\cos(2x) \\] in the interval \\((0, \\pi / 4)\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{12} + \\frac{\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 35406,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cube with side length 10 is suspended above a plane. The vertex closest to the plane is labeled $A$. The three vertices adjacent to vertex $A$ are at heights 10, 11, and 12 above the plane. The distance from vertex $A$ to the plane can be expressed as $ \\frac{r-\\sqrt{s}}{t}... | math | {
"style": "rule",
"ground_truth": "330"
} | {
"split": "train",
"index": 35407,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the sum $$\\frac{1}{2\\lfloor\\sqrt{1}\\rfloor+1}+\\frac{1}{2\\lfloor\\sqrt{2}\\rfloor+1}+\\frac{1}{2\\lfloor\\sqrt{3}\\rfloor+1}+\\cdots+\\frac{1}{2\\lfloor\\sqrt{100}\\rfloor+1}$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "190/21"
} | {
"split": "train",
"index": 35408,
"solution": "The first three terms all equal $1 / 3$, then the next five all equal $1 / 5$; more generally, for each $a=1,2, \\ldots, 9$, the terms $1 /(2\\lfloor\\sqrt{a^{2}}\\rfloor+1)$ to $1 /(2\\lfloor\\sqrt{a^{2}+2 a}\\rfloor+1)$ all equal $1 /(2 a+1)$, and there are $2 a+... |
deepscaler | [
{
"role": "user",
"content": "The polynomial \\( x^8 - 4x^7 + 7x^6 + \\cdots + a_0 \\) has all its roots positive and real numbers. Find the possible values for \\( a_0 \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{256}"
} | {
"split": "train",
"index": 35409,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Johan has a large number of identical cubes. He has made a structure by taking a single cube and then sticking another cube to each face. He wants to make an extended structure in the same way so that each face of the current structure will have a cube stuck to it. How many ext... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 35410,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the curve $x^{2}-y-2\\ln \\sqrt{x}=0$ and the line $4x+4y+1=0$, find the shortest distance from any point $P$ on the curve to the line. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{\\sqrt{2}(1+\\ln2)}{2}"
} | {
"split": "train",
"index": 35411,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the graph of the power function $y=f(x)$ passes through the point $(9, \\frac{1}{3})$, find the value of $f(25)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"split": "train",
"index": 35412,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a finite sequence $\\{a\\_1\\}, \\{a\\_2\\}, \\ldots \\{a\\_m\\} (m \\in \\mathbb{Z}^+)$ that satisfies the conditions: $\\{a\\_1\\} = \\{a\\_m\\}, \\{a\\_2\\} = \\{a\\_{m-1}\\}, \\ldots \\{a\\_m\\} = \\{a\\_1\\}$, it is called a \"symmetric sequence\" with the additional... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 35413,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\sin(\\omega x+\\varphi)$, which is monotonically increasing on the interval ($\\frac{\\pi}{6}$,$\\frac{{2\\pi}}{3}$), and the lines $x=\\frac{\\pi}{6}$ and $x=\\frac{{2\\pi}}{3}$ are the two symmetric axes of the graph of the function $y=f(x)$, find $... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 35414,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A$ be a subset of $\\{1, 2, 3, \\ldots, 50\\}$ with the property: for every $x,y\\in A$ with $x\\neq y$ , it holds that\n\\[\\left| \\frac{1}{x}- \\frac{1}{y}\\right|>\\frac{1}{1000}.\\]\nDetermine the largest possible number of elements that the set $A$ can have.... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 35415,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Several consecutive natural numbers are written on the board. Exactly 52% of them are even. How many even numbers are written on the board? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 35416,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Distribute 5 volunteers from the Shanghai World Expo to work in the pavilions of China, the United States, and the United Kingdom. Each pavilion must have at least one volunteer, with the requirement that two specific volunteers, A and B, do not work in the same pavilion. How m... | math | {
"style": "rule",
"ground_truth": "114"
} | {
"split": "train",
"index": 35417,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sample contains 5 individuals with values a, 0, 1, 2, 3, and the average value of the sample is 1, calculate the standard deviation of the sample. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 35418,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A total of 1000 senior high school students from a certain school participated in a mathematics exam. The scores in this exam follow a normal distribution N(90, σ²). If the probability of a score being within the interval (70, 110] is 0.7, estimate the number of students with s... | math | {
"style": "rule",
"ground_truth": "150"
} | {
"split": "train",
"index": 35419,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For all positive integers $x$, let \\[f(x)=\\begin{cases}1 & \\text{if }x = 1\\\\ \\frac x{10} & \\text{if }x\\text{ is divisible by 10}\\\\ x+1 & \\text{otherwise}\\end{cases}\\] and define a sequence as follows: $x_1=x$ and $x_{n+1}=f(x_n)$ for all positive integers $n$. Let ... | math | {
"style": "rule",
"ground_truth": "511"
} | {
"split": "train",
"index": 35420,
"solution": "We backcount the number of ways. Namely, we start at $x_{20} = 1$, which can only be reached if $x_{19} = 10$, and then we perform $18$ operations that either consist of $A: (-1)$ or $B: (\\times 10)$. We represent these operations in a string format, starting with... |
deepscaler | [
{
"role": "user",
"content": "A sphere is inscribed in a cube, and the cube has a surface area of 24 square meters. A second cube is then inscribed within the sphere. What is the surface area in square meters of the inner cube? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 35421,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many distinct divisors do the following numbers have:\n1) \\(2^{7}\\);\n2) \\(5^{4}\\);\n3) \\(2^{7} \\cdot 5^{4}\\);\n4) \\(2^{m} \\cdot 5^{n} \\cdot 3^{k}\\);\n5) 3600;\n6) \\(42^{5}\\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "216"
} | {
"split": "train",
"index": 35422,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In 1960, there were 450,000 cases of measles reported in the U.S. In 1996, there were 500 cases reported. How many cases of measles would have been reported in 1987 if the number of cases reported from 1960 to 1996 decreased linearly? Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "112,\\!875"
} | {
"split": "train",
"index": 35423,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The base of a right prism is an isosceles trapezoid \\(ABCD\\) with \\(AB = CD = 13\\), \\(BC = 11\\), and \\(AD = 21\\). The area of the diagonal cross-section of the prism is 180. Find the total surface area of the prism. Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "906"
} | {
"split": "train",
"index": 35424,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many distinct products can you obtain by multiplying two or more distinct elements from the set $\\{1, 2, 3, 5, 7, 11\\}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 35425,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The product $(1.8)(40.3 + .07)$ is closest to Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "74"
} | {
"split": "train",
"index": 35426,
"solution": "1. **Identify the expression to approximate:** The given expression is $(1.8)(40.3 + 0.07)$.\n\n2. **Simplify the expression inside the parentheses:** \n \\[\n 40.3 + 0.07 = 40.37\n \\]\n So, the expression becomes $(1.8)(40.37)$.\n\n3. **Approximate the pr... |
deepscaler | [
{
"role": "user",
"content": "Given that positive real numbers $x$ and $y$ satisfy $4x+3y=4$, find the minimum value of $\\frac{1}{2x+1}+\\frac{1}{3y+2}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{8}+\\frac{\\sqrt{2}}{4}"
} | {
"split": "train",
"index": 35427,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The least common multiple of $x$ and $y$ is $18$, and the least common multiple of $y$ and $z$ is $20$. Determine the least possible value of the least common multiple of $x$ and $z$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 35428,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A semicircle and a circle each have a radius of 5 units. A square is inscribed in each. Calculate the ratio of the perimeter of the square inscribed in the semicircle to the perimeter of the square inscribed in the circle. Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{10}}{5}"
} | {
"split": "train",
"index": 35429,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the triangular prism \\( P-ABC \\),\n\\[\n\\begin{array}{l}\n\\angle APB = \\angle BPC = \\angle CPA = 90^{\\circ}, \\\\\nPA = 4, \\, PB = PC = 3.\n\\end{array}\n\\]\n\nFind the minimum sum of the squares of the distances from any point on the base \\( ABC \\) to the three l... | math | {
"style": "rule",
"ground_truth": "\\frac{144}{41}"
} | {
"split": "train",
"index": 35430,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, $\\triangle ABE$, $\\triangle BCE$ and $\\triangle CDE$ are right-angled, with $\\angle AEB=\\angle BEC = \\angle CED = 45^\\circ$, and $AE=28$. Find the length of $CE$, given that $CE$ forms the diagonal of a square $CDEF$. Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 35431,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the acute triangle \\( \\triangle ABC \\), the sides \\( a, b, c \\) are opposite to the angles \\( \\angle A, \\angle B, \\angle C \\) respectively, and \\( a, b, c \\) form an arithmetic sequence. Also, \\( \\sin (A - C) = \\frac{\\sqrt{3}}{2} \\). Find \\( \\sin (A + C) \... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{39}}{8}"
} | {
"split": "train",
"index": 35432,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If you add 2 to the last digit of the quotient, you get the penultimate digit. If you add 2 to the third digit from the right of the quotient, you get the fourth digit from the right. For example, the quotient could end in 9742 or 3186.\n\nWe managed to find only one solution. ... | math | {
"style": "rule",
"ground_truth": "9742"
} | {
"split": "train",
"index": 35433,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that angle DEF is a right angle and the sides of triangle DEF are the diameters of semicircles, the area of the semicircle on segment DE equals $18\\pi$, and the arc of the semicircle on segment DF has length $10\\pi$. Determine the radius of the semicircle on segment EF.... | math | {
"style": "rule",
"ground_truth": "\\sqrt{136}"
} | {
"split": "train",
"index": 35434,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Using the numbers from 1 to 22 exactly once each, Antoine writes 11 fractions. For example, he could write the fractions \\(\\frac{10}{2}, \\frac{4}{3}, \\frac{15}{5}, \\frac{7}{6}, \\frac{8}{9}, \\frac{11}{19}, \\frac{12}{14}, \\frac{13}{17}, \\frac{22}{21}, \\frac{18}{16}, \\... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 35435,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Nine lines parallel to the base of a triangle divide the other sides each into $10$ equal segments and the area into $10$ distinct parts. If the area of the largest of these parts is $38$ , then the area of the original triangle is Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "200"
} | {
"split": "train",
"index": 35436,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The distance between points A and B is 1200 meters. Dachen starts from point A, and 6 minutes later, Xiaogong starts from point B. After another 12 minutes, they meet. Dachen walks 20 meters more per minute than Xiaogong. How many meters does Xiaogong walk per minute? Let's thi... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 35437,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "To obtain the graph of the function $y=2\\cos \\left(2x-\\frac{\\pi }{6}\\right)$, all points on the graph of the function $y=2\\sin 2x$ need to be translated $\\frac{\\pi }{6}$ units to the left. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi }{6}"
} | {
"split": "train",
"index": 35438,
"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 $\\angle A=45^{\\circ}$, $a=6$.\n(1) If $\\angle C=105^{\\circ}$, find $b$;\n(2) Find the maximum area of $\\triangle ABC$. Let's think step by step and put only ... | math | {
"style": "rule",
"ground_truth": "9(1+\\sqrt{2})"
} | {
"split": "train",
"index": 35439,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $AB=AC$, and $D$ is the midpoint of both $\\overline{AB}$ and $\\overline{CE}$. If $\\overline{BC}$ is 14 units long, determine the length of $\\overline{CD}$. Express your answer as a decimal to the nearest tenth. Let's think step by step and put only the fi... | math | {
"style": "rule",
"ground_truth": "14.0"
} | {
"split": "train",
"index": 35440,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Of the 36 students in Richelle's class, 12 prefer chocolate pie, 8 prefer apple, and 6 prefer blueberry. Half of the remaining students prefer cherry pie and half prefer lemon. For Richelle's pie graph showing this data, how many degrees should she use for cherry pie? Let's t... | math | {
"style": "rule",
"ground_truth": "50^{\\circ}"
} | {
"split": "train",
"index": 35441,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle and two distinct lines are drawn on a sheet of paper. What is the largest possible number of points of intersection of these figures? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 35442,
"solution": "To determine the largest possible number of points of intersection involving a circle and two distinct lines, we need to consider the maximum number of intersections each pair of figures can have:\n\n1. **Intersections between a line and a circle**: A line can inte... |
deepscaler | [
{
"role": "user",
"content": "Given that positive numbers $x$ and $y$ satisfy $x + 4y = 2$, find the minimum value of $\\frac{x + 40y + 4}{3xy}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 35443,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Out of a batch of 5000 electric lamps, a self-random non-repeating sample of 300 was selected. The average burning time of the lamps in the sample was found to be 1450 hours, and the variance was 40,000. What is the probability that the average burning time of the lamps in the ... | math | {
"style": "rule",
"ground_truth": "0.99964"
} | {
"split": "train",
"index": 35444,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-1^{2023}-\\sqrt{2\\frac{1}{4}}+\\sqrt[3]{-1}+\\frac{1}{2}$;<br/>$(2)2\\sqrt{3}+|1-\\sqrt{3}|-\\left(-1\\right)^{2022}+2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3\\sqrt{3}"
} | {
"split": "train",
"index": 35445,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The surface of a 3 x 3 x 3 Rubik's Cube consists of 54 cells. What is the maximum number of cells you can mark such that the marked cells do not share any vertices? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 35446,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$ABCDEFGH$ is a cube. Find $\\sin \\angle BAE$, where $E$ is the top vertex directly above $A$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{\\sqrt{2}}"
} | {
"split": "train",
"index": 35447,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\(\\sin x + \\sin y = 0.6\\) and \\(\\cos x + \\cos y = 0.8\\), find \\(\\cos x \\cdot \\cos y\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{11}{100}"
} | {
"split": "train",
"index": 35448,
"solution": ""
} |
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