data_source large_stringclasses 1
value | prompt listlengths 1 1 | reward_model dict | extra_info dict |
|---|---|---|---|
math | [
{
"content": "A cone is formed from a 270-degree sector of a circle of radius 18 by aligning the two straight sides. What is the result when the volume of the cone is divided by $\\pi$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "60.75\\sqrt{141.75}",
"style": "rule"
} | {
"index": "35300",
"split": "train"
} |
math | [
{
"content": "If $\\alpha, \\beta, \\gamma$ are the roots of the equation $x^3 - x - 1 = 0$, find the value of $\\frac{1 + \\alpha}{1 - \\alpha} + \\frac{1 + \\beta}{1 - \\beta} + \\frac{1 + \\gamma}{1 - \\gamma}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-7",
"style": "rule"
} | {
"index": "35301",
"split": "train"
} |
math | [
{
"content": "Equilateral $\\triangle ABC$ has side length $2$, and shapes $ABDE$, $BCHT$, $CAFG$ are formed outside the triangle such that $ABDE$ and $CAFG$ are squares, and $BCHT$ is an equilateral triangle. What is the area of the geometric shape formed by $DEFGHT$?\nA) $3\\sqrt{3} - 1$\nB) $3\\sqrt{3} - 2$\... | {
"ground_truth": "3\\sqrt{3} - 2",
"style": "rule"
} | {
"index": "35302",
"split": "train"
} |
math | [
{
"content": "5 people are standing in a row for a photo, among them one person must stand in the middle. There are ways to arrange them. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "24",
"style": "rule"
} | {
"index": "35303",
"split": "train"
} |
math | [
{
"content": "Given sets $A=\\{1,2,3,4,5\\}$, $B=\\{0,1,2,3,4\\}$, and a point $P$ with coordinates $(m,n)$, where $m\\in A$ and $n\\in B$, find the probability that point $P$ lies below the line $x+y=5$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\dfrac{2}{5}",
"style": "rule"
} | {
"index": "35304",
"split": "train"
} |
math | [
{
"content": "How many integers between 100 and 300 are multiples of both 5 and 7, but are not multiples of 10? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"index": "35305",
"split": "train"
} |
math | [
{
"content": "From a group of $3$ orthopedic surgeons, $4$ neurosurgeons, and $5$ internists, a medical disaster relief team of $5$ people is to be formed. How many different ways can the team be selected such that there is at least one person from each specialty? Please output the final answer within \\boxed{}... | {
"ground_truth": "590",
"style": "rule"
} | {
"index": "35306",
"split": "train"
} |
math | [
{
"content": "In the figure, $PA$ is tangent to semicircle $SAR$, $PB$ is tangent to semicircle $RBT$, and $SRT$ is a straight line. If arc $AS$ is $58^\\circ$ and arc $BT$ is $37^\\circ$, then find $\\angle APB$, in degrees.\n\n[asy]\nimport graph;\n\nunitsize(1.5 cm);\n\npair A, B, P, R, S, T;\npair[] O;\nre... | {
"ground_truth": "95^\\circ",
"style": "rule"
} | {
"index": "35307",
"split": "train"
} |
math | [
{
"content": "An 8.5-meter ladder is leaning against a vertical wall. How many meters is its base from the wall if the ladder reaches 7.5 meters up the wall? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"index": "35308",
"split": "train"
} |
math | [
{
"content": "Simplify the expression $(-\\frac{1}{343})^{-2/3}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "49",
"style": "rule"
} | {
"index": "35309",
"split": "train"
} |
math | [
{
"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 the value of $\\frac{\... | {
"ground_truth": "\\frac{2016}{2017}",
"style": "rule"
} | {
"index": "35310",
"split": "train"
} |
math | [
{
"content": "Evaluate the expression \\[ \\frac{a+3}{a+1} \\cdot \\frac{b-2}{b-3} \\cdot \\frac{c + 9}{c+7} , \\] given that $c = b-11$, $b = a+3$, $a = 5$, and none of the denominators are zero. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"index": "35311",
"split": "train"
} |
math | [
{
"content": "Let $S_n=1-2+3-4+\\cdots +(-1)^{n-1}n$, where $n=1,2,\\cdots$. Then $S_{17}+S_{33}+S_{50}$ equals: Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1",
"style": "rule"
} | {
"index": "35312",
"split": "train"
} |
math | [
{
"content": "Sarah is leading a class of $35$ students. Initially, all students are standing. Each time Sarah waves her hands, a prime number of standing students sit down. If no one is left standing after Sarah waves her hands $3$ times, what is the greatest possible number of students that could have bee... | {
"ground_truth": "31",
"style": "rule"
} | {
"index": "35313",
"split": "train"
} |
math | [
{
"content": "A clock takes $7$ seconds to strike $9$ o'clock starting precisely from $9:00$ o'clock. If the interval between each strike increases by $0.2$ seconds as time progresses, calculate the time it takes to strike $12$ o'clock. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "12.925",
"style": "rule"
} | {
"index": "35314",
"split": "train"
} |
math | [
{
"content": "Let $n \\ge 3$ be an integer. Rowan and Colin play a game on an $n \\times n$ grid of squares, where each square is colored either red or blue. Rowan is allowed to permute the rows of the grid, and Colin is allowed to permute the columns of the grid. A grid coloring is $orderly$ if:\nno matter how... | {
"ground_truth": "\\[ 2 \\cdot n! + 2 \\]",
"style": "rule"
} | {
"index": "35315",
"split": "train"
} |
math | [
{
"content": "A scale drawing of a park shows that one inch represents 800 feet. A line segment in the drawing that is 4.75 inches long represents how many feet? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3800",
"style": "rule"
} | {
"index": "35316",
"split": "train"
} |
math | [
{
"content": "Consider the set $M=\\{1,2,3,...,2020\\}.$ Find the smallest positive integer $k$ such that for any subset $A$ of $M$ with $k$ elements, there exist $3$ distinct numbers $a,b,c$ from $M$ such that $a+b, b+c$ and $c+a$ are all in $A.$ Please output the final answer within \\box... | {
"ground_truth": "1011",
"style": "rule"
} | {
"index": "35317",
"split": "train"
} |
math | [
{
"content": "Two numbers \\( x \\) and \\( y \\) satisfy the equation \\( 26x^2 + 23xy - 3y^2 - 19 = 0 \\) and are respectively the sixth and eleventh terms of a decreasing arithmetic progression consisting of integers. Find the common difference of this progression. Please output the final answer within \\box... | {
"ground_truth": "-3",
"style": "rule"
} | {
"index": "35318",
"split": "train"
} |
math | [
{
"content": "Suppose $a_{1}, a_{2}, \\ldots, a_{100}$ are positive real numbers such that $$a_{k}=\\frac{k a_{k-1}}{a_{k-1}-(k-1)}$$ for $k=2,3, \\ldots, 100$. Given that $a_{20}=a_{23}$, compute $a_{100}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "215",
"style": "rule"
} | {
"index": "35319",
"split": "train"
} |
math | [
{
"content": "The cross below is made up of five congruent squares. The perimeter of the cross is $72$ . Find its area.\n[asy]\nimport graph;\nsize(3cm);\npair A = (0,0);\npair temp = (1,0);\npair B = rotate(45,A)*temp;\npair C = rotate(90,B)*A;\npair D = rotate(270,C)*B;\npair E = rotate(270,D)*C;\npair F = r... | {
"ground_truth": "180",
"style": "rule"
} | {
"index": "35320",
"split": "train"
} |
math | [
{
"content": "In the trapezoid $ABCD$, $CD$ is three times the length of $AB$. Given that the area of the trapezoid is $30$ square units, determine the area of $\\triangle ABC$.\n\n[asy]\ndraw((0,0)--(1,4)--(7,4)--(12,0)--cycle);\ndraw((1,4)--(0,0));\nlabel(\"$A$\",(1,4),NW);\nlabel(\"$B$\",(7,4),NE);\nlabel(\"... | {
"ground_truth": "7.5",
"style": "rule"
} | {
"index": "35321",
"split": "train"
} |
math | [
{
"content": "In Mrs. Marsh's algebra class, 30 of the 36 students took the Chapter 4 test, and their mean score was $72 \\%$. The next day the other six students took the test and their mean score was $78 \\%$. What is the new class mean? Express your answer as a percent. Please output the final answer within ... | {
"ground_truth": "73\\%",
"style": "rule"
} | {
"index": "35322",
"split": "train"
} |
math | [
{
"content": "The surface of a clock is circular, and on its circumference, there are 12 equally spaced points representing the hours. Calculate the total number of rectangles that can have these points as vertices. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "15",
"style": "rule"
} | {
"index": "35323",
"split": "train"
} |
math | [
{
"content": "Four families visit a tourist spot that has four different routes available for exploration. Calculate the number of scenarios in which exactly one route is not visited by any of the four families. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "144",
"style": "rule"
} | {
"index": "35324",
"split": "train"
} |
math | [
{
"content": "Given in the polar coordinate system, circle $C$: $p=2\\cos (\\theta+ \\frac {\\pi}{2})$ and line $l$: $\\rho\\sin (\\theta+ \\frac {\\pi}{4})= \\sqrt {2}$, point $M$ is a moving point on circle $C$. Find the maximum distance from point $M$ to line $l$. Please output the final answer within \\boxe... | {
"ground_truth": "\\frac {3 \\sqrt {2}}{2}+1",
"style": "rule"
} | {
"index": "35325",
"split": "train"
} |
math | [
{
"content": "Let $u$ and $v$ be real numbers satisfying the inequalities $2u + 3v \\le 10$ and $4u + v \\le 9.$ Find the largest possible value of $u + 2v$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "6.1",
"style": "rule"
} | {
"index": "35326",
"split": "train"
} |
math | [
{
"content": "What is the area of the quadrilateral formed by the points of intersection of the circle \\(x^2 + y^2 = 16\\) and the ellipse \\((x-3)^2 + 4y^2 = 36\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "14",
"style": "rule"
} | {
"index": "35327",
"split": "train"
} |
math | [
{
"content": "Let $f(x)=\\frac{3x^2+5x+8}{x^2-x+4}$ and $g(x)=x-1$. Find $f(g(x))+g(f(x))$, evaluated when $x=1$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "5",
"style": "rule"
} | {
"index": "35328",
"split": "train"
} |
math | [
{
"content": "Nine balls numbered $1, 2, \\cdots, 9$ are placed in a bag. These balls differ only in their numbers. Person A draws a ball from the bag, the number on the ball is $a$, and after returning it to the bag, person B draws another ball, the number on this ball is $b$. The probability that the inequali... | {
"ground_truth": "61/81",
"style": "rule"
} | {
"index": "35329",
"split": "train"
} |
math | [
{
"content": "In \\(\\triangle ABC\\), \\(AC = AB = 25\\) and \\(BC = 40\\). From \\(D\\), perpendiculars are drawn to meet \\(AC\\) at \\(E\\) and \\(AB\\) at \\(F\\), calculate the value of \\(DE + DF\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "24",
"style": "rule"
} | {
"index": "35330",
"split": "train"
} |
math | [
{
"content": "Find the number of cubic centimeters in the volume of the cylinder formed by rotating a rectangle with side lengths 8 cm and 16 cm about its longer side. Express your answer in terms of \\(\\pi\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "256\\pi",
"style": "rule"
} | {
"index": "35331",
"split": "train"
} |
math | [
{
"content": "Below is a portion of the graph of a function, $y=f(x)$:\n\n[asy]\nimport graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=5.25,ymin=-3.25,ymax=4.25;\n\npen cqcqcq=rgb(0.75,0.75,0.75);\n\n/*grid*/ pen gs=linewidth(0.7)+cqcqcq+... | {
"ground_truth": "2",
"style": "rule"
} | {
"index": "35332",
"split": "train"
} |
math | [
{
"content": "For how many values of $c$ in the interval $[0, 1000]$ does the equation \\[7 \\lfloor x \\rfloor + 2 \\lceil x \\rceil = c\\]have a solution for $x$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "223",
"style": "rule"
} | {
"index": "35333",
"split": "train"
} |
math | [
{
"content": "Given the sequence $\\{a_k\\}_{k=1}^{11}$ of real numbers defined by $a_1=0.5$, $a_2=(0.51)^{a_1}$, $a_3=(0.501)^{a_2}$, $a_4=(0.511)^{a_3}$, and in general,\n\n$a_k=\\begin{cases}\n(0.\\underbrace{501\\cdots 01}_{k+1\\text{ digits}})^{a_{k-1}} & \\text{if } k \\text{ is odd,} \\\\\n(0.\\underbrac... | {
"ground_truth": "30",
"style": "rule"
} | {
"index": "35334",
"split": "train"
} |
math | [
{
"content": "In right triangle $ABC$, we have $\\sin A = \\frac{3}{5}$ and $\\sin B = 1$. Find $\\sin C$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{4}{5}",
"style": "rule"
} | {
"index": "35335",
"split": "train"
} |
math | [
{
"content": "The number of distinct pairs $(x,y)$ of real numbers satisfying both of the following equations: \n\\[x=x^2+y^2\\] \\[y=2xy\\] \nis Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4",
"style": "rule"
} | {
"index": "35336",
"split": "train"
} |
math | [
{
"content": "Kevin has four red marbles and eight blue marbles. He arranges these twelve marbles randomly, in a ring. Determine the probability that no two red marbles are adjacent. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{7}{33}",
"style": "rule"
} | {
"index": "35337",
"split": "train"
} |
math | [
{
"content": "Experts and Viewers play \"What? Where? When?\" until one side wins six rounds—the first to win six rounds wins the game. The probability of the Experts winning a single round is 0.6, and there are no ties. Currently, the Experts are losing with a score of $3:4$. Find the probability that the Expe... | {
"ground_truth": "0.4752",
"style": "rule"
} | {
"index": "35338",
"split": "train"
} |
math | [
{
"content": "A four-digit number $2\\Box\\Box5$ is divisible by $45$. How many such four-digit numbers are there? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "11",
"style": "rule"
} | {
"index": "35339",
"split": "train"
} |
math | [
{
"content": "Find the smallest integer $n \\geq 5$ for which there exists a set of $n$ distinct pairs $\\left(x_{1}, y_{1}\\right), \\ldots,\\left(x_{n}, y_{n}\\right)$ of positive integers with $1 \\leq x_{i}, y_{i} \\leq 4$ for $i=1,2, \\ldots, n$, such that for any indices $r, s \\in\\{1,2, \\ldots, n\\}$ (... | {
"ground_truth": "8",
"style": "rule"
} | {
"index": "35340",
"split": "train"
} |
math | [
{
"content": "Javier is going to Disneyland during spring break. He plans on visiting four particular attractions all before lunch. In how many orders could he visit all four attractions once? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "24",
"style": "rule"
} | {
"index": "35341",
"split": "train"
} |
math | [
{
"content": "Find the focus of the parabola $y = -3x^2 - 6x.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\left( -1, \\frac{35}{12} \\right)",
"style": "rule"
} | {
"index": "35342",
"split": "train"
} |
math | [
{
"content": "The operation $\\otimes$ is defined for all nonzero numbers by $a \\otimes b = \\frac{a^{2}}{b}$. Determine $[(1 \\otimes 2) \\otimes 3] - [1 \\otimes (2 \\otimes 3)]$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-\\frac{2}{3}",
"style": "rule"
} | {
"index": "35343",
"split": "train"
} |
math | [
{
"content": "How many non-congruent triangles with perimeter 7 have integer side lengths? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"index": "35344",
"split": "train"
} |
math | [
{
"content": "Four identical isosceles triangles $A W B, B X C, C Y D$, and $D Z E$ are arranged with points $A, B, C, D$, and $E$ lying on the same straight line. A new triangle is formed with sides the same lengths as $A X, A Y,$ and $A Z$. If $A Z = A E$, find the largest integer value of $x$ such that the a... | {
"ground_truth": "22",
"style": "rule"
} | {
"index": "35345",
"split": "train"
} |
math | [
{
"content": "Simplify the expression $20(x+y)-19(y+x)$ for all values of $x$ and $y$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "x+y",
"style": "rule"
} | {
"index": "35346",
"split": "train"
} |
math | [
{
"content": "Given the ellipse $C$: $\\frac{x^{2}}{a^{2}}+ \\frac{y^{2}}{b^{2}}=1 (a > b > 0)$ with a focal length of $2\\sqrt{2}$, and passing through the point $A(\\frac{3}{2}, -\\frac{1}{2})$.\n(1) Find the equation of the ellipse;\n(2) Find the coordinates of a point $P$ on the ellipse $C$ such that its di... | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"index": "35347",
"split": "train"
} |
math | [
{
"content": "We have a $100\\times100$ garden and we’ve plant $10000$ trees in the $1\\times1$ squares (exactly one in each.). Find the maximum number of trees that we can cut such that on the segment between each two cut trees, there exists at least one uncut tree. Please output the final answer within ... | {
"ground_truth": "2500",
"style": "rule"
} | {
"index": "35348",
"split": "train"
} |
math | [
{
"content": "Let $M = 39 \\cdot 48 \\cdot 77 \\cdot 150$. Calculate the ratio of the sum of the odd divisors of $M$ to the sum of the even divisors of $M$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{62}",
"style": "rule"
} | {
"index": "35349",
"split": "train"
} |
math | [
{
"content": "In triangle $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is known that $4a = \\sqrt{5}c$ and $\\cos C = \\frac{3}{5}$. \n$(Ⅰ)$ Find the value of $\\sin A$. \n$(Ⅱ)$ If $b = 11$, find the area of $\\triangle ABC$. Please output the final a... | {
"ground_truth": "22",
"style": "rule"
} | {
"index": "35350",
"split": "train"
} |
math | [
{
"content": "Calculate the area of the polygon with vertices at $(2,1)$, $(4,3)$, $(6,1)$, $(4,-2)$, and $(3,4)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{11}{2}",
"style": "rule"
} | {
"index": "35351",
"split": "train"
} |
math | [
{
"content": "Given $|a|=1$, $|b|=2$, and $a+b=(1, \\sqrt{2})$, the angle between vectors $a$ and $b$ is _______. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{2\\pi}{3}",
"style": "rule"
} | {
"index": "35352",
"split": "train"
} |
math | [
{
"content": "Let $g$ be defined by \\[g(x) = \\left\\{\n\\begin{array}{cl}\nx+3 & \\text{ if } x \\leq 2, \\\\\nx^2 - 4x + 5 & \\text{ if } x > 2.\n\\end{array}\n\\right.\\]Calculate $g^{-1}(1)+g^{-1}(6)+g^{-1}(11)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2 + \\sqrt{5} + \\sqrt{10}",
"style": "rule"
} | {
"index": "35353",
"split": "train"
} |
math | [
{
"content": "The 12 numbers from 1 to 12 on a clock face divide the circumference into 12 equal parts. Using any 4 of these division points as vertices to form a quadrilateral, find the total number of rectangles that can be formed. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "15",
"style": "rule"
} | {
"index": "35354",
"split": "train"
} |
math | [
{
"content": "Given that there are 25 cities in the County of Maplewood, and the average population per city lies between $6,200$ and $6,800$, estimate the total population of all the cities in the County of Maplewood. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "162,500",
"style": "rule"
} | {
"index": "35355",
"split": "train"
} |
math | [
{
"content": "How many of the numbers from the set $\\{1,\\ 2,\\ 3,\\ldots,\\ 100\\}$ have a perfect square factor other than one? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "40",
"style": "rule"
} | {
"index": "35356",
"split": "train"
} |
math | [
{
"content": "Triangle $ABC$ has an area 1. Points $E,F,G$ lie, respectively, on sides $BC$, $CA$, $AB$ such that $AE$ bisects $BF$ at point $R$, $BF$ bisects $CG$ at point $S$, and $CG$ bisects $AE$ at point $T$. Find the area of the triangle $RST$. Please output the final answer within \\boxed{}.",
"role... | {
"ground_truth": "\\frac{7 - 3 \\sqrt{5}}{4}",
"style": "rule"
} | {
"index": "35357",
"split": "train"
} |
math | [
{
"content": "What is the sum of the number of faces, edges and vertices of a triangular prism?\n\n[asy]\ndraw((0,0)--(10,0)--(5,8.7)--cycle);\ndraw((0,0)--(20,20),dashed);\ndraw((10,0)--(30,20));\ndraw((5,8.7)--(25,28.7));\ndraw((25,28.7)--(30,20)--(20,20)--cycle,dashed);\ndraw((25,28.7)--(30,20));\n[/asy] Ple... | {
"ground_truth": "20",
"style": "rule"
} | {
"index": "35358",
"split": "train"
} |
math | [
{
"content": "A car's clock is running at a constant speed but is inaccurate. One day, when the driver begins shopping, he notices both the car clock and his wristwatch (which is accurate) show 12:00 noon. After shopping, the wristwatch reads 12:30, and the car clock reads 12:35. Later that day, he loses his wr... | {
"ground_truth": "6:00",
"style": "rule"
} | {
"index": "35359",
"split": "train"
} |
math | [
{
"content": "Toner Drum and Celery Hilton are both running for president. A total of $129$ million people cast their vote in a random order, with exactly $63$ million and $66$ million voting for Toner Drum and Celery Hilton, respectively. The Combinatorial News Network displays the face of the leading ca... | {
"ground_truth": "1/43",
"style": "rule"
} | {
"index": "35360",
"split": "train"
} |
math | [
{
"content": "Sandwiches at Joe's Fast Food cost $3 each and sodas cost $2 each. How many dollars will it cost to purchase 5 sandwiches and 8 sodas? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "31",
"style": "rule"
} | {
"index": "35361",
"split": "train"
} |
math | [
{
"content": "A running track is the ring formed by two concentric circles. If the circumferences of the two circles differ by $10\\pi $ feet, how wide is the track in feet?\n\n[asy]size(100); path g=scale(2)*unitcircle;\nfilldraw(unitcircle^^g,evenodd+grey,black);\n[/asy] Please output the final answer within ... | {
"ground_truth": "5",
"style": "rule"
} | {
"index": "35362",
"split": "train"
} |
math | [
{
"content": "A bag contains four balls, each labeled with one of the characters \"美\", \"丽\", \"惠\", \"州\". Balls are drawn with replacement until both \"惠\" and \"州\" are drawn, at which point the drawing stops. Use a random simulation method to estimate the probability that the drawing stops exactly on the t... | {
"ground_truth": "\\frac{1}{8}",
"style": "rule"
} | {
"index": "35363",
"split": "train"
} |
math | [
{
"content": "Let $\\mathcal{S}$ be the set of all perfect squares whose rightmost three digits in base $10$ are $256$. Let $\\mathcal{T}$ be the set of all numbers of the form $\\frac{x-256}{1000}$, where $x$ is in $\\mathcal{S}$. In other words, $\\mathcal{T}$ is the set of numbers that result when the last t... | {
"ground_truth": "170",
"style": "rule"
} | {
"index": "35364",
"split": "train"
} |
math | [
{
"content": "An uncrossed belt is fitted without slack around two circular pulleys with radii of $14$ inches and $4$ inches. \nIf the distance between the points of contact of the belt with the pulleys is $24$ inches, then the distance \nbetween the centers of the pulleys in inches is Please output the final a... | {
"ground_truth": "26",
"style": "rule"
} | {
"index": "35365",
"split": "train"
} |
math | [
{
"content": "$\\frac{16+8}{4-2}=$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "12",
"style": "rule"
} | {
"index": "35366",
"split": "train"
} |
math | [
{
"content": "Given a circle of radius 3, there are many line segments of length 4 that are tangent to the circle at their midpoints. Find the area of the region consisting of all such line segments.\nA) $9\\pi$\nB) $\\pi$\nC) $4\\pi$\nD) $13\\pi$\nE) $16\\pi$ Please output the final answer within \\boxed{}.",
... | {
"ground_truth": "4\\pi",
"style": "rule"
} | {
"index": "35367",
"split": "train"
} |
math | [
{
"content": "Construct a square such that two adjacent vertices lie on a circle with a unit radius, and the side connecting the other two vertices is tangent to the circle. Calculate the sides of the square! Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "8/5",
"style": "rule"
} | {
"index": "35368",
"split": "train"
} |
math | [
{
"content": "How many four-digit positive integers have at least one digit that is a 2 or a 3? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "5416",
"style": "rule"
} | {
"index": "35369",
"split": "train"
} |
math | [
{
"content": "A point $Q$ is chosen within $\\triangle DEF$ such that lines drawn through $Q$, parallel to the sides of $\\triangle DEF$, divide it into three smaller triangles with areas $9$, $16$, and $25$ respectively. Determine the area of $\\triangle DEF$. Please output the final answer within \\boxed{}.",... | {
"ground_truth": "144",
"style": "rule"
} | {
"index": "35370",
"split": "train"
} |
math | [
{
"content": "Two cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a Queen and the second card is a $\\diamondsuit$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\dfrac{289}{15068}",
"style": "rule"
} | {
"index": "35371",
"split": "train"
} |
math | [
{
"content": "In a store, there are 50 light bulbs in stock, 60% of which are produced by Factory A and 40% by Factory B. The first-class rate of the light bulbs produced by Factory A is 90%, and the first-class rate of the light bulbs produced by Factory B is 80%.\n\n(1) If one light bulb is randomly selected ... | {
"ground_truth": "1.08",
"style": "rule"
} | {
"index": "35372",
"split": "train"
} |
math | [
{
"content": "Let \\( ABC \\) be a right triangle with the hypotenuse \\( BC \\) measuring \\( 4 \\) cm. The tangent at \\( A \\) to the circumcircle of \\( ABC \\) meets the line \\( BC \\) at point \\( D \\). Suppose \\( BA = BD \\). Let \\( S \\) be the area of triangle \\( ACD \\), expressed in square centi... | {
"ground_truth": "27",
"style": "rule"
} | {
"index": "35373",
"split": "train"
} |
math | [
{
"content": "In the arithmetic sequence $\\{a_n\\}$, $a_2=4$, $a_4+a_7=15$. \n(Ⅰ) Find the general term formula of sequence $\\{a_n\\}$. \n(Ⅱ) Let $b_{n}= \\frac {1}{a_{n}a_{n+1}}$, find the value of $b_1+b_2+b_3+\\ldots+b_{10}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{10}{39}",
"style": "rule"
} | {
"index": "35374",
"split": "train"
} |
math | [
{
"content": "It is known that the ellipse $C_1$ and the parabola $C_2$ have a common focus $F(1,0)$. The center of $C_1$ and the vertex of $C_2$ are both at the origin. A line $l$ passes through point $M(4,0)$ and intersects the parabola $C_2$ at points $A$ and $B$ (with point $A$ in the fourth quadrant).\n1. ... | {
"ground_truth": "\\sqrt{34}",
"style": "rule"
} | {
"index": "35375",
"split": "train"
} |
math | [
{
"content": "Bobbo starts swimming at 2 feet/s across a 100 foot wide river with a current of 5 feet/s. Bobbo doesn't know that there is a waterfall 175 feet from where he entered the river. He realizes his predicament midway across the river. What is the minimum speed that Bobbo must increase to make it to th... | {
"ground_truth": "3 \\text{ feet/s}",
"style": "rule"
} | {
"index": "35376",
"split": "train"
} |
math | [
{
"content": "A line $l$ with an inclination angle of $45^\\circ$ passes through the focus $F$ of the parabola $y^2=8x$ and intersects the parabola at points $A$ and $B$. Find the value of $|\\overrightarrow{FA}| \\cdot |\\overrightarrow{FB}|$. Please output the final answer within \\boxed{}.",
"role": "use... | {
"ground_truth": "32",
"style": "rule"
} | {
"index": "35377",
"split": "train"
} |
math | [
{
"content": "How many ten digit positive integers with distinct digits are multiples of $11111$ ? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3456",
"style": "rule"
} | {
"index": "35378",
"split": "train"
} |
math | [
{
"content": "Find the constant term in the expansion of $\\left( \\sqrt {x}+ \\dfrac {1}{2 \\sqrt {x}}\\right)^{8}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\dfrac {35}{8}",
"style": "rule"
} | {
"index": "35379",
"split": "train"
} |
math | [
{
"content": "A triangle with side lengths $5,7,8$ is inscribed in a circle $C$. The diameters of $C$ parallel to the sides of lengths 5 and 8 divide $C$ into four sectors. What is the area of either of the two smaller ones? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{49}{18} \\pi",
"style": "rule"
} | {
"index": "35380",
"split": "train"
} |
math | [
{
"content": "What is the largest $4$ digit integer congruent to $15 \\pmod{22}?$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "9981",
"style": "rule"
} | {
"index": "35381",
"split": "train"
} |
math | [
{
"content": "Let \\(\\left\\{a_{n}\\right\\}\\) be a sequence of positive integers such that \\(a_{1}=1\\), \\(a_{2}=2009\\) and for \\(n \\geq 1\\), \\(a_{n+2} a_{n} - a_{n+1}^{2} - a_{n+1} a_{n} = 0\\). Determine the value of \\(\\frac{a_{993}}{100 a_{991}}\\). Please output the final answer within \\boxed{}... | {
"ground_truth": "89970",
"style": "rule"
} | {
"index": "35382",
"split": "train"
} |
math | [
{
"content": "What is the sum of the digits of \\(10^{2008} - 2008\\)? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "18063",
"style": "rule"
} | {
"index": "35383",
"split": "train"
} |
math | [
{
"content": "Let $f$ be a function defined on the positive integers, such that\n\\[f(xy) = f(x) + f(y)\\]for all positive integers $x$ and $y.$ Given $f(10) = 14$ and $f(40) = 20,$ find $f(500).$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "39",
"style": "rule"
} | {
"index": "35384",
"split": "train"
} |
math | [
{
"content": "Out of 1500 people surveyed, $25\\%$ do not like television, and out of those who do not like television, $15\\%$ also do not like books. How many people surveyed do not like both television and books? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "56",
"style": "rule"
} | {
"index": "35385",
"split": "train"
} |
math | [
{
"content": "Find all solutions to the equation\\[ \\sqrt[4]{x} = \\frac{12}{7 - \\sqrt[4]{x}}.\\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "81, 256",
"style": "rule"
} | {
"index": "35386",
"split": "train"
} |
math | [
{
"content": "Three balls are lying on a table, each pair touching each other. The radii of the balls form a geometric progression with a common ratio \\( q \\neq 1 \\). The radius of the middle ball is 2012. Find the ratio of the sum of the squares of the sides of the triangle formed by the points of contact o... | {
"ground_truth": "4024",
"style": "rule"
} | {
"index": "35387",
"split": "train"
} |
math | [
{
"content": "Given the function $f(x) = x^{3} + ax^{2} - 2x + 1$ has an extremum at $x=1$. \n$(1)$ Find the value of $a$; \n$(2)$ Determine the monotonic intervals and extremum of $f(x)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"index": "35388",
"split": "train"
} |
math | [
{
"content": "Given $f(x)=\\cos x\\cdot\\ln x$, $f(x_{0})=f(x_{1})=0(x_{0}\\neq x_{1})$, find the minimum value of $|x_{0}-x_{1}|$ ___. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\dfrac {\\pi}{2}-1",
"style": "rule"
} | {
"index": "35389",
"split": "train"
} |
math | [
{
"content": "If an integer of two digits is $k$ times the sum of its digits, the number formed by interchanging the digits is the sum of the digits multiplied by Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "11-k",
"style": "rule"
} | {
"index": "35390",
"split": "train"
} |
math | [
{
"content": "The diagonals of a rhombus are 6 inches and 8 inches. What is the perimeter, in inches, of the rhombus below? [asy]\nimport geometry; size(150); defaultpen(linewidth(0.8));\npair A = (0,0),B = (8,6),C = (16,0),D = (8,-6), E = (8,0);\ndraw(A--B--C--D--cycle);\ndraw(A--C,StickIntervalMarker(2,2,10))... | {
"ground_truth": "20",
"style": "rule"
} | {
"index": "35391",
"split": "train"
} |
math | [
{
"content": "Ten points are spaced evenly along the perimeter of a rectangle measuring $3 \\times 2$ units. What is the probability that the two points are one unit apart? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{2}{9}",
"style": "rule"
} | {
"index": "35392",
"split": "train"
} |
math | [
{
"content": "In how many different places in the $xy$-plane can a third point, $R$, be placed so that $PQ = QR = PR$ if points $P$ and $Q$ are two distinct points in the $xy$-plane? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"index": "35393",
"split": "train"
} |
math | [
{
"content": "How many integers $n>1$ are there such that $n$ divides $x^{13}-x$ for every positive integer $x$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "31",
"style": "rule"
} | {
"index": "35394",
"split": "train"
} |
math | [
{
"content": "Find the smallest sum of distances from an arbitrary point on the plane to the vertices of a unit square.\n\nA problem of the shortest connection for four points. Four points: \\(A, B, C,\\) and \\(D\\) are the vertices of a square with side length 1. How should these points be connected by roads ... | {
"ground_truth": "2\\sqrt{2}",
"style": "rule"
} | {
"index": "35395",
"split": "train"
} |
math | [
{
"content": "A class is scheduled to have 6 classes in one day: Chinese, Mathematics, Politics, English, PE, and Art. It is required that the Mathematics class is scheduled within the first 3 periods, and the PE class cannot be scheduled in the first period. The number of different scheduling methods is ______... | {
"ground_truth": "312",
"style": "rule"
} | {
"index": "35396",
"split": "train"
} |
math | [
{
"content": "Determine the number of six-letter words where the first and last two letters are the same (e.g., \"aabbaa\"). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "456976",
"style": "rule"
} | {
"index": "35397",
"split": "train"
} |
math | [
{
"content": "In square \\(ABCD\\) with a side length of 10, points \\(P\\) and \\(Q\\) lie on the segment joining the midpoints of sides \\(AD\\) and \\(BC\\). Connecting \\(PA\\), \\(PC\\), \\(QA\\), and \\(QC\\) divides the square into three regions of equal area. Find the length of segment \\(PQ\\). Please ... | {
"ground_truth": "20/3",
"style": "rule"
} | {
"index": "35398",
"split": "train"
} |
math | [
{
"content": "A sports equipment store purchaser needs to purchase a total of 100 basketballs and volleyballs from the manufacturer, with a total payment not exceeding $11,815. The wholesale prices from the two types of balls and the retail prices at the store are shown in the table below. Solve the following q... | {
"ground_truth": "2,600",
"style": "rule"
} | {
"index": "35399",
"split": "train"
} |
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