data_source large_stringclasses 1
value | prompt listlengths 1 1 | reward_model dict | extra_info dict |
|---|---|---|---|
math | [
{
"content": "Find the sum of $10_{10} + 23_{10}$, first by converting each number to base 3, performing the addition in base 3, and then converting the result back to base 10. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "33",
"style": "rule"
} | {
"index": "7900",
"split": "train"
} |
math | [
{
"content": "In triangle $ABC$, $AC = 13$, $BC = 14$, and $AB=15$. Points $M$ and $D$ lie on $AC$ with $AM=MC$ and $\\angle ABD = \\angle DBC$. Points $N$ and $E$ lie on $AB$ with $AN=NB$ and $\\angle ACE = \\angle ECB$. Let $P$ be the point, other than $A$, of intersection of the circumcircles of $\\triangle ... | {
"ground_truth": "218",
"style": "rule"
} | {
"index": "7901",
"split": "train"
} |
math | [
{
"content": "Given the area of rectangle $ABCD$ is $8$, when the perimeter of the rectangle is minimized, fold $\\triangle ACD$ along the diagonal $AC$, then the surface area of the circumscribed sphere of the pyramid $D-ABC$ is ______. Please output the final answer within \\boxed{}.",
"role": "user"
}
... | {
"ground_truth": "16\\pi",
"style": "rule"
} | {
"index": "7902",
"split": "train"
} |
math | [
{
"content": "When the radius $r$ of a circle is increased by $5$, the area is quadrupled. What was the original radius $r$? Additionally, find the new perimeter of the circle after this radius increase.\nA) Original radius: 4, New perimeter: $18\\pi$\nB) Original radius: 5, New perimeter: $20\\pi$\nC) Original... | {
"ground_truth": "20\\pi",
"style": "rule"
} | {
"index": "7903",
"split": "train"
} |
math | [
{
"content": "Triangle $PQR$ has $PQ = 28.$ The incircle of the triangle evenly trisects the median $PS.$ If the area of the triangle is $p \\sqrt{q}$ where $p$ and $q$ are integers, and $q$ is prime, find $p+q.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "199",
"style": "rule"
} | {
"index": "7904",
"split": "train"
} |
math | [
{
"content": "Let\n\\[f(x)=\\cos(x^3-4x^2+5x-2).\\]\nIf we let $f^{(k)}$ denote the $k$ th derivative of $f$ , compute $f^{(10)}(1)$ . For the sake of this problem, note that $10!=3628800$ . Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "907200",
"style": "rule"
} | {
"index": "7905",
"split": "train"
} |
math | [
{
"content": "Let $a,b$ be positive reals such that $\\frac{1}{a}+\\frac{1}{b}\\leq2\\sqrt2$ and $(a-b)^2=4(ab)^3$ . Find $\\log_a b$ . Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-1",
"style": "rule"
} | {
"index": "7906",
"split": "train"
} |
math | [
{
"content": "Given vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ that satisfy $|\\overrightarrow{a}| = 1$, $|\\overrightarrow{b}| = \\sqrt{3}$, and $(3\\overrightarrow{a} - 2\\overrightarrow{b}) \\perp \\overrightarrow{a}$, find the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b}$. Pleas... | {
"ground_truth": "\\frac{\\pi}{6}",
"style": "rule"
} | {
"index": "7907",
"split": "train"
} |
math | [
{
"content": "Given that Alice is 1.6 meters tall, can reach 50 centimeters above her head, and the ceiling is 3 meters tall, find the minimum height of the stool in centimeters needed for her to reach a ceiling fan switch located 15 centimeters below the ceiling. Please output the final answer within \\boxed{}... | {
"ground_truth": "63",
"style": "rule"
} | {
"index": "7908",
"split": "train"
} |
math | [
{
"content": "Let a positive integer \\(n\\) be called a cubic square if there exist positive integers \\(a, b\\) with \\(n=\\operatorname{gcd}\\left(a^{2}, b^{3}\\right)\\). Count the number of cubic squares between 1 and 100 inclusive. Please output the final answer within \\boxed{}.",
"role": "user"
}
... | {
"ground_truth": "13",
"style": "rule"
} | {
"index": "7909",
"split": "train"
} |
math | [
{
"content": "Circles $P$, $Q$, and $R$ are externally tangent to each other and internally tangent to circle $S$. Circles $Q$ and $R$ are congruent. Circle $P$ has radius 2 and passes through the center of $S$. What is the radius of circle $Q$? Please output the final answer within \\boxed{}.",
"role": "us... | {
"ground_truth": "\\frac{16}{9}",
"style": "rule"
} | {
"index": "7910",
"split": "train"
} |
math | [
{
"content": "What is the maximum number of cells in an $8 \\times 8$ square that can be colored such that the centers of any four colored cells do not form the vertices of a rectangle with sides parallel to the edges of the square? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "24",
"style": "rule"
} | {
"index": "7911",
"split": "train"
} |
math | [
{
"content": "What is the smallest positive integer that is a multiple of each of 3, 5, 7, and 9? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "315",
"style": "rule"
} | {
"index": "7912",
"split": "train"
} |
math | [
{
"content": "A firecracker was thrown vertically upwards with a speed of $20 \\mathrm{~m/s}$. Three seconds after the start of the flight, it exploded into two fragments of equal mass. The first fragment flew horizontally immediately after the explosion with a speed of $48 \\mathrm{~m/s}$. Find the speed of th... | {
"ground_truth": "52",
"style": "rule"
} | {
"index": "7913",
"split": "train"
} |
math | [
{
"content": "From the 20 numbers 11, 12, 13, 14, ... 30, how many numbers at a minimum must be taken to ensure that among the selected numbers, there will definitely be a pair whose sum is a multiple of ten? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "11",
"style": "rule"
} | {
"index": "7914",
"split": "train"
} |
math | [
{
"content": "Find the product of all constants $t$ such that the quadratic $x^2 + tx - 12$ can be factored in the form $(x+a)(x+b)$, where $a$ and $b$ are integers. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1936",
"style": "rule"
} | {
"index": "7915",
"split": "train"
} |
math | [
{
"content": "Let $\\mathcal{T}$ be the set of ordered triples $(x,y,z)$ of nonnegative real numbers that lie in the plane $x+y+z=1.$ Let us say that $(x,y,z)$ supports $(a,b,c)$ when exactly two of the following are true: $x\\ge a, y\\ge b, z\\ge c.$ Let $\\mathcal{S}$ consist of those triples in $\\mathcal{T}... | {
"ground_truth": "\\frac{7}{18}",
"style": "rule"
} | {
"index": "7916",
"split": "train"
} |
math | [
{
"content": "Segment $AB$ is both a diameter of a circle of radius $1$ and a side of an equilateral triangle $ABC$. The circle also intersects $AC$ and $BC$ at points $D$ and $E$, respectively. The length of $AE$ is Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"index": "7917",
"split": "train"
} |
math | [
{
"content": "What is the value of the expression $(25 + 8)^2 - (8^2 +25^2)$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "400",
"style": "rule"
} | {
"index": "7918",
"split": "train"
} |
math | [
{
"content": "One morning at 9:00 AM, a pedestrian named Fedya left the village of Fedino and headed towards the village of Novoverandovo. At the same time, a cyclist named Vera left Novoverandovo heading towards Fedya. It is known that by the time they met, Fedya had covered one-third of the distance between t... | {
"ground_truth": "11:00",
"style": "rule"
} | {
"index": "7919",
"split": "train"
} |
math | [
{
"content": "In the triangular pyramid $A B C D$ with a base $A B C$, the lateral edges are pairwise perpendicular, $D A=D B=5$, and $D C=1$. From a point on the base, a light ray is emitted. After reflecting exactly once from each of the lateral faces (without reflecting from the edges), the ray hits a point ... | {
"ground_truth": "\\frac{10\\sqrt{3}}{9}",
"style": "rule"
} | {
"index": "7920",
"split": "train"
} |
math | [
{
"content": "Triangle $PQR$ has side-lengths $PQ = 20, QR = 40,$ and $PR = 30.$ The line through the incenter of $\\triangle PQR$ parallel to $\\overline{QR}$ intersects $\\overline{PQ}$ at $X$ and $\\overline{PR}$ at $Y.$ What is the perimeter of $\\triangle PXY?$ Please output the final answer within \\boxed... | {
"ground_truth": "50",
"style": "rule"
} | {
"index": "7921",
"split": "train"
} |
math | [
{
"content": "Calculate the arc lengths of the curves given by the equations in the rectangular coordinate system.\n\n$$\ny=2-e^{x}, \\ln \\sqrt{3} \\leq x \\leq \\ln \\sqrt{8}\n$$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1 + \\frac{1}{2} \\ln \\frac{3}{2}",
"style": "rule"
} | {
"index": "7922",
"split": "train"
} |
math | [
{
"content": "Joel now selects an acute angle $x$ (between 0 and 90 degrees) and writes $\\sin x$, $\\cos x$, and $\\tan x$ on three different cards. Each student, Malvina, Paulina, and Georgina, receives one card, but Joel chooses a value $\\sin x$ that is a commonly known value, $\\sin x = \\frac{1}{2}$. The ... | {
"ground_truth": "\\frac{\\sqrt{3}}{2}",
"style": "rule"
} | {
"index": "7923",
"split": "train"
} |
math | [
{
"content": "Given the definition that an arithmetic sequence is a sequence in which the difference between any term and its preceding term is a constant. For example, the sequence $2, 4, 6, 8, \\ldots$ is an arithmetic sequence. A second-order arithmetic sequence is defined as a sequence in which the differen... | {
"ground_truth": "4050157",
"style": "rule"
} | {
"index": "7924",
"split": "train"
} |
math | [
{
"content": "A regular dodecagon \\(Q_1 Q_2 \\dotsb Q_{12}\\) is drawn in the coordinate plane with \\(Q_1\\) at \\((1,0)\\) and \\(Q_7\\) at \\((3,0)\\). If \\(Q_n\\) is the point \\((x_n,y_n),\\) compute the numerical value of the product\n\\[(x_1 + y_1 i)(x_2 + y_2 i)(x_3 + y_3 i) \\dotsm (x_{12} + y_{12} i... | {
"ground_truth": "4095",
"style": "rule"
} | {
"index": "7925",
"split": "train"
} |
math | [
{
"content": "Given the cubic function $f(x) = x^3 - 9x^2 + 20x - 4$, and the arithmetic sequence $\\{a_n\\}$ with $a_5 = 3$, find the value of $f(a_1) + f(a_2) + ... + f(a_9)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "18",
"style": "rule"
} | {
"index": "7926",
"split": "train"
} |
math | [
{
"content": "Let $S$ be a set of $2020$ distinct points in the plane. Let \n\\[M=\\{P:P\\text{ is the midpoint of }XY\\text{ for some distinct points }X,Y\\text{ in }S\\}.\\]\n\nFind the least possible value of the number of points in $M$ . Please output the final answer within \\boxed{}.",
"role": "u... | {
"ground_truth": "4037",
"style": "rule"
} | {
"index": "7927",
"split": "train"
} |
math | [
{
"content": "How many integers from 1 through 9999, inclusive, do not contain any of the digits 2, 3, 4 or 5? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1295",
"style": "rule"
} | {
"index": "7928",
"split": "train"
} |
math | [
{
"content": "Let $\\triangle ABC$ be a triangle in the plane, and let $D$ be a point outside the plane of $\\triangle ABC$, so that $DABC$ is a pyramid whose faces are all triangles.\n\nSuppose that every edge of $DABC$ has length $20$ or $45$, but no face of $DABC$ is equilateral. Then what is the surface are... | {
"ground_truth": "40 \\sqrt{1925}",
"style": "rule"
} | {
"index": "7929",
"split": "train"
} |
math | [
{
"content": "In triangle $\\triangle ABC$, the opposite sides of angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $\\tan A = 2\\tan B$, $b = \\sqrt{2}$, find the value of $a$ when the area of $\\triangle ABC$ is maximized. Please output the final answer within \\boxed{}.",
"role": "u... | {
"ground_truth": "\\sqrt{5}",
"style": "rule"
} | {
"index": "7930",
"split": "train"
} |
math | [
{
"content": "Find a number \\( N \\) with five digits, all different and none zero, which equals the sum of all distinct three-digit numbers whose digits are all different and are all digits of \\( N \\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "35964",
"style": "rule"
} | {
"index": "7931",
"split": "train"
} |
math | [
{
"content": "Consider all the subsets of $\\{1,2,3, \\ldots, 2018,2019\\}$ having exactly 100 elements. For each subset, take the greatest element. Find the average of all these greatest elements. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2000",
"style": "rule"
} | {
"index": "7932",
"split": "train"
} |
math | [
{
"content": "Let \\(z=\\frac{1+i}{\\sqrt{2}}.\\)What is \\(\\left(z^{1^2}+z^{2^2}+z^{3^2}+\\dots+z^{{12}^2}\\right) \\cdot \\left(\\frac{1}{z^{1^2}}+\\frac{1}{z^{2^2}}+\\frac{1}{z^{3^2}}+\\dots+\\frac{1}{z^{{12}^2}}\\right)?\\) Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "36",
"style": "rule"
} | {
"index": "7933",
"split": "train"
} |
math | [
{
"content": "Given an ellipse $C$: $\\frac{x^2}{a^2}+\\frac{y^2}{b^2}=1\\left(a \\gt b \\gt 0\\right)$ with the left and right foci $F_{1}$ and $F_{2}$ respectively. Let $F_{1}$ be the center of a circle with radius $|F_{1}F_{2}|$, intersecting the $y$-axis at points $A$ and $B$ (both points $A$ and $B$ are ou... | {
"ground_truth": "\\sqrt{3} - 1",
"style": "rule"
} | {
"index": "7934",
"split": "train"
} |
math | [
{
"content": "After folding the long rope in half 6 times, calculate the number of segments the rope will be cut into. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "65",
"style": "rule"
} | {
"index": "7935",
"split": "train"
} |
math | [
{
"content": "Arrange for 7 staff members to be on duty from May 1st to May 7th. Each person is on duty for one day, with both members A and B not being scheduled on May 1st and 2nd. The total number of different scheduling methods is $\\_\\_\\_\\_\\_\\_\\_$. Please output the final answer within \\boxed{}.",
... | {
"ground_truth": "2400",
"style": "rule"
} | {
"index": "7936",
"split": "train"
} |
math | [
{
"content": "Let \\( p, q, r, s, t, u, v, w \\) be real numbers such that \\( pqrs = 16 \\) and \\( tuvw = 25 \\). Find the minimum value of\n\\[ (pt)^2 + (qu)^2 + (rv)^2 + (sw)^2. \\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "400",
"style": "rule"
} | {
"index": "7937",
"split": "train"
} |
math | [
{
"content": "Three circles have the same center O. Point X divides segment OP in the ratio 1:3, with X being closer to O. Calculate the ratio of the area of the circle with radius OX to the area of the circle with radius OP. Next, find the area ratio of a third circle with radius 2*OX to the circle with radius... | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"index": "7938",
"split": "train"
} |
math | [
{
"content": "In the right triangle \\(ABC\\) with an acute angle of \\(30^\\circ\\), an altitude \\(CD\\) is drawn from the right angle vertex \\(C\\). Find the distance between the centers of the inscribed circles of triangles \\(ACD\\) and \\(BCD\\), if the shorter leg of triangle \\(ABC\\) is 1. Please outp... | {
"ground_truth": "\\frac{\\sqrt{3}-1}{\\sqrt{2}}",
"style": "rule"
} | {
"index": "7939",
"split": "train"
} |
math | [
{
"content": "The numbers in the sequence $101$, $104$, $109$, $116$,$\\ldots$ are of the form $a_n=100+n^2$, where $n=1,2,3,\\ldots$ For each $n$, let $d_n$ be the greatest common divisor of $a_n$ and $a_{n+1}$. Find the maximum value of $d_n$ as $n$ ranges through the positive integers. Please output the fina... | {
"ground_truth": "401",
"style": "rule"
} | {
"index": "7940",
"split": "train"
} |
math | [
{
"content": "Consider a list of numbers \\[8, 3, x, 3, 7, 3, y\\]. When the mean, median, and mode of this list are arranged in increasing order, they form a non-constant arithmetic progression. What is the sum of all possible values of \\(y\\) if \\(x=6\\)?\nA) $\\frac{51}{13}$ \nB) $33$ \nC) $\\frac{480}{1... | {
"ground_truth": "\\frac{480}{13}",
"style": "rule"
} | {
"index": "7941",
"split": "train"
} |
math | [
{
"content": "If two distinct numbers from the set $\\{ 5, 15, 21, 35, 45, 63, 70, 90 \\}$ are randomly selected and multiplied, what is the probability that the product is a multiple of 105? Express your answer as a common fraction. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"index": "7942",
"split": "train"
} |
math | [
{
"content": "A triangle has vertices $(0,0)$, $(1,1)$, and $(6m,0)$. The line $y = mx$ divides the triangle into two triangles of equal area. What is the sum of all possible values of $m$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "- \\frac {1}{6}",
"style": "rule"
} | {
"index": "7943",
"split": "train"
} |
math | [
{
"content": "A circle is inscribed in quadrilateral $ABCD$, tangent to $\\overline{AB}$ at $P$ and to $\\overline{CD}$ at $Q$. Given that $AP=19$, $PB=26$, $CQ=37$, and $QD=23$, find the square of the radius of the circle. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "647",
"style": "rule"
} | {
"index": "7944",
"split": "train"
} |
math | [
{
"content": "Two integers are relatively prime if they have no common factors other than 1 or -1. What is the probability that a positive integer less than or equal to 30 is relatively prime to 30? Express your answer as a common fraction. Please output the final answer within \\boxed{}.",
"role": "user"
... | {
"ground_truth": "\\frac{4}{15}",
"style": "rule"
} | {
"index": "7945",
"split": "train"
} |
math | [
{
"content": "If exactly three of the balls match the numbers of their boxes, calculate the number of different ways to place the balls. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "10",
"style": "rule"
} | {
"index": "7946",
"split": "train"
} |
math | [
{
"content": "Let $u$ and $v$ be integers satisfying $0 < v < u$. Let $A = (u,v)$, let $B$ be the reflection of $A$ across the line $y = x$, let $C$ be the reflection of $B$ across the y-axis, let $D$ be the reflection of $C$ across the x-axis, and let $E$ be the reflection of $D$ across the y-axis. The area of... | {
"ground_truth": "21",
"style": "rule"
} | {
"index": "7947",
"split": "train"
} |
math | [
{
"content": "How many non-congruent right triangles with positive integer leg lengths have areas that are numerically equal to $3$ times their perimeters? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "7",
"style": "rule"
} | {
"index": "7948",
"split": "train"
} |
math | [
{
"content": "Given $f(x)={x}^{2023}+a{x}^{3}-\\frac{b}{x}-8$, $f\\left(-2\\right)=10$, find $f\\left(2\\right)=\\_\\_\\_\\_\\_\\_$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-26",
"style": "rule"
} | {
"index": "7949",
"split": "train"
} |
math | [
{
"content": "The function $f$, defined on the set of ordered pairs of positive integers, satisfies the following properties: \\[f(x, x) = x,\\; f(x, y) = f(y, x), {\\rm \\ and\\ } (x+y)f(x, y) = yf(x, x+y).\\] Calculate $f(14,52)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "364",
"style": "rule"
} | {
"index": "7950",
"split": "train"
} |
math | [
{
"content": "If the measure of angle $C$ is double the measure of angle $B$, what is the measure of angle $A$ in triangle $ABC$?\n\n[asy]\n\npair A,B,C;\n\nA=(0,0);\nB=(5,0);\nC=(-0.8,2.5);\n\ndraw(A--B--C--A);\n\nlabel(\"$A$\",A,SW);\nlabel(\"$B$\",B,SE);\nlabel(\"$C$\",C,N);\n\ndraw((4,0.6)..(3.8,0.4)..(3.9,... | {
"ground_truth": "117^\\circ",
"style": "rule"
} | {
"index": "7951",
"split": "train"
} |
math | [
{
"content": "Given the polynomial $f(x) = 12 + 35x - 8x^2 + 79x^3 + 6x^4 + 5x^5 + 3x^6$, use Horner's Rule to calculate the value of $v_4$ when $x = -4$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "220",
"style": "rule"
} | {
"index": "7952",
"split": "train"
} |
math | [
{
"content": "Given a random variable $\\xi$ follows the normal distribution $N(0, \\sigma^2)$. If $P(\\xi > 2) = 0.023$, calculate $P(-2 \\leq \\xi \\leq 2)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "0.954",
"style": "rule"
} | {
"index": "7953",
"split": "train"
} |
math | [
{
"content": "Let $ABCDE$ be a regular pentagon. The star $ACEBD$ has area 1. $AC$ and $BE$ meet at $P$ , while $BD$ and $CE$ meet at $Q$ . Find the area of $APQD$ . Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1/2",
"style": "rule"
} | {
"index": "7954",
"split": "train"
} |
math | [
{
"content": "In \\\\(\\Delta ABC\\\\), given that \\\\(a= \\sqrt{3}, b= \\sqrt{2}, B=45^{\\circ}\\\\), find \\\\(A, C\\\\) and \\\\(c\\\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{\\sqrt{6}- \\sqrt{2}}{2}",
"style": "rule"
} | {
"index": "7955",
"split": "train"
} |
math | [
{
"content": "30 students from 5 grades participated in answering 40 questions. Each student answered at least 1 question. Every two students from the same grade answered the same number of questions, and students from different grades answered a different number of questions. How many students answered only 1 ... | {
"ground_truth": "26",
"style": "rule"
} | {
"index": "7956",
"split": "train"
} |
math | [
{
"content": "Let $S$ be the set of the $2005$ smallest positive multiples of $4$, and let $T$ be the set of the $2005$ smallest positive multiples of $6$. How many elements are common to $S$ and $T$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "668",
"style": "rule"
} | {
"index": "7957",
"split": "train"
} |
math | [
{
"content": "A recent study found that 60$\\%$ of men and 80$\\%$ of women surveyed support increased funding for particular medical research. The study surveyed 100 men and 900 women. What was the overall percent of the people surveyed who supported increased funding? Please output the final answer within \\b... | {
"ground_truth": "78\\%",
"style": "rule"
} | {
"index": "7958",
"split": "train"
} |
math | [
{
"content": "Evaluate the expression \\(\\dfrac{\\sqrt[4]{7}}{\\sqrt[6]{7}}\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "7^{\\frac{1}{12}}",
"style": "rule"
} | {
"index": "7959",
"split": "train"
} |
math | [
{
"content": "A unit purchased a vacant lot for 21.6 million yuan, planning to build a building of at least 10 floors, with each floor being 2000 square meters. It is calculated that if the building is built to $x$ ($x \\geqslant 10$) floors, then the average construction cost per square meter is $560+48x$ (uni... | {
"ground_truth": "15",
"style": "rule"
} | {
"index": "7960",
"split": "train"
} |
math | [
{
"content": "The necessary and sufficient condition for the graph of the function $y=f(x)$ to be symmetric with respect to the origin is that the function $y=f(x)$ is an odd function. This can be extended as follows: The necessary and sufficient condition for the graph of the function $y=f(x)$ to be symmetric ... | {
"ground_truth": "-8086",
"style": "rule"
} | {
"index": "7961",
"split": "train"
} |
math | [
{
"content": "Define a positive integer $n$ to be a factorial tail if there is some positive integer $m$ such that the decimal representation of $m!$ ends with exactly $n$ zeroes. How many positive integers less than $2500$ are not factorial tails? Please output the final answer within \\boxed{}.",
"role": ... | {
"ground_truth": "500",
"style": "rule"
} | {
"index": "7962",
"split": "train"
} |
math | [
{
"content": "Given that the terminal side of angle $\\alpha$ is in the second quadrant and intersects the unit circle at point $P(m, \\frac{\\sqrt{15}}{4})$. \n$(1)$ Find the value of the real number $m$; \n$(2)$ Let $f(\\alpha) = \\frac{\\cos(2\\pi - \\alpha) + \\tan(3\\pi + \\alpha)}{\\sin(\\pi - \\alpha) ... | {
"ground_truth": "-\\frac{4 + 16\\sqrt{15}}{15}",
"style": "rule"
} | {
"index": "7963",
"split": "train"
} |
math | [
{
"content": "Given the parabola C: y² = 3x with focus F, and a line l with slope $\\frac{3}{2}$ intersecting C at points A and B, and the x-axis at point P.\n(1) If |AF| + |BF| = 4, find the equation of line l;\n(2) If $\\overrightarrow{AP}$ = 3$\\overrightarrow{PB}$, find |AB|. Please output the final answer ... | {
"ground_truth": "\\frac{4\\sqrt{13}}{3}",
"style": "rule"
} | {
"index": "7964",
"split": "train"
} |
math | [
{
"content": "Given vectors $\\overrightarrow{a}=(m,1)$ and $\\overrightarrow{b}=(4-n,2)$, with $m > 0$ and $n > 0$. If $\\overrightarrow{a}$ is parallel to $\\overrightarrow{b}$, find the minimum value of $\\frac{1}{m}+\\frac{8}{n}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{9}{2}",
"style": "rule"
} | {
"index": "7965",
"split": "train"
} |
math | [
{
"content": "Given that \\(a, b, c, a+b-c, a+c-b, b+c-a, a+b+c\\) are 7 distinct prime numbers, and the sum of any two of \\(a, b, c\\) is 800. Let \\(d\\) be the difference between the largest and smallest of these 7 prime numbers. Find the maximum possible value of \\(d\\). Please output the final answer wit... | {
"ground_truth": "1594",
"style": "rule"
} | {
"index": "7966",
"split": "train"
} |
math | [
{
"content": "Find the number of integers \\( n \\) that satisfy\n\\[ 20 < n^2 < 200. \\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "20",
"style": "rule"
} | {
"index": "7967",
"split": "train"
} |
math | [
{
"content": "Given that the base of the tetrahedron \\( S-ABC \\) is an isosceles right triangle with \\( AB \\) as the hypotenuse, and \\( SA = SB = SC = AB = 2 \\). Assume that the points \\( S, A, B, \\) and \\( C \\) lie on a spherical surface with center \\( O \\). Find the distance from point \\( O \\) t... | {
"ground_truth": "\\frac{\\sqrt{3}}{3}",
"style": "rule"
} | {
"index": "7968",
"split": "train"
} |
math | [
{
"content": "Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will t... | {
"ground_truth": "9",
"style": "rule"
} | {
"index": "7969",
"split": "train"
} |
math | [
{
"content": "Mady has an infinite number of balls and empty boxes available to her. The empty boxes, each capable of holding four balls, are arranged in a row from left to right. At the first step, she places a ball in the first box (the leftmost box) of the row. At each subsequent step, she places a ball in t... | {
"ground_truth": "6",
"style": "rule"
} | {
"index": "7970",
"split": "train"
} |
math | [
{
"content": "Given that $4:5 = 20 \\div \\_\\_\\_\\_\\_\\_ = \\frac{()}{20} = \\_\\_\\_\\_\\_\\_ \\%$, find the missing values. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "80",
"style": "rule"
} | {
"index": "7971",
"split": "train"
} |
math | [
{
"content": "The graphs of $y=3-x^2+x^3$ and $y=1+x^2+x^3$ intersect in multiple points. Find the maximum difference between the $y$-coordinates of these intersection points. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2",
"style": "rule"
} | {
"index": "7972",
"split": "train"
} |
math | [
{
"content": "In a modified game, each of 5 players rolls a standard 6-sided die. The winner is the player who rolls the highest number. If there is a tie for the highest roll, those involved must roll again. This continues until only one person has the highest number. If Cecilia is one of the players, what is ... | {
"ground_truth": "\\frac{256}{1555}",
"style": "rule"
} | {
"index": "7973",
"split": "train"
} |
math | [
{
"content": "[i]Version 1[/i]. Let $n$ be a positive integer, and set $N=2^{n}$. Determine the smallest real number $a_{n}$ such that, for all real $x$,\n\\[\n\\sqrt[N]{\\frac{x^{2 N}+1}{2}} \\leqslant a_{n}(x-1)^{2}+x .\n\\]\n[i]Version 2[/i]. For every positive integer $N$, determine the smallest real number... | {
"ground_truth": "{a_n = 2^{n-1}}",
"style": "rule"
} | {
"index": "7974",
"split": "train"
} |
math | [
{
"content": "Given that $α$ and $β$ belong to the interval $(0, \\frac{π}{2})$, and they satisfy the equation $\\tan(α + β) = 9\\tan(β)$, find the maximum value of $\\tan(α)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{4}{3}",
"style": "rule"
} | {
"index": "7975",
"split": "train"
} |
math | [
{
"content": "Find the least positive integer $k$ so that $k + 25973$ is a palindrome (a number which reads the same forward and backwards). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "89",
"style": "rule"
} | {
"index": "7976",
"split": "train"
} |
math | [
{
"content": "A shop sells two kinds of products $A$ and $B$ at the price $\\$ 2100$. Product $A$ makes a profit of $20\\%$, while product $B$ makes a loss of $20\\%$. Calculate the net profit or loss resulting from this deal. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-175",
"style": "rule"
} | {
"index": "7977",
"split": "train"
} |
math | [
{
"content": "How many of the 20 perfect squares $1^{2}, 2^{2}, 3^{2}, \\ldots, 19^{2}, 20^{2}$ are divisible by 9? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "6",
"style": "rule"
} | {
"index": "7978",
"split": "train"
} |
math | [
{
"content": "Given \\((a + b i)^2 = 3 + 4i\\), where \\(a, b \\in \\mathbf{R}\\), and \\(i\\) is the imaginary unit, find the value of \\(a^2 + b^2\\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "25",
"style": "rule"
} | {
"index": "7979",
"split": "train"
} |
math | [
{
"content": "Let $\\triangle PQR$ be a right triangle with $Q$ as the right angle. A circle with diameter $QR$ intersects side $PR$ at point $S$. If the area of $\\triangle PQR$ is $200$ and $PR = 40$, find the length of $QS$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "10",
"style": "rule"
} | {
"index": "7980",
"split": "train"
} |
math | [
{
"content": "Contractor Steve agreed to complete a job in 30 days. After 6 days he found that the 8 people assigned to the work had already done $\\frac{1}{3}$ of the job. If everyone works at the same rate, what is the least number of people he must keep on the job to ensure that the job will be completed on ... | {
"ground_truth": "4",
"style": "rule"
} | {
"index": "7981",
"split": "train"
} |
math | [
{
"content": "In the Sweet Tooth store, they are thinking about what promotion to announce before March 8. Manager Vasya suggests reducing the price of a box of candies by $20\\%$ and hopes to sell twice as many goods as usual because of this. Meanwhile, Deputy Director Kolya says it would be more profitable to... | {
"ground_truth": "6000",
"style": "rule"
} | {
"index": "7982",
"split": "train"
} |
math | [
{
"content": "Compute\n\\[\\begin{vmatrix} 1 & \\cos (a - b) & \\cos a \\\\ \\cos(a - b) & 1 & \\cos b \\\\ \\cos a & \\cos b & 1 \\end{vmatrix}.\\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "0",
"style": "rule"
} | {
"index": "7983",
"split": "train"
} |
math | [
{
"content": "The first term of a geometric sequence is 1024, and the 6th term is 125. What is the positive, real value for the 4th term? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "2000",
"style": "rule"
} | {
"index": "7984",
"split": "train"
} |
math | [
{
"content": "In a school cafeteria line, there are 16 students alternating between boys and girls (starting with a boy, followed by a girl, then a boy, and so on). Any boy, followed immediately by a girl, can swap places with her. After some time, all the girls end up at the beginning of the line and all the b... | {
"ground_truth": "36",
"style": "rule"
} | {
"index": "7985",
"split": "train"
} |
math | [
{
"content": "How many whole numbers between 1 and 2000 do not contain the digit 2? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "6560",
"style": "rule"
} | {
"index": "7986",
"split": "train"
} |
math | [
{
"content": "A worker first receives a 25% cut in wages, then undergoes a 10% increase on the reduced wage. Determine the percent raise on his latest wage that the worker needs to regain his original pay. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "21.21\\%",
"style": "rule"
} | {
"index": "7987",
"split": "train"
} |
math | [
{
"content": "Two wholesalers, A and B, sell the same brand of teapots and teacups at the same price, with the teapot priced at 30 yuan each and the teacup at 5 yuan each. Both stores are offering a promotional sale: Store A has a 'buy one get one free' promotion (buy a teapot and get a teacup for free), while ... | {
"ground_truth": "20",
"style": "rule"
} | {
"index": "7988",
"split": "train"
} |
math | [
{
"content": "Equilateral $\\triangle ABC$ is inscribed in a circle of radius $2$. Extend $\\overline{AB}$ through $B$ to point $D$ so that $AD=13,$ and extend $\\overline{AC}$ through $C$ to point $E$ so that $AE = 11.$ Through $D,$ draw a line $l_1$ parallel to $\\overline{AE},$ and through $E,$ draw a line $... | {
"ground_truth": "865",
"style": "rule"
} | {
"index": "7989",
"split": "train"
} |
math | [
{
"content": "Define the derivative of the $(n-1)$th derivative as the $n$th derivative $(n \\in N^{*}, n \\geqslant 2)$, that is, $f^{(n)}(x)=[f^{(n-1)}(x)]'$. They are denoted as $f''(x)$, $f'''(x)$, $f^{(4)}(x)$, ..., $f^{(n)}(x)$. If $f(x) = xe^{x}$, then the $2023$rd derivative of the function $f(x)$ at th... | {
"ground_truth": "-\\frac{2023}{2024}",
"style": "rule"
} | {
"index": "7990",
"split": "train"
} |
math | [
{
"content": "Given that the moving points $P$, $M$, and $N$ are respectively on the $x$-axis, the circle $\\Gamma_{1}$: $(x-1)^{2}+(y-2)^{2}=1$, and the circle $\\Gamma_{2}$: $(x-3)^{2}+(y-4)^{2}=3$, find the minimum value of $|PM| + |PN|$. Please output the final answer within \\boxed{}.",
"role": "user"
... | {
"ground_truth": "2\\sqrt{10} - \\sqrt{3} - 1",
"style": "rule"
} | {
"index": "7991",
"split": "train"
} |
math | [
{
"content": "What is the result of subtracting $7.305$ from $-3.219$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-10.524",
"style": "rule"
} | {
"index": "7992",
"split": "train"
} |
math | [
{
"content": "In a trapezoid, the lengths of the diagonals are known to be 6 and 8, and the length of the midsegment is 5. Find the height of the trapezoid. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4.8",
"style": "rule"
} | {
"index": "7993",
"split": "train"
} |
math | [
{
"content": "Given the radii of the inner and outer circles are $4$ and $8$, respectively, with the inner circle divided into regions with point values 3, 1, 1, and the outer circle divided into regions with point values 2, 3, 3, calculate the probability that the score sum of two darts hitting this board is o... | {
"ground_truth": "\\frac{4}{9}",
"style": "rule"
} | {
"index": "7994",
"split": "train"
} |
math | [
{
"content": "Distribute 3 male and 2 female freshmen, a total of 5 students, into two classes, Class A and Class B, with each class receiving no fewer than 2 students, and Class A must have at least 1 female student. The number of different distribution schemes is ______. Please output the final answer within ... | {
"ground_truth": "16",
"style": "rule"
} | {
"index": "7995",
"split": "train"
} |
math | [
{
"content": "Xiaoming's family raises chickens and pigs in a ratio of 26:5, and sheep to horses in a ratio of 25:9, while the ratio of pigs to horses is 10:3. Find the ratio of chickens, pigs, horses, and sheep. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "156:30:9:25",
"style": "rule"
} | {
"index": "7996",
"split": "train"
} |
math | [
{
"content": "Given that $\\operatorname{log}_{8}(p) = \\operatorname{log}_{12}(q) = \\operatorname{log}_{18}(p-q)$, calculate the value of $\\frac{q}{p}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{\\sqrt{5} - 1}{2}",
"style": "rule"
} | {
"index": "7997",
"split": "train"
} |
math | [
{
"content": "Four people can paint a house in six hours. How many hours would it take three people to paint the same house, assuming everyone works at the same rate? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "8",
"style": "rule"
} | {
"index": "7998",
"split": "train"
} |
math | [
{
"content": "If point $P$ is any point on the curve $y=x^{2}-\\ln x$, then the minimum distance from point $P$ to the line $y=x-2$ is ____. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"index": "7999",
"split": "train"
} |
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