data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "In triangle $\\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and it is given that $(2a-c)\\cos B = b\\cos C$. \n\n(1) Find the size of angle $B$; \n(2) If the area of $\\triangle ABC$ is $T$ and $b=\\sqrt{3}$, find the value of... | math | {
"style": "rule",
"ground_truth": "\\sqrt{ \\frac{30}{2} }"
} | {
"split": "train",
"index": 20049,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $m$ be a positive integer, and let $a_0, a_1, \\dots , a_m$ be a sequence of real numbers such that $a_0 = 37$, $a_1 = 72$, $a_m=0$, and $$ a_{k+1} = a_{k-1} - \\frac{3}{a_k} $$for $k = 1,\n2, \\dots, m-1$. Find $m$. Let's think step by step and put only the final answer wi... | math | {
"style": "rule",
"ground_truth": "889"
} | {
"split": "train",
"index": 20050,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the cubes whose vertices lie on the surface of a given cube. Which one is the smallest among them? 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": 20051,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the tetrahedron $P-ABC$, $\\Delta ABC$ is an equilateral triangle, and $PA=PB=PC=3$, $PA \\perp PB$. The volume of the circumscribed sphere of the tetrahedron $P-ABC$ is __________. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{27\\sqrt{3}\\pi}{2}"
} | {
"split": "train",
"index": 20052,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given real numbers \\( x \\) and \\( y \\in (1, +\\infty) \\), and \\( x y - 2 x - y + 1 = 0 \\). Find the minimum value of \\( \\frac{3}{2} x^{2} + y^{2} \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 20053,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $k$ be a real number such that the product of real roots of the equation $$ X^4 + 2X^3 + (2 + 2k)X^2 + (1 + 2k)X + 2k = 0 $$ is $-2013$ . Find the sum of the squares of these real roots. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4027"
} | {
"split": "train",
"index": 20054,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The line joining the midpoints of the diagonals of a trapezoid has length $3$. If the longer base is $97,$ then the shorter base is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "91"
} | {
"split": "train",
"index": 20055,
"solution": "1. **Identify the properties of the trapezoid**: In a trapezoid, the line segment joining the midpoints of the diagonals is parallel to the bases and its length is equal to half the difference of the lengths of the bases.\n\n2. **Set up the equation**: Let $x$ be t... |
deepscaler | [
{
"role": "user",
"content": "Distribute 6 volunteers into 4 groups, with each group having at least 1 and at most 2 people, and assign them to four different exhibition areas of the fifth Asia-Europe Expo. The number of different allocation schemes is ______ (answer with a number). Let's think step by step... | math | {
"style": "rule",
"ground_truth": "1080"
} | {
"split": "train",
"index": 20056,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the volume of the region in space defined by\n\\[|x + y + 2z| + |x + y - 2z| \\le 12\\]\nand $x, y, z \\ge 0$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "54"
} | {
"split": "train",
"index": 20057,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle with center $C$ is tangent to the positive $x$ and $y$-axes and externally tangent to the circle centered at $(3,0)$ with radius $1$. What is the sum of all possible radii of the circle with center $C$? Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 20058,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two positive integers $m$ and $n$ are both less than $500$ and $\\text{lcm}(m,n) = (m-n)^2$ . What is the maximum possible value of $m+n$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "840"
} | {
"split": "train",
"index": 20059,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Emma writes down the smallest positive multiple of 30 that is a perfect square, the smallest positive multiple of 30 that is a perfect cube, and all the multiples of 30 between them. How many integers are in Emma's list? Let's think step by step and put only the final answer wi... | math | {
"style": "rule",
"ground_truth": "871"
} | {
"split": "train",
"index": 20060,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the result when $\\frac{2}{3}$ is subtracted from $2\\frac{1}{4}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1\\frac{7}{12}"
} | {
"split": "train",
"index": 20061,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $A=120^{\\circ}$, $c=5$, $a=7$, find the value of $\\frac{\\sin B}{\\sin C}$____. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 20062,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The vertex of the parabola $y^2 = 4x$ is $O$, and the coordinates of point $A$ are $(5, 0)$. A line $l$ with an inclination angle of $\\frac{\\pi}{4}$ intersects the line segment $OA$ (but does not pass through points $O$ and $A$) and intersects the parabola at points $M$ and $... | math | {
"style": "rule",
"ground_truth": "8\\sqrt{2}"
} | {
"split": "train",
"index": 20063,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A right circular cone is placed on a table, pointing upwards. The vertical cross-section triangle, perpendicular to the base, has a vertex angle of 90 degrees. The diameter of the cone's base is 16 inches. A sphere is placed inside the cone so that it touches the sides of the c... | math | {
"style": "rule",
"ground_truth": "\\frac{256}{3}\\pi"
} | {
"split": "train",
"index": 20064,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle is inscribed in quadrilateral $EFGH$, tangent to $\\overline{EF}$ at $R$ and to $\\overline{GH}$ at $S$. Given that $ER=24$, $RF=31$, $GS=40$, and $SH=29$, find the square of the radius of the circle. Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "945"
} | {
"split": "train",
"index": 20065,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Higher Secondary P4\n\nIf the fraction $\\dfrac{a}{b}$ is greater than $\\dfrac{31}{17}$ in the least amount while $b<17$ , find $\\dfrac{a}{b}$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{11}{6}"
} | {
"split": "train",
"index": 20066,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rhombus $PQRS$ is inscribed in rectangle $ABCD$ so that vertices $P$, $Q$, $R$, and $S$ are interior points on sides $\\overline{AB}$, $\\overline{BC}$, $\\overline{CD}$, and $\\overline{DA}$, respectively. It is given that $PB=15$, $BQ=20$, $PR=30$, and $QS=40$. Let $m/n$, in ... | math | {
"style": "rule",
"ground_truth": "677"
} | {
"split": "train",
"index": 20067,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Maya lists all the positive divisors of $2010^2$. She then randomly selects two distinct divisors from this list. Let $p$ be the probability that exactly one of the selected divisors is a perfect square. The probability $p$ can be expressed in the form $\\frac {m}{n}$, where $m... | math | {
"style": "rule",
"ground_truth": "107"
} | {
"split": "train",
"index": 20068,
"solution": "$2010^2 = 2^2\\cdot3^2\\cdot5^2\\cdot67^2$. Thus there are $(2+1)^4$ divisors, $(1+1)^4$ of which are squares (the exponent of each prime factor must either be $0$ or $2$). Therefore the probability is \\[\\frac {2\\cdot2^4\\cdot(3^4 - 2^4)}{3^4(3^4 - 1)} = \\frac ... |
deepscaler | [
{
"role": "user",
"content": "Let \\( p, q, r, \\) and \\( s \\) be the roots of the polynomial \n\\[ x^4 + 10x^3 + 20x^2 + 15x + 6 = 0. \\]\nFind the value of \n\\[ \\frac{1}{pq} + \\frac{1}{pr} + \\frac{1}{ps} + \\frac{1}{qr} + \\frac{1}{qs} + \\frac{1}{rs}. \\] Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "\\frac{10}{3}"
} | {
"split": "train",
"index": 20069,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the largest integer \\( n \\) such that \n\n$$\n\\frac{\\sqrt{7}+2 \\sqrt{n}}{2 \\sqrt{7}-\\sqrt{n}}\n$$\n\nis an integer? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "343"
} | {
"split": "train",
"index": 20070,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In right triangle $BCD$ with $\\angle D = 90^\\circ$, we have $BC = 9$ and $BD = 4$. Find $\\sin B$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{65}}{9}"
} | {
"split": "train",
"index": 20071,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a$ be the proportion of teams that correctly answered problem 1 on the Guts round. Estimate $A=\\lfloor 10000a\\rfloor$. An estimate of $E$ earns $\\max (0,\\lfloor 20-|A-E| / 20\\rfloor)$ points. If you have forgotten, question 1 was the following: Two hexagons are attach... | math | {
"style": "rule",
"ground_truth": "2539"
} | {
"split": "train",
"index": 20072,
"solution": "689 teams participated in the guts round. Of these, - 175 teams submitted 3, the correct answer; - 196 teams submitted 4; - 156 teams submitted 10 (the correct answer if the hexagons had to be regular); - 64 teams submitted 6 (the correct answer if one of the hexag... |
deepscaler | [
{
"role": "user",
"content": "Calculate the value of $v_4$ for the polynomial $f(x) = 12 + 35x - 8x^2 + 79x^3 + 6x^4 + 5x^5 + 3x^6$ using the Horner's method when $x = -4$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "220"
} | {
"split": "train",
"index": 20073,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A parabola with equation $y = x^2 + bx + c$ passes through the points $(2,3)$ and $(4,3)$. What is $c$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 20074,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the coefficient of $x^2$ when $3(x^2 - x^3) +2(x - 2x^2 + 3x^5) -(4x^3 - x^2)$ is simplified. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 20075,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a convex pentagon \\(ABCDE\\), \\(AB = BC\\), \\(CD = DE\\), \\(\\angle ABC = 100^\\circ\\), \\(\\angle CDE = 80^\\circ\\), and \\(BD^2 = \\frac{100}{\\sin 100^\\circ}\\). Find the area of the pentagon. Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 20076,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose a point P(m, n) is formed by using the numbers m and n obtained from rolling a dice twice as its horizontal and vertical coordinates, respectively. The probability that point P(m, n) falls below the line x+y=4 is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{12}"
} | {
"split": "train",
"index": 20077,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an old estate, the house is surrounded by tall trees arranged in a circle, including spruces, pines, and birches. There are 96 trees in total. These trees have a peculiar property: for any coniferous tree, among the two trees that are two trees away from it, one is coniferou... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 20078,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nRain drops fall vertically at a speed of $v = 2 \\, \\text{m/s}$. The rear window of a car is inclined at an angle of $\\alpha = 60^{\\circ}$ to the horizontal. At what speed $u$ must the car travel on a horizontal, flat road so that its rear window remains dry? Let's think s... | math | {
"style": "rule",
"ground_truth": "1.15"
} | {
"split": "train",
"index": 20079,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three lathes \\( A, B, C \\) each process the same type of standard parts at a certain work efficiency. Lathe \\( A \\) starts 10 minutes earlier than lathe \\( C \\), and lathe \\( C \\) starts 5 minutes earlier than lathe \\( B \\). After lathe \\( B \\) has been working for ... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 20080,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $r$ be the result of doubling both the base and exponent of $a^b$, and $b$ does not equal to $0$. \nIf $r$ equals the product of $a^b$ by $x^b$, then $x$ equals: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4a"
} | {
"split": "train",
"index": 20081,
"solution": "1. **Identify the expression for $r$:** \n Given that $r$ is the result of doubling both the base and the exponent of $a^b$, we have:\n \\[ r = (2a)^{2b} \\]\n\n2. **Set up the equation using the given condition:** \n According to the problem, $r$ equals th... |
deepscaler | [
{
"role": "user",
"content": "Al, Bill, and Cal will each randomly be assigned a whole number from $1$ to $10$, inclusive, with no two of them getting the same number. What is the probability that Al's number will be a whole number multiple of Bill's and Bill's number will be a whole number multiple of Cal'... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{80}"
} | {
"split": "train",
"index": 20082,
"solution": "To solve this problem, we need to count the number of valid assignments of numbers to Al, Bill, and Cal such that Al's number is a multiple of Bill's number, and Bill's number is a multiple of Cal's number. We then divide this count by the total number of ways to a... |
deepscaler | [
{
"role": "user",
"content": "It is known that there are a total of $n$ students in the first grade of Shuren High School, with $550$ male students. They are divided into layers based on gender, and $\\frac{n}{10}$ students are selected to participate in a wetland conservation knowledge competition. It is g... | math | {
"style": "rule",
"ground_truth": "1000"
} | {
"split": "train",
"index": 20083,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the product $\\frac{1}{2} \\times \\frac{3}{2} \\times \\frac{4}{3} \\times \\frac{5}{4} \\times \\cdots \\times \\frac{2010}{2009}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "502.5"
} | {
"split": "train",
"index": 20084,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The arithmetic mean of the nine numbers in the set $\\{9, 99, 999, 9999, \\ldots, 999999999\\}$ is a $9$-digit number $M$, all of whose digits are distinct. The number $M$ doesn't contain the digit Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 20085,
"solution": "1. **Identify the pattern in the set**: The set given is $\\{9, 99, 999, 9999, \\ldots, 999999999\\}$. Each number in the set is composed of repeated digits of $9$, increasing by one $9$ at each step.\n\n2. **Express each number as a sum**: Each number in the set c... |
deepscaler | [
{
"role": "user",
"content": "Five people are sitting at a round table. Let $f\\geq 0$ be the number of people sitting next to at least 1 female and $m\\geq0$ be the number of people sitting next to at least one male. The number of possible ordered pairs $(f,m)$ is\n$\\mathrm{(A) \\ 7 } \\qquad \\mathrm{(B)... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 20086,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The lateral surface area of a circular truncated cone is given by the formula, find the value for the lateral surface area of the cone where the radii of the upper and lower bases are $r=1$ and $R=4$ and the height is $4$. Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "25\\pi"
} | {
"split": "train",
"index": 20087,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of pairs of integers $x, y$ with different parities such that $\\frac{1}{x}+\\frac{1}{y} = \\frac{1}{2520}$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 20088,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The World Cup football tournament is held in Brazil, and the host team Brazil is in group A. In the group stage, the team plays a total of 3 matches. The rules stipulate that winning one match scores 3 points, drawing one match scores 1 point, and losing one match scores 0 poin... | math | {
"style": "rule",
"ground_truth": "0.5"
} | {
"split": "train",
"index": 20089,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a circle with center \\(O\\) and radius \\(OD\\) perpendicular to chord \\(AB\\), intersecting \\(AB\\) at point \\(C\\). Line segment \\(AO\\) is extended to intersect the circle at point \\(E\\). If \\(AB = 8\\) and \\(CD = 2\\), calculate the area of \\(\\triangle BCE\... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 20090,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"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 $g^{-1}(1)+g^{-1}(6)+g^{-1}(11)$. Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "2 + \\sqrt{5} + \\sqrt{10}"
} | {
"split": "train",
"index": 20091,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many ways are there to place 31 knights in the cells of an $8 \\times 8$ unit grid so that no two attack one another? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "68"
} | {
"split": "train",
"index": 20092,
"solution": "Consider coloring the squares of the chessboard so that 32 are black and 32 are white, and no two squares of the same color share a side. Then a knight in a square of one color only attacks squares of the opposite color. Any arrangement of knights in which all 31 a... |
deepscaler | [
{
"role": "user",
"content": "We are given $2n$ natural numbers\n\\[1, 1, 2, 2, 3, 3, \\ldots, n - 1, n - 1, n, n.\\]\nFind all $n$ for which these numbers can be arranged in a row such that for each $k \\leq n$, there are exactly $k$ numbers between the two numbers $k$. Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "n=3,4,7,8"
} | {
"split": "train",
"index": 20093,
"solution": "\nWe are given \\(2n\\) natural numbers: \n\\[\n1, 1, 2, 2, 3, 3, \\ldots, n-1, n-1, n, n.\n\\]\nand we need to find all values of \\(n\\) for which these numbers can be arranged such that there are exactly \\(k\\) numbers between the two occurrences of the number ... |
deepscaler | [
{
"role": "user",
"content": "Eight students from Adams school worked for $4$ days, six students from Bentley school worked for $6$ days, and seven students from Carter school worked for $10$ days. If a total amount of $\\ 1020$ was paid for the students' work, with each student receiving the same amount fo... | math | {
"style": "rule",
"ground_truth": "517.39"
} | {
"split": "train",
"index": 20094,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Arrange the numbers in the set \\(\\left\\{2^{x}+2^{y} \\mid x, y\\ \\text{are non-negative integers,}\\ x < y\\right\\}\\) in ascending order. What is the 60th number? (Answer in digits). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2064"
} | {
"split": "train",
"index": 20095,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The degree of $(x^2+1)^4 (x^3+1)^3$ as a polynomial in $x$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 20096,
"solution": "To find the degree of the polynomial $(x^2+1)^4 (x^3+1)^3$, we need to consider the highest degree terms from each factor when expanded.\n\n1. **Analyzing the first factor $(x^2+1)^4$:**\n - The highest degree term in $x^2+1$ is $x^2$.\n - When raised to the fo... |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC,$ the side lengths $a,$ $b,$ and $c$ satisfy $a + 2b + 2c = a^2$ and $a + 2b - 2c = -3.$ Find the largest angle of the triangle, in degrees.\n\nNote: $a$ is the side length opposite $\\angle A,$ etc. Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "120^\\circ"
} | {
"split": "train",
"index": 20097,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the sum of all positive integers \\( p \\) such that the expression \\((x-p)(x-13)+4\\) can be expressed in the form \\((x+q)(x+r)\\) for distinct integers \\( q \\) and \\( r \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 20098,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Using $600$ cards, $200$ of them having written the number $5$ , $200$ having a $2$ , and the other $200$ having a $1$ , a student wants to create groups of cards such that the sum of the card numbers in each group is $9$ . What is the maximum amount of groups that ... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 20099,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of permutations $(a_1, a_2, a_3, a_4, a_5, a_6)$ of $(1,2,3,4,5,6)$ that satisfy\n\\[\\frac{a_1 + 1}{2} \\cdot \\frac{a_2 + 2}{2} \\cdot \\frac{a_3 + 3}{2} \\cdot \\frac{a_4 + 4}{2} \\cdot \\frac{a_5 + 5}{2} \\cdot \\frac{a_6 + 6}{2} > 6!.\\] Let's think step by... | math | {
"style": "rule",
"ground_truth": "719"
} | {
"split": "train",
"index": 20100,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Function $f(x, y): \\mathbb N \\times \\mathbb N \\to \\mathbb Q$ satisfies the conditions:\n\n(i) $f(1, 1) =1$ ,\n\n(ii) $f(p + 1, q) + f(p, q + 1) = f(p, q)$ for all $p, q \\in \\mathbb N$ , and\n\n(iii) $qf(p + 1, q) = pf(p, q + 1)$ for all $p, q \\in \\mathbb N$ ... | math | {
"style": "rule",
"ground_truth": "\\frac{30! \\cdot 1989!}{2020!}"
} | {
"split": "train",
"index": 20101,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ali Baba and the 40 thieves are dividing their loot. The division is considered fair if any 30 participants receive at least half of the loot in total. What is the maximum share that Ali Baba can receive in a fair division? Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 20102,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A truncated right circular cone has a large base radius of 10 cm and a small base radius of 5 cm. The height of the truncated cone is 10 cm. Calculate the volume of this solid. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "583.33\\pi"
} | {
"split": "train",
"index": 20103,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many integers $x$ does a triangle with side lengths $10, 24$ and $x$ have all its angles acute? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 20104,
"solution": "To determine the number of integers $x$ for which a triangle with sides $10, 24,$ and $x$ has all acute angles, we need to consider both the triangle inequality and the condition for all angles to be acute.\n\n#### Step 1: Apply the Triangle Inequality\nThe triangl... |
deepscaler | [
{
"role": "user",
"content": "Two different numbers are randomly selected from the set $\\{-3, -2, 0, 0, 5, 6, 7\\}$. What is the probability that the product of these two numbers is $0$?\n**A)** $\\frac{1}{4}$\n**B)** $\\frac{1}{5}$\n**C)** $\\frac{5}{21}$\n**D)** $\\frac{1}{3}$\n**E)** $\\frac{1}{2}$ Let'... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{21}"
} | {
"split": "train",
"index": 20105,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a revised dataset given in the following stem-and-leaf plot, where $7|1$ represents 71:\n\n\\begin{tabular}{|c|c|}\\hline\n\\textbf{Tens} & \\textbf{Units} \\\\ \\hline\n2 & $0 \\hspace{2mm} 0 \\hspace{2mm} 1 \\hspace{2mm} 1 \\hspace{2mm} 2$ \\\\ \\hline\n3 & $3 \\hspa... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 20106,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A pebble is shaped as the intersection of a cube of side length 1 with the solid sphere tangent to all of the cube's edges. What is the surface area of this pebble? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{6 \\sqrt{2}-5}{2} \\pi"
} | {
"split": "train",
"index": 20107,
"solution": "Imagine drawing the sphere and the cube. Take a cross section, with a plane parallel to two of the cube's faces, passing through the sphere's center. In this cross section, the sphere looks like a circle, and the cube looks like a square (of side length 1) inscribe... |
deepscaler | [
{
"role": "user",
"content": "For real numbers $x$ and $y$, define $x\\spadesuit y = (x + y)(x - y)$. What is $3\\spadesuit(4\\spadesuit 5)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-72"
} | {
"split": "train",
"index": 20108,
"solution": "To solve the problem, we first need to evaluate $4 \\spadesuit 5$ using the operation defined as $x \\spadesuit y = (x + y)(x - y)$.\n\n1. **Calculate $4 \\spadesuit 5$:**\n \\[\n 4 \\spadesuit 5 = (4 + 5)(4 - 5) = 9 \\times (-1) = -9\n \\]\n\n2. **Next, calc... |
deepscaler | [
{
"role": "user",
"content": "Which integers from 1 to 60,000 (inclusive) are more numerous and by how much: those containing only even digits in their representation, or those containing only odd digits in their representation? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "780"
} | {
"split": "train",
"index": 20109,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The term containing \\(x^7\\) in the expansion of \\((1 + 2x - x^2)^4\\) arises when \\(x\\) is raised to the power of 3 in three factors and \\(-x^2\\) is raised to the power of 1 in one factor. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-8"
} | {
"split": "train",
"index": 20110,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "All positive integers whose digits add up to 14 are listed in increasing order: $59, 68, 77, ...$. What is the fifteenth number in that list? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "266"
} | {
"split": "train",
"index": 20111,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 13 students in a class (one of them being the monitor) and 13 seats in the classroom. Every day, the 13 students line up in random order and then enter the classroom one by one. Except for the monitor, each student will randomly choose an unoccupied seat and sit down.... | math | {
"style": "rule",
"ground_truth": "7/13"
} | {
"split": "train",
"index": 20112,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If infinitely many values of $y$ satisfy the equation $2(4+cy) = 12y+8$, then what is the value of $c$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 20113,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the rectangular coordinate system $xoy$, the parametric equations of the curve $C$ are $x=3\\cos \\alpha$ and $y=\\sin \\alpha$ ($\\alpha$ is the parameter). In the polar coordinate system with the origin as the pole and the positive semi-axis of $x$ as the polar axis, the p... | math | {
"style": "rule",
"ground_truth": "\\frac{18\\sqrt{2}}{5}"
} | {
"split": "train",
"index": 20114,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a table lie 140 different cards with numbers $3, 6, 9, \\ldots, 417, 420$ (each card has exactly one number, and each number appears exactly once). In how many ways can you choose 2 cards so that the sum of the numbers on the selected cards is divisible by $7?$ Let's think s... | math | {
"style": "rule",
"ground_truth": "1390"
} | {
"split": "train",
"index": 20115,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a prime $p$ and an integer $a$, we say that $a$ is a $\\textit{primitive root} \\pmod p$ if the set $\\{a,a^2,a^3,\\ldots,a^{p-1}\\}$ contains exactly one element congruent to each of $1,2,3,\\ldots,p-1\\pmod p$.\n\nFor example, $2$ is a primitive root $\\pmod 5$ because ... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 20116,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3127"
} | {
"split": "train",
"index": 20117,
"solution": "1. **Identify the smallest primes greater than 50**: The problem specifies that the number must not have any prime factors less than 50. The smallest primes greater than 50 are 53 and 59.\n\n2. **Calculate the product of the smallest primes**: To find the smallest ... |
deepscaler | [
{
"role": "user",
"content": "Add together all natural numbers less than 1980 for which the sum of their digits is even! Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "979605"
} | {
"split": "train",
"index": 20118,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A student recorded the exact percentage frequency distribution for a set of measurements, as shown below.\nHowever, the student neglected to indicate $N$, the total number of measurements. What is the smallest possible value of $N$?\n\\begin{tabular}{c c}\\text{measured value}&... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 20119,
"solution": "1. **Understanding the Problem:**\n The problem provides a frequency distribution in percentages for a set of measurements. We need to find the smallest possible total number of measurements, $N$, such that all the given percentages can be converted into integer ... |
deepscaler | [
{
"role": "user",
"content": "$ABCD$ is a rectangle whose area is 12 square units. How many square units are contained in the area of trapezoid $EFBA$?\n\n[asy]\n\nsize(4cm,4cm);\n\nfor(int i=0; i < 4; ++i){\nfor(int k=0; k < 5; ++k){\ndraw((0,i)--(4,i));\ndraw((k,0)--(k,3));\n} }\n\ndraw((0,0)--(1,3));\ndr... | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 20120,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a function $f(x) = \\cos x \\sin \\left( x + \\frac{\\pi}{3} \\right) - \\sqrt{3} \\cos^2 x + \\frac{\\sqrt{3}}{4}$, where $x \\in \\mathbb{R}$,\n(1) Find the smallest positive period of $f(x)$ and the interval where $f(x)$ is monotonically decreasing;\n(2) Find the maxim... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2}"
} | {
"split": "train",
"index": 20121,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the length of \\(PQ\\) in the triangle below, where \\(PQR\\) is a right triangle with \\( \\angle RPQ = 45^\\circ \\) and the length \\(PR\\) is \\(10\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10\\sqrt{2}"
} | {
"split": "train",
"index": 20122,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nA uniform cubic die with faces numbered $1, 2, 3, 4, 5, 6$ is rolled three times independently, resulting in outcomes $a_1, a_2, a_3$. Find the probability of the event \"$|a_1 - a_2| + |a_2 - a_3| + |a_3 - a_1| = 6$\". Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "1/4"
} | {
"split": "train",
"index": 20123,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a bag of marbles, $\\frac{3}{5}$ of the marbles are blue and the rest are red. If the number of red marbles is doubled and the number of blue marbles stays the same, what fraction of the marbles will be red? Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{7}"
} | {
"split": "train",
"index": 20124,
"solution": "1. **Identify the fraction of blue and red marbles initially:**\n Let the total number of marbles be $x$. Given that $\\frac{3}{5}$ of the marbles are blue, the number of blue marbles is $\\frac{3}{5}x$. The rest of the marbles are red, so the number of red marbl... |
deepscaler | [
{
"role": "user",
"content": "How many four-digit whole numbers are there such that the leftmost digit is a prime number, the second digit is even, and all four digits are different? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1064"
} | {
"split": "train",
"index": 20125,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the minimum value of\n\\[\ny^2 + 9y + \\frac{81}{y^3}\n\\]\nfor \\(y > 0\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 20126,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are five distinct nonzero natural numbers; the smallest one is 7. If one of them is decreased by 20, and the other four numbers are each increased by 5, the resulting set of numbers remains the same. What is the sum of these five numbers? Let's think step by step and put ... | math | {
"style": "rule",
"ground_truth": "85"
} | {
"split": "train",
"index": 20127,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the tetrahedron $P-ABC$, edges $PA$, $AB$, and $AC$ are mutually perpendicular, and $PA = AB = AC$. Points $E$ and $F$ are the midpoints of segments $AB$ and $PC$, respectively. Find the sine of the angle between line $EF$ and plane $PBC$. Let's think step by step and put on... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 20128,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many paths are there from point $A$ to point $B$ in a $7 \\times 6$ grid, if every step must be up or to the right, and you must not pass through the cell at position $(3,3)$?\n[asy]size(4cm,4cm);int w=7;int h=6;int i;pen p=fontsize(9);for (i=0; i<h; ++i){draw((0,i) -- (w-1... | math | {
"style": "rule",
"ground_truth": "262"
} | {
"split": "train",
"index": 20129,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The function $f$ takes nonnegative integers to real numbers, such that $f(1) = 1,$ and\n\\[f(m + n) + f(m - n) = \\frac{f(2m) + f(2n)}{2}\\]for all nonnnegative integers $m \\ge n.$ Find the sum of all possible values of $f(10).$ Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 20130,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the sequence $\\left\\{a_{i}\\right\\}_{i=0}^{\\infty}$ be defined by $a_{0}=\\frac{1}{2}$ and $a_{n}=1+\\left(a_{n-1}-1\\right)^{2}$. Find the product $$\\prod_{i=0}^{\\infty} a_{i}=a_{0} a_{1} a_{2}$$ Let's think step by step and put only the final answer within \\boxed{}... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 20131,
"solution": "Let $\\left\\{b_{i}\\right\\}_{i=0}^{\\infty}$ be defined by $b_{n}=a_{n}-1$ and note that $b_{n}=b_{n-1}^{2}$. The infinite product is then $$\\left(1+b_{0}\\right)\\left(1+b_{0}^{2}\\right)\\left(1+b_{0}^{4}\\right) \\ldots\\left(1+b_{0}^{2^{k}}\\right) \\ldots$$... |
deepscaler | [
{
"role": "user",
"content": "In isosceles trapezoid $ABCD$, parallel bases $\\overline{AB}$ and $\\overline{CD}$ have lengths $500$ and $650$, respectively, and $AD=BC=333$. The angle bisectors of $\\angle{A}$ and $\\angle{D}$ meet at $P$, and the angle bisectors of $\\angle{B}$ and $\\angle{C}$ meet at $Q... | math | {
"style": "rule",
"ground_truth": "242"
} | {
"split": "train",
"index": 20132,
"solution": "This will be my first solution on AoPS. My apologies in advance for any errors.\n Angle bisectors can be thought of as the locus of all points equidistant from the lines whose angle they bisect. It can thus be seen that $P$ is equidistant from $AB, AD,$ and $CD$ an... |
deepscaler | [
{
"role": "user",
"content": "Ana and Luíza train every day for the Big Race that will take place at the end of the year at school, each running at the same speed. The training starts at point $A$ and ends at point $B$, which are $3000 \\mathrm{~m}$ apart. They start at the same time, but when Luíza finishe... | math | {
"style": "rule",
"ground_truth": "125"
} | {
"split": "train",
"index": 20133,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sphere is inscribed in a cube with edge length 9 inches. Then a smaller cube is inscribed in the sphere. How many cubic inches are in the volume of the inscribed cube? Express your answer in simplest radical form. Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "81\\sqrt{3}"
} | {
"split": "train",
"index": 20134,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve for $x>0$ in the following arithmetic sequence: $1^2, x^2, 3^2, \\ldots$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{5}"
} | {
"split": "train",
"index": 20135,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many integers $n$ satisfy the inequality $-\\frac{9\\pi}{2} \\leq n \\leq 12\\pi$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "53"
} | {
"split": "train",
"index": 20136,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two arithmetic sequences, $C$ and $D$, begin with the terms 25 and 40 respectively, both with common differences of absolute value 15, with sequence $C$ increasing and sequence $D$ decreasing. What is the absolute value of the difference between the 60th terms of sequences $C$ ... | math | {
"style": "rule",
"ground_truth": "1755"
} | {
"split": "train",
"index": 20137,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The electronic clock on the International Space Station displayed time in the format HH:MM. Due to an electromagnetic storm, the device malfunctioned, and each digit on the display either increased by 1 or decreased by 1. What was the actual time of the storm if the clock displ... | math | {
"style": "rule",
"ground_truth": "11:18"
} | {
"split": "train",
"index": 20138,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A herder has forgotten the number of cows she has, and does not want to count them all of them. She remembers these four facts about the number of cows: \n\n\n- It has $3$ digits.\n- It is a palindrome.\n- The middle digit is a multiple of $4$ .\n- It is divisible by $11$ .... | math | {
"style": "rule",
"ground_truth": "726"
} | {
"split": "train",
"index": 20139,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Sector $OAB$ is a quarter of a circle of radius 3 cm. A circle is drawn inside this sector, tangent at three points as shown. What is the number of centimeters in the radius of the inscribed circle? Express your answer in simplest radical form. [asy]\nimport olympiad; import ge... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{2}-3"
} | {
"split": "train",
"index": 20140,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( S = \\{1, 2, \\cdots, 2005\\} \\). If in any set of \\( n \\) pairwise coprime numbers in \\( S \\) there is at least one prime number, find the minimum value of \\( n \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 20141,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If an angle of a triangle remains unchanged but each of its two including sides is doubled, then the area is multiplied by: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 20142,
"solution": "1. **Identify the original setup**: Let the angle be $\\theta$ and the sides enclosing it be $a$ and $b$. The area of the triangle can be expressed using the formula for the area of a triangle given two sides and the included angle:\n \\[\n A = \\frac{a \\cdot ... |
deepscaler | [
{
"role": "user",
"content": "A stack of logs has 15 logs on the bottom row, and each successive row has two fewer logs, ending with five special logs at the top. How many total logs are in the stack, and how many are the special logs? Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 20143,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the number of tuples $\\left(a_{0}, a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\\right)$ of (not necessarily positive) integers such that $a_{i} \\leq i$ for all $0 \\leq i \\leq 5$ and $$a_{0}+a_{1}+\\cdots+a_{5}=6$$ Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "2002"
} | {
"split": "train",
"index": 20144,
"solution": "Let $b_{i}=i-a_{i}$, so $b_{i} \\geq 0$. Then $$15-\\left(b_{0}+b_{1}+\\cdots+b_{5}\\right)=6 \\Longrightarrow b_{0}+b_{1}+\\cdots+b_{5}=9$$ By stars and bars, the answer is $\\binom{14}{5}=2002$."
} |
deepscaler | [
{
"role": "user",
"content": "What is $(a^3+b^3)\\div(a^2-ab+b^2+c)$ for $a=7$, $b=6$, and $c=1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{559}{44}"
} | {
"split": "train",
"index": 20145,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Circle $\\omega$ has radius 5 and is centered at $O$. Point $A$ lies outside $\\omega$ such that $OA=13$. The two tangents to $\\omega$ passing through $A$ are drawn, and points $B$ and $C$ are chosen on them (one on each tangent), such that line $BC$ is tangent to $\\omega$ an... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 20146,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Chloe chooses a real number uniformly at random from the interval $[ 0,2017 ]$. Independently, Laurent chooses a real number uniformly at random from the interval $[ 0 , 4034 ]$. What is the probability that Laurent's number is greater than Chloe's number? Let's think step by s... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 20147,
"solution": "1. **Define the random variables:**\n Let $x$ be the number chosen by Chloe, uniformly at random from the interval $[0, 2017]$. Thus, $0 \\leq x \\leq 2017$.\n Let $y$ be the number chosen by Laurent, uniformly at random from the interval $[0, 4034]$. Thus, $0 ... |
deepscaler | [
{
"role": "user",
"content": "Let $A=\\{m-1,-3\\}$, $B=\\{2m-1,m-3\\}$. If $A\\cap B=\\{-3\\}$, then determine the value of the real number $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 20148,
"solution": ""
} |
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