data_source stringclasses 1 value | prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"content": "Let $a, b, c, d$ be real numbers such that $a + b + c + d = 10$ and $ab + ac + ad + bc + bd + cd = 20$. Find the largest possible value of $d$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5 + \\sqrt{105}}{2}",
"style": "rule"
} | {
"difficulty": 81.25,
"index": 3243,
"split": "train"
} |
deepscaler | [
{
"content": "Cátia leaves school every day at the same time and returns home by bicycle. When she pedals at $20 \\mathrm{~km/h}$, she arrives home at $4:30$ PM. If she pedals at $10 \\mathrm{~km/h}$, she arrives home at $5:15$ PM. At what speed should she pedal to arrive home at $5:00$ PM? Let's think step by ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"difficulty": 77.34375,
"index": 4288,
"split": "train"
} |
deepscaler | [
{
"content": "Given that $S_{n}=\\sin \\frac{\\pi}{7}+\\sin \\frac{2\\pi}{7}+\\cdots+\\sin \\frac{n\\pi}{7}$, determine the number of positive values in the sequence $S_{1}$, $S_{2}$, …, $S_{100}$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "86",
"style": "rule"
} | {
"difficulty": 97.65625,
"index": 875,
"split": "train"
} |
deepscaler | [
{
"content": "In the plane rectangular coordinate system $xOy$, the parametric equations of the line $l$ are $\\left\\{{\\begin{array}{l}{x=t}\\\\{y=-1+\\sqrt{3}t}\\end{array}}\\right.$ (where $t$ is a parameter). Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive ha... | math | {
"ground_truth": "\\frac{2\\sqrt{3} + 1}{3}",
"style": "rule"
} | {
"difficulty": 75.78125,
"index": 4425,
"split": "train"
} |
deepscaler | [
{
"content": "The Hoopers, coached by Coach Loud, have 15 players. George and Alex are the two players who refuse to play together in the same lineup. Additionally, if George plays, another player named Sam refuses to play. How many starting lineups of 6 players can Coach Loud create, provided the lineup does n... | math | {
"ground_truth": "3795",
"style": "rule"
} | {
"difficulty": 99.21875,
"index": 583,
"split": "train"
} |
deepscaler | [
{
"content": "Points $P$ and $Q$ lie in a plane with $PQ=8$. How many locations for point $R$ in this plane are there such that the triangle with vertices $P$, $Q$, and $R$ is a right triangle with area $12$ square units? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"difficulty": 66.40625,
"index": 5444,
"split": "train"
} |
deepscaler | [
{
"content": "Grain warehouses A and B each originally stored a certain number of full bags of grain. If 90 bags are transferred from warehouse A to warehouse B, the number of bags in warehouse B will be twice the number in warehouse A. If an unspecified number of bags are transferred from warehouse B to wareho... | math | {
"ground_truth": "153",
"style": "rule"
} | {
"difficulty": 87.5,
"index": 3539,
"split": "train"
} |
deepscaler | [
{
"content": "Given that $F_{1}$ and $F_{2}$ are two foci of the hyperbola $C: x^{2}-\\frac{{y}^{2}}{3}=1$, $P$ and $Q$ are two points on $C$ symmetric with respect to the origin, and $\\angle PF_{2}Q=120^{\\circ}$, find the area of quadrilateral $PF_{1}QF_{2}$. Let's think step by step and output the final ans... | math | {
"ground_truth": "6\\sqrt{3}",
"style": "rule"
} | {
"difficulty": 88.28125,
"index": 3553,
"split": "train"
} |
deepscaler | [
{
"content": "The sixth graders were discussing how old their principal is. Anya said, \"He is older than 38 years.\" Borya said, \"He is younger than 35 years.\" Vova: \"He is younger than 40 years.\" Galya: \"He is older than 40 years.\" Dima: \"Borya and Vova are right.\" Sasha: \"You are all wrong.\" It tur... | math | {
"ground_truth": "39",
"style": "rule"
} | {
"difficulty": 64.84375,
"index": 6936,
"split": "train"
} |
deepscaler | [
{
"content": "A line passing through the intersection point of the medians of triangle \\(ABC\\) intersects the sides \\(BA\\) and \\(BC\\) at points \\(A^{\\prime}\\) and \\(C_1\\) respectively. Given that:\n\n\\(BA^{\\prime} < BA = 3\\), \\(BC = 2\\), and \\(BA^{\\prime} \\cdot BC_1 = 3\\). Find \\(BA^{\\prim... | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"difficulty": 75.78125,
"index": 4597,
"split": "train"
} |
deepscaler | [
{
"content": "A right triangle has side lengths $a, b$, and $\\sqrt{2016}$ in some order, where $a$ and $b$ are positive integers. Determine the smallest possible perimeter of the triangle. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "48+\\sqrt{2016}",
"style": "rule"
} | {
"difficulty": 99.21875,
"index": 647,
"split": "train"
} |
deepscaler | [
{
"content": "The graphs of five functions are labelled from **(1) through (5)**. Provided below are descriptions of three:\n 1. The domain of function (2) is from $$\\{-6,-5,-4,-3,-2,-1,0,1,2,3\\}.$$ It is graphed as a set of discrete points.\n 2. Function (4) is defined by the equation $$y = x^3$$ and is ... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"difficulty": 75.78125,
"index": 3931,
"split": "train"
} |
deepscaler | [
{
"content": "In $\\triangle A B C$, the incircle centered at $I$ touches sides $A B$ and $B C$ at $X$ and $Y$, respectively. Additionally, the area of quadrilateral $B X I Y$ is $\\frac{2}{5}$ of the area of $A B C$. Let $p$ be the smallest possible perimeter of a $\\triangle A B C$ that meets these conditions... | math | {
"ground_truth": "2 \\sqrt{5}",
"style": "rule"
} | {
"difficulty": 94.53125,
"index": 864,
"split": "train"
} |
deepscaler | [
{
"content": "In triangle \\(PQR\\) with side \\(PQ = 3\\), a median \\(PM = \\sqrt{14}\\) and an altitude \\(PH = \\sqrt{5}\\) are drawn from vertex \\(P\\) to side \\(QR\\).\n\nFind side \\(PR\\), given that \\(\\angle QPR + \\angle PRQ < 90^\\circ\\). Let's think step by step and output the final answer with... | math | {
"ground_truth": "\\sqrt{21}",
"style": "rule"
} | {
"difficulty": 92.96875,
"index": 825,
"split": "train"
} |
deepscaler | [
{
"content": "Let vectors $\\overrightarrow{a}$, $\\overrightarrow{b}$, $\\overrightarrow{c}$ satisfy $|\\overrightarrow{a}|=|\\overrightarrow{b}|=1$, $\\overrightarrow{a}\\cdot \\overrightarrow{b}= \\frac{1}{2}$, and $(\\overrightarrow{a}- \\overrightarrow{c})\\cdot(\\overrightarrow{b}- \\overrightarrow{c})=0$... | math | {
"ground_truth": "\\frac{\\sqrt{3}+1}{2}",
"style": "rule"
} | {
"difficulty": 86.71875,
"index": 2364,
"split": "train"
} |
deepscaler | [
{
"content": "How many ways can you mark 8 squares of an $8 \\times 8$ chessboard so that no two marked squares are in the same row or column, and none of the four corner squares is marked? (Rotations and reflections are considered different.) Let's think step by step and output the final answer within \\boxed{... | math | {
"ground_truth": "21600",
"style": "rule"
} | {
"difficulty": 64.84375,
"index": 5747,
"split": "train"
} |
deepscaler | [
{
"content": "The function $f(x)$ satisfies\n\\[f(x) + f \\left( \\frac{x + 1}{1 - 3x} \\right) = x\\]for all $x \\neq \\frac{1}{3}.$ Find $f(2).$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{48}{35}",
"style": "rule"
} | {
"difficulty": 60.9375,
"index": 5603,
"split": "train"
} |
deepscaler | [
{
"content": "How many groups of integer solutions are there for the equation $xyz = 2009$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "72",
"style": "rule"
} | {
"difficulty": 81.25,
"index": 3213,
"split": "train"
} |
deepscaler | [
{
"content": "Consider the sequence of numbers defined recursively by $t_1=1$ and for $n>1$ by $t_n=1+t_{n/2}$ when $n$ is even and by $t_n=\\frac{1}{t_{n-1}}$ when $n$ is odd. Given that $t_n=\\frac{19}{87}$, find $n.$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
... | math | {
"ground_truth": "1905",
"style": "rule"
} | {
"difficulty": 66.40625,
"index": 6304,
"split": "train"
} |
deepscaler | [
{
"content": "Tim plans a weeklong prank to repeatedly steal Nathan's fork during lunch. He involves different people each day:\n- On Monday, he convinces Joe to do it.\n- On Tuesday, either Betty or John could undertake the prank.\n- On Wednesday, there are only three friends from whom he can seek help, as Joe... | math | {
"ground_truth": "48",
"style": "rule"
} | {
"difficulty": 85.9375,
"index": 2319,
"split": "train"
} |
deepscaler | [
{
"content": "Suppose $a$ and $b$ are single-digit positive integers chosen independently and at random. What is the probability that the point $(a,b)$ lies above the parabola $y=ax^2-bx$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{19}{81}",
"style": "rule"
} | {
"difficulty": 88.28125,
"index": 3089,
"split": "train"
} |
deepscaler | [
{
"content": "A rectangular garden that is $14$ feet wide and $19$ feet long is paved with $2$-foot square pavers. Given that a bug walks from one corner to the opposite corner in a straight line, determine the total number of pavers the bug visits, including the first and the last paver. Let's think step by st... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"difficulty": 65.625,
"index": 5402,
"split": "train"
} |
deepscaler | [
{
"content": "What is the sum of the six positive integer factors of 30? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "72",
"style": "rule"
} | {
"difficulty": 68.75,
"index": 5744,
"split": "train"
} |
deepscaler | [
{
"content": "There is an opaque bag containing 4 identical balls labeled with the numbers 1, 2, 3, and 4.\n(Ⅰ) If balls are drawn one by one without replacement twice, calculate the probability that the first ball drawn has an even number and the sum of the two balls’ numbers is divisible by 3.\n(Ⅱ) If a ball ... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"difficulty": 67.96875,
"index": 6065,
"split": "train"
} |
deepscaler | [
{
"content": "A circle with a circumscribed and an inscribed square centered at the origin of a rectangular coordinate system with positive $x$ and $y$ axes is shown in each figure I to IV below.\n\nThe inequalities\n\\(|x|+|y| \\leq \\sqrt{2(x^{2}+y^{2})} \\leq 2\\mbox{Max}(|x|, |y|)\\)\nare represented geomet... | math | {
"ground_truth": "II",
"style": "rule"
} | {
"difficulty": 71.09375,
"index": 5381,
"split": "train"
} |
deepscaler | [
{
"content": "Given in the tetrahedron P-ABC, PA is perpendicular to the plane ABC, AB=AC=PA=2, and in triangle ABC, ∠BAC=120°, then the volume of the circumscribed sphere of the tetrahedron P-ABC is \\_\\_\\_\\_\\_\\_. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
... | math | {
"ground_truth": "\\frac{20\\sqrt{5}\\pi}{3}",
"style": "rule"
} | {
"difficulty": 82.03125,
"index": 3175,
"split": "train"
} |
deepscaler | [
{
"content": "Jacob uses the following procedure to write down a sequence of numbers. First he chooses the first term to be 6. To generate each succeeding term, he flips a fair coin. If it comes up heads, he doubles the previous term and subtracts 1. If it comes up tails, he takes half of the previous term and ... | math | {
"ground_truth": "\\frac{5}{8}",
"style": "rule"
} | {
"difficulty": 83.59375,
"index": 3002,
"split": "train"
} |
deepscaler | [
{
"content": "We place planes through each edge and the midpoint of the edge opposite to it in a tetrahedron. Into how many parts do these planes divide the tetrahedron, and what are the volumes of these parts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "24",
"style": "rule"
} | {
"difficulty": 63.28125,
"index": 6201,
"split": "train"
} |
deepscaler | [
{
"content": "Given a cube \\( ABCD-A_1B_1C_1D_1 \\) with edge length 1, a point \\( M \\) is taken on the diagonal \\( A_1D \\) and a point \\( N \\) is taken on \\( CD_1 \\) such that the line segment \\( MN \\) is parallel to the diagonal plane \\( A_1ACC_1 \\), find the minimum value of \\( |MN| \\). Let's ... | math | {
"ground_truth": "\\frac{\\sqrt{3}}{3}",
"style": "rule"
} | {
"difficulty": 89.84375,
"index": 2408,
"split": "train"
} |
deepscaler | [
{
"content": "The sum of the digits of the result of the expression $\\underbrace{99 \\cdots 99}_{2021 \\text{ digits}} \\times \\underbrace{99 \\cdots 99}_{2020 \\text{ digits}}$ is $\\qquad$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "18189",
"style": "rule"
} | {
"difficulty": 78.125,
"index": 3749,
"split": "train"
} |
deepscaler | [
{
"content": "A straight one-way city street has 8 consecutive traffic lights. Every light remains green for 1.5 minutes, yellow for 3 seconds, and red for 1.5 minutes. The lights are synchronized so that each light turns red 10 seconds after the preceding one turns red. Calculate the longest interval of time, ... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"difficulty": 75,
"index": 4619,
"split": "train"
} |
deepscaler | [
{
"content": "A truck delivered 4 bags of cement. They are stacked in the truck. A worker can carry one bag at a time either from the truck to the gate or from the gate to the shed. The worker can carry the bags in any order, each time taking the top bag, carrying it to the respective destination, and placing i... | math | {
"ground_truth": "\\frac{1}{8}",
"style": "rule"
} | {
"difficulty": 92.96875,
"index": 44,
"split": "train"
} |
deepscaler | [
{
"content": "If the fractional equation $\\frac{3}{{x-2}}+1=\\frac{m}{{4-2x}}$ has a root, then the value of $m$ is ______. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"difficulty": 72.65625,
"index": 5027,
"split": "train"
} |
deepscaler | [
{
"content": "Xiaoqiang conducts an experiment while drinking a beverage. He inserts a chopstick vertically into the bottom of the cup and measures the wetted part, which is exactly 8 centimeters. He then turns the chopstick around and inserts the other end straight into the bottom of the cup. He finds that the... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"difficulty": 89.0625,
"index": 3477,
"split": "train"
} |
deepscaler | [
{
"content": "Let $ABC$ be a triangle and $\\Gamma$ the $A$ - exscribed circle whose center is $J$ . Let $D$ and $E$ be the touchpoints of $\\Gamma$ with the lines $AB$ and $AC$ , respectively. Let $S$ be the area of the quadrilateral $ADJE$ , Find the maximum value that $\\frac{S}{AJ^2}$ ... | math | {
"ground_truth": "1/2",
"style": "rule"
} | {
"difficulty": 60.15625,
"index": 5497,
"split": "train"
} |
deepscaler | [
{
"content": "What is the value of $\\sqrt{64 \\times \\sqrt{49}}$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "8\\sqrt{7}",
"style": "rule"
} | {
"difficulty": 67.1875,
"index": 6741,
"split": "train"
} |
deepscaler | [
{
"content": "Two fair, eight-sided dice are rolled. What is the probability that the sum of the two numbers showing is less than 12? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{49}{64}",
"style": "rule"
} | {
"difficulty": 93.75,
"index": 1223,
"split": "train"
} |
deepscaler | [
{
"content": "The letters L, K, R, F, O and the digits 1, 7, 8, 9 are \"cycled\" separately and put together in a numbered list. Determine the line number on which LKRFO 1789 will appear for the first time. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule"
} | {
"difficulty": 63.28125,
"index": 5690,
"split": "train"
} |
deepscaler | [
{
"content": "The sum of three different numbers is 100. The two larger numbers differ by 8 and the two smaller numbers differ by 5. What is the value of the largest number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{121}{3}",
"style": "rule"
} | {
"difficulty": 92.1875,
"index": 935,
"split": "train"
} |
deepscaler | [
{
"content": "A scientist begins an experiment with a cell culture that starts with some integer number of identical cells. After the first second, one of the cells dies, and every two seconds from there another cell will die (so one cell dies every odd-numbered second from the starting time). Furthermore, afte... | math | {
"ground_truth": "61",
"style": "rule"
} | {
"difficulty": 82.03125,
"index": 2625,
"split": "train"
} |
deepscaler | [
{
"content": "Let $ a_1, a_2,\\ldots ,a_8$ be $8$ distinct points on the circumference of a circle such that no three chords, each joining a pair of the points, are concurrent. Every $4$ of the $8$ points form a quadrilateral which is called a *quad*. If two chords, each joining a pair of the $8$ poi... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"difficulty": 82.03125,
"index": 2499,
"split": "train"
} |
deepscaler | [
{
"content": "Jeremy wakes up at 6:00 a.m., catches the school bus at 7:00 a.m., has 7 classes that last 45 minutes each, enjoys 45 minutes for lunch, and spends an additional 2.25 hours (which includes 15 minutes for miscellaneous activities) at school. He takes the bus home and arrives at 5:00 p.m. Calculate ... | math | {
"ground_truth": "105",
"style": "rule"
} | {
"difficulty": 75.78125,
"index": 5389,
"split": "train"
} |
deepscaler | [
{
"content": "Given a geometric sequence $\\{a_n\\}$ whose sum of the first $n$ terms is $S_n$, and $a_1=2$, if $\\frac {S_{6}}{S_{2}}=21$, then the sum of the first five terms of the sequence $\\{\\frac {1}{a_n}\\}$ is \n\nA) $\\frac {1}{2}$ or $\\frac {11}{32}$\n\nB) $\\frac {1}{2}$ or $\\frac {31}{32}$\n\nC)... | math | {
"ground_truth": "\\frac {31}{32}",
"style": "rule"
} | {
"difficulty": 87.5,
"index": 2269,
"split": "train"
} |
deepscaler | [
{
"content": "A high school offers three separate elective classes for the senior two-grade mathematics course. After the selection process, four students request to change their math class. However, each class can accept at most two more students. Determine the number of different ways the students can be redi... | math | {
"ground_truth": "54",
"style": "rule"
} | {
"difficulty": 71.875,
"index": 4258,
"split": "train"
} |
deepscaler | [
{
"content": "Someone bought 5 consecutive train ticket numbers, and the sum of these 5 ticket numbers is 120. What is the product of these 5 ticket numbers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "7893600",
"style": "rule"
} | {
"difficulty": 81.25,
"index": 3413,
"split": "train"
} |
deepscaler | [
{
"content": "If $A = 3009 \\div 3$, $B = A \\div 3$, and $Y = A - B$, then what is the value of $Y$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "669",
"style": "rule"
} | {
"difficulty": 72.65625,
"index": 4795,
"split": "train"
} |
deepscaler | [
{
"content": "Let \\( x_{1}, y_{1}, x_{2}, y_{2} \\) be real numbers satisfying the equations \\( x_{1}^{2}+5 x_{2}^{2}=10 \\), \\( x_{2} y_{1}-x_{1} y_{2}=5 \\) and \\( x_{1} y_{1}+5 x_{2} y_{2}=\\sqrt{105} \\). Find the value of \\( y_{1}^{2}+5 y_{2}^{2} \\). Let's think step by step and output the final answ... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"difficulty": 66.40625,
"index": 7107,
"split": "train"
} |
deepscaler | [
{
"content": "In triangle $ABC$, $BD$ is a median. $CF$ intersects $BD$ at $E$ so that $\\overline{BE}=\\overline{ED}$. Point $F$ is on $AB$. Then, if $\\overline{BF}=5$, $\\overline{BA}$ equals: Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"difficulty": 75.78125,
"index": 4825,
"split": "train"
} |
deepscaler | [
{
"content": "The sides of rhombus \\( EFGH \\) are the hypotenuses of the isosceles right triangles \\( EAF, FDG, GCH, \\) and \\( HBE \\), and all these triangles have common interior points with the rhombus \\( EFGH \\). The sum of the areas of quadrilateral \\( ABCD \\) and rhombus \\( EFGH \\) is 12. Find ... | math | {
"ground_truth": "2\\sqrt{3}",
"style": "rule"
} | {
"difficulty": 79.6875,
"index": 3693,
"split": "train"
} |
deepscaler | [
{
"content": "How many multiples of 4 are between 70 and 300? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "57",
"style": "rule"
} | {
"difficulty": 92.96875,
"index": 1012,
"split": "train"
} |
deepscaler | [
{
"content": "How many distinct sequences of four letters can be made from the letters in \"EXAMPLE\" if each letter can be used only once and each sequence must begin with X and not end with E? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "80",
"style": "rule"
} | {
"difficulty": 94.53125,
"index": 972,
"split": "train"
} |
deepscaler | [
{
"content": "The segment connecting the centers of two intersecting circles is divided by their common chord into segments of 4 and 1. Find the length of the common chord, given that the radii of the circles are in the ratio $3:2$. Let's think step by step and output the final answer within \\boxed{}.",
"r... | math | {
"ground_truth": "2 \\sqrt{11}",
"style": "rule"
} | {
"difficulty": 72.65625,
"index": 4946,
"split": "train"
} |
deepscaler | [
{
"content": "A factory produces two types of products, A and B, with profits P and Q (in ten thousand yuan), respectively. The relationship between the profits and the invested capital m (in ten thousand yuan) follows the empirical formulas P = (1/3)m + 65 and Q = 76 + 4√m. Now, 150 ten thousand yuan of capita... | math | {
"ground_truth": "203",
"style": "rule"
} | {
"difficulty": 67.96875,
"index": 6665,
"split": "train"
} |
deepscaler | [
{
"content": "There are more than 20 and fewer than 30 children in Miss Tree's class. They are all standing in a circle. Anna notices that there are six times as many children between her and Zara going round the circle clockwise, as there are going round anti-clockwise. How many children are there in the class... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"difficulty": 70.3125,
"index": 4715,
"split": "train"
} |
deepscaler | [
{
"content": "At 9:00, a pedestrian set off on a journey. An hour later, a cyclist set off from the same starting point. At 10:30, the cyclist caught up with the pedestrian and continued ahead, but after some time, the bicycle broke down. After repairing the bike, the cyclist resumed the journey and caught up w... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"difficulty": 63.28125,
"index": 6773,
"split": "train"
} |
deepscaler | [
{
"content": "Given that the sum of the first $n$ terms of the positive arithmetic geometric sequence ${a_n}$ is $S_n$, if $S_2=3$, $S_4=15$, find the common ratio $q$ and $S_6$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "63",
"style": "rule"
} | {
"difficulty": 60.15625,
"index": 6971,
"split": "train"
} |
deepscaler | [
{
"content": "Compute the sum of the squares of the roots of the equation \\[x\\sqrt{x} - 8x + 9\\sqrt{x} - 2 = 0,\\] given that all of the roots are real and nonnegative. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "46",
"style": "rule"
} | {
"difficulty": 85.9375,
"index": 3286,
"split": "train"
} |
deepscaler | [
{
"content": "Given the integers \\( 1, 2, 3, \\ldots, 40 \\), find the greatest possible sum of the positive differences between the integers in twenty pairs, where the positive difference is either 1 or 3. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "58",
"style": "rule"
} | {
"difficulty": 81.25,
"index": 2653,
"split": "train"
} |
deepscaler | [
{
"content": "Let n be the smallest positive integer such that n is divisible by 20, n^2 is a perfect square, and n^3 is a perfect fifth power. Find the value of n. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3200000",
"style": "rule"
} | {
"difficulty": 75.78125,
"index": 5123,
"split": "train"
} |
deepscaler | [
{
"content": "The measure of each exterior angle of a regular polygon is \\(20^\\circ\\). What is the sum of the measures of the interior angles and the total number of diagonals of this polygon? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "135",
"style": "rule"
} | {
"difficulty": 75,
"index": 4295,
"split": "train"
} |
deepscaler | [
{
"content": "How many positive integers \\( n \\) exist such that both \\(\\frac{n+1}{3}\\) and \\(3n+1\\) are three-digit integers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"difficulty": 89.0625,
"index": 3483,
"split": "train"
} |
deepscaler | [
{
"content": "The repeating decimals $0.abab\\overline{ab}$ and $0.abcabc\\overline{abc}$ satisfy\n\\[0.abab\\overline{ab}+0.abcabc\\overline{abc}=\\frac{33}{37},\\]\nwhere $a$, $b$, and $c$ are (not necessarily distinct) digits. Find the three digit number $abc$.\n Let's think step by step and output the final... | math | {
"ground_truth": "447",
"style": "rule"
} | {
"difficulty": 60.9375,
"index": 6943,
"split": "train"
} |
deepscaler | [
{
"content": "A grocer sets up a pyramid display for a store promotion, where the topmost row has three cans and each succeeding row below has three more cans than the row immediately above it. If the grocer uses 225 cans in total for this display, how many rows are there in the display? Let's think step by ste... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"difficulty": 68.75,
"index": 5697,
"split": "train"
} |
deepscaler | [
{
"content": "Squares $ABCD$, $EFGH$, and $GHIJ$ are equal in area. Points $C$ and $D$ are the midpoints of sides $IH$ and $HE$, respectively. What is the ratio of the area of the shaded pentagon $AJICB$ to the sum of the areas of the three squares? Let's think step by step and output the final answer within \\... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"difficulty": 78.90625,
"index": 3937,
"split": "train"
} |
deepscaler | [
{
"content": "How many positive integers \\( n \\) between 10 and 1000 have the property that the sum of the digits of \\( n \\) is 3? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"difficulty": 82.03125,
"index": 2451,
"split": "train"
} |
deepscaler | [
{
"content": "The GDP of a certain city last year was 84,300,000 ten thousand yuan. Represent this number in scientific notation. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "8.43 \\times 10^7",
"style": "rule"
} | {
"difficulty": 88.28125,
"index": 3268,
"split": "train"
} |
deepscaler | [
{
"content": "The sides opposite to the internal angles $A$, $B$, and $C$ of $\\triangle ABC$ are $a$, $b$, and $c$ respectively. It is given that $b\\sin C + c\\sin B = 4a\\sin B\\sin C$ and $b^2 + c^2 - a^2 = 8$. The area of $\\triangle ABC$ is __________. Let's think step by step and output the final answer ... | math | {
"ground_truth": "\\frac{2\\sqrt{3}}{3}",
"style": "rule"
} | {
"difficulty": 64.0625,
"index": 5416,
"split": "train"
} |
deepscaler | [
{
"content": "The area of the region in the $xy$ -plane satisfying the inequality \\[\\min_{1 \\le n \\le 10} \\max\\left(\\frac{x^2+y^2}{4n^2}, \\, 2 - \\frac{x^2+y^2}{4n^2-4n+1}\\right) \\le 1\\] is $k\\pi$ , for some integer $k$ . Find $k$ .\n\n*Proposed by Michael Tang* Let's think step by step and outp... | math | {
"ground_truth": "210",
"style": "rule"
} | {
"difficulty": 68.75,
"index": 6195,
"split": "train"
} |
deepscaler | [
{
"content": "Given \\( f(x) = x^{5} + a_{1} x^{4} + a_{2} x^{3} + a_{3} x^{2} + a_{4} x + a_{5} \\), and \\( f(m) = 2017m \\) for \\( m = 1, 2, 3, 4 \\), find \\( f(10) - f(-5) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "75615",
"style": "rule"
} | {
"difficulty": 76.5625,
"index": 4087,
"split": "train"
} |
deepscaler | [
{
"content": "$3-i(i)$ is a root of the equation $x^{2}+px+10=0(p∈R)$ with respect to $x$. Find the value of $p$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"difficulty": 82.03125,
"index": 1863,
"split": "train"
} |
deepscaler | [
{
"content": "Each of the $20$ balls is tossed independently and at random into one of the $5$ bins. Let $p$ be the probability that some bin ends up with $3$ balls, another with $5$ balls, and the other three with $4$ balls each. Let $q$ be the probability that every bin ends up with $4$ balls. What is $\\frac... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"difficulty": 97.65625,
"index": 969,
"split": "train"
} |
deepscaler | [
{
"content": "What is the probability that Claudia gets at least 2 more heads than tails if she flips 12 coins? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{793}{2048}",
"style": "rule"
} | {
"difficulty": 88.28125,
"index": 1844,
"split": "train"
} |
deepscaler | [
{
"content": "The centers of the three circles A, B, and C are collinear with the center of circle B lying between the centers of circles A and C. Circles A and C are both externally tangent to circle B, and the three circles share a common tangent line. Given that circle A has radius $12$ and circle B has ra... | math | {
"ground_truth": "147",
"style": "rule"
} | {
"difficulty": 95.3125,
"index": 817,
"split": "train"
} |
deepscaler | [
{
"content": "The sequence \\(\\{a_n\\}\\) is a geometric sequence with a common ratio of \\(q\\), where \\(|q| > 1\\). Let \\(b_n = a_n + 1 (n \\in \\mathbb{N}^*)\\), if \\(\\{b_n\\}\\) has four consecutive terms in the set \\(\\{-53, -23, 19, 37, 82\\}\\), find the value of \\(q\\). Let's think step by step a... | math | {
"ground_truth": "-\\dfrac{3}{2}",
"style": "rule"
} | {
"difficulty": 96.875,
"index": 1378,
"split": "train"
} |
deepscaler | [
{
"content": "On a line passing through the center $O$ of a circle with radius 12, points $A$ and $B$ are chosen such that $OA=15$, $AB=5$, and $A$ lies between $O$ and $B$. Tangents are drawn from points $A$ and $B$ to the circle, with the points of tangency lying on the same side of the line $OB$. Find the ar... | math | {
"ground_truth": "150/7",
"style": "rule"
} | {
"difficulty": 97.65625,
"index": 965,
"split": "train"
} |
deepscaler | [
{
"content": "Li Shuang rides a bike from location $A$ to location $B$ at a speed of 320 meters per minute. On the way, due to a bike malfunction, he pushes the bike and continues walking for 5 minutes to a location 1800 meters from $B$ to repair the bike. Fifteen minutes later, he resumes riding towards $B$ at... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"difficulty": 93.75,
"index": 1602,
"split": "train"
} |
deepscaler | [
{
"content": "Marie does three equally time-consuming tasks in a row without taking breaks. She begins the first task at $1\\!:\\!00$ PM and finishes the second task at $2\\!:\\!40$ PM. When does she finish the third task? Let's think step by step and output the final answer within \\boxed{}.",
"role": "use... | math | {
"ground_truth": "3:30 PM",
"style": "rule"
} | {
"difficulty": 98.4375,
"index": 959,
"split": "train"
} |
deepscaler | [
{
"content": "Given that the terminal side of angle $\\alpha$ passes through point $P(m, 2\\sqrt{2})$, $\\sin{\\alpha} = \\frac{2\\sqrt{2}}{3}$, and $\\alpha$ is in the second quadrant.\n\n(1) Find the value of $m$;\n\n(2) If $\\tan{\\beta} = \\sqrt{2}$, find the value of $\\frac{\\sin{\\alpha}\\cos{\\beta} + 3... | math | {
"ground_truth": "\\frac{\\sqrt{2}}{11}",
"style": "rule"
} | {
"difficulty": 63.28125,
"index": 5884,
"split": "train"
} |
deepscaler | [
{
"content": "Given that $sinα + cosα = \\frac{\\sqrt{2}}{3}, α ∈ (0, π)$, find the value of $sin(α + \\frac{π}{12})$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2\\sqrt{2} + \\sqrt{3}}{6}",
"style": "rule"
} | {
"difficulty": 96.09375,
"index": 134,
"split": "train"
} |
deepscaler | [
{
"content": "Three friends are in the park. Bob and Clarise are standing at the same spot and Abe is standing 10 m away. Bob chooses a random direction and walks in this direction until he is 10 m from Clarise. What is the probability that Bob is closer to Abe than Clarise is to Abe? Let's think step by step a... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"difficulty": 88.28125,
"index": 3046,
"split": "train"
} |
deepscaler | [
{
"content": "Given $x^3y = k$ for a positive constant $k$, find the percentage decrease in $y$ when $x$ increases by $20\\%$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "42.13\\%",
"style": "rule"
} | {
"difficulty": 69.53125,
"index": 5901,
"split": "train"
} |
deepscaler | [
{
"content": "Determine the area of the triangle bounded by the axes and the curve $y = (x-5)^2 (x+3)$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "300",
"style": "rule"
} | {
"difficulty": 61.71875,
"index": 6506,
"split": "train"
} |
deepscaler | [
{
"content": "Let $a, b$ and $c$ be positive real numbers such that $$\\begin{aligned} a^{2}+a b+b^{2} & =9 \\\\ b^{2}+b c+c^{2} & =52 \\\\ c^{2}+c a+a^{2} & =49 \\end{aligned}$$ Compute the value of $\\frac{49 b^{2}-33 b c+9 c^{2}}{a^{2}}$. Let's think step by step and output the final answer within \\boxed{}.... | math | {
"ground_truth": "52",
"style": "rule"
} | {
"difficulty": 99.21875,
"index": 1401,
"split": "train"
} |
deepscaler | [
{
"content": "In triangle \\( ABC \\), \\( \\angle ABC \\) is obtuse. Point \\( D \\) lies on side \\( AC \\) such that \\( \\angle ABD \\) is right, and point \\( E \\) lies on side \\( AC \\) between \\( A \\) and \\( D \\) such that \\( BD \\) bisects \\( \\angle EBC \\). Find \\( CE \\), given that \\( AC =... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"difficulty": 96.09375,
"index": 1114,
"split": "train"
} |
deepscaler | [
{
"content": "Let $b_0 = \\sin^2 \\left( \\frac{\\pi}{30} \\right)$ and for $n \\geq 0$,\n\\[ b_{n + 1} = 4b_n (1 - b_n). \\]\nFind the smallest positive integer $n$ such that $b_n = b_0$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"difficulty": 61.71875,
"index": 5945,
"split": "train"
} |
deepscaler | [
{
"content": "An event occurs many years ago. It occurs periodically in $x$ consecutive years, then there is a break of $y$ consecutive years. We know that the event occured in $1964$ , $1986$ , $1996$ , $2008$ and it didn't occur in $1976$ , $1993$ , $2006$ , $2013$ . What is the first year in tha... | math | {
"ground_truth": "2018",
"style": "rule"
} | {
"difficulty": 87.5,
"index": 2508,
"split": "train"
} |
deepscaler | [
{
"content": "For each real number \\( x \\), \\( f(x) \\) is defined to be the minimum of the values of \\( 2x + 3 \\), \\( 3x - 2 \\), and \\( 25 - x \\). What is the maximum value of \\( f(x) \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{53}{3}",
"style": "rule"
} | {
"difficulty": 66.40625,
"index": 6020,
"split": "train"
} |
deepscaler | [
{
"content": "Determine the greatest number m such that the\nsystem \u001a $x^2$ + $y^2$ = 1; | $x^3$ - $y^3$ |+|x-y|= $m^3$ has a solution. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt[3]{2}",
"style": "rule"
} | {
"difficulty": 71.09375,
"index": 3871,
"split": "train"
} |
deepscaler | [
{
"content": "In a game show, Bob is faced with 7 doors, 2 of which hide prizes. After he chooses a door, the host opens three other doors, of which one is hiding a prize. Bob chooses to switch to another door. What is the probability that his new door is hiding a prize? Let's think step by step and output the ... | math | {
"ground_truth": "\\frac{5}{21}",
"style": "rule"
} | {
"difficulty": 90.625,
"index": 62,
"split": "train"
} |
deepscaler | [
{
"content": "A circular grass plot 12 feet in diameter is cut by a straight gravel path 3 feet wide, one edge of which passes through the center of the plot. The number of square feet in the remaining grass area is Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}... | math | {
"ground_truth": "30\\pi - 9\\sqrt3",
"style": "rule"
} | {
"difficulty": 99.21875,
"index": 466,
"split": "train"
} |
deepscaler | [
{
"content": "Let $f(x)$ be a function defined on $\\mathbb{R}$ with a period of 2. On the interval $[-1,1)$, $f(x)$ is given by\n$$\nf(x) = \\begin{cases}\nx+a & \\text{for } -1 \\leq x < 0,\\\\\n\\left| \\frac{2}{5} - x \\right| & \\text{for } 0 \\leq x < 1,\n\\end{cases}\n$$\nwhere $a \\in \\mathbb{R}$. If $... | math | {
"ground_truth": "-\\frac{2}{5}",
"style": "rule"
} | {
"difficulty": 67.1875,
"index": 6905,
"split": "train"
} |
deepscaler | [
{
"content": "In Rivertown, car plates each contain three symbols: two letters followed by a digit. The first letter is chosen from the set ${A, B, G, H, T}$, the second letter from ${E, I, O, U}$, and the digit from $0$ to $9$. \n\nTo accommodate an increase in the number of cars, Rivertown decides to expand e... | math | {
"ground_truth": "130",
"style": "rule"
} | {
"difficulty": 73.4375,
"index": 3806,
"split": "train"
} |
deepscaler | [
{
"content": "In the Cartesian coordinate system $xOy$, with $O$ as the pole and the non-negative half-axis of the $x$-axis as the polar axis, a polar coordinate system is established. The polar coordinates of point $P$ are $(3, \\frac{\\pi}{4})$. The parametric equation of curve $C$ is $\\rho=2\\cos (\\theta- ... | math | {
"ground_truth": "\\frac{\\sqrt{10}-1}{2}",
"style": "rule"
} | {
"difficulty": 72.65625,
"index": 5387,
"split": "train"
} |
deepscaler | [
{
"content": "Given that each side of a large square is divided into four equal parts, a smaller square is inscribed in such a way that its corners are at the division points one-fourth and three-fourths along each side of the large square, calculate the ratio of the area of this inscribed square to the area of... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"difficulty": 67.1875,
"index": 6436,
"split": "train"
} |
deepscaler | [
{
"content": "In a particular sequence, the first term is $a_1=1007$ and the second term is $a_2=1008$. Furthermore, the values of the remaining terms are chosen so that $a_n + a_{n+1} + a_{n+2} = 2n$ for all $n \\geq 1$. Determine $a_{500}$. Let's think step by step and output the final answer within \\boxed{}... | math | {
"ground_truth": "1339",
"style": "rule"
} | {
"difficulty": 99.21875,
"index": 1740,
"split": "train"
} |
deepscaler | [
{
"content": "It is known that $\\tan\\alpha$ and $\\tan\\beta$ are the two roots of the equation $x^2+6x+7=0$, and $\\alpha, \\beta \\in \\left(-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right)$. What is the value of $\\alpha + \\beta$? Let's think step by step and output the final answer within \\boxed{}.",
"role... | math | {
"ground_truth": "- \\frac{3\\pi}{4}",
"style": "rule"
} | {
"difficulty": 60.9375,
"index": 6603,
"split": "train"
} |
deepscaler | [
{
"content": "Triangle $XYZ$ has vertices $X(1, 9)$, $Y(3, 1)$, and $Z(9, 1)$. A line through $Y$ cuts the area of $\\triangle XYZ$ in half. Find the sum of the slope and the $y$-intercept of this line. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"difficulty": 67.96875,
"index": 5984,
"split": "train"
} |
deepscaler | [
{
"content": "The acronym XYZ is displayed on a rectangular grid similarly spaced 1 unit apart. The acronym starts X having length 2 units at the top and the bottom and slanted sides making triangles on both ends. Y is made with a vertical line of 3 units and two slanted lines extending from the midpoint down t... | math | {
"ground_truth": "13 + 4\\sqrt{2} + \\sqrt{10}",
"style": "rule"
} | {
"difficulty": 83.59375,
"index": 3236,
"split": "train"
} |
deepscaler | [
{
"content": "Find the area of triangle $ABC$ below.\n\n[asy]\nunitsize(1inch);\npair A, B, C;\nA = (0,0);\nB= (sqrt(2),0);\nC = (0,sqrt(2));\ndraw (A--B--C--A, linewidth(0.9));\ndraw(rightanglemark(B,A,C,3));\nlabel(\"$A$\",A,S);\nlabel(\"$B$\",B,S);\nlabel(\"$C$\",C,N);\nlabel(\"$8$\",(B+C)/2,NE);\nlabel(\"$4... | math | {
"ground_truth": "32",
"style": "rule"
} | {
"difficulty": 91.40625,
"index": 758,
"split": "train"
} |
deepscaler | [
{
"content": "Schools A and B are having a sports competition with three events. In each event, the winner gets 10 points and the loser gets 0 points, with no draws. The school with the highest total score after the three events wins the championship. It is known that the probabilities of school A winning in th... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"difficulty": 82.8125,
"index": 3109,
"split": "train"
} |
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