data_source stringclasses 1 value | prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Find the sum of the roots of the equation \\[(3x^4 + 2x^3 - 9x^2 + 5x - 15)(4x^3 - 16x^2 + x + 7) - 10 = 0.\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{10}{3}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "On one particular Wednesday, Jack worked \\( t-2 \\) hours and earned \\( 3t-2 \\) dollars per hour. His coworker Bob worked 1.5 times more hours than Jack but earned \\( 2t-7 \\) dollars per hour less than Jack. After paying a fixed tax of $10 each, they both netted the same amount of earnings. D... | math | {
"ground_truth": "\\frac{19}{3}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Calculate $300,000$ times $300,000$ times $3$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "270,000,000,000",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Chef Aria, an acclaimed Australian chef and television personality, is preparing a special dish using her favorite local produce. She decides to use 5 different types of vegetables for her dish. Each vegetable costs $3, and she needs 4 of each type to serve her guests. Additionally, she wants to a... | math | {
"ground_truth": "82",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Given that there are 10 children and a total of 26 wheels, determine the number of tricycles.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "In right triangle $ABC$ with $\\angle A = 90^\\circ$, the sides $AB = 8$ and $BC = 17$. Find $\\sin C$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{8}{17}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Medians $\\overline{DP}$ and $\\overline{EQ}$ of $\\triangle DEF$ are perpendicular. If $DP= 24$ and $EQ = 32$, then what is ${DE}$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{80}{3}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Compute the definite integral:\n\n$$\n\\int_{\\pi / 2}^{\\pi} 2^{4} \\cdot \\sin ^{6} x \\cos ^{2} x \\, dx\n$$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5\\pi}{16}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Find all $t\\in \\mathbb Z$ such that: exists a function $f:\\mathbb Z^+\\to \\mathbb Z$ such that: $f(1997)=1998$ $\\forall x,y\\in \\mathbb Z^+ , \\text{gcd}(x,y)=d : f(xy)=f(x)+f(y)+tf(d):P(x,y)$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
... | math | {
"ground_truth": "t = -1",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "For how many bases between four and twelve inclusive does the representation of $1024_{10}$ have a final digit of 1?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Determine the number of ways to arrange the letters of the word BANANAS such that no 'A' appears at the first position.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "240",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "How many perfect squares are between 50 and 250?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Convert the point $( -5, 0, -8 )$ in rectangular coordinates to cylindrical coordinates. Enter your answer in the form $(r,\\theta,z),$ where $r > 0$ and $0 \\le \\theta < 2 \\pi.$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "(5,\\pi,-8)",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Given a triangle \\(ABC\\) and a point \\(P_0\\) on the side \\(AB\\). Construct points \\(P_i, Q_i, R_i\\) as follows: \\(Q_i\\) is the foot of the perpendicular from \\(P_i\\) to \\(BC\\), \\(R_i\\) is the foot of the perpendicular from \\(Q_i\\) to \\(AC\\) and \\(P_{i+1}\\) is the foot of the ... | math | {
"ground_truth": "P",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "For how many positive integers $n$ is $\\frac{n}{40-n}$ also a positive integer?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "How many positive integers \\( n \\) less than 2007 can we find such that \\(\\left\\lfloor \\frac{n}{2} \\right\\rfloor + \\left\\lfloor \\frac{n}{3} \\right\\rfloor + \\left\\lfloor \\frac{n}{6} \\right\\rfloor = n\\), where \\(\\left\\lfloor x \\right\\rfloor\\) is the greatest integer less tha... | math | {
"ground_truth": "334",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "What is the value of $x$ if a cube's volume is $5x$ cubic units and its surface area is $x$ square units?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "5400",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "The measure of angle $ACB$ is 50 degrees. If ray $CA$ is rotated 540 degrees about point $C$ in a clockwise direction, what will be the positive measure of the new acute angle $ACB$, in degrees?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "50 \\text{ degrees}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "In Central High School, a dodgeball league includes 12 students, among them are Dexter and Sam. Students split into two teams of 6 players each during their sports period. Over the course of a term, each group of six players team up exactly once. Determine how many times Dexter played in the same ... | math | {
"ground_truth": "210",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "How many 3-digit numbers have the property that the units digit is exactly twice the tens digit?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "45",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "At a particular school with 43 students, each student takes chemistry, biology, or both. The chemistry class is three times as large as the biology class, and 5 students are taking both classes. How many people are in the chemistry class?\nPlease reason step by step, and put your final answer with... | math | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Given the fraction $\\frac{987654321}{2^{30}\\cdot 5^5}$, calculate the minimum number of digits to the right of the decimal point needed to express the fraction as a decimal.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "The length of the segment between the points $(3a, 2a-5)$ and $(5, 0)$ is $3\\sqrt{10}$ units. What is the product of all possible values for $a$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{40}{13}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "A line with a slope of 2 and a line with a slope of -4 each have a $y$-intercept of 6. The distance between the $x$-intercepts of these lines is:\n(A) 2\n(B) 6\n(C) $\\frac{3}{2}$\n(D) $\\frac{5}{2}$\n(E) $\\frac{9}{2}$\nPlease reason step by step, and put your final answer within \\boxed{}.",
... | math | {
"ground_truth": "\\frac{9}{2}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Simplify $\\frac{\\sqrt{3}}{\\sqrt{5}} \\cdot \\frac{\\sqrt{7}}{\\sqrt{11}} \\cdot \\frac{\\sqrt{15}}{\\sqrt{2}}$ and rationalize the denominator of the resulting fraction.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3\\sqrt{154}}{22}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Determine the base \\( b \\) such that the number \\( 256_{10} \\) has exactly \\( 4 \\) digits in base \\( b \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Find the number of different monic quadratic polynomials (i.e., with the leading coefficient equal to 1) with integer coefficients such that they have two different roots which are powers of 5 with natural exponents, and their coefficients do not exceed in absolute value $125^{48}$.\nPlease reason... | math | {
"ground_truth": "5112",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Let \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) be an odd function, i.e., a function that satisfies \\( -f(x) = f(-x) \\) for all \\( x \\in \\mathbb{R} \\). Suppose that \\( f(x+5) = f(x) \\) for all \\( x \\in \\mathbb{R} \\) and that \\( f(1/3) = 1 \\). Determine the value of the sum:\n\n\\... | math | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Let $w_{1}$ and $w_{2}$ denote the circles $x^{2}+y^{2}+10x-24y-87=0$ and $x^{2}+y^{2}-10x-24y+153=0$ , respectively. Let $m$ be the smallest positive value of $a$ for which the line $y=ax$ contains the center of a circle that is externally tangent to $w_{2}$ and internally tangent ... | math | {
"ground_truth": "169",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "We are given that $$54+(98\\div14)+(23\\cdot 17)-200-(312\\div 6)=200.$$Now, let's remove the parentheses: $$54+98\\div14+23\\cdot 17-200-312\\div 6.$$What does this expression equal?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "200",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "An abundant number is a positive integer such that the sum of its proper divisors is greater than the number itself. What is the smallest abundant number that is not a multiple of 5?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Compute $\\sin 240^\\circ$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{\\sqrt{3}}{2}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Seventy cards, numbered 1-70, are placed in a box. One card is randomly selected. What is the probability that the number on the card is prime and is a multiple of 11? Express your answer as a common fraction.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "... | math | {
"ground_truth": "\\frac{1}{70}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "In a class of 150 students, all taking the same test, what is the maximum number of students who can receive a score above the class average?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "149",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "The numbers \\(a_1, a_2, a_3, a_4,\\) and \\(a_5\\) form a geometric progression. Among them, there are both rational and irrational numbers. What is the maximum number of terms in this progression that can be rational numbers?\nPlease reason step by step, and put your final answer within \\boxed{... | math | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Suppose the graph of a function $y=g(x)$ has the property that if it is shifted $30$ units to the right, then the resulting graph is identical to the original graph of $y=g(x)$.\n\nWhat is the smallest positive $b$ such that if the graph of $y=g\\left(\\frac{x}{3}\\right)$ is shifted $b$ units to ... | math | {
"ground_truth": "90",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "A square is divided into 2016 triangles, with no vertex of any triangle lying on the sides or inside any other triangle. The sides of the square are sides of some of the triangles in the division. How many total points, which are the vertices of the triangles, are located inside the square?\nPleas... | math | {
"ground_truth": "1007",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "The diagram shows the miles traveled by cyclists Carlos and Diana. After three hours, how many more miles has Carlos cycled than Diana? [asy]\n/* Adapted AMC8-like problem */\ndraw((0,0)--(5,0)--(5,3.75)--(0,3.75)--cycle);\nfor(int x=0; x <= 5; ++x) {\nfor(real y=0; y <=3.75; y+=0.75) {\ndot((x, y... | math | {
"ground_truth": "15",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "A binary operation $\\diamondsuit$ has the properties that $a\\,\\diamondsuit\\, (b\\,\\diamondsuit \\,c) = (a\\,\\diamondsuit \\,b)\\cdot c$ and that $a\\,\\diamondsuit \\,a=1$ for all nonzero real numbers $a, b,$ and $c$. (Here $\\cdot$ represents multiplication). Find the solution to the equati... | math | {
"ground_truth": "\\frac{25}{84}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Given the equation $(x\\sqrt{x})^x = x^{x\\sqrt{x}}$, find the sum of the real roots of this equation.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{13}{4}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "The Happy Baker baked a round cake with a boundary described by the equation \\(x^2 + y^2 + 1 = 2x + 6y\\). She needs to determine the size of her cake to properly decorate it. What is the radius of the cake?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "u... | math | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Alex, a mid-career attorney, is considering opening a solo practice. Currently, Alex earns $120,000 per year working at a law firm. To set up the solo practice, Alex estimates the following initial costs: $15,000 for office rent, $8,000 for office furniture, $10,000 for a computer and software set... | math | {
"ground_truth": "16166.67",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "If \\( x + \\frac{1}{x} = 5 \\), find the value of \\( x^3 + \\frac{1}{x^3} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "110",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "The taxi fare in Rivertown is $3.00 for the first $\\frac{3}{4}$ mile and additional mileage charged at the rate of $0.25 for each additional 0.1 mile. You plan to give the driver a $3 tip. Determine the number of miles that can be ridden for a total of $15.\nPlease reason step by step, and put yo... | math | {
"ground_truth": "4.35",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "What is the sum and the average of the prime numbers between 20 and 40?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "As shown in the figure, point $D$ is an interior point of $\\triangle ABC$. $BD$ intersects $AC$ at $E$, and $CD$ intersects $AB$ at $F$, with $AF = BF = CD$ and $CE = DE$. Find the measure of $\\angle BFC$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "us... | math | {
"ground_truth": "120^\\circ",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Given $\\begin{vmatrix} x & y \\\\ z & w \\end{vmatrix} = 5$, find the value of:\n\\[\\begin{vmatrix} x & 2x + 4y \\\\ z & 2z + 4w \\end{vmatrix}\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Find the angle $\\theta$ in degrees for the expression\n\\[\n\\text{cis } 55^\\circ + \\text{cis } 65^\\circ + \\text{cis } 75^\\circ + \\dots + \\text{cis } 145^\\circ\n\\]\nexpressed in the form $r \\, \\text{cis } \\theta$, where $r > 0$ and $0^\\circ \\le \\theta < 360^\\circ$.\nPlease reason ... | math | {
"ground_truth": "100^\\circ",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "$n$ points are located at the vertices of a convex $n$-gon. Inside this $n$-gon, $k$ points are marked. It turns out that any three of the $n+k$ points do not lie on the same straight line and form the vertices of an isosceles triangle. What can be the value of $k$?\nPlease reason step by step, an... | math | {
"ground_truth": "k = 0 \\text{ or } 1",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "The Sunnydale Farm has 5 chickens, 3 dogs, 4 cats, and 3 rabbits. How many ways can these 15 animals be placed in a row of 15 cages, such that all of the animals of each type are next to each other? Each animal within a species remains distinguishable from others.\nPlease reason step by step, and ... | math | {
"ground_truth": "2,\\!488,\\!320",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Andrew's grandfather's age is fifteen times Andrew's age. If Andrew's grandfather was 55 years old when Andrew was born, how old is Andrew now?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{55}{14}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Suppose that the roots of $x^3 + 4x^2 + 5x - 14 = 0$ are $p$, $q$, and $r$, and the roots of $x^3 + ux^2 + vx + w = 0$ are $p+q$, $q+r$, and $r+p$. Find the value of $w$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "34",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "The integers \\( x, y, z \\), and \\( p \\) satisfy the equation \\( x^2 + xz - xy - yz = -p \\). Given that \\( p \\) is prime, what is the value of \\( |y+z| \\) in terms of \\( p \\) ? Your answer should refer to the variable \\( p \\) so that it works for every prime number \\( p \\).\nPlease ... | math | {
"ground_truth": "p+1",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Find the product of all $x$ such that the expression $\\frac{x^2 - 4x + 4}{x^2 - 5x + 6}$ is undefined.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Positive real numbers $a$ , $b$ , $c$ satisfy $a+b+c=1$ . Find the smallest possible value of $$ E(a,b,c)=\\frac{a^3}{1-a^2}+\\frac{b^3}{1-b^2}+\\frac{c^3}{1-c^2}. $$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{8}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "What is the area enclosed by the graph of $|x| + |3y| = 12$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "96",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"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 $f(10).$\nPlease reason step by step, and put your final answer within \\box... | math | {
"ground_truth": "100",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "A sports coach distributes 40 water bottles among 25 athletes before a game, with each athlete receiving at least one water bottle. Calculate the maximum number of water bottles one athlete could have received, assuming everyone received at least one.\nPlease reason step by step, and put your fina... | math | {
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "In how many ways can one arrange all the natural numbers from 1 to \\(2n\\) in a circle so that each number is a divisor of the sum of its two adjacent numbers? (Arrangements that differ by rotation and symmetry are considered the same.)\nPlease reason step by step, and put your final answer withi... | math | {
"ground_truth": "1 \\text{ variant}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Determine the solution of the equation $9^{x+6} = 10^x$ in the form $x = \\log_c 9^6$. Identify the value of $c$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{10}{9}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Professor Smith is an English literature professor who recently came across a collection of Islamic poetry while researching for her next lecture. She decides to include a few poems in her syllabus and plans to allocate a certain number of days for her students to study them. Professor Smith has 4... | math | {
"ground_truth": "Sunday",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "A 4x4x4 cube is made of $64$ normal dice, where opposites sum to $7$. Calculate the smallest possible sum of all the values visible on the $6$ faces of the giant cube.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "144",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Given real numbers $t$, consider the point of intersection of the lines $3x + 4y = 12t + 6$ and $2x + 3y = 8t - 1$. All plotted points from various values of $t$ lie on a line. Determine the slope of this line.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": ... | math | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "A classroom has $30$ seats arranged into $5$ rows of $6$ seats. Thirty students of distinct heights come to class every day, each sitting in a random seat. The teacher stands in front of all the rows, and if any student seated in front of you (in the same column) is taller than you, then the... | math | {
"ground_truth": "\\frac{163}{10}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "What is the modular inverse of $13$, modulo $997$?\n\nExpress your answer as an integer from $0$ to $996$, inclusive.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "767",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "(a) Determine all pairs $(x, y)$ of (real) numbers with $0 < x < 1$ and $0 <y < 1$ for which $x + 3y$ and $3x + y$ are both integer. An example is $(x,y) =( \\frac{8}{3}, \\frac{7}{8}) $ , because $ x+3y =\\frac38 +\\frac{21}{8} =\\frac{24}{8} = 3$ and $ 3x+y = \\frac98 + \\frac78 ... | math | {
"ground_truth": "m = 11",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "The roots of the polynomial $P(x) = x^3 + 5x + 4$ are $r$ , $s$ , and $t$ . Evaluate $(r+s)^4 (s+t)^4 (t+r)^4$ .\n\n*Proposed by Eugene Chen*\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "256",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "What is the smallest positive integer $x$ that, when multiplied by $450$, produces a product that is a multiple of $648$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "36",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Two lines enclose an angle of $36^{\\circ}$. A grasshopper jumps back and forth from one line to the other such that the length of each of its jumps is always the same. Show that it can reach at most ten different points.\nPlease reason step by step, and put your final answer within \\boxed{}.",
... | math | {
"ground_truth": "10",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "The infinite sequence $T=\\{t_1,t_2,t_3,\\ldots\\}$ is defined by $t_1=11$ and $t_n=11^{t_{n-1}}$ for each integer $n>1$. What is the remainder when $t_{100}$ is divided by $7$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "You have a whole pizza in the refrigerator. On your first trip to the refrigerator, you eat one-third of the pizza. On each successive trip, you eat one-third of the remaining pizza. After six trips to the refrigerator, what fractional part of the pizza have you eaten?\nPlease reason step by step,... | math | {
"ground_truth": "\\frac{665}{729}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Evaluate the expression \n\\[\n\\left(d^d - d(d-2)^d + (d-1)!\\right)^2\n\\]\nwhen $d = 4$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "39204",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "In spherical coordinates, the point $\\left( 4, \\frac{\\pi}{3}, \\frac{7 \\pi}{4} \\right)$ is equivalent to what other point, in the standard spherical coordinate representation? Enter your answer in the form $(\\rho,\\theta,\\phi),$ where $\\rho > 0,$ $0 \\le \\theta < 2 \\pi,$ and $0 \\le \\ph... | math | {
"ground_truth": "\\left( 4, \\frac{4 \\pi}{3}, \\frac{\\pi}{4} \\right)",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "There are 5 people standing in a line numbered 1 through 5 in a left to right order.\nEach person has the following attributes: Job, Food, Beverage, Nationality, Sport.\nThe attributes have the following possible values:\n- Job: accountant, dressmaker, project-manager, security-guard, videographe... | math | {
"ground_truth": "turkish",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Points A and B lie on a circle centered at O, and ∠AOB = 60°. A second circle is internally tangent to the first and tangent to both OA and OB. What is the ratio of the area of the smaller circle to that of the larger circle?\nPlease reason step by step, and put your final answer within \\boxed{}.... | math | {
"ground_truth": "\\frac{1}{9}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Consider a sequence $F_0=2$ , $F_1=3$ that has the property $F_{n+1}F_{n-1}-F_n^2=(-1)^n\\cdot2$ . If each term of the sequence can be written in the form $a\\cdot r_1^n+b\\cdot r_2^n$ , what is the positive difference between $r_1$ and $r_2$ ?\nPlease reason step by step, and put your fin... | math | {
"ground_truth": "\\frac{\\sqrt{17}}{2}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Determine the number of ways to arrange the letters of the word TOOTH.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Factor $x^2 + 6x + 9 - 64x^4$ into two quadratic polynomials with integer coefficients. Submit your answer in the form $(ax^2 + bx + c)(dx^2 + ex + f)$, with $a < d$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "(-8x^2+x+3)(8x^2+x+3)",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "What is the measure, in degrees, of the acute angle formed by the minute hand and the hour hand on a standard clock when it indicates 4:50?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "155^\\circ",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "John works on three tasks sequentially. The second task takes twice as long as the first, and the third task takes the same amount of time as the first. He starts the first task at 9:00 AM and completes the second task by 11:30 AM. Determine the completion time of the third task.\nPlease reason st... | math | {
"ground_truth": "12:20 \\text{ PM}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "A car rental company owns 100 cars. When the monthly rental fee per car is 3000 Yuan, all the cars are rented out. For every 50 Yuan increase in the monthly rental fee per car, one more car remains unrented. The maintenance cost for each rented car is 150 Yuan per month, and the maintenance cost f... | math | {
"ground_truth": "307050 \\text{ yuan}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Let $f(n)$ be the smallest prime which divides $n^4+1$. Determine the remainder when the sum $f(1)+f(2)+\\cdots+f(2014)$ is divided by 8$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Given an isosceles triangle \\(ABC\\) where \\(AB = AC\\) and \\(\\angle ABC = 53^\\circ\\), point \\(K\\) is such that \\(C\\) is the midpoint of segment \\(AK\\). Point \\(M\\) is chosen such that:\n\n- \\(B\\) and \\(M\\) lie on the same side of line \\(AC\\);\n- \\(KM = AB\\);\n- the angle \\(... | math | {
"ground_truth": "44",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Three dice with faces numbered 1 through 6 are placed vertically in a stack as described. The visible numbers on these dice are 2, 2, 3, 3, 4, 5, 6. Calculate the total number of dots that are NOT visible on these dice.\nPlease reason step by step, and put your final answer within \\boxed{}.",
... | math | {
"ground_truth": "38",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "All seats at King Arthur's round table are numbered clockwise, with equal distances between adjacent seats.\n\nOne day, King Arthur sat in seat number 10, and Sir Lancelot sat directly opposite him in seat number 29. How many seats are there in total at the round table?\nPlease reason step by step... | math | {
"ground_truth": "38",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "A positive two-digit number is even and is a multiple of 11. The product of its digits is a perfect cube. What is this two-digit number?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "88",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Consider a regular polygon with $2^n$ sides, for $n \\ge 2$ , inscribed in a circle of radius $1$ . Denote the area of this polygon by $A_n$ . Compute $\\prod_{i=2}^{\\infty}\\frac{A_i}{A_{i+1}}$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
... | math | {
"ground_truth": "\\frac{2}{\\pi}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "In the isosceles triangle \\(ABC\\), \\(\\angle ACB = \\angle ABC = 40^\\circ\\). On the ray \\(AC\\), mark off the segment \\(AD\\) such that \\(AD = BC\\). What is the measure of \\(\\angle BDC\\)?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
... | math | {
"ground_truth": "30^\\circ",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Given a regular 15-sided polygon with a side length of \\(2a\\). What is the area of the annulus bounded by the circles inscribed in and circumscribed around the 15-sided polygon?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\pi a^2",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Given that the inequality $1+\\sqrt{n^2-9n+20} > \\sqrt{n^2-7n+12}$ holds true, determine the number of positive integer $n$ satisfying this inequality.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Find the reflection of \\(\\begin{pmatrix} 2 \\\\ 3 \\\\ 1 \\end{pmatrix}\\) over the vector \\(\\begin{pmatrix} 4 \\\\ -1 \\\\ 2 \\end{pmatrix}\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\begin{pmatrix} \\frac{2}{3} \\\\ -\\frac{11}{3} \\\\ \\frac{1}{3} \\end{pmatrix}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "For all composite integers $n$ that are multiples of $4$, what is the largest integer that always divides into the difference between $n^3$ and $n^2$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "16",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "A cylinder \\( C \\) and a cone \\( K \\) are circumscribed around a sphere; the volumes of the cylinder and cone are denoted by \\( V_{1} \\) and \\( V_{2} \\), respectively. What is the minimum possible value of \\( v \\) if \\( V_{1} = 1 \\)? What is the angle at the apex of the axial section o... | math | {
"ground_truth": "\\frac{4}{3}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Let $m = \\underbrace{333333333}_{\\text{9 digits}}$ and $n = \\underbrace{9999999999}_{\\text{10 digits}}$.\n\nDetermine $\\gcd(m, n)$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Every member, starting from the third one, of two sequences $\\{a_n\\}$ and $\\{b_n\\}$ equals to the sum of two preceding ones. First members are: $a_1 = 1, a_2 = 2, b_1 = 2, b_2 = 1$ . How many natural numbers are encountered in both sequences (may be on the different places)?\nPlease reaso... | math | {
"ground_truth": "3",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Suppose that $p$ is prime and $1014_p + 307_p + 114_p + 126_p + 7_p = 143_p + 272_p + 361_p$. How many possible values of $p$ are there?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "Given non-negative real numbers $a_{1}, a_{2}, \\cdots, a_{2008}$ whose sum equals 1, determine the maximum value of $a_{1} a_{2} + a_{2} a_{3} + \\cdots + a_{2007} a_{2008} + a_{2008} a_{1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "How many positive integers smaller than $500,000$ are powers of $2$, but are not powers of $4$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "A student, Ellie, was supposed to calculate $x-y-z$, but due to a misunderstanding, she computed $x-(y+z)$ and obtained 18. The actual answer should have been 6. What is the value of $x-y$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
DigitalLearningGmbH/MATH-lighteval | [
{
"content": "A geometric sequence of positive integers starts with a first term of 5. The third term in this sequence is 120. What is the fifth term of the sequence?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "2880",
"style": "rule-lighteval/MATH_v2"
} | {
"dataset": "orz_math_57k"
} |
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