data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the complex number $z= \\frac {i}{1-i}$. Then calculate the modulus of the conjugate of $z$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $XYZ$, we have $\\angle X = 90^\\circ$, $YZ = 20$, and $\\tan Z = 3\\cos Y$. What is $XY$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{40\\sqrt{2}}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the value of $\\sqrt{49 \\times \\sqrt{25 \\times \\sqrt{9}}}$?",
"role": "user"
}
] | math | {
"ground_truth": "5\\sqrt{7} \\sqrt[4]{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=(x^{2}+x+m)e^{x}$ (where $m\\in R$, $e$ is the base of the natural logarithm), if the function $f(x)$ has a maximum value at $x=-3$, then the minimum val... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Princeton’s Math Club recently bought a stock for $\\$ 2 $ and sold it for $ \\ $9$ thirteen days later. Given that the stock either increases or decreases by $\\$ 1 $ every d... | math | {
"ground_truth": "273",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The greatest common divisor of 459 and 357 is.",
"role": "user"
}
] | math | {
"ground_truth": "51",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the ordered triple of natural numbers $(x,y,z)$ such that $x \\le y \\le z$ and $x^x+y^y+z^z = 3382.$ [i]Proposed by Evan Fang",
"role": "user"
}
] | math | {
"ground_truth": "(1, 4, 5)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\alpha$ and $\\beta$ are the roots of the equation $x^2 - 3x - 2 = 0,$ find the value of $5 \\alpha^4 + 12 \\beta^3.$",
"role": "user"
}
] | math | {
"ground_truth": "672.5 + 31.5\\sqrt{17}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sequence \\( x, y, z, w \\) satisfying \\( xy + 2yz + zw \\leq A(x^2 + y^2 + z^2 + w^2) \\), find the minimum value of the real number \\( A \\).",
"role": "user"
... | math | {
"ground_truth": "\\frac{1+\\sqrt{2}}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A clock face is designed with ten equally spaced rays emanating from its center, dividing the clock into ten equal segments. One ray points at 12 o'clock (due north). Calculate t... | math | {
"ground_truth": "108^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "To welcome the arrival of the \"May Day holiday,\" a certain shopping mall is carrying out a promotional activity. Customers who spend over $200$ yuan in the mall can participate... | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of two numbers is $S$. Suppose $4$ is added to each number and then each of the resulting numbers is tripled. Calculate the sum of the final two numbers.",
"role": "u... | math | {
"ground_truth": "3S + 24",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the base-10 integer 678 when expressed in base 7?",
"role": "user"
}
] | math | {
"ground_truth": "1656_7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the least integer a greater than $14$ so that the triangle with side lengths $a - 1$ , $a$ , and $a + 1$ has integer area?",
"role": "user"
}
] | math | {
"ground_truth": "52",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given vectors $\\overrightarrow{a}=(\\cos \\frac{3}{2}x, \\sin \\frac{3}{2}x)$ and $\\overrightarrow{b}=(\\cos \\frac{1}{2}x, -\\sin \\frac{1}{2}x)$, where $x \\in [0, \\frac{\\p... | math | {
"ground_truth": "\\lambda = \\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ f(x) = x^3 - x + 1$. Suppose $ h$ is a cubic polynomial such that $ h(0) = 1$, and the roots of $ h$ are the squares of the roots of $ f$. Find $ h(4)$.",
"role": "user... | math | {
"ground_truth": "-3599",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three fair, six-sided dice are rolled. What is the probability that the sum of the three numbers showing is less than 16?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{103}{108}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the complex number $z$ satisfying the equation $3z - 5\\bar{z} = -4 - 60i - 8$.",
"role": "user"
}
] | math | {
"ground_truth": "6 - 7.5i",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A standard deck of 52 cards, containing cards of 13 ranks and 4 suits, is shuffled randomly. What is the probability that the top card is any King (King of $\\spadesuit$, King of... | math | {
"ground_truth": "\\frac{1}{13}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A mother is walking with a stroller around a lake and completes one lap in 12 minutes. Vanya rides a scooter on the same path in the same direction and overtakes the mother every... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For what real values of \\( k > 0 \\) is it possible to dissect a \\( 1 \\times k \\) rectangle into two similar but noncongruent polygons?",
"role": "user"
}
] | math | {
"ground_truth": "\\text{The dissection is possible for all } k > 0 \\text{ except for } k = 1.",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Ahn chooses a two-digit integer, subtracts it from 300, and triples the result. Find the smallest number Ahn can get.",
"role": "user"
}
] | math | {
"ground_truth": "603",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There is a regular $17$ -gon $\\mathcal{P}$ and its circumcircle $\\mathcal{Y}$ on the plane. \nThe vertices of $\\mathcal{P}$ are coloured in such a way that $A,B \\in \... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A Senate committee consists of 6 Democrats and 4 Republicans. In how many ways can they sit around a circular table if no two Republicans are allowed to sit next to each other?",... | math | {
"ground_truth": "43,\\!200",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify the expression: \\[(7x^{12} + 2x^{10} + x^9) + (3x^{11} + x^{10} + 6x^9 + 5x^7) + (x^{12} + 4x^{10} + 2x^9 + x^3).\\]",
"role": "user"
}
] | math | {
"ground_truth": "8x^{12} + 3x^{11} + 7x^{10} + 9x^9 + 5x^7 + x^3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( n \\) be the number of real values of \\( p \\) for which the roots of the equation \\( x^2 - (p+1)x + p = 0 \\) are equal. Find \\( n \\).",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A certain function $f$ has the properties that $f(3x)=3f(x)$ for all positive real values of $x$ , and that $f(x)=1-\\mid x-2 \\mid$ for $1\\leq x \\leq 3$ . Find the sma... | math | {
"ground_truth": "429",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Positive integers $a$, $b$, and $c$ are randomly and independently selected with replacement from the set $\\{1, 2, 3,\\dots, 5000\\}$. What is the probability that $abc + ab + a... | math | {
"ground_truth": "\\text{(B)}\\ \\frac{25}{64}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When the amount of water is tripled while keeping the amount of alcohol constant, calculate the fraction of the mixture that will now be alcohol.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{Therefore, the fraction of the mixture that is alcohol after tripling the volume of water is }\\frac{2}{5}.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three congruent circles of radius $2$ are drawn in the plane so that each circle passes through the centers of the other two circles. The region common to all three circles has... | math | {
"ground_truth": "300",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For $ k>0 $, let $ I_k\\equiv10\\ldots064 $ , where there are $ k $ zeros between the $ 1 $ and the $ 6 $ . Let $ N(k) $ be the number of factors of $ 2 $ in the prime factorizat... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=2\\sin \\left(x+ \\frac{\\pi}{6}\\right), x\\in\\left[ \\frac{\\pi}{2},\\pi\\right]$.\n\n$(1)$ If $\\sin x= \\frac{4}{5}$, find the value of the function... | math | {
"ground_truth": "[1,2]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Twelve people sit down for dinner where there are three choices of meals. Four people order the beef meal, four order the chicken meal, and four order the fish meal. The waiter s... | math | {
"ground_truth": "211200",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A fixed circumcircle is given around an acute-angled triangle \\(ABC\\) with vertex \\(C\\). The orthocenter \\(H\\) moves along a circle centered at point \\(C\\). Find the locu... | math | {
"ground_truth": "\\text{Arc of a circle centered at } Q \\text{ with radius } \\frac{1}{2} CH, \\text{ bounded by } A_2B_2 \\text{.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangle and a regular pentagon have the same perimeter. Let $A$ be the area of the circle circumscribed about the rectangle, with the rectangle having side lengths in the rat... | math | {
"ground_truth": "\\frac{5(5-\\sqrt{5})}{64}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An integer $n>0$ is written in decimal system as $\\overline{a_ma_{m-1}\\ldots a_1}$ . Find all $n$ such that\n\\[n=(a_m+1)(a_{m-1}+1)\\cdots (a_1+1)\\]",
"role": "user"... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two celestial bodies, located at a given distance ( $d$ ) from each other, are moving towards each other with given velocities ( $v$ and $v_{1}$ ). Determine the point at which t... | math | {
"ground_truth": "\\frac{v d}{v + v_{1}}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many integer Fahrenheit temperatures between 50 and 500 inclusive, does the original temperature, after conversion to Celsius, rounded to the nearest integer, converted b... | math | {
"ground_truth": "35",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Mike has two similar pentagons. The first pentagon has a perimeter of $18$ and an area of $8 \\frac{7}{16}$ . The second pentagon has a perimeter of $24$ . Find the area of ... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Person A and person B start simultaneously from points A and B, respectively, and move towards each other. When person A reaches the midpoint C of A and B, person B is still 240 ... | math | {
"ground_truth": "144 \\, \\text{meters}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a real number $a$, let $\\lfloor a \\rfloor$ denote the [greatest integer](https://artofproblemsolving.com/wiki/index.php/Ceiling_function) less than or equal to $a$. Let $\\... | math | {
"ground_truth": "164",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For each prime \\( p \\), find the largest natural power of \\( p \\) that divides the number \\( (p^2)! \\).",
"role": "user"
}
] | math | {
"ground_truth": "p+1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The range of the function $f(x) = 2 - \\log_2{x}$ is $(1, +\\infty)$. Find the range of $f^{-1}(x)$.",
"role": "user"
}
] | math | {
"ground_truth": "(0, 2)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle \\(K M N\\), it is known that \\(\\sin \\angle K N M = \\frac{\\sqrt{3}}{2}\\) and \\(\\cos \\angle K M N = \\frac{1}{3}\\). Find the ratio of the lengths of the alti... | math | {
"ground_truth": "\\frac{4 \\sqrt{6}}{9}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 6 seats in a row, and now 3 people are going to sit down. Calculate the number of different seating arrangements where exactly two empty seats are adjacent.",
"role... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the following equation:\n\n$\\operatorname{tg} x+\\operatorname{tg} 2 x+\\operatorname{tg} 3 x+\\operatorname{tg} 4 x=0$.",
"role": "user"
}
] | math | {
"ground_truth": "0^\\circ, 36^\\circ, 72^\\circ, 108^\\circ, 144^\\circ, 25^\\circ 5', 154^\\circ 55', 56^\\circ 29', 123^\\circ 31'",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $10^{\\log_{10}7} = 5x + 8$, solve for $x$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{5}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be an equilateral triangle with $AB=1.$ Let $M$ be the midpoint of $BC,$ and let $P$ be on segment $AM$ such that $AM/MP=4.$ Find $BP.$",
"role": "us... | math | {
"ground_truth": "\\frac{\\sqrt{7}}{5}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The arithmetic mean of four numbers is 90. If the largest of these numbers is 105, and the smallest of these numbers is 75, calculate the mean of the remaining two numbers.",
... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\log_a b \\cdot \\log_b a$, calculate the product.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $k \\in \\mathbb{N}^+$ . A sequence of subset of the integer set $\\mathbb{Z} \\supseteq I_1 \\supseteq I_2 \\supseteq \\cdots \\supseteq I_k$ is called a $k-chain$ ... | math | {
"ground_truth": "(k+1)^2 \\binom{k+3}{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Cagney can frost a cupcake every 15 seconds, and Lacey can frost a cupcake every 25 seconds. Lacey starts working 30 seconds after Cagney starts. Find the number of cupcakes that... | math | {
"ground_truth": "62",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle \\( \\triangle ABC \\), let the sides opposite to angles \\( \\angle A \\), \\( \\angle B \\), and \\( \\angle C \\) be \\( a \\), \\( b \\), and \\( c \\) respective... | math | {
"ground_truth": "1009",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sylvia has a bag of 10 coins. Nine are fair coins, but the tenth has tails on both sides. Sylvia draws a coin at random from the bag and flips it without looking. If the coin com... | math | {
"ground_truth": "\\frac{2}{11}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the sum of all primes $p$ such that $7^p - 6^p + 2$ is divisible by 43?",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jeff will pick a card at random from twelve cards numbered 1 through 12. The number on this card will indicate his starting point on the number line. He will then spin a fair spi... | math | {
"ground_truth": "\\frac{1}{8}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each of the numbers \\(x_{1}, x_{2}, \\ldots, x_{2004}\\) can be equal to \\(\\sqrt{2}-1\\) or \\(\\sqrt{2}+1\\). How many distinct integer values can the sum\n\n\\[ \n\\sum_{k=1... | math | {
"ground_truth": "502",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an acute-angled triangle \\( ABC \\), the altitude \\( AA_1 \\) is drawn. \\( H \\) is the orthocenter of triangle \\( ABC \\). It is known that \\( AH = 3 \\), \\( A_1H = 2 \... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Six equilateral triangles, each with a side length of 3 units, are arranged sequentially along a straight line, with each triangle sharing a vertex with the next. The midpoint of... | math | {
"ground_truth": "10.6875\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A street has 25 houses on each side, for a total of 50 houses. The addresses on the south side of the street form an arithmetic sequence, as do the addresses on the north side of... | math | {
"ground_truth": "125",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that all three vertices of $\\bigtriangleup ABC$ lie on the parabola defined by $y=2x^2$, with $A$ at the origin and $\\overline{BC}$ parallel to the $x$-axis, calculate th... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In 2020, the sum of the year's digits is $4$. What is the first year after 2020 in which the sum of the digits is 7 again?",
"role": "user"
}
] | math | {
"ground_truth": "2021",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, which is right-angled at $B$, segments $AD=15$, $BE=9$, and $CF=27$ are drawn from the vertices of triangle $ABC$, each perpendicular to a straight line $RS$, ... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the sum of the squares of all real numbers that satisfy the equation \\(x^{81} - 3^{36} = 0\\).\n**A)** 6561\n**B)** 13122\n**C)** 162\n**D)** 324\n**E)** 1296",
"r... | math | {
"ground_truth": "**B)** 13122",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given \\( x_1, x_2, \\cdots, x_{1993} \\) that satisfy\n\\[\n\\begin{array}{l}\n\\left|x_1 - x_2\\right| + \\left|x_2 - x_3\\right| + \\cdots + \\left|x_{1992} - x_{1993}\\right|... | math | {
"ground_truth": "1992",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a $5 \\times 5$ grid, place 6 crosses such that each row and each column contains at least one cross. How many ways can this be done?",
"role": "user"
}
] | math | {
"ground_truth": "4200",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "let $x,y,z$ be positive reals , such that $x+y+z=1399$ find the\n $$ \\max( [x]y + [y]z + [z]x ) $$ \n( $[a]$ is the biggest integer not exceeding $a$ )",
"role"... | math | {
"ground_truth": "\\max( \\lfloor x \\rfloor y + \\lfloor y \\rfloor z + \\lfloor z \\rfloor x ) = 652400",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle. An interior point $P$ of $ABC$ is said to be *good*if we can find exactly $27$ rays emanating from $P$ intersecting the sides of the triangle ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the equation in natural numbers: \\( x + \\frac{1}{y + \\frac{1}{z}} = \\frac{10}{7} \\).",
"role": "user"
}
] | math | {
"ground_truth": "x = 1, y = 2, z = 3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The parallel sides of a trapezoid are $ 3$ and $ 9$ . The non-parallel sides are $ 4$ and $ 6$ . A line parallel to the bases divides the trapezoid into two trapezoids of e... | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $a,n\\ge1$ such that for all primes $p$ dividing $a^n-1$ , there exists a positive integer $m<n$ such that $p\\mid a^m-1$ .",
"role": "user... | math | {
"ground_truth": "(1, c), (2^c - 1, 2) \\text{ for all } c \\in \\mathbb{N}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Call a number prime-looking if it is composite but not divisible by $2, 3, 5,$ or $7$. The three smallest prime-looking numbers are $121, 143$, and $169$. There are $95$ prime nu... | math | {
"ground_truth": "D) 60",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( x \\) and \\( y \\) be two distinct real numbers such that \\( x^2 - 2000x = y^2 - 2000y \\). What is the value of \\( x + y \\)?",
"role": "user"
}
] | math | {
"ground_truth": "2000",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jose is 4 years younger than Zack, Zack is 3 years older than Inez, and Inez is 15 years old. Find Jose's age.",
"role": "user"
}
] | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function defined on \\(\\mathbf{R}^{+}\\), \\( f(x) = \n\\begin{cases} \n\\left|\\log_3(x) - 1\\right| & \\text{if } 0 < x \\leq 9,\\\\ \n4 - \\sqrt{x} & \\text{if } x ... | math | {
"ground_truth": "(81, 144)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $2a + 3 = 2b + 4 = 2c + 5 = 2d + 6 = a + b + c + d + 10$. Find the value of $a + b + c + d$.\nA) -4 \nB) -10 \nC) -11 \nD) -19 \nE) -20",
"role": "user"
}
] | math | {
"ground_truth": "C) -11",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the maximum and minimum values of the function:\n\n1) \\( z = x^{2} - y^{2} + 2a^{2} \\) in the circle \\( x^{2} + y^{2} \\leqslant a^{2} \\);\n\n2) \\( v = 2x^{3} + 4x^{2} ... | math | {
"ground_truth": "0 \\text{ and } 32",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the real part is equal to the imaginary part for the complex number $$\\frac {2+ai}{1+2i}$$, find the real number $a$.",
"role": "user"
}
] | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find a monic polynomial of degree $4,$ in $x,$ with rational coefficients such that $\\sqrt{2} + \\sqrt{5}$ is a root of the polynomial.",
"role": "user"
}
] | math | {
"ground_truth": "x^4 - 14x^2 + 9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given \\(2^{\\log_{2}(5)} = 3x + 4\\), solve for the value of \\(x\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A bug (of negligible size) starts at the origin of the coordinate plane. For its first move, it travels 2 units right to $(2,0)$. It then continues following a sequence where eac... | math | {
"ground_truth": "\\text{(B)} \\ \\left(1.6, 1.2\\right)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A torus (donut shape) with an inner radius of $3$ and an outer radius of $5$ is placed on a flat table. Determine the radius of the largest spherical ball that can be positioned ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all values of $x$ in the interval $0 \\leq x \\leq 2\\pi$ which satisfy the inequality \\[ 2 \\cos{x} \\leq \\sqrt{1+\\sin{2x}}-\\sqrt{1-\\sin{2x}} \\leq \\sqrt{2}.... | math | {
"ground_truth": "x \\in \\left[\\frac{\\pi}{4}, \\frac{7\\pi}{4}\\right]",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A triangle has side lengths of 7, 24, and 25. Determine the inradius of the triangle.\nA) 2\nB) 3\nC) 4\nD) 5",
"role": "user"
}
] | math | {
"ground_truth": "The correct answer is B) 3.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given is a natural number $n \\geq 3$ . Solve the system of equations: $\\[\n\\begin{cases}\n\\tan (x_1) + 3 \\cot (x_1) &= 2 \\tan (x_2) \n\\tan (x_2) + 3 \\cot (x_2) &= 2 \\ta... | math | {
"ground_truth": "(x_1, x_2, \\ldots, x_n) \\in \\pi \\mathbb{Z}^n \\pm \\left( \\frac{\\pi}{3}, \\frac{\\pi}{3}, \\ldots, \\frac{\\pi}{3} \\right)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the sequence $\\left\\{a_{n}\\right\\}$, $a_{4}=1$ and $a_{11}=9$, and the sum of any three consecutive terms is 15. Find $a_{2016}$.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( S = \\{1, 2, 3, \\ldots, 20\\} \\) be the set of all positive integers from 1 to 20. Suppose that \\( N \\) is the smallest positive integer such that exactly eighteen nu... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $Q$ be a point inside triangle $DEF$. Let $H_1$, $H_2$, and $H_3$ be the centroids of triangles $QEF$, $QFD$, and $QDE$, respectively. If the area of triangle $DEF$ is 24, fi... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\( 3 \\cdot 4^{x} + \\frac{1}{3} \\cdot 9^{x+2} = 6 \\cdot 4^{x+1} - \\frac{1}{2} \\cdot 9^{x+1} \\).",
"role": "user"
}
] | math | {
"ground_truth": "x = -\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Paul fi\flls in a $7\\times7$ grid with the numbers $1$ through $49$ in a random arrangement. He then erases his work and does the same thing again, to obtain two diff\u000... | math | {
"ground_truth": "73.5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Maria and Bilyana play the following game. Maria has $2024$ fair coins and Bilyana has $2023$ fair coins. They toss every coin they have. Maria wins if she has strictly more ... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On an island, there are knights, who always tell the truth, and liars, who always lie.\n\nOne day, 80 islanders gathered, each wearing a T-shirt numbered from 1 to 80 (with diffe... | math | {
"ground_truth": "70",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the solution set of the inequality $|kx - 4| \\leq 2$ is $\\{x|1 \\leq x \\leq 3\\}$, then the real number $k$ is equal to \\_\\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $\\frac{9}{7\\times 53}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{0.9}{0.7 \\times 53}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that line segment $\\overline{AB}$ is a diameter of a circle with $AB=24$, find the area of the region bounded by the curve traced out by the centroid of $\\triangle{ABC}$.... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "James has 6 ounces of tea in a ten-ounce mug and 6 ounces of milk in a separate ten-ounce mug. He first pours one-third of the tea from the first mug into the second mug and stir... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate: $\\sqrt{4}+\\sqrt[3]{-8}-\\frac{\\sqrt{6}-\\sqrt{24}}{\\sqrt{2}}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Mark conversely starts with $\\frac{1}{16}$ displayed on a calculator with the reciprocal key. What is the fewest number of times he must depress the $\\boxed{\\frac{1}{x}}$ key ... | math | {
"ground_truth": "B) 2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all $(m, n)$ positive integer pairs such that both $\\frac{3n^2}{m}$ and $\\sqrt{n^2+m}$ are integers.",
"role": "user"
}
] | math | {
"ground_truth": "n = a, m = 3a^2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(2016·Hebei Huanghua) Choose the appropriate numbers to fill in the corresponding brackets (each number can only be chosen once). \n150 1 1.5 1350 50 15 \nXiaojun is a six... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
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