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": "Lark has noted down some clues about her new locker combination, which is again a sequence of three numbers. Each number in the combination is within the range from 1 to 50. The ... | math | {
"ground_truth": "3750",
"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 value of the number $7.845\\times 10^{-6}$, $\\frac{7845}{1000}\\times 10^{-6}$, $78.45\\times 10^{-7}$, $\\frac{785}{100000000}$ in scientific notation, and find t... | math | {
"ground_truth": "\\textbf{(C)}\\ 785\\times 10^{-9}",
"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": "For each integer $1\\le j\\le 2017$ , let $S_j$ denote the set of integers $0\\le i\\le 2^{2017} - 1$ such that $\\left\\lfloor \\frac{i}{2^{j-1}} \\right\\rfloor$ is an o... | math | {
"ground_truth": "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": "Given nine cubes with volumes $512$, $343$, $216$, $125$, $64$, $27$, $8$, $1$, and $0.125$ cubic units, stacked vertically from bottom to top in decreasing order, find the total... | math | {
"ground_truth": "948.25",
"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": "If $A$ and $B$ are fixed points on a given circle and $XY$ is a variable diameter of the same circle, determine the locus of the point of intersection of lines $AX$ and $BY$. You... | math | {
"ground_truth": "x^2 + \\left(y - \\frac{1}{b}\\right)^2 = \\frac{a^2}{b^2}",
"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": "Calculate the result of $(\\sqrt{3}-2)(\\sqrt{3}-2)$.",
"role": "user"
}
] | math | {
"ground_truth": "7-4\\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": "Given nonzero numbers $p$, $q$, and $r$, define\n$$\n\\text{{J}}(p, q, r) = \\frac{p}{q} + \\frac{q}{r} + \\frac{r}{p}\n$$\nand\n$$\n\\text{{K}}(p, q, r) = \\frac{p+q}{r} + \\fra... | math | {
"ground_truth": "13.5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an isosceles triangle $ABC$ with $AB = AC = 40$ units and $BC = 24$ units, let $CX$ be the angle bisector of $\\angle BCA$. Find the ratio of the area of $\\triangle BCX$ t... | math | {
"ground_truth": "\\frac{3}{5}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute the integral\n\n$$\nI = \\int_{1}^{i} \\frac{\\ln ^{3} z}{z} \\, d z\n$$\n\nalong the arc of the circle $|z| = 1$ ($\\ln z$ is the principal value of the logarithm, $\\ln... | math | {
"ground_truth": "\\frac{\\pi^4}{64}",
"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": "$\\frac{900^2}{306^2-294^2}$ can be simplified to a positive value.",
"role": "user"
}
] | math | {
"ground_truth": "112.5",
"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": "Given that the product of Kiana's age and the ages of her two older twin brothers is $128$, calculate the sum of their three ages.",
"role": "user"
}
] | math | {
"ground_truth": "18",
"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": "Circle \\(P\\) is located on the coordinate plane with its center at \\((5, -4)\\). One endpoint of a diameter is at \\((0, -9)\\). What are the coordinates of the other endpoint... | math | {
"ground_truth": "(10, 1)",
"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 a triangle \\(ABC\\), let \\(D\\), \\(E\\), and \\(F\\) be the midpoints of sides \\(BC\\), \\(AC\\), and \\(AB\\) respectively.\n\nThe two medians \\(AD\\) and \\(BE\\) ar... | math | {
"ground_truth": "22.5",
"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": "The graph of the function $f(x)=\\sin(\\omega x+\\frac{π}{6})(\\omega>0)$ is shifted to the left by $\\frac{π}{2\\omega}$ to obtain the graph of $g(x)$. If the function $g(x)$ is... | math | {
"ground_truth": "(0,\\frac{5}{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": "Given the geometric sequence $\\{a_n\\}$, where $a_1$ and $a_5$ are the two real roots of the equation $x^2-12x+9=0$, find the value of $a_3$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "An ordered pair $(a, c)$ of integers, each of which has an absolute value less than or equal to 6, is chosen at random. What is the probability that the equation $ax^2 - 3ax + c ... | math | {
"ground_truth": "\\frac{167}{169}",
"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 square sheet of paper with sides of length $10$ cm is initially folded in half horizontally. The folded paper is then folded diagonally corner to corner, forming a triangular s... | math | {
"ground_truth": "\\frac{15 + \\sqrt{125}}{40}",
"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 volume of a cube whose surface area is three times that of a cube with volume 8 cubic units?\nA) $12\\sqrt{3}$\nB) $24$\nC) $24\\sqrt{3}$\nD) $48$\nE) $72$",
"rol... | math | {
"ground_truth": "C) \\ 24\\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": "The probability it will rain on Friday is $30\\%$, the probability it will rain on Saturday is $50\\%$, and the probability it will rain on Sunday is $40\\%$. Assuming the probab... | math | {
"ground_truth": "10.5\\%",
"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 regular hexagon has a side length of 12 cm. A rhombus is formed by joining the midpoints of alternating sides of the hexagon. Calculate the area of this rhombus in square centi... | math | {
"ground_truth": "72\\sqrt{3} \\text{ cm}^2",
"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 relatively prime date is defined as a date where the day and the month number are coprime. Determine how many relatively prime dates are in the month with 31 days and the highe... | math | {
"ground_truth": "11",
"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 $0 < \\alpha < \\frac{\\pi}{2}$ and $0 < \\beta < \\frac{\\pi}{2}$, if $\\sin\\left(\\frac{\\pi}{3}-\\alpha\\right) = \\frac{3}{5}$ and $\\cos\\left(\\frac{\\beta}{2} ... | math | {
"ground_truth": "\\frac{11\\sqrt{5}}{25}",
"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 roots of the equation \\((x^2-5x+6)(x-3)(x+2)=0\\).",
"role": "user"
}
] | math | {
"ground_truth": "-2, 2, 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 the parabola $x^2=4y$ with focus $F$, and $P$ is a moving point on the parabola. \n(1) When $|PF|=2$, find the coordinates of point $P$; \n(2) A line passing through $F$ ... | math | {
"ground_truth": "4\\sqrt{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": "BdMO National 2016 Higher Secondary \n\n<u>**Problem 4:**</u>\nConsider the set of integers $ \\left \\{ 1, 2, ......... , 100 \\right \\} $ . Let $ \\left \\{ x_1, x_2, ...... | math | {
"ground_truth": "198",
"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": "(1) If $x > 0$, find the minimum value of $f(x)=\\frac{12}{x}+3x$;\n\n(2) Given $0 < x < \\frac{1}{3}$, find the maximum value of $f(x)=x(1-3x)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{12}",
"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": "x is chosen at random from the interval [0, a] (with the uniform distribution). y is chosen similarly from [0, b], and z from [0, c]. The three numbers are chosen independently, ... | math | {
"ground_truth": "\\frac{c^2}{2} \\left(\\frac{1}{a} + \\frac{1}{b} + \\frac{1}{c}\\right)\n- \\frac{2c^3}{3} \\left(\\frac{1}{ab} + \\frac{1}{bc} + \\frac{1}{ca}\\right)\n+ \\frac{3c^4}{4abc}",
"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": "Consider the numbers $\\{24,27,55,64,x\\}$ . Given that the mean of these five numbers is prime and the median is a multiple of $3$ , compute the sum of all possible positive i... | math | {
"ground_truth": "60",
"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": "Calculate the sum\n\n$$\nS=\\frac{2015}{3 \\cdot 8}+\\frac{2015}{8 \\cdot 13}+\\frac{2015}{13 \\cdot 18}+\\ldots+\\frac{2015}{2008 \\cdot 2013}\n$$\n\nIn the answer, indicate the... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two circles with equations $x^2 + y^2 - 6x + 4y - 8 = 0$ and $x^2 + y^2 - 8x + 2y + 4 = 0$ intersect at points $C$ and $D$. Compute the slope of line $\\overline{CD}$.",
"rol... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $a_1, a_2, a_3, . . . , a_{99}$ is a permutation of $1, 2, 3, . . . , 99,$ find the maximum possible value of $$ |a_1 - 1| + |a_2 - 2| + |a_3 - 3| + \\dots + |a_{... | math | {
"ground_truth": "4900",
"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 mustache is created by taking the set of points $(x, y)$ in the $xy$ -coordinate plane that satisfy $4 + 4 \\cos(\\pi x/24) \\le y \\le 6 + 6\\cos(\\pi x/24)$ and $-24 \\... | math | {
"ground_truth": "96",
"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 price of an article is cut by $20\\%$. To restore it to its original price, the new price must be increased by:\nA) 20%\nB) 22.5%\nC) 25%\nD) 27.5%\nE) none of these answers"... | math | {
"ground_truth": "C) 25%",
"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": "Petya created all the numbers that can be made from the digits 2, 0, 1, 8 (each digit can be used no more than once). Find their total sum.",
"role": "user"
}
] | math | {
"ground_truth": "78331",
"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": "Select points $T_1,T_2$ and $T_3$ in $\\mathbb{R}^3$ such that $T_1=(0,1,0)$ , $T_2$ is at the origin, and $T_3=(1,0,0)$ . Let $T_0$ be a point on the line $x=y=0$ ... | 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": "The expression $\\circ \\ 1\\ \\circ \\ 2 \\ \\circ 3 \\ \\circ \\dots \\circ \\ 2012$ is written on a blackboard. Catherine places a $+$ sign or a $-$ sign into each blan... | math | {
"ground_truth": "1006",
"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": "Which of the following statements is incorrect? \n① Inductive reasoning and analogical reasoning both involve reasoning from specific to general. \n② When making an analogy, it... | math | {
"ground_truth": "①②④",
"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": "Given that the focus of the parabola $y^{2}=8x$ is $F$, two perpendicular lines $l_{1}$ and $l_{2}$ are drawn passing through point $F$. Let these lines intersect the parabola at... | math | {
"ground_truth": "128",
"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": "David drives from his house to a meeting location. In the first hour, he drives 40 miles, but he calculates that he will be 40 minutes late if he continues at this rate. He incre... | math | {
"ground_truth": "B) 120 miles",
"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": "Trapezoid $EFGH$ has bases $EF = 24$ units and $GH = 36$ units. Diagonals $EG$ and $FH$ intersect at point $Y$. The area of trapezoid $EFGH$ is $360$ square units. Determine the ... | math | {
"ground_truth": "57.6 \\text{ square units}",
"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 certain population grows by $10\\%$ from year $1$ to year $2$ and then by $20\\%$ from year $2$ to year $3$. What is the total percentage increase in the population from year $... | math | {
"ground_truth": "C) 32%",
"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 $ABC$, a point $E$ lies on side $\\overline{BC}$ such that $BE=EC$, and point $F$ lies on $\\overline{AC}$ such that $\\overline{BF}$ is the angle bisector of $\\angl... | math | {
"ground_truth": "\\textbf{(B) }67.5^\\circ",
"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": "Ninety-eight apples who always lie and one banana who always tells the truth are randomly arranged along a line. The first fruit says \"One of the first forty fruit is the banana... | math | {
"ground_truth": "21",
"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 ratio of $a$ to $b$ is to be determined where $b = a+3d$. Calculate the ratio of $a$ to $b$.",
"role": "user"
}
] | 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": "All angles of $ABC$ are in $(30,90)$ . Circumcenter of $ABC$ is $O$ and circumradius is $R$ . Point $K$ is projection of $O$ to angle bisector of $\\angle B$ , point... | math | {
"ground_truth": "60^\\circ",
"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": "If $x, y > 0$ and $x \\neq y$, evaluate the expression $\\log_x y \\cdot \\log_y x \\cdot \\log_x x$.\nA) 0\nB) 1\nC) x\nD) y",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(B)}\\ 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": "Find the general solution of the equation\n\n$$\ny'' + 3y' + 2y = 2x^2 - 4x - 17\n$$",
"role": "user"
}
] | math | {
"ground_truth": "y = C_1 e^{-x} + C_2 e^{-2x} + x^2 - 5x - 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": "If\n\\[\\frac{\\sin x}{\\cos y} + \\frac{\\sin y}{\\cos x} = 2 \\quad \\text{and} \\quad \\frac{\\cos x}{\\sin y} + \\frac{\\cos y}{\\sin x} = 3,\\]\nthen find \\(\\frac{\\tan x}... | math | {
"ground_truth": "\\frac{1}{2}",
"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 circles $A$ and $B$ each have a radius of 1, and they share one point of tangency, and circle $C$ has a radius of 2 and touches the midpoint of line segment $\\overline{AB}... | math | {
"ground_truth": "\\frac{10\\pi}{3} + 2\\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": "Let $f$ be a real-valued function defined on the positive integers satisfying the following condition: For all $n>1$ there exists a prime divisor $p$ of $n$ such that $f... | math | {
"ground_truth": "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": "Consider all possible 100-digit natural numbers that contain only the digits 1 and 2 in their decimal representation. How many of them are divisible by 3?",
"role": "user"
... | math | {
"ground_truth": "\\frac{2^{100} + 2}{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": "Given that the car ran exclusively on its battery for the first $60$ miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of $0.03$ gallons ... | math | {
"ground_truth": "108",
"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": "If the tangent line to the curve $y=x^2+ax+b$ at the point $(0, b)$ is $y=x+1$, then $a=\\ $, $b=\\ $.",
"role": "user"
}
] | math | {
"ground_truth": "1, 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": "If $\\tan \\theta = -2$, then calculate $\\frac{\\sin \\theta(1+\\sin 2\\theta)}{\\sin \\theta+\\cos \\theta}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2}{5}",
"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 lateral edge of a pyramid is divided into 100 equal parts, and through the points of division, planes parallel to the base are drawn. Find the ratio of the areas of the large... | math | {
"ground_truth": "9801",
"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 \\( F_n \\) be the \\( n \\)th number in the modified Fibonacci sequence, where \\( F_1 = 2 \\), \\( F_2 = 3 \\), and \\( F_{n+1} = F_n + F_{n-1} \\). Calculate:\n\\[\n\\prod... | math | {
"ground_truth": "(50, 51)",
"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": "Convex pentagon $ABCDE$ is inscribed in circle $\\gamma$ . Suppose that $AB=14$ , $BE=10$ , $BC=CD=DE$ , and $[ABCDE]=3[ACD]$ . Then there are two possible values for the ... | math | {
"ground_truth": "417",
"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 circular disc with diameter $D$ is placed on an $8\\times 8$ checkerboard with width $D$ so that the centers coincide. Find the number of checkerboard squares which are complet... | math | {
"ground_truth": "32",
"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": "Determine the least value of \\(x\\) for which \\(4x^2 + 8x + 3 = 1\\).",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"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 \\(a_0=-3, b_0=2\\), and for \\(n\\geq 0\\), define:\n\\begin{align*}\na_{n+1} &= a_n + b_n + 2\\sqrt{a_n^2 + b_n^2},\\\\\nb_{n+1} &= a_n + b_n - 2\\sqrt{a_n^2 + b_n^2}.\n\\e... | math | {
"ground_truth": "-\\frac{1}{6}",
"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 $H$ be the orthocenter and $Q$ the centroid of triangle $ABC.$ For all points $P$ on the circumcircle of triangle $ABC,$\n\\[PA^2 + PB^2 + PC^2 + QA^2 + QB^2 + QC^2 - PH^2 - ... | math | {
"ground_truth": "a^2 + b^2 + c^2 - 4R^2",
"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": "If $F_1$ and $F_2$ are the left and right foci of the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$, determine the eccentricity of the hyperbola $C$.",
"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": "The ratio of rabbits to guinea pigs in a pet shop is 5:4. If there are 25 rabbits, how many guinea pigs are there?",
"role": "user"
}
] | math | {
"ground_truth": "20",
"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": "Calculate the area of a polygon with vertices at (2,1), (4,3), (6,1), and (4,6).",
"role": "user"
}
] | math | {
"ground_truth": "6",
"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 that $m$, $n$, and $4$ are the lengths of the sides of an isosceles triangle (which is not an equilateral triangle), and $m$ and $n$ are the two roots of the quadratic equa... | math | {
"ground_truth": "6$ or $7",
"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 mean age of Amanda's 4 cousins is 8, and their median age is 5. Calculate the sum of the ages of Amanda's youngest and oldest cousins.",
"role": "user"
}
] | math | {
"ground_truth": "22",
"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": "In each cell of the table $4 \\times 4$ , in which the lines are labeled with numbers $1,2,3,4$ , and columns with letters $a,b,c,d$ , one number is written: $0$ or $1$ ... | math | {
"ground_truth": "90",
"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 real solutions of the equation: $$ x=\\frac{2z^2}{1+z^2} $$ $$ y=\\frac{2x^2}{1+x^2} $$ $$ z=\\frac{2y^2}{1+y^2} $$",
"role": "user"
}
] | math | {
"ground_truth": "(0, 0, 0)",
"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 kingdom's road map is given. Cities are represented by numbers, and the segments represent roads. Once, a wandering knight started his journey in one of the kingdom's cities an... | math | {
"ground_truth": "2 \\text{ and } 6",
"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 $z=1+i$, then $|{iz+3\\overline{z}}|=\\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | math | {
"ground_truth": "2\\sqrt{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 $m \\in \\mathbb{R}$, and the complex number $z = m^2-1+(m+1)i$ represents a pure imaginary number. Find the value of $m$.",
"role": "user"
}
] | 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": "Let $ m,n > 1$ are integers which satisfy $ n|4^m \\minus{} 1$ and $ 2^m|n \\minus{} 1$ . Is it a must that $ n \\equal{} 2^{m} \\plus{} 1$ ?",
"role": "user"
}
] | math | {
"ground_truth": "n = 2^m + 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": "Arnaldo and Bernaldo play a game where they alternate saying natural numbers, and the winner is the one who says $0$ . In each turn except the first the possible moves are deter... | math | {
"ground_truth": "0",
"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 triangle $\\triangle ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$ respectively. Given that $b^{2}+c^{2}-a^{2}=ac\\cos C+c^{2}\\... | 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": "Let \\( A \\) and \\( B \\) be non-empty subsets of \\(\\{1, 2, \\cdots, 10\\}\\), with the condition that the smallest element of set \\( A \\) is not less than the largest elem... | math | {
"ground_truth": "9217",
"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": "Half of the yellow flowers are tulips, two-thirds of the red flowers are daffodils, and four-sevenths of the flowers are yellow. Calculate the percentage of the flowers that are ... | math | {
"ground_truth": "57\\%",
"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": "The circle is defined by the equation \\( x^2 + y^2 = 25 \\) and it intersects with the line \\( y = x + 3 \\). Find the distance between the two intersection points of the line ... | math | {
"ground_truth": "C) \\ 6\\sqrt{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": "Given a circle $\\omega$ with radius $1$ . Let $T$ be a set of triangles good, if the following conditions apply:\n(a) the circumcircle of each triangle in the set $T$ is ... | 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": "For a positive integer $n$ and nonzero digits $a$, $b$, and $d$, let $A_n$ be the $n$-digit integer each of whose digits is equal to $a$; let $B_n$ be the $n$-digit integer each ... | math | {
"ground_truth": "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": "In a game of Chomp, two players alternately take bites from a 5-by-7 grid of [unit squares](https://artofproblemsolving.com/wiki/index.php/Unit_square). To take a bite, a player ... | math | {
"ground_truth": "330",
"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": "Find the number of ordered pairs of positive integers \\( (a, b) \\) such that \\( a + b = 500 \\) and neither \\( a \\) nor \\( b \\) has a zero digit.",
"role": "user"
}
... | math | {
"ground_truth": "414",
"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 the function $f(x)$ is an odd function defined on $\\mathbb{R}$, and for $x > 0$, $f(x) = x^2 - 2x - 3$, find the number of integer solutions for the inequality $f(x) ... | math | {
"ground_truth": "4",
"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 $P$ and $Q$ be the midpoints of sides $AB$ and $BC,$ respectively, of $\\triangle ABC.$ Suppose $\\angle A = 30^{\\circ}$ and $\\angle PQC = 110^{\\circ}.$ Find... | math | {
"ground_truth": "80^\\circ",
"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 power function f(x) passes through the point (3, 9), determine the interval of monotonic increase for the function f(x).",
"role": "user"
}
] | math | {
"ground_truth": "[0, +\\infty)",
"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": "Determine the approximate interval containing the roots of the function $f(x)=\\log_{2} x + 2x - 4$.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{A: (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": "What is the maximum number of coins can be arranged in cells of the table $n \\times n$ (each cell is not more of the one coin) so that any coin was not simultaneously below an... | math | {
"ground_truth": "f(n) = \\frac{n^2}{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": "Let the plane region \\( T = \\{(x, y) \\mid x > 0, y > 0, x y \\leq 48\\} \\). Determine the number of lattice points inside \\( T \\).",
"role": "user"
}
] | math | {
"ground_truth": "202",
"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 circular base of a hemisphere of radius $2$ rests on the base of a square pyramid of height $6$. The hemisphere is tangent to the other four faces of the pyramid. Find the ed... | math | {
"ground_truth": "3",
"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": "An object moves $8$ cm in a straight line from $A$ to $B$, turns at an angle $\\alpha$, measured in radians and chosen at random from the interval $(0,\\pi)$, and moves $5$ cm in... | math | {
"ground_truth": "\\frac{1}{3}",
"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": "Let $\\mathcal S$ be the sphere with center $(0,0,1)$ and radius $1$ in $\\mathbb R^3$ . A plane $\\mathcal P$ is tangent to $\\mathcal S$ at the point $(x_0,y_0,z_0... | math | {
"ground_truth": "\\frac{40}{21}",
"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": "An object in the plane moves from the origin and takes a ten-step path, where at each step the object may move one unit to the right, one unit to the left, one unit up, or one un... | math | {
"ground_truth": "221",
"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 $\\triangle ABC$, $AB=6$, $BC=8$, $AC=10$, and $D$ is on $\\overline{AC}$ such that $BD=6$, calculate the ratio of $AD:DC$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{16}",
"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": "Fold rectangle $ABCD$ as shown in the accompanying diagram, so that triangle $DCF$ falls onto the position of triangle $DEF$, with vertex $E$ exactly landing on edge $AB$. Given ... | math | {
"ground_truth": "40^\\circ",
"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": "An insect lives on the surface of a cube with edges of length 2. It wishes to travel from the midpoint of one edge to the midpoint of an opposite edge (not sharing a face) on the... | math | {
"ground_truth": "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": "Let \\( p \\) and \\( q \\) be real numbers so that the roots of\n\\[ z^2 + (12 + pi) z + (30 + qi) = 0 \\]\nare complex conjugates. Determine the ordered pair \\( (p, q) \\).",
... | math | {
"ground_truth": "(0,0)",
"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 inequality about $x$, $m - |x - 2| \\geq 1$, its solution set is $[0, 4]$.\n(Ⅰ) Find the value of $m$;\n(Ⅱ) If $a$ and $b$ are both positive real numbers, and satisfy $... | math | {
"ground_truth": "\\frac{9}{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 the sum\n\n$$\na^{2000}+\\frac{1}{a^{2000}}\n$$\n\nif $a^{2}-a+1=0$.",
"role": "user"
}
] | math | {
"ground_truth": "-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": "A box contains 10 red balls and 8 green balls. 4 balls are drawn at random. What is the probability of drawing 2 red balls and 2 green balls?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{7}{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 that $0 < m < \\frac{1}{2}$, find the maximum value of $k$ such that $\\frac{1}{m} + \\frac{2}{1-2m} \\geq k$ always holds true.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"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": "Given $\\sqrt{x+2}=3$, calculate the value of $(x+2)^3$.",
"role": "user"
}
] | math | {
"ground_truth": "729",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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