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": "Rationalize the denominator of \\(\\frac{4}{\\sqrt[3]{5} - \\sqrt[3]{2}}\\). Provide your answer in the form \\(\\frac{\\sqrt[3]{A} + \\sqrt[3]{B} + \\sqrt[3]{C}}{D}\\), where th... | math | {
"ground_truth": "159",
"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 vectors $\\overrightarrow {p} =(\\sin A, \\cos A)$ and $\\overrightarrow {q} = (\\sqrt {3}\\cos A, -\\cos A)$ (where $\\overrightarrow {q} \\neq \\overrightarrow {0}$),... | math | {
"ground_truth": "\\frac{\\sqrt{3}}{2} < b + c \\leq 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": "A line $l$ passes through the focus $F$ of the parabola $y^2=2px(p > 0)$ and has an inclination angle of $\\frac{\\pi}{3}$, intersecting the parabola at points $A$ and $B$ in the... | 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": "For what value of $k$ does the line represented by the equation $3kx - k = -4y - 2$ contain the point $(2, 1)$?",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{6}{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 set $T$ of points in the $xy$-plane is symmetric about both coordinate axes and the line $y=-x$. If $(1,4)$ is in $T$, calculate the smallest number of points in $T$.",
"ro... | 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": "A merchant bought several sacks of salt in Tver and sold them in Moscow with a profit of 100 rubles. With all the money earned, he bought salt again in Tver (at Tver prices) and ... | math | {
"ground_truth": "500",
"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": "Rectangle $ABCD$ is inscribed in triangle $PQR$ such that side $AD$ of the rectangle lies along side $QR$ of the triangle, as shown. The triangle's altitude from $P$ to side $QR$... | math | {
"ground_truth": "27",
"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 set $T$ of points in the $xy$-plane is symmetric about the origin, both coordinate axes, and the line $y = x$, and that the point $(1,4)$ is in $T$, find the smalles... | 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": "Determine constants $a_1$ and $a_2$ such that:\n\\[a_1 \\begin{pmatrix} 3 \\\\ 4 \\end{pmatrix} + a_2 \\begin{pmatrix} -3 \\\\ 6 \\end{pmatrix} = \\begin{pmatrix} 0 \\\\ 5 \\end{... | math | {
"ground_truth": "\\left(\\frac{1}{2}, \\frac{1}{2}\\right)",
"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 expression $kxy^2$, if the value of $x$ is decreased by 25% and the value of $y$ is decreased by 35%, find the new value of the expression in terms of its original valu... | math | {
"ground_truth": "\\frac{507}{1600}kxy^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 the function \\( f(x)=\\sin \\left(x+\\frac{\\pi}{6}\\right)+\\sin \\left(x-\\frac{\\pi}{6}\\right)+a \\cos x+b \\) (where \\(a\\) and \\(b\\) are real constants),\n\n1. Fi... | math | {
"ground_truth": "a=-1, b=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": "The natural numbers from 1 to 100 are arranged on a circle with the characteristic that each number is either larger as their two neighbours or smaller than their two neighbours.... | math | {
"ground_truth": "51",
"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 four points $P(-5,0), Q(0,-5), R(0,10),$ and $S(15,k)$ are placed on the Cartesian plane. If segment $PQ$ is parallel to segment $RS$, what is the value of $k$?",
"role":... | math | {
"ground_truth": "k = -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": "If a positive function \\( f(x) \\) defined on a set \\( D \\) satisfies the following inequality for any \\( x, y \\in D \\):\n$$\nf(x) f(y) \\leqslant\\left[f\\left(\\frac{x+y}... | math | {
"ground_truth": "f\\left(x_1\\right) f\\left(x_2\\right) \\cdots f\\left(x_n\\right) \\leqslant \\left[f\\left(\\frac{x_1 + x_2 + \\cdots + x_n}{n}\\right)\\right]^n",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For the nonzero numbers $x$, $y$, and $z$, define $$\n\\text{K}(x,y,z) = \\frac{x}{y} + \\frac{y}{z} + \\frac{z}{x}.\n$$ Find $\\text{K}(3, 27, 12)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{229}{36}",
"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 four times the reciprocal of the circumference of a circle equals the diameter of the circle, find the area of the circle.",
"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 a cube with side length $10$ and balls of clay with radius $3$, find the maximum number of balls that can completely fit inside the cube.",
"role": "user"
}
] | 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": "Let \\(\\mathbf{d} = \\begin{pmatrix} -4 \\\\ 12 \\\\ 2 \\end{pmatrix},\\) \\(\\mathbf{e} = \\begin{pmatrix} 6 \\\\ 2\\pi \\\\ 1 \\end{pmatrix},\\) and \\(\\mathbf{f} = \\begin{p... | math | {
"ground_truth": "328 - 136\\pi",
"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": "How many minutes will pass before the clock next shows a time with all digits identical?",
"role": "user"
}
] | math | {
"ground_truth": "316",
"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 torpedo boat is anchored 9 km from the nearest point on the shore. A messenger needs to be sent from the boat to a camp located 15 km along the shore from the nearest point of ... | math | {
"ground_truth": "12",
"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 power function $f(x)$ passes through the point $(2, 16)$. Therefore, $f(x) = \\boxed{x^4}$.",
"role": "user"
}
] | math | {
"ground_truth": "x^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": "An artist has 20 cubes, each with an edge of 1 meter. He arranges them on the ground to form a four-layer sculpture. The top layer has 1 cube, the second layer has 4 cubes, the t... | math | {
"ground_truth": "42",
"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": "Point $A(1,2)$, $B(-2,0)$, if a point $P$ on the line $l: x-y+3=0$ makes $PA+PB$ the smallest, then the coordinates of point $P$ are.",
"role": "user"
}
] | math | {
"ground_truth": "\\left(- \\dfrac{5}{3}, \\dfrac{4}{3}\\right)",
"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 a number $N,N \\ne 0$, diminished by five times its reciprocal and increased by the square of $N$, equals a given real constant $R$, find the sum of all such possible values o... | 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": "In a classroom of 48 students, 15 prefer chocolate pie, 10 prefer apple, and 9 prefer blueberry. Half of the remaining students prefer cherry pie, and the other half prefer banan... | math | {
"ground_truth": "52.5^\\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": "Let \\( z_{n} = \\left(\\frac{1-\\mathrm{i}}{2}\\right)^{n}, n \\in \\mathbf{N}_{+} \\). Define \\( S_{n} = \\sum_{k=1}^{n}\\left|z_{k+1} - z_{k}\\right| \\). Find \\( \\lim_{n \... | math | {
"ground_truth": "1 + \\frac{\\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": "Solve the following system of equations:\n\n$$\n\\begin{aligned}\n2 x_{1}-2 x_{2} & =A \\\\\n-x_{1}+4 x_{2}-3 x_{3} & =0 \\\\\n-2 x_{2}+6 x_{3}-4 x_{4} & =0 \\\\\n-3 x_{3}+8 x_{4... | math | {
"ground_truth": "x_i = \\frac{(n+1-i) A + i B}{i (n + 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 number of ounces of water needed to dilute 12 ounces of a shaving lotion containing 60% alcohol to a lotion containing 25% alcohol is to be calculated.",
"role": "user"
... | math | {
"ground_truth": "16.8",
"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": "The ellipse \\( x^{2} + 2y^{2} = 3 \\) is rotated one full revolution around the y-axis to form a surface of revolution \\(\\Sigma\\). Let \\( P(x, y, z) \\) be a point on \\(\\S... | math | {
"ground_truth": "x^2 + 2y^2 + z^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": "Let $n$ be a positive integer. Find, with proof, the least positive integer $d_{n}$ which cannot be expressed in the form \\[\\sum_{i=1}^{n}(-1)^{a_{i}}2^{b_{i}},\\]\nwhere ... | math | {
"ground_truth": "d_n = 2 \\frac{4^n - 1}{3} + 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": "Given $\\left(x-1\\right)^{10}=a_{0}+a_{1}x+a_{2}x^{2}+\\ldots +a_{10}x^{10}$, calculate the value of $a_{1}+a_{2}+\\ldots +a_{10}$.",
"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": "A regiment of cuirassiers buys a certain number of horses for 11,250 francs. A regiment of dragoons buys fifteen more horses for 16,000 francs. Each dragoon horse is 50 francs ch... | math | {
"ground_truth": "\\begin{array}{l}\n\\text{Number of cuirassier horses: } 25 \\\\\n\\text{Number of dragoon horses: } 40 \\\\\n\\text{Cost per cuirassier horse: } 450 \\text{ francs} \\\\\n\\text{Cost per dragoon horse: } 400 \\text{ francs}\n\\end{array}",
"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 function \\( f \\) maps the set of positive integers onto itself and satisfies the equation\n\n\\[ \nf(f(n)) + f(n) = 2n + 6 \n\\]\n\nWhat could this function be?",
"role... | math | {
"ground_truth": "f(n) = n + 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 booklet contains 154 pages. Each page has the same number of words, and each page has no more than 120 words on it. The total number of words in the booklet is congruent to 207... | math | {
"ground_truth": "100",
"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 the number of intersection points of the three lines $x+y+1=0$, $2x-y+8=0$, and $ax+3y-5=0$ does not exceed 2, then the set of all possible values of $a$ is __________.",
... | 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": "There are $n$ lamps in a row. Some of which are on. Every minute all the lamps already on go off. Those which were off and were adjacent to exactly one lamp which was on will g... | math | {
"ground_truth": "n \\neq 1, 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": "How many Fridays that fall on the 12th can there be in a year? (at most? at least?) And if the year is a leap year?",
"role": "user"
}
] | math | {
"ground_truth": "\\text{Maximum non bissextile : 3} \\\\ \\text{Maximum bissextile : 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": "What is the value of $\\dfrac{(5 \\times 3) + 4}{7}?$",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{19}{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": "The orthocenter of triangle $ABC$ lies on its circumcircle. One of the angles of $ABC$ must equal:\n(The orthocenter of a triangle is the point where all three altitudes inte... | math | {
"ground_truth": "90^\\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 $f(x)=x^{k^{2}-2k-3}(k\\in\\mathbb{N}^{*})$ whose graph is symmetric about the $y$-axis and is a decreasing function in the interval $(0,+\\infty)$, \n$... | math | {
"ground_truth": "(\\ln a)^{0.7} > (\\ln a)^{0.6}",
"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": "The workday decreased from 8 to 7 hours. By what percentage should labor productivity be increased so that, at the same rates, wages increase by 5%?",
"role": "user"
}
] | math | {
"ground_truth": "20",
"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 certain television entertainment game show, each participant needs to complete three events $A$, $B$, and $C$. It is known that the probabilities for contestant Jia to compl... | math | {
"ground_truth": "\\mathbb{E}(X) = \\frac{243a}{128}",
"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": "Alex launches his boat into a river and heads upstream at a constant speed. At the same time at a point $8$ miles upstream from Alex, Alice launches her boat and heads downstre... | 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": "If \\( x, y, \\) and \\( k \\) are positive real numbers such that \n\\[\n4 = k^2\\left(\\dfrac{x^2}{y^2}+\\dfrac{y^2}{x^2}\\right) + k\\left(\\dfrac{x}{y}+\\dfrac{y}{x}\\right),... | math | {
"ground_truth": "1.5",
"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 natural number \\( n \\) is called \"good\" if appending it to the right of any natural number results in a number divisible by \\( n \\). List ten \"good\" numbers that are le... | math | {
"ground_truth": "1, 2, 5, 10, 20, 25, 50, 100, 125, 200",
"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 sunset was reported to be at $8:15\\textsc{pm}$, and the length of daylight was 10 hours and 24 minutes. If the sunrise was at $6:57\\textsc{am}$, determine the actual time o... | math | {
"ground_truth": "5:21\\textsc{pm}",
"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": "There are $n$ boxes which is numbere from $1$ to $n$ . The box with number $1$ is open, and the others are closed. There are $m$ identical balls ( $m\\geq n$ ). One of ... | math | {
"ground_truth": "\\binom{m+n-2}{n-1} - \\binom{m+n-2}{n-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": "For what value of $x$ does $2^{2x} \\cdot 8^{x} = 32^{3}$?\nA) 1 \nB) 2 \nC) 3 \nD) 4 \nE) 5",
"role": "user"
}
] | math | {
"ground_truth": "\\textbf{(C)}\\;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 $f(x) = 5x^2 - 4$ and $g(f(x)) = x^2 + 2x + 3$. Find the sum of all possible values of $g(49)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{136}{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": "Find all permutations $(a_1, a_2,...,a_{2021})$ of $(1,2,...,2021)$ , such that for every two positive integers $m$ and $n$ with difference bigger than $20^{21}$ , the fo... | math | {
"ground_truth": "a_i = i \\text{ for } i = 1, 2, \\ldots, 2021",
"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 rectangle ABCD, where A=(6,-22), B=(2006,178), and D=(8,y), for some integer y, find the area of rectangle ABCD.",
"role": "user"
}
] | math | {
"ground_truth": "40400",
"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 point on the line defined by\n\\[\n\\begin{pmatrix} 3 \\\\ -2 \\\\ 2 \\end{pmatrix} + s \\begin{pmatrix} -1 \\\\ 4 \\\\ -2 \\end{pmatrix}\n\\]\nthat is closest to the po... | math | {
"ground_truth": "\\left( \\frac{17}{7}, \\frac{10}{7}, \\frac{6}{7} \\right)",
"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": "Through $S$ and $V$ are denoted the surface area and volume of a regular $n$-sided pyramid.\n\na) For given values of $n$ and $S$, find the maximum value of $V$.\n\nb) Find the s... | math | {
"ground_truth": "a_1 = 2\\sqrt{2}, \\quad h_1 = 24 \\quad \\text{and} \\quad a_2 = 8, \\quad h_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 three rectangles each with a common base width of $2$ have lengths of $1$, $8$, and $27$, find the sum of the areas of these three rectangles.",
"role": "user"
}... | math | {
"ground_truth": "72",
"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 are six rock specimens with weights of 8.5 kg, 6 kg, 4 kg, 4 kg, 3 kg, and 2 kg. They need to be distributed into three backpacks such that the heaviest backpack is as ligh... | math | {
"ground_truth": "10 \\text{ kg}",
"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": "Four squares, each with a side length of 2 inches, are arranged horizontally. The second square from the left is rotated 45 degrees. Then it is centered and lowered into its orig... | 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": "If \\(x\\), \\(y\\), and \\(z\\) are positive integers with \\(xy = 18\\), \\(xz = 3\\), and \\(yz = 6\\), find the value of \\(x + y + z\\).",
"role": "user"
}
] | math | {
"ground_truth": "10",
"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 a regular star polygon with $n$ points. Each point of the star has two angles associated with it: one at $C_i$ and one at $D_i$ for $i = 1, 2, \\ldots, n$. All $C_i$ ang... | math | {
"ground_truth": "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": "Let $\\mathbf{C}$ and $\\mathbf{D}$ be matrices such that\n\\[\\mathbf{C} + \\mathbf{D} = \\mathbf{C} \\mathbf{D}.\\]\nIf $\\mathbf{C} \\mathbf{D} = \\begin{pmatrix} 5 & 2 \\\\ -... | math | {
"ground_truth": "\\begin{pmatrix} 5 & 2 \\\\ -3 & 6 \\end{pmatrix}",
"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 $\\ell$ be a line with negative slope passing through the point $(20,16)$ . What is the minimum possible area of a triangle that is bounded by the $x$ -axis, $y$ -axis, ... | math | {
"ground_truth": "640",
"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 hyperbola \\[\\frac{(x-5)^2}{7^2} - \\frac{(y+3)^2}{11^2} = 1\\] has two foci, which have different $x-$coordinates. Find the coordinates of the one with the larger $x-$coord... | math | {
"ground_truth": "(5 + \\sqrt{170}, -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": "Determine the value of $c-a$ where the parabolas defined by the equations $y = 3x^2 - 2x + 1$ and $y = -2x^2 + 4x + 1$ intersect at points $(a, b)$ and $(c, d)$, with $c \\geq a$... | math | {
"ground_truth": "\\frac{6}{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": "Find the smallest positive integer $k$ which is representable in the form $k=19^n-5^m$ for some positive integers $m$ and $n$ .",
"role": "user"
}
] | math | {
"ground_truth": "14",
"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 a $10 \\times 10$ chessboard, consisting of ten horizontal and ten vertical lines. Determine the number $r$ of rectangles and the number $s$ of squares that can be forme... | math | {
"ground_truth": "44",
"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 the distance from a point $P$ on the parabola $y^{2}=8x$ to its focus is $9$, find the coordinates of point $P$.",
"role": "user"
}
] | math | {
"ground_truth": "(7,±2 \\sqrt {14})",
"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 $n \\times n$ complex matrix $A$ is called \\emph{t-normal} if $AA^t = A^t A$ where $A^t$ is the transpose of $A$ . For each $n$ ,\ndetermine the maximum dimension o... | math | {
"ground_truth": "\\frac{n(n+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": "Find the smallest positive multiple of 9 that can be written using only the digits: (a) 0 and 1; (b) 1 and 2.",
"role": "user"
}
] | math | {
"ground_truth": "12222",
"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 $\\triangle ABC$, points $D$ and $E$ are on $\\overline{BC}$ and $\\overline{AC}$, respectively. If $\\overline{AD}$ and $\\overline{BE}$ intersect at $T$ so that $AT/DT=2$ an... | 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": "A circle of radius $3$ has center at $(3,0)$. A circle of radius $2$ has center at $(8,0)$. A line is tangent to these two circles at points in the first quadrant. What is the $y... | math | {
"ground_truth": "\\frac{15\\sqrt{26}}{26}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Observe the following equations and answer the following question:<br/>$\\sqrt{1+\\frac{1}{1^2}+\\frac{1}{2^2}}=1+\\frac{1}{1}-\\frac{1}{1+1}=1\\frac{1}{2}$;<br/>②$\\sqrt{1+\\fra... | math | {
"ground_truth": "\\sqrt{1+\\frac{1}{n^2}+\\frac{1}{(n+1)^2}} = 1+\\frac{1}{n(n+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": "Three machine tools, A, B, and C, independently process the same type of parts. The probability that a part processed by machine A is of the first grade and the part processed by... | math | {
"ground_truth": "\\frac{5}{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": "**\nWhat is the smallest three-digit integer \\( n \\) that satisfies \\( 77n \\equiv 231 \\pmod{385} \\)?\n\n**",
"role": "user"
}
] | math | {
"ground_truth": "113",
"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 $\\frac{b}{a} = 3$ and $\\frac{c}{b} = 4$, and if $d = 2b - a$, determine the ratio of $a + b + d$ to $b + c + d$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{20}",
"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 constants $a$ and $b$ such that\n\\[a \\begin{pmatrix} 3 \\\\ 4 \\end{pmatrix} + b \\begin{pmatrix} 1 \\\\ -2 \\end{pmatrix} = \\begin{pmatrix} 5 \\\\ 0 \\end{pmatrix}.... | math | {
"ground_truth": "(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": "On the trip home from the meeting where this AMC $10$ was constructed, the Contest Chair noted that his airport parking receipt had digits of the form $bbcac$, where $0 \\le a < ... | math | {
"ground_truth": "20",
"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 semi-axes of an ellipse are $a$ and $b$, find the maximum area of a triangle that can be inscribed in the ellipse.",
"role": "user"
}
] | math | {
"ground_truth": "ab \\frac{3\\sqrt{3}}{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": "Consider the graphs of \n\\[(1)\\qquad y = x^3 - x^2 - \\frac{1}{2}x + 2\\]\nand\n\\[(2)\\qquad y = x^2 + \\frac{3}{2}x + 4\\]\non the same set of axes. Determine the relative po... | math | {
"ground_truth": "\\textbf{B)} \\((2)\\) passes from below upwards through \\((1)\\) on the left side.",
"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 value of the positive real number \\( k \\) such that for any positive real numbers \\( a \\) and \\( b \\), the following inequality holds:\n$$\n\\sqrt{a^{2}+k ... | math | {
"ground_truth": "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": "If $\\log_5 \\Big(\\log_4 (\\log_3 x) \\Big) = 1$, then $x^{-1/3}$ equals\nA) $\\frac{1}{3^{341}}$\nB) $\\frac{1}{3^{342}}$\nC) $\\frac{1}{3^{340}}$\nD) $\\frac{1}{3^{341.\\overl... | math | {
"ground_truth": "\\frac{1}{3^{341.\\overline{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 \\(i^{2} = -1\\), determine the number of values of \\(n\\) that make \\((n+i)^{4}\\) an integer.",
"role": "user"
}
] | math | {
"ground_truth": "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": "For some positive integers \\( n \\), the fraction \\( \\frac{n+2}{3n^2 + 7} \\) is not in its simplest form. Find the smallest value of \\( n \\).",
"role": "user"
}
] | math | {
"ground_truth": "17",
"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 four-digit number $n$ is said to be *literally 1434* if, when every digit is replaced by its remainder when divided by $5$ , the result is $1434$ . For example, $1984$ is... | math | {
"ground_truth": "67384",
"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 the sum of the real roots of the equation $x^4-4x^3+5x^2-4x+1 = 0$.",
"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": "Given the functions $f_1(x)=x^2+x$, $f_2(x)=2x^2-x$, $f_3(x)=x^2+x$, $g_1(x)=x-2$, $g_2(x)=2x$, and $g_3(x)=x+2$, determine the tuple $(F_1,F_2,F_3)$ by evaluating whether $h(x)=... | math | {
"ground_truth": "(0, 0, 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": "A cone-shaped mountain has its base on the ocean floor and has a total height of 10000 feet. The top $\\frac{2}{5}$ of the volume of the mountain is above water. If the radius of... | math | {
"ground_truth": "1566",
"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 cylindrical tank has a radius of 10 meters and a length of 30 meters. The tank is lying on its side on a flat surface and is filled with water to a depth of 5 meters. Water is ... | math | {
"ground_truth": "(1250, 1500, 750, 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 the sequence $\\{a_n\\}$, let $S_n$ denote the sum of the first $n$ terms of the sequence $\\{\\frac{1}{a_n}\\}$. If $\\frac{S_5}{5} + \\frac{S_{11}}{11} = 12$, calculate $... | math | {
"ground_truth": "48",
"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 ABC\\\\), \\\\(\\angle A = \\frac{2\\pi}{3}\\\\), \\\\(a = \\sqrt{3}c\\\\), then \\\\(\\frac{b}{c} =\\\\) \\_\\_\\_\\_\\_\\_.",
"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": "In $\\triangle ABC, AB = 16, BC = 17$ and $CA = 15$. Let $M$ be the midpoint of side $AB$ and $H$ be the foot of the altitude from $A$ to $BC$. Determine the length of $HM$.\n**A... | math | {
"ground_truth": "The final correct answer is **E) 5.76**",
"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": "Suppose that $x,$ $y,$ and $z$ are three positive numbers that satisfy the equations $xyz = 1,$ $x + \\frac{1}{z} = 4,$ and $y + \\frac{1}{x} = 20.$ Find $z + \\frac{1}{y}.$",
... | math | {
"ground_truth": "\\frac{26}{79}",
"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": "How many ways are there to put 7 balls into 3 boxes if the balls are not distinguishable and neither are the boxes?",
"role": "user"
}
] | 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": "A Yule log is shaped like a right cylinder with height $10$ and diameter $5$ . Freya cuts it parallel to its bases into $9$ right cylindrical slices. After Freya cut it, the... | math | {
"ground_truth": "100",
"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 total number of days from the year 2010 through 2015, inclusive.",
"role": "user"
}
] | math | {
"ground_truth": "2191",
"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 $\\cos \\left(\\alpha +\\dfrac{\\pi }{6}\\right)=\\dfrac{1}{3}$, find the value of $\\sin \\left(2\\alpha -\\dfrac{\\pi }{6}\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{7}{9}",
"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 we let $g(n)$ denote the sum of all the positive divisors of the integer $n$, how many integers $j$ exist such that $1 \\le j \\le 5041$ and $g(j) = 1 + \\sqrt{j} + j$?",
... | 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": "Express the sum as a common fraction: $0.\\overline{6} + 0.\\overline{3}$.",
"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 $f(n)$ be the smallest prime which divides $n^4+1$. Determine the remainder when the sum $f(1)+f(2)+\\cdots+f(2014)$ is divided by 8$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "In the Cartesian plane \\( xOy \\), let point \\( P \\) be in the first quadrant, and points \\( A \\) and \\( B \\) be on the \\( Ox \\) and \\( Oy \\) axes respectively, such t... | math | {
"ground_truth": "2 + 2\\sqrt{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": "Find the sum $2i + 3i^2 + 4i^3 + ... + 2003i^{2003}.$\nA) $-1000 + 999i$\nB) $-999 + 997i$\nC) $-1001 + 997i$\nD) $-1000 + 997i$\nE) $997i$",
"role": "user"
}
] | math | {
"ground_truth": "\\text{(D) } -1000 + 997i",
"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 function $f(x) = e^x - 2x + a$ has a zero, determine the range of values for $a$.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, 2\\ln{2} - 2]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
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