data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that in $\\triangle ABC$, $\\angle B = 90^{\\circ}$ and $AB = 15$, squares $ABXY$ and $BCWZ$ are constructed outside of the triangle. The points $X$, $Y$, $Z$, and $W$ lie ... | math | {
"ground_truth": "15 + 5\\sqrt{3} + 5\\sqrt{6}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 five-digit number is called indivisible if it cannot be factored into the product of two three-digit numbers.\n\nWhat is the largest number of consecutive indivisible five-digi... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a circle, $15$ equally spaced points are drawn and arbitrary triangles are formed connecting $3$ of these points. How many non-congruent triangles can be drawn?",
"rol... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Martin, Tomáš and Jirka guessed the result of the following expression:\n\n$$\n2.4 - 1.5 \\cdot 3.6 \\div 2 =\n$$\n\nTheir average guess differed from the correct result by 0.4. ... | math | {
"ground_truth": "-0.2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Positive integers $a$, $b$, and $c$ are randomly and independently selected with replacement from the set $\\{1, 2, 3,\\dots, 100\\}$. Find the probability that $abc + ab + ac + ... | math | {
"ground_truth": "5. \\text{ Sum Probabilities:} \\Pr(a(bc + b + c + 1) \\equiv 0 \\pmod{4) = \\frac{1}{4} + \\frac{3}{8} = \\frac{2}{8} + \\frac{3}{8} = \\frac{5}{8}}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 Bernardo and Silvia each pick 3 distinct numbers from their respective sets, and form 3-digit numbers in descending order, find the probability that Bernardo's number is la... | math | {
"ground_truth": "\\frac{37}{56}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"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 \\\\(z\\\\) be a complex number, \\\\(w=z+ \\dfrac{1}{z} \\\\) be a real number, and \\\\(-1 < w < 2\\\\).\n\n\\\\((1)\\\\) Find the value of \\\\(\\left|z\\right| \\\\) and ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f: N \\to N$ satisfy $n=\\sum_{d|n} f(d), \\forall n \\in N$ . Then sum of all possible values of $f(100)$ is?",
"role": "user"
}
] | math | {
"ground_truth": "40",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three balls are randomly and independently tossed into bins numbered with the positive integers such that the probability of ball ending up in bin \\(i\\) is \\(3^{-i}\\) for \\(... | math | {
"ground_truth": "341",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 lines $y=k_{1}x$ and $y=k_{2}x(k_{1} \\gt k_{2})$ are two tangent lines of the curve $y=ax+2\\ln |x|\\left(a\\in R\\right)$, find the value of $k_{1}-k_{2}$.",
... | math | {
"ground_truth": "\\frac{4}{e}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 right triangle $DEF$, where angle $E$ is the right angle, it is given that $\\cos{F} = \\frac{5\\sqrt{34}}{34}$. Find the length of side $DE$.\n\n[asy]\ndraw((0,0)--(7,0)--(0,... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 minimum value of\n\\[\n\\frac{x^2 + 8}{\\sqrt{x^2 + 4}}\n\\]\nover all real numbers $x$.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$ M$ is a subset of $ \\{1, 2, 3, \\ldots, 15\\}$ such that the product of any three distinct elements of $ M$ is not a square. Determine the maximum number of elements in ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 set $A=\\{x\\in\\mathbb{R}|x > 1\\}$, $B=\\{x\\in\\mathbb{R}|x^{2}\\leqslant 4\\}$, then find $A\\cup B$.",
"role": "user"
}
] | math | {
"ground_truth": "A\\cup B=\\{x|-2\\leqslant x<\\infty\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Considering all numbers of the form $n = \\lfloor \\frac{k^3}{2012} \\rfloor$ , where $\\lfloor x \\rfloor$ denotes the greatest integer less than or equal to $x$ , and $k$ ... | math | {
"ground_truth": "1995",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 how many (not necessarily positive) integer values of \\(n\\) is the value of \\(3200 \\cdot \\left(\\frac{2}{5}\\right)^n\\) an integer?\nA) 5\nB) 7\nC) 9\nD) 10\nE) 11",
... | math | {
"ground_truth": "C) 9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "100 students participated in a school quiz. After summarizing the results, it turned out that any 66 of them together earned at least 50% of the total prize points. What is the m... | math | {
"ground_truth": "25 \\%",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The proposition \"The complement of any angle is not less than the angle itself\" is a $\\boxed{\\text{true or false}}$ proposition. If it is a false proposition, provide a count... | math | {
"ground_truth": "\\text{false, a }60^\\circ\\text{ angle is smaller than its complement}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that $a$ cows give $b$ gallons of milk in $c$ days during the summer. If the rate of milk production doubles during the winter, calculate the number of gallons of milk th... | math | {
"ground_truth": "\\frac{3bde}{ac}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate $f(g(-3))$ where $f(x) = 3 - \\sqrt{x}$ and $g(x) = -x + 3x^2$.",
"role": "user"
}
] | math | {
"ground_truth": "3 - \\sqrt{30}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "John is running at a constant speed of 7 miles per hour in the same direction as Jane, who is cycling at a constant speed of 3 miles per hour. Determine the time in minutes that ... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 how many ways can segments of length \\(7 \\mathrm{~cm}\\) and \\(12 \\mathrm{~cm}\\) be used to form a segment of length 1 meter?",
"role": "user"
}
] | math | {
"ground_truth": "(4, 6)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\(4 \\sin^{3} x \\cos 3x + 4 \\cos^{3} x \\sin 3x = 3 \\sin 2x\\).",
"role": "user"
}
] | math | {
"ground_truth": "x_1 = \\frac{\\pi}{6}(2n+1), x_2 = k\\pi",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A 20-quart container is fully filled with water. Five quarts are removed and replaced with pure antifreeze liquid. Then, five quarts of the mixture are removed and replaced with ... | math | {
"ground_truth": "\\frac{243}{1024}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 $p$ and $q$ so that $x^{4} + p x^{2} + q$ is divisible by $x^{2} - 6x + 5$.",
"role": "user"
}
] | math | {
"ground_truth": "p = -26 \\text{ and } q = 25",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle. Point $P$ lies in the interior of $\\triangle ABC$ such that $\\angle ABP = 20^\\circ$ and $\\angle ACP = 15^\\circ$ . Compute $\\angle BPC -... | math | {
"ground_truth": "35^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the value of $a + b$ if the four points $(2,a,b)$, $(a,3,b)$, $(a,b,4)$, and $(5,b,a)$ are collinear.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Evaluate the expression $\\left(\\frac{1}{3}\\right)^{6} \\cdot \\left(\\frac{2}{5}\\right)^{-4}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{625}{11664}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When Cathy the cat just lazes around, she drinks $60 \\mathrm{ml}$ of milk per day. However, each day she chases mice she drinks a third more milk. Also, each day she gets chased... | math | {
"ground_truth": "E \\, 1100 \\, \\text{ml}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three concentric circles have diameters of $2$ inches, $4$ inches, and $6$ inches, respectively. The smallest circle is painted red, the area between the smallest and the middle ... | math | {
"ground_truth": "\\textbf{(C)} 5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 how many integers \\( n \\) is \\( \\frac{n}{15-n} \\) the square of an integer?\nA) 0 \nB) 1\nC) 2 \nD) 3 \nE) 4",
"role": "user"
}
] | math | {
"ground_truth": "The correct answer is C) 2.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 $R$ be the rectangle in the Cartesian plane with vertices at $(0,0)$ , $(2,0)$ , $(2,1)$ , and $(0,1)$ . $R$ can be divided into two unit squares, as shown. [asy]size... | math | {
"ground_truth": "\\frac{3}{4}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 frog is standing in a center of a $3 \\times 3$ grid of lilypads. Each minute, the frog chooses a square that shares exactly one side with their current square uniformly at r... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 cyclist planned to travel from point A to point F in 5 hours, moving at a constant speed. He traveled at the planned speed until the halfway point, then increased his speed by ... | math | {
"ground_truth": "4 \\, \\text{hours 30 minutes}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Kevin is trying to solve an economics question which has six steps. At each step, he has a probability $p$ of making a sign error. Let $q$ be the probability that Kevin makes... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 set $M = \\{x \\in \\mathbb{N} | 8 - x \\in \\mathbb{N}\\}$, calculate the number of elements in set $M$.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 large cube with edge length $5$ cm is cut into $N$ smaller cubes, where each edge of the smaller cubes is a whole number of centimeters. Determine the value of $N$.",
"role... | math | {
"ground_truth": "118",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 positive sequence $\\{a_n\\}$ satisfies: $a_1=1+\\sqrt 2$ and $(a_n-a_{n-1})(a_n+a_{n-1}-2\\sqrt n)=2(n\\geq 2).$ (1)Find the general formula of $\\{a_n\\}$ ;\n(2)Find t... | math | {
"ground_truth": "\\{ n \\in \\mathbb{Z} \\mid 1021026 \\leq n \\leq 1022121 \\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 second degree polynomial $d(x)=x^{2}+ax+b$ with integer coefficients, so that there exists an integer coefficient polynomial $p(x)$ and a non-zero integer coefficien... | math | {
"ground_truth": "d(x) = x^2 + ax + b",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two numbers are randomly selected from interval $I = [0, 1]$ . Given $\\alpha \\in I$ , what is the probability that the smaller of the two numbers does not exceed $\\alpha$ ?... | math | {
"ground_truth": "2\\alpha - \\alpha^2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 rectangle is called amazing if the number of square units in its area is equal to three times the number of units in its perimeter. The rectangle must have integer side lengths... | math | {
"ground_truth": "942",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the first digit (from left to right) of the base $8$ representation of $391_{10}$?",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the slope of the line passing through the points \\((1, 2)\\) and \\((4, 8)\\)?",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 different real numbers \\(x\\) satisfy the equation \\[(x^2 - 7)^2 = 36?\\]\nA) 0\nB) 2\nC) 4\nD) 8\nE) 16",
"role": "user"
}
] | math | {
"ground_truth": "The correct answer is \\(\\textbf{(C) }4\\).",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three different numbers are chosen at random from the list \\(1, 3, 5, 7, 9, 11, 13, 15, 17, 19\\). The probability that one of them is the mean of the other two is \\(p\\). What... | math | {
"ground_truth": "720",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The population of Canada in 1980 was approximately 24,343,181. The area of Canada is 3,855,103 square miles. Given there are \\( (5280)^2 \\) square feet in one square mile, calc... | math | {
"ground_truth": "4,413,171",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Aerith rolls a fair die until she gets a roll that is greater than or equal to her previous roll. Find the expected number of times she will roll the die before stopping.",
"... | math | {
"ground_truth": "2.52",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the set of all rectangles with a given area $S$ . \nFind the largest value o $ M = \\frac{16-p}{p^2+2p}$ where $p$ is the perimeter of the rectangle.",
"role":... | math | {
"ground_truth": "\\frac{4 - \\sqrt{S}}{4S + 2\\sqrt{S}}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 non-zero numbers $x$ and $y$ such that $x = 1/y$, simplify the expression $\\left(x-\\frac{1}{x}\\right)\\left(y+\\frac{1}{y}\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "x^2 - y^2",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"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 positive integer $n$ is chosen such that the probability of choosing $n$ is $p$ if $n\\le 60$ and $3p$ if $n > 60$, find the probability that a perfect square is chosen."... | math | {
"ground_truth": "0.0667",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 natural number is equal to the cube of the number of its thousands. Find all such numbers.",
"role": "user"
}
] | math | {
"ground_truth": "32768",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given ten tiles numbered 1 through 10 are turned face down and a die is rolled, calculate the probability that the product of the numbers on the tile and the die will be a square... | math | {
"ground_truth": "\\frac{11}{60}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three squares $ABCD$, $EFGH$, and $GHIJ$ each have side $s$. Points $C$ and $D$ are no longer midpoints but instead are at $\\frac{1}{3}$ and $\\frac{2}{3}$ along sides $IH$ and ... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 40 files, with 5 files taking up 0.9 MB, 15 files taking up 0.8 MB, and the rest taking up 0.5 MB, determine the smallest number of disks of 2.0 MB capacity that are needed... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We have a collection of identical spheres that we stack to form a tetrahedron where all edges have $n$ spheres. Calculate, as a function of $n$, the total number of points of tan... | math | {
"ground_truth": "n^3 - n",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $f(x)$ is an odd function on $\\mathbb{R}$, and $f(x+4)=f(x)$, $f(1)=2$, calculate $f(7)$.",
"role": "user"
}
] | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Circle $C$ has its center at $(-4, 5)$ and a radius of $13$ units. What is the sum of the $y$-coordinates of the two points on circle $C$ that are also on the $y$-axis?",
"ro... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 integers $x$ such that $2x^2+x-6$ is a positive integral power of a prime positive integer.",
"role": "user"
}
] | math | {
"ground_truth": "-3, 2, 5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=x\\ln x+(1-k)x+k$, where $k\\in R$.\n\n(I) When $k=1$, find the monotonic intervals of the function $f(x)$;\n\n(II) When $x > 1$, find the maximum intege... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 $ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$, respectively. It is given that $a\\sin A+c\\sin C- \\sqrt {2}a\\sin C=b\\sin B... | math | {
"ground_truth": "c=\\sqrt{6}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 tetrahedron \\(PQRS\\),\n\\[\\angle PRS = \\angle PSQ = \\angle QRS = 90^\\circ.\\]\nAlso, let \\(a = \\sin \\angle PQS\\) and \\(b = \\sin \\angle PRQ\\). Express \\(\\cos \\... | math | {
"ground_truth": "\\frac{a^2 - b^2}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 Jane has to take one red pill and one blue pill each day for three weeks to treat her condition, each red pill costs $\\textdollar 2$ more than a blue pill, and the to... | math | {
"ground_truth": "22.5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 two circles $⊙C_{1}$: $x^{2}+(y+1)^{2}=25$ and $⊙C_{2}$: $x^{2}+(y-2)^{2}=1$, find the trajectory equation of the moving circle's center $M$ that is internally tangent to $... | math | {
"ground_truth": "\\frac {y^{2}}{9}+ \\frac {x^{2}}{5}=1(y\\neq 3)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 how many positive divisors the number $30$ has.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify first, then evaluate: $b^{2}-a^{2}+2(a^{2}+ab)-(a^{2}+b^{2})$, where $a=\\frac{1}{2}$ and $b=-\\frac{1}{3}$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice, Bob, Dave, and Carol take turns tossing a die. The order is always Alice, then Bob, then Dave, and finally Carol, and this sequence repeats indefinitely. Determine the pro... | math | {
"ground_truth": "\\frac{125}{671}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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+6\\) cows give \\(x+9\\) cans of milk in \\(x+4\\) days, determine how many days will it take \\(x+4\\) cows to give \\(x+11\\) cans of milk.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{(x+11)(x+6)}{x+9}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 central angle of a sector is $60^{\\circ}$ and the arc length is $\\pi$, find the radius of the sector.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Real numbers $x$ and $y$ satisfy\n\\begin{align*}\nx^2 + y^2 &= 2023 \n(x-2)(y-2) &= 3.\n\\end{align*}\nFind the largest possible value of $|x-y|$ .\n\n*Proposed by Howard H... | math | {
"ground_truth": "13\\sqrt{13}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 number of ordered triples $(x,y,z)$ of real numbers such that $x + y = 3$ and $xy - z^2 = 4.$",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 the hyperbola \\( C: \\frac{x^{2}}{4} - \\frac{y^{2}}{5} = 1 \\),\n\\( F_1 \\) and \\( F_2 \\) are the left and right foci of the hyperbola \\( C \\), and \\( P \\) is a point... | math | {
"ground_truth": "x = 6 \\text{ with vertical properties/scaled specifics }",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find how many nonzero complex numbers $z$ are there such that $0, z,$ and $2z^3$, when represented by points in the complex plane, form the vertices of an equilateral triangle?\n... | math | {
"ground_truth": "\\textbf{(C) }2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$\\tan 5^{\\circ}+\\tan 40^{\\circ}+\\tan 5^{\\circ}\\tan 40^{\\circ}=\\_\\_\\_\\_\\_\\_.$",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 each positive integer $n$, let $f_1(n)$ be twice the number of positive integer divisors of $n$, and for $j \\ge 2$, let $f_j(n) = f_1(f_{j-1}(n))$. Calculate the number of v... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the base four equivalent of $185_{10}$?",
"role": "user"
}
] | math | {
"ground_truth": "2321_4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 arithmetic sequence $\\{a_n\\}$ with the first term $1$ and common difference $2$, and the sum of the first $n$ terms is $S_n$, then $\\lim_{n\\rightarrow \\infty} \\fra... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify the expression\n\\[\\frac{\\sin{40^\\circ} + \\sin{80^\\circ}}{\\cos{40^\\circ} + \\cos{80^\\circ}}.\\]\nProvide your answer as a trigonometric function evaluated at an ... | math | {
"ground_truth": "\\tan 60^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 $$\\frac{m}{1+i}=1-ni$$ where $m, n$ are real numbers and $i$ is the imaginary unit, find the value of $m-n$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 $T$ be the set of all ordered triples of integers $(b_1, b_2, b_3)$ with $1 \\leq b_1, b_2, b_3 \\leq 15$. Each ordered triple in $T$ generates a sequence based on the rule $... | math | {
"ground_truth": "855",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 units digit of $27 \\cdot 46$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 minimum positive period of the function \\( y = \\sin x |\\cos x| \\) is to be calculated.",
"role": "user"
}
] | math | {
"ground_truth": "2\\pi",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The least common multiple of two integers is 72 and their greatest common divisor is 8. What is the product of the two numbers?",
"role": "user"
}
] | math | {
"ground_truth": "576",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 vertex of a parabola is on the x-axis and its directrix is the y-axis. The nearest distance from the point \\(\\Lambda (4,0)\\) to this parabola is 2. Find the equ... | math | {
"ground_truth": "y^2 = 8(x - 2)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integer $n$ that is divisible by $100$ and has exactly $100$ divisors.",
"role": "user"
}
] | math | {
"ground_truth": "162000",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify the expression: \\[[(3+4+5+6)\\div3] + [(3\\cdot6+12)\\div4].\\]",
"role": "user"
}
] | math | {
"ground_truth": "13.5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 non-similar triangles have angles whose degree measures are distinct positive integers in an arithmetic progression, with the middle angle being \\(45\\) degrees?",
... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Assume we have a modified calendrical system in which leap years normally happen every four years, except every 100th year is not a leap year unless it is also divisible by 400. ... | math | {
"ground_truth": "48",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 $f(x)=|x+1|+|x-2|$,\n(I) Find the range of real number $a$ such that the inequality $f(x) < 2a-1$ has real number solutions;\n(II) Solve the inequality $f(x)\\geqslant x^{2... | math | {
"ground_truth": "[-1,2+ \\sqrt {3}]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 expected value and standard deviation of a normally distributed random variable \\( X \\) are 10 and 2, respectively. Find the probability that \\( X \\) will take a value in... | math | {
"ground_truth": "0.1359",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangle is divided into three congruent rectangles, as shown in an imaginary diagram. Each smaller rectangle has a perimeter of 40 inches. If the width of the initial rectang... | math | {
"ground_truth": "72 \\text{ inches}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 function $f$ is defined such that $f(3x-1)=x^3 + x^2 + x + 1$ for all real numbers $x$. What is $f(5)$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{140}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 $f(x) = x^2 + 3xf''(1)$, calculate $f''(2)$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 function $f\\left(x\\right)=\\left\\{\\begin{array}{l}{{2}^{x},x≤0}\\\\{x-1,x＞0}\\end{array}\\right.$, if $f\\left(a\\right)=\\frac{1}{2}$, then the real number $a=$___... | math | {
"ground_truth": "-1\\, \\text{or}\\, \\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 university student drove $150$ miles to visit a friend and averaged $25$ miles per gallon using a sedan. On the return trip, the student borrowed their friend's pickup truck an... | math | {
"ground_truth": "18.75",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 $\\log_{10}{\\left(m^2\\right)} = b - 2\\log_{10}{n}$, then find $m$.\n**A)** $\\frac{10^b}{n}$\n**B)** $\\frac{10^{b/2}}{n}$\n**C)** $\\pm \\frac{10^{b/2}}{n}$\n**D)** $\\fra... | math | {
"ground_truth": "\\textbf{(C)}\\ \\pm \\frac{10^{b/2}}{n}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 polynomial $1976(x+x^2+ \\cdots +x^n)$ is decomposed into a sum of polynomials of the form $a_1x + a_2x^2 + \\cdots + a_nx^n$ , where $a_1, a_2, \\ldots , a_n$ are disti... | math | {
"ground_truth": "7, 103, 1975",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 project requires 12 man-days to finish. If 4 men are originally planned to work on it with an efficiency rate of 1.5 man-days per man per day, how long will it take for 6 men w... | math | {
"ground_truth": "B) 1 day",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 pile you have 100 stones. A partition of the pile in $ k$ piles is *good* if:\r\n\r\n1) the small piles have different numbers of stones;\r\n\r\n2) for any partition of on... | math | {
"ground_truth": "k_{\\text{max}} = 13",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 equation \\[ 4x^3 \\plus{} 4x^2y \\minus{} 15xy^2 \\minus{} 18y^3 \\minus{} 12x^2 \\plus{} 6xy \\plus{} 36y^2 \\plus{} 5x \\minus{} 10y \\equal{} 0,\\] find all positiv... | math | {
"ground_truth": "(x, y) = (2a, a) \\text{ for any positive integer } a \\text{ and } (1, 1)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 an $h$-meter race, Sunny is exactly $2d$ meters ahead of Windy when Sunny finishes the race. The next time they race, Sunny sportingly starts $2d$ meters behind Windy, who is ... | math | {
"ground_truth": "\\frac{4d^2}{h}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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