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": "What is the maximum value of $\\frac{(3^t - 2t)t}{9^t}$ for integer values of $t$?\n**A)** $\\frac{1}{8}$ \n**B)** $\\frac{1}{10}$ \n**C)** $\\frac{1}{12}$ \n**D)** $\\frac{1}... | math | {
"ground_truth": "\\frac{1}{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": "Tom's Hat Shoppe increased all original prices by $30\\%$. Then, the shoppe is having a sale where all prices are $10\\%$ off these increased prices. What is the sale price of an... | math | {
"ground_truth": "1.17",
"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": "Anna Lisa bought three dozen apples for $\\$$24.00. At the same rate, how much would five dozen of these apples cost if a 10% discount is applied to purchases exceeding four doze... | math | {
"ground_truth": "\\$36.00",
"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": "Hossna is playing with a $m*n$ grid of points.In each turn she draws segments between points with the following conditions.\n\n**1.** No two segments intersect.\n\n**2.** Each... | math | {
"ground_truth": "2mn",
"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 $\\triangle ABC$ is isosceles with base $AC$, and $AC=AP=PQ=QB$, calculate the measure of $\\angle B$ in degrees.",
"role": "user"
}
] | math | {
"ground_truth": "25\\frac{5}{7}^\\circ",
"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": "A chord intercepted on the circle with center at $(2,-1)$ by the line $x-y-1=0$ has a length of $2 \\sqrt {2}$. Determine the equation of this circle.",
"role": "user"
}
] | math | {
"ground_truth": "(x-2)^2+(y+1)^2=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": "Using the garden's wall and the three pieces of fence, determine the maximum area Bahman can enclose in square meters.",
"role": "user"
}
] | math | {
"ground_truth": "50\\sqrt{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": "Given that the derivative of the function $f(x)$ is $f'(x)$, and it satisfies $f(x) = 2xf'(2) + x^3$, calculate the value of $f'(2)$.",
"role": "user"
}
] | math | {
"ground_truth": "-12",
"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": "$A$ and $B$ together can complete a job in $3$ days; $B$ and $C$ can do it in $6$ days; $A$ and $C$ in $4$ days. Determine the number of days required for $A$ to do the job alone... | math | {
"ground_truth": "4.8",
"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": "A certain natural number $m$ satisfies $m^2$ giving a remainder of 1 when divided by 7, and $m^3$ gives a remainder of 6 when divided by 7. What is the remainder when $m$ is divi... | 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": "Given $i$ is the imaginary unit, if $(1-i)(a+i) = 3-bi$ ($a, b \\in \\mathbb{R}$), find the value of $a+b$.",
"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": "There are 2016 points arranged in a circle. We are allowed to jump 2 or 3 points in a clockwise direction as we please.\n\nWhat is the minimum number of jumps needed to reach all... | math | {
"ground_truth": "673",
"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 $ 2n$ distinct points on a circle be given. Arrange them into disjoint pairs in an arbitrary way and join the couples by chords. Determine the probability that no two of th... | math | {
"ground_truth": "\\frac{2^n}{(n+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": "Given the function $f(x)={\\left\\{{\\begin{array}{l}{x-2({x>0})}\\\\{{e^{x+1}}({x\\leq0})}\\end{array}}\\right.}$, calculate $f\\left(f\\left(-1\\right)\\right)$.",
"role": ... | 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": "In a relay race, Ainslee runs the first lap in 72 seconds. Bridget runs the next lap at $\\frac{9}{10}$ of Ainslee's speed, Cecilia runs the next lap at $\\frac{4}{3}$ of Bridget... | math | {
"ground_truth": "4 \\text{ minutes, } 22 \\text{ seconds}",
"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": "Ben starts with an integer greater than $9$ and subtracts the sum of its digits from it to get a new integer. He repeats this process with each new integer he gets until he get... | math | {
"ground_truth": "9",
"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 a positive integer $ n,$ $ a_{n}\\equal{}n\\sqrt{5}\\minus{} \\lfloor n\\sqrt{5}\\rfloor$ . Compute the maximum value and the minimum value of $ a_{1},a_{2},\\ldots ,a_{2... | math | {
"ground_truth": "1597",
"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": "What is the minimum value of the diameter of a convex $n$-gon ($n=4,5,6$), all of whose sides are equal to 1?",
"role": "user"
}
] | math | {
"ground_truth": "1.41, 1.61, 1.93",
"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 $f(x)$ is an odd function on $\\mathbb{R}$, and when $x > 0$, $f(x) = 3^x$. Find the value of $f(\\log_{\\frac{1}{2}}4)$.",
"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": "The domain of the function $y=\\sqrt{2-x}+{\\log_2}({x-1})$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "\\{x|1 < x \\leq 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": "What is the area of the region in the complex plane consisting of all points $z$ satisfying both $|\\tfrac{1}{z}-1|<1$ and $|z-1|<1$ ? ( $|z|$ denotes the magnitude of a co... | math | {
"ground_truth": "\\frac{\\pi}{3} + \\frac{\\sqrt{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": "In the sum below, identical letters represent identical digits, and different letters represent different digits.\n\n$$\n\\begin{array}{ccc} \n& & X \\\\\n+ & & X \\\\\n& Y & Y \... | math | {
"ground_truth": "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": "Evaluate the expression \\( 5^{\\log_5 3} \\).",
"role": "user"
}
] | math | {
"ground_truth": "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": "Ryan is learning number theory. He reads about the *Möbius function* $\\mu : \\mathbb N \\to \\mathbb Z$ , defined by $\\mu(1)=1$ and\n\\[ \\mu(n) = -\\sum_{\\substack{d\\mid ... | math | {
"ground_truth": "14013",
"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": "Instead of walking along two adjacent sides of a rectangular field, a boy took a shortcut along the diagonal of the field and saved a distance equal to $\\frac{1}{3}$ of the long... | math | {
"ground_truth": "\\frac{5}{12}",
"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": "Joey, Chloe, and their son Liam all share the same birthday. Joey is 3 years older than Chloe, and Liam is exactly 2 years old today. Today marks the first out of the 7 birthdays... | math | {
"ground_truth": "B) 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 function $f(x)$ is an odd function, and for $x < 0$, $f(x) = 2x^2 - 1$, find the value of $f(1)$.",
"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": "The circumcenter $O$ , the incenter $I$ , and the midpoint $M$ of a diagonal of a bicentral quadrilateral were marked. After this the quadrilateral was erased. Restore it.",
... | math | {
"ground_truth": "z = \\frac{y^2}{x - y}",
"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 $ n > 1$ be an odd positive integer and $ A = (a_{ij})_{i, j = 1..n}$ be the $ n \\times n$ matrix with \r\n\\[ a_{ij}= \\begin{cases}2 & \\text{if }i = j 1 & \\text{i... | math | {
"ground_truth": "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": "Let $ S_i$ be the set of all integers $ n$ such that $ 100i\\leq n < 100(i \\plus{} 1)$ . For example, $ S_4$ is the set $ {400,401,402,\\ldots,499}$ . How many of the ... | 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": "Calculate the value of $\\frac{3}{80}$.",
"role": "user"
}
] | math | {
"ground_truth": "0.0375",
"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 the xy-plane, what is the length of the shortest path from $(0,0)$ to $(20,25)$ that does not go inside the circle $(x-10)^{2}+(y-12.5)^{2}= 64$?\nA) \\( 27.732 + 2\\pi \\)\nB... | math | {
"ground_truth": "B) \\( 27.732 + \\frac{8\\pi}{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": "If $\\log_{3x+1} (343) = x$, solve for $x$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Given the expression $\\frac{2^{2x-3}}{4^{-1} + 2^{-2}}$, evaluate this expression.",
"role": "user"
}
] | math | {
"ground_truth": "2^{2x-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": "Square \\(ABCD\\) has a side length of \\(1\\). Points \\(P\\) and \\(Q\\) are located on segments \\(AB\\) and \\(AD\\) respectively. If the perimeter of \\(\\triangle APQ\\) is... | math | {
"ground_truth": "45^\\circ",
"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 set \\( M \\) is obtained from a plane by removing three distinct points \\( A \\), \\( B \\), and \\( C \\). Find the minimum number of convex sets whose union is the set \\... | math | {
"ground_truth": "3",
"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 $b > 0$, and let $Q(x)$ be a polynomial with integer coefficients such that\n\\[Q(1) = Q(4) = Q(7) = Q(10) = b\\]\nand\n\\[Q(2) = Q(5) = Q(8) = Q(11) = -b.\\]\nWhat is the sm... | math | {
"ground_truth": "1260",
"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": "Vasya wrote a set of distinct natural numbers on the board, each of which does not exceed 2023. It turned out that for any two written numbers \\(a\\) and \\(b\\), the number \\(... | math | {
"ground_truth": "675",
"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": "For what real value of $b$ in the interval $[-10, 0]$ is the expression $2b^2 + 8b - 4$ minimized?",
"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": "Three friends, Rowan, Sara, and Tim, are playing a monetary game. Each starts with $3. A bell rings every 20 seconds, and with each ring, any player with money chooses one of the... | math | {
"ground_truth": "\\frac{1}{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": "Let $ABC$ be a non-degenerate triangle with perimeter $4$ such that $a=bc\\sin^2A$ . If $M$ is the maximum possible area of $ABC$ and $m$ is the minimum possible area ... | math | {
"ground_truth": "199",
"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 that the terminal side of angle $\\alpha$ passes through point $P\\left(\\frac{3}{5},-\\frac{4}{5}\\right)$, find the value of $\\cos \\alpha -\\sin \\alpha$.",
"role":... | math | {
"ground_truth": "\\frac{7}{5}",
"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 an $m \\times n$ grid, each square is either filled or not filled. For each square, its *value* is defined as $0$ if it is filled and is defined as the number of neighbour... | math | {
"ground_truth": "C = 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 right circular cone has base radius 1. The vertex is K. P is a point on the circumference of the base. The distance KP is 3. A particle travels from P around the cone and back ... | math | {
"ground_truth": "\\frac{3}{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": "If $\\log_3 m + \\log_3 n = 4$, calculate the minimum value of $m + n$.",
"role": "user"
}
] | math | {
"ground_truth": "18",
"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 arithmetic mean of four numbers is 92. Given that the largest of these numbers is 108, calculate the mean of the remaining three numbers.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{260}{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 vectors $\\overrightarrow{a} = (1, 2)$, $\\overrightarrow{b} = (-3, 2)$.\n\n(1) Find $|\\overrightarrow{a} + \\overrightarrow{b}|$ and $|\\overrightarrow{a} - \\overrightar... | 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": "Given a nonempty set \\( M \\) satisfying\n\\[ \nM \\subseteq \\{0,1, \\cdots, n\\} \\quad \\text{(where \\( n \\geq 2 \\), \\( n \\) is a positive integer)}.\n\\]\n\nIf there ex... | math | {
"ground_truth": "31",
"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 the expression $\\frac{13! - 11!}{10!}$, evaluate the result.",
"role": "user"
}
] | math | {
"ground_truth": "1705",
"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": "Consider the equation of the parabola \\( y = x^2 + 2x - 6 \\). Let \\( L(m) \\) denote the \\( x \\)-coordinate of the left endpoint of the intersection of the graphs of \\( y =... | math | {
"ground_truth": "\\frac{1}{\\sqrt{7}}",
"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": "Consider the following sequence of pieces, in which piece number 1 is a small square.\n\n(a) How many small squares make up piece number 50?\n\n(b) How many small squares are the... | math | {
"ground_truth": "5050",
"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 \\( A \\) be an \\( m \\times m \\) matrix. Let \\( X_{i} \\) be the set of entries in the \\( i \\)-th row and \\( Y_{j} \\) the set of entries in the \\( j \\)-th column, \... | math | {
"ground_truth": "13",
"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": "For every positive integer $k$ , let $\\mathbf{T}_k = (k(k+1), 0)$ , and define $\\mathcal{H}_k$ as the homothety centered at $\\mathbf{T}_k$ with ratio $\\tfrac{1}{2}$ i... | math | {
"ground_truth": "256",
"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": "If the sequence $\\{b_n\\}$ satisfies $b_{n+1}=|b_n-b_{n-1}|$ and $b_1=1$, $b_2=a$, where $a \\neq 0$, determine the sum of the first 2017 terms when the period of the sequence $... | math | {
"ground_truth": "1345",
"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 proposition:\n\nIf point $O$ is on line segment $AB$, then $|$\\overrightarrow{OB}$|$·$$\\overrightarrow{OA}$ + $|$\\overrightarrow{OA}$|$·$$\\overrightarrow{OB}$ = 0$.... | math | {
"ground_truth": "V_{O-BCD}·$$\\overrightarrow{OA}$ + V_{O-ACD}·$$\\overrightarrow{OB}$ + V_{O-ABD}·$$\\overrightarrow{OC}$ + V_{O-ABC}·$$\\overrightarrow{OD}$ = 0",
"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 that $A$, $B$, $C$, and $D$ are distinct digits, in the addition shown below, determine the number of different values possible for $D$.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"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 the function $f(x) = 45|2x + 3| + |2x - 1|$. \n(Ⅰ) Solve the inequality $f(x) < 8$; \n(Ⅱ) If the inequality $f(x) \\leqslant |3m + 1|$ has a solution, find the range of t... | math | {
"ground_truth": "m \\leqslant -\\dfrac{5}{3} \\text{ or } m \\geqslant 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": "The height \\( AH \\) of triangle \\( ABC \\) is equal to its median \\( BM \\). On the extension of side \\( AB \\) beyond point \\( B \\), point \\( D \\) is marked such that \... | math | {
"ground_truth": "30^\\circ",
"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": "To each positive integer $ n$ it is assigned a non-negative integer $f(n)$ such that the following conditions are satisfied:\n\n(1) $ f(rs) \\equal{} f(r)\\plus{}f(s)$ (2) ... | math | {
"ground_truth": "0",
"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 that integers are between $1000$ and $9999$, inclusive, and have only even digits, how many of them are divisible by $5$?",
"role": "user"
}
] | math | {
"ground_truth": "100",
"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": "When $x \\in (-\\infty, 1]$, the inequality $\\frac{1+2^{x}+4^{x} \\cdot a}{a^{2}-a+1} > 0$ always holds. Determine the range of values for the real number $a$\\_.",
"role": ... | math | {
"ground_truth": "(-\\frac{3}{4},+\\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": "Kanga likes jumping on the number line. She always makes two large jumps of length 3, followed by three small jumps of length 1, and then repeats this over and over again. She st... | math | {
"ground_truth": "84",
"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 the ellipse C: $$\\frac{{x}^{2}}{{a}^{2}}+ \\frac{{y}^{2}}{{b}^{2}}=1$$ (where $a>b>0$) passes through the point $(0, \\sqrt{2})$, and satisfies $a+b=3\\sqrt{2}$.\n1. Find ... | math | {
"ground_truth": "0",
"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 a triangular pyramid with all edge lengths of $\\sqrt {2}$, find the volume of the pyramid.",
"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": "Let \\( P \\) be the midpoint of the height \\( VH \\) of a regular square pyramid \\( V-ABCD \\). If the distance from point \\( P \\) to a lateral face is 3 and the distance to... | math | {
"ground_truth": "750",
"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 image of a point with coordinates $(2,3)$ under the reflection across the line $y=mx+b$ is the point with coordinates $(8,6)$. Find $m+b$.",
"role": "user"
}
] | math | {
"ground_truth": "12.5",
"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": "Given the expression \\[\n\\left(\\frac{x^3+1}{x}\\right)\\left(\\frac{y^3+1}{y}\\right)+\\left(\\frac{x^3-1}{y}\\right)\\left(\\frac{y^3-1}{x}\\right), \\quad xy \\neq 0\n\\], s... | math | {
"ground_truth": "2x^2y^2 + \\frac{2}{xy}",
"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": "Find \\(\\sum_{k=0}^n \\frac{(-1)^k \\binom{n}{k}}{k^3 + 9k^2 + 26k + 24}\\), where \\(\\binom{n}{k} = \\frac{n!}{k!(n-k)!}\\).",
"role": "user"
}
] | math | {
"ground_truth": "0",
"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 the binomial expansion of $( \\sqrt[3]{x}- \\frac {2}{x})^{n}$, the sum of the binomial coefficients is $128$. Find the coefficient of the $x$ term in the expansion.",
"ro... | math | {
"ground_truth": "-14",
"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": "How many consecutive \"0\"s are there at the end of the product \\(5 \\times 10 \\times 15 \\times 20 \\times \\cdots \\times 2010 \\times 2015\\)?",
"role": "user"
}
] | math | {
"ground_truth": "398",
"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 the function $f\\left(x\\right)=2\\sin x\\sin \\left(x+\\frac{π}{3}\\right)-\\frac{1}{2}$.<br/>$(1)$ Find the minimum positive period of $f\\left(x\\right)$;<br/>$(2)$ If $... | math | {
"ground_truth": "\\frac{11}{14}",
"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": "Find the least positive integer $n$ such that when $3^n$ is written in base $143$, its two right-most digits in base $143$ are $01$.",
"role": "user"
}
] | math | {
"ground_truth": "195",
"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": "Find the solution set of the inequality $\\log_{2}(4 - x) > \\log_{2}(3x)$.",
"role": "user"
}
] | math | {
"ground_truth": "(0, 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": "Given a tetrahedron \\( ABCD \\) with \\( AD = BC = 26 \\), \\( AC = BD = 42 \\), and \\( AB = CD = 50 \\). For any point \\( Y \\) in space, define \\( g(Y) = AY + BY + CY + DY ... | math | {
"ground_truth": "654",
"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 $(1+\\sin x)(1+\\cos x) = \\frac{9}{4}$ and $(1-\\sin x)(1-\\cos x) = p - \\sqrt{q},$ where $p$ and $q$ are positive integers, determine the value of $p+q$.",
"role": "... | math | {
"ground_truth": "p+q = 1",
"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 line on a graph can be represented by the equation $y = mx + b$. This particular line passes through the point (-1, -3) and intersects the y-axis at y = -1. Calculate the value... | 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": "Triangle $ABC$ is right angled such that $\\angle ACB=90^{\\circ}$ and $\\frac {AC}{BC} = 2$ . Let the line parallel to side $AC$ intersects line segments $AB$ and $BC$... | math | {
"ground_truth": "90^\\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": "Let $ABCD$ be a convex quadrilateral. $O$ is the intersection of $AC$ and $BD$ . $AO=3$ , $BO=4$ , $CO=5$ , $DO=6$ . $X$ and $Y$ are points in segment $AB$ and ... | math | {
"ground_truth": "10a + b + c = 10 \\cdot 2 + 3 + 10 = 23",
"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": "Koalas absorb \\(35\\%\\) of the fiber they eat. A koala absorbed \\(14.7\\) ounces of fiber on one day and \\(9.8\\) ounces on the next day. How many total ounces of fiber did t... | math | {
"ground_truth": "70 \\text{ ounces}",
"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 circle $C$: $x^{2}+y^{2}=4$, and line $l$: $ax+y+2a=0$, when line $l$ intersects with circle $C$ at points $A$ and $B$, and $|AB|=2 \\sqrt {2}$, find the equation of line $... | math | {
"ground_truth": "x-y+2=0",
"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 $a_1 = 1$ , and that for all $n \\ge 2$ , $a_n = a_{n-1} + 2a_{n-2} + 3a_{n-3} + \\ldots + (n-1)a_1.$ Suppose furthermore that $b_n = a_1 + a_2 + \\ldots + a_n$... | math | {
"ground_truth": "2022",
"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 $10^{x}\\cdot 1000^{2x}=100^{6}$, solve for $x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{12}{7}",
"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 \\(s\\) be a complex number such that \\(s^7 = 1\\) and \\(s \\neq 1.\\) Compute\n\\[\n(s - 1)(s^2 - 1)(s^3 - 1)(s^4 - 1)(s^5 - 1)(s^6 - 1).\n\\]",
"role": "user"
}
] | 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": "Calculate: \n(1) Calculate $27^{ \\frac {2}{3}} - 2^{ \\log_{2}3} \\times \\log_{2} \\frac {1}{8} + \\log_{2}3 \\times \\log_{3}4$; \n(2) Given $0 < x < 1$, and $x + x^{-1} = 3... | 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": "If the average (arithmetic mean) age of a group consisting of teachers and engineers is 45, the average age of teachers is 40, and the average age of engineers is 55, determine t... | math | {
"ground_truth": "2:1",
"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 $ABCD$ be a rectangle. Circles with diameters $AB$ and $CD$ meet at points $P$ and $Q$ inside the rectangle such that $P$ is closer to segment $BC$ than $Q$ . ... | math | {
"ground_truth": "80^\\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": "Given the sequences $\\left\\{a_{n}\\right\\}$ and $\\left\\{b_{n}\\right\\}$ satisfy the following conditions:\n\\[\n\\begin{array}{l}\na_{1}=-1, b_{1}=2, \\\\\na_{n+1}=-b_{n}, ... | math | {
"ground_truth": "-24",
"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": "Determine how many integers $i$ exist such that $1 \\le i \\le 5000$ and $f(i) = 1 + \\sqrt{i} + i + \\sqrt[3]{i}$?",
"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": "The equation of the tangent line to the curve $f(x)=\\ln x+\\frac{2}{x}$ at the point $\\left(1,2\\right)$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "x+y-3=0",
"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 a finite set of naturals $(C)$ , the product of its elements is going to be noted $P(C)$ . We are going to define $P (\\phi) = 1$ . Calculate the value of the expression ... | math | {
"ground_truth": "n+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": "Let $x<y$ be positive integers and $P=\\frac{x^3-y}{1+xy}$ . Find all integer values that $P$ can take.",
"role": "user"
}
] | math | {
"ground_truth": "p \\geq 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": "Elberta has 10% more money than Anjou, and Anjou has one-fourth of what Granny Smith has, and Granny Smith has $75. Determine the amount of money Elberta has.",
"role": "user... | math | {
"ground_truth": "21",
"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": "What is the largest multiple of 11 less than 100?",
"role": "user"
}
] | math | {
"ground_truth": "99",
"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 equation of the line through $(4,3)$ and $(12,-3)$ is $\\frac{x}{a}+\\frac{y}{b}=1$. Find $a$.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"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 the function \\(y=\\cos x\\), if we shrink the \\(x\\)-coordinates of all points on its graph to half of their original value (while keeping the \\(y\\)-coordinates unchang... | math | {
"ground_truth": "\\cos \\left(2x + \\frac{\\pi}{2}\\right)",
"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 that the universal set is the set of real numbers $R$, $M={x|x∈R|x≤\\sqrt{5}}$ and $N={1,2,3,4}$, find $∁_{R}M∩N$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{3,4\\}",
"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": "In the polar coordinate system, the polar coordinate equation of circle C is ρ=4cosθ. Taking the pole as the origin and the direction of the polar axis as the positive direction ... | math | {
"ground_truth": "\\frac{7}{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": "Let $S$ be a set of positive integers, each of them having exactly $100$ digits in base $10$ representation. An element of $S$ is called *atom* if it is not divisible by ... | math | {
"ground_truth": "\\binom{19}{10} - 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 a high school, there are two self-study classrooms, A and B. If three students, X, Y, and Z, randomly choose one of the classrooms to study in, the probability that they all c... | math | {
"ground_truth": "\\frac{1}{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": "**H**orizontal parallel segments $AB=10$ and $CD=15$ are the bases of trapezoid $ABCD$ . Circle $\\gamma$ of radius $6$ has center within the trapezoid and is tangent to... | math | {
"ground_truth": "\\frac{225}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
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