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": "Find the quotient of the division $(3z^4 - 5z^3 + 5z^2 - 11z + 2)/(1 + 1.5z)$.",
"role": "user"
}
] | math | {
"ground_truth": "2z^3 - \\frac{4}{3}z^2 + \\frac{38}{9}z - \\frac{68}{27}",
"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 lengths of the sides of a non-degenerate triangle are \\(x\\), 15, and 40 units. How many integer values of \\(x\\) are possible?",
"role": "user"
}
] | math | {
"ground_truth": "29",
"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 pen, a pencil, and an ink refill together cost $\\;\\$2.40$. The pen costs $\\;\\$1.50$ more than the ink refill, and the pencil costs $\\;\\$0.40$ less than the ink refill. Wh... | math | {
"ground_truth": "0.03",
"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 regular octagon (8 sides) is inscribed in a circle with radius \\( s \\) inches. Calculate the area of the octagon, in square inches.\nA) \\(2s^2\\)\nB) \\(2\\sqrt{2}s^2\\)\nC)... | math | {
"ground_truth": "\\textbf{(B)}\\ 2\\sqrt{2}s^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 a set of sample data: $56$, $62$, $63$, $63$, $65$, $66$, $68$, $69$, $71$, $74$, $76$, $76$, $77$, $78$, $79$, $79$, $82$, $85$, $87$, $88$, $95$, $98$, find the sum of th... | math | {
"ground_truth": "148",
"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": "Consider the following sequence of sets: $ \\{ 1,2\\} ,\\{ 3,4,5\\}, \\{ 6,7,8,9\\} ,... $ **a)** Find the samllest element of the $ 100\\text{-th} $ term.**b)** Is $ 2015 $ ... | math | {
"ground_truth": "2015",
"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": "Consider the equation $3^{x+1} + 3^{x+1} + 3^{x+1} = 243$. Find the value of $x^2 - 1$.",
"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": "Mark has $\\frac{5}{6}$ of a dollar, Carolyn has $\\frac{3}{10}$ of a dollar, and Jim has $\\frac{1}{2}$ of a dollar. How many dollars do they have altogether? (Give your answer ... | math | {
"ground_truth": "\\$1.63",
"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 a regular hexagon, a circle is drawn circumscribing it and another circle is drawn inscribing it. The ratio of the area of the larger circle to the area of the smaller circ... | math | {
"ground_truth": "7",
"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": "Add $45.92$ to $68.453$ and round your answer to the nearest tenth.",
"role": "user"
}
] | math | {
"ground_truth": "114.4",
"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": "Determine all functions $f:\\mathbb{R}\\to\\mathbb{R}$ for which there exists a function $g:\\mathbb{R}\\to\\mathbb{R}$ such that $f(x)+f(y)=\\lfloor g(x+y)\\rfloor$ for al... | math | {
"ground_truth": "f(x) = \\frac{n}{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 basket contains a certain number of grapes. If the grapes are distributed as evenly as possible among 7 children, what is the maximum number of grapes that could be left over a... | 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": "Let $n,k$ be positive integers so that $n \\ge k$ .Find the maximum number of binary sequances of length $n$ so that fixing any arbitary $k$ bits they do not produce all b... | math | {
"ground_truth": "\\sum_{i=0}^{k-1} \\binom{n}{i}",
"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 $r$ and $s$ are the roots of the quadratic equation $x^2 - px - q = 0$, find the value of $r^3 + s^3$.\n**A)** $p^3 - 3pq$ \n**B)** $p^3 + 3pq$ \n**C)** $p^3 - pq$ \n**D)*... | math | {
"ground_truth": "\\textbf{(B)}\\ p^3 + 3pq",
"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 an isosceles trapezoid, there are two touching circles of radii $R$, each of which touches both bases and one of the lateral sides, and the centers of the circles lie on the d... | math | {
"ground_truth": "2R\\sqrt{2}, 2R\\sqrt{2}, 2R\\sqrt{2}, 2R(2 + \\sqrt{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": "There are 2019 numbers written on the board. One of them occurs more frequently than the others - 10 times. What is the minimum number of different numbers that could be written ... | math | {
"ground_truth": "225",
"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": "What is the two-digit number which, when divided by the digit in the units place, results in a quotient of 9 and a remainder of 6?",
"role": "user"
}
] | math | {
"ground_truth": "78",
"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 diagonal $DB$ of rectangle $ABCD$ is divided into three segments of length $1$ by parallel lines $L$ and $L'$ that pass through $A$ and $C$ and are perpendicular to $DB$.",... | math | {
"ground_truth": "4.2",
"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": "Consider each positive integer $n$, let $g_1(n)$ be thrice the number of positive integer divisors of $n$ raised to the power of 2, and for $j \\ge 2$, let $g_j(n) = g_1(g_{j-1}(... | math | {
"ground_truth": "0",
"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": "Point $P$ is located inside a square $ABCD$ of side length $10$ . Let $O_1$ , $O_2$ , $O_3$ , $O_4$ be the circumcenters of $P AB$ , $P BC$ , $P CD$ , and $P DA$ , ... | math | {
"ground_truth": "5001",
"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 $w_{1}$ and $w_{2}$ be two circles which intersect at points $A$ and $B$ . Consider $w_{3}$ another circle which cuts $w_{1}$ in $D,E$ , and it is tangent to $w_... | 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": "The sequence $\\left\\{a_{n}\\right\\}$ satisfies $a_{1} = 1$, and for each $n \\in \\mathbf{N}^{*}$, $a_{n}$ and $a_{n+1}$ are the roots of the equation $x^{2} + 3n x + b_{n} = ... | math | {
"ground_truth": "6385",
"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": "Suppose $3x - 2y - 4z = 0$ and $2x + y - 9z = 0$, for $z \\neq 0$. Determine the numerical value of $\\frac{x^2 - 2xy}{y^2 + 2z^2}$.\n**A)** $-\\frac{24}{25}$ \n**B)** $-\\frac{6... | math | {
"ground_truth": "-\\frac{24}{25}",
"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 the remainder when \\( x^{101} \\) is divided by \\( (x+1)^4 \\).",
"role": "user"
}
] | math | {
"ground_truth": "166650x^3 - 3520225x^2 + 67605570x - 1165299255",
"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 circle's radius is increased by 50%, and its circumference is also increased by 50%. Determine the percentage increase in the area of the circle.",
"role": "user"
}
] | math | {
"ground_truth": "125\\%",
"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": "Calculate the coefficient of $x^5$ in the expansion of the series $(1+x)^5 + (1+x)^6 + (1+x)^7 + \\ldots + (1+x)^{2009}$.\nA) $\\binom{2009}{5}$\nB) $\\binom{2010}{5}$\nC) $\\bin... | math | {
"ground_truth": "\\binom{2010}{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": "Circle \\(\\omega\\) has radius 5 and is centered at \\(O\\). Point \\(A\\) lies outside \\(\\omega\\) such that \\(OA = 13\\). The two tangents to \\(\\omega\\) passing through ... | math | {
"ground_truth": "17",
"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": "What is the degree measure of an interior angle of a regular octagon?",
"role": "user"
}
] | math | {
"ground_truth": "135^\\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": "Find the sum of all roots for the polynomial $3x^3 - 9x^2 - 48x - 12 = 0$.",
"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": "A $ 20\\times20\\times20$ block is cut up into 8000 non-overlapping unit cubes and a number is assigned to each. It is known that in each column of 20 cubes parallel to any edg... | math | {
"ground_truth": "333",
"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 Cartesian coordinate system $xy$, a circle with center O is tangent to the line $x - \\sqrt{3}y = 4$.\n(I) Find the equation of circle O.\n(II) The circle O intersects the... | math | {
"ground_truth": "[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": "How many different routes are there from point $A$ to point $B$ if you can only move to the right, down, or diagonally to the right-down along the drawn segments on a 3x3 grid?\n... | math | {
"ground_truth": "24",
"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 initially 2 inches long grows following this pattern:\n\\[ 2 + \\frac{1}{3} + \\frac{1}{3}\\sqrt{3} + \\frac{1}{9} + \\frac{1}{9}\\sqrt{3} + \\frac{1}{27} + \\frac{1}{27}\... | math | {
"ground_truth": "\\frac{5 + \\sqrt{3}}{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": "John's car achieves a fuel efficiency of $40$ miles per gallon. Currently, the cost of gas is $\\$5$ per gallon. How many miles can John drive on $\\$25$ worth of gas?",
"rol... | math | {
"ground_truth": "200",
"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 triangle \\(ABC\\), it is known that \\(\\angle A=\\alpha, \\angle C=\\beta, AB=a\\); \\(AD\\) is the angle bisector. Find \\(BD\\).",
"role": "user"
}
] | math | {
"ground_truth": "a \\cdot \\frac{\\sin \\frac{\\alpha}{2}}{\\sin (\\frac{\\alpha}{2} + \\beta)}",
"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": "Five more than four times \\(C\\) is equal to 25. What is the value of \\(C\\)?",
"role": "user"
}
] | 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": "Compute \\[\\sum_{k=1}^{100} \\log_2\\left(1 + \\frac{1}{k}\\right) \\log_k 2 \\log_{k+1} 2.\\]",
"role": "user"
}
] | math | {
"ground_truth": "0.8498",
"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": "Compute the value of the infinite series \\[\n\\sum_{n=3}^{\\infty} \\frac{n^4 + 2n^3 + 9n^2 + 18n + 24}{2^n \\cdot \\left(n^4 + 2n^3 + 5n^2 + 8n + 8\\right)}\n\\]",
"role": ... | math | {
"ground_truth": "\\frac{227}{448}",
"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 sum of two numbers is \\( t \\) and the positive difference between the squares of these two numbers is 208. What is the larger of the two numbers?",
"role": "user"
}
] | math | {
"ground_truth": "53",
"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": "How many $n$-digit numbers ($n \\geq 3$) can be formed using the digits $1, 2, 3$, where each digit is used at least once?",
"role": "user"
}
] | math | {
"ground_truth": "3^n - 3 \\cdot 2^n + 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 $n \\ge 3$ be an integer and $S$ be a set of $n$ elements. Determine the largest integer $k_n$ such that: for each selection of $k_n$ $3-$ subsets of $S$ , there ... | math | {
"ground_truth": "k_n = 6",
"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 a bag containing only black and white balls, with 2 white balls and n black balls, a ball is randomly drawn, recorded, and then returned to the bag. After a large number of... | 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": "Let $k$ be a natural number such that $k\\ge 7$ . How many $(x,y)$ such that $0\\le x,y<2^k$ satisfy the equation $73^{73^x}\\equiv 9^{9^y} \\pmod {2^k}$ ?\n\n*Proposed b... | math | {
"ground_truth": "2^{k+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": "For each positive integer $n$, find the number of $n$-digit positive integers that satisfy both of the following conditions:\n$\\bullet$ no two consecutive digits are equal, and\... | math | {
"ground_truth": "\\frac{2}{5} (9^n + (-1)^{n+1})",
"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 that $O$ is the origin, $P$ is any point on the line $2x + y - 2 = 0$, and $\\vec{a} = (m, n)$ is a non-zero vector. If the dot product of $\\vec{OP}$ and $\\vec{a}$ is alw... | math | {
"ground_truth": "\\frac{m}{n} = 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": "Ella works for 4 hours a day and is paid $1.00 per hour for each full year of her age. During a year, Ella worked 180 days and her pay totaled $7920. Ella had her birthday during... | math | {
"ground_truth": "B) 60 days",
"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 vectors $\\mathbf{a},$ $\\mathbf{b},$ $\\mathbf{c},$ and $\\mathbf{d}$ be such that $\\mathbf{a} + \\mathbf{b} + \\mathbf{c} = \\mathbf{d}.$ There exists a scalar $k$ such th... | math | {
"ground_truth": "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": "Masha came up with the number \\( A \\), and Pasha came up with the number \\( B \\). It turned out that \\( A + B = 2020 \\), and the fraction \\( \\frac{A}{B} \\) is less than ... | math | {
"ground_truth": "\\frac{403}{1617}",
"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": "Calculate the volume of tetrahedron PQRS where PQ = 3, PR = 4, PS = 5, QR = √17, QS = 2√10, and RS = √29.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Circle $A$ has a radius of $100$. Circle $B$ has an integer radius $r<100$ and remains internally tangent to circle $A$ as it rolls once around the circumference of circle $A$. T... | math | {
"ground_truth": "8",
"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 expression $\\frac{x + 1}{x - 1}$, where each $x$ is replaced by $\\frac{x + 1}{x - 1}$, evaluate the resulting expression for $x = \\frac{1}{2}$.",
"role": "user"
... | math | {
"ground_truth": "-3",
"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": "Tessa has a unit cube, on which each vertex is labeled by a distinct integer between 1 and 8 inclusive. She also has a deck of 8 cards, 4 of which are black and 4 of which are wh... | math | {
"ground_truth": "42648",
"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 total area of metal wasted when a circular disc is cut out from a square metallic sheet of side length \\( s \\), and then a rectangle (with the rectangle's longer side ... | math | {
"ground_truth": "\\frac{s^2}{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 that $f(x)$ is a quadratic function, if $f(0)=0$, and $f(x+1)=f(x)+x+1$\n(1) Find the explicit formula for the function $f(x)$;\n(2) Find the range of the function $y=f(x^2... | math | {
"ground_truth": "[-\\frac{1}{8}, +\\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": "Calculate the number of trailing zeroes in $1500!$. Additionally, determine the smallest non-zero digit at the end of $1500!$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "For all real numbers $r$ , denote by $\\{r\\}$ the fractional part of $r$ , i.e. the unique real number $s\\in[0,1)$ such that $r-s$ is an integer. How many real numbers... | math | {
"ground_truth": "2^{2017}",
"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 $i(1-z)=1$, calculate the value of $z+\\overline{z}$.",
"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 area and perimeter of a rectangle are 18, find the ordered pairs $(w, l)$ where $w$ is the width and $l$ is the length of the rectangle.",
"role": "user"
}
] | math | {
"ground_truth": "(6, 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": "Find $r$ if $4(r - 10) = 3(3 - 3r) + 9$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{58}{13}",
"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 center of a square, there is a police officer, and in one of the vertices, there is a gangster. The police officer can run throughout the whole square, while the gangster ... | math | {
"ground_truth": "\\text{1/3}",
"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": "The polynomial equation \\[x^3 + ax^2 + bx + c = 0,\\] where $a$, $b$, and $c$ are rational numbers, has $2-\\sqrt{5}$ as a root. It also has an integer root. What is the integer... | 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": "What is ${-\\frac{1}{2} \\choose 100} \\div {\\frac{1}{2} \\choose 100}$?",
"role": "user"
}
] | math | {
"ground_truth": "-199",
"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": "Sandy's daughter has upgraded her playhouse in the backyard. She plans to cover one exterior wall measuring 10 feet wide by 7 feet high and the two identical sloped roof faces, e... | math | {
"ground_truth": "\\$70",
"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 the limit of the function:\n\\[\n\\lim _{x \\rightarrow \\frac{\\pi}{4}}\\left(\\frac{\\ln (\\tan x)}{1-\\cot x}\\right)^{\\frac{1}{x+\\frac{\\pi}{4}}}\n\\]",
"role... | math | {
"ground_truth": "1",
"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 \\[f(x) =\n\\begin{cases}\nx/3 &\\quad \\text{if } x \\text{ is divisible by 3}, \\\\\n5x+2 &\\quad \\text{if } x \\text{ is not divisible by 3}.\n\\end{cases}\n\\] What is $... | math | {
"ground_truth": "4687",
"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": "Consider the lines with equations \\( y = mx \\) and \\( y = -2x + 28 \\) where \\( m \\) is some real number. The area enclosed by the two lines and the \\( x \\)-axis in the fi... | 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": "A line is described by the equation $\\frac{x}{4} + \\frac{y}{3} = 1$. Determine the slope of this line and calculate the midpoint of the segment formed by the intercepts of this... | math | {
"ground_truth": "(2, 1.5)",
"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": "1. (Optional question on coordinate systems and parametric equations) If the polar equation of a curve is $p=2\\sin\\theta+4\\cos\\theta$, and a Cartesian coordinate system is es... | math | {
"ground_truth": "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": "Given that the sequence $\\{a_n\\}$ is an arithmetic sequence, and $a_1+a_2+a_3=15$, the sequence $\\{b_n\\}$ is a geometric sequence, and $b_1b_2b_3=27$, with $a_1=b_2$ and $a_4... | math | {
"ground_truth": "2n^2+4n+\\frac{3}{2}\\cdot3^n-\\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": "Buses from Austin to San Antonio leave every 30 minutes on the hour and the half hour. Buses from San Antonio to Austin leave every 45 minutes starting from 15 minutes past every... | math | {
"ground_truth": "The correct answer is D) 10.",
"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 $a \\oplus b$ means $4a + 2b$, find the value of $y$ if $3 \\oplus (4 \\oplus y) = -14$.",
"role": "user"
}
] | math | {
"ground_truth": "-14.5",
"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": "Find all positive integers \\( n > 2 \\) for which \\( \\left(1 + n + \\frac{n(n-1)}{2} + \\frac{n(n-1)(n-2)}{6} \\right) \\) divides \\( 2^{2000} \\).",
"role": "user"
}
] | math | {
"ground_truth": "n = 3, 7, \\text{or } 23",
"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": "$P, Q, R,$ and $S$ are distinct positive integers such that the product $PQ = 72$, the product $RS = 72$, and $P + Q = R - S$. What is $P$?",
"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": "Let $n\\geq 3$ be an integer. $n$ balls are arranged in a circle, and are labeled with numbers $1,2,\\cdots,n$ by their order. There are $10$ colors, and each ball is col... | math | {
"ground_truth": "24",
"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": "Alice has three daughters, each of whom has two daughters, each of Alice's six grand-daughters has one daughter. How many sets of women from the family of $16$ can be chosen su... | math | {
"ground_truth": "793",
"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 definite integral:\n\n$$\n\\int_{0}^{2 \\pi} (3 - 7x^2) \\cos(2x) \\, dx\n$$",
"role": "user"
}
] | math | {
"ground_truth": "-7\\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": "Given that Alex received $150$ points in a $60$-question multiple choice math contest, where $5$ points are awarded for a correct answer, $0$ points for an answer left blank, and... | math | {
"ground_truth": "38",
"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 quadratic function $y=5x^{2}$, first shift its graph $3$ units to the right and then $2$ units down, and determine the resulting analytical expression.",
"role": "u... | math | {
"ground_truth": "y = 5(x-3)^{2} - 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": "Compute $\\gcd(47^5+1, 47^5 + 47^3 + 1)$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Let $n$ be a positive integer and $d(n)$ be the number of positive divisors of $n$ .\nFind all $n$ such that $n^{d(n)+1}(n+21)^{d(n)}$ is a square.",
"role": "user"
... | math | {
"ground_truth": "4 \\text{ and } 100",
"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 $y+4=(x-2)^2$ and $x+4=(y-2)^2$, find the value of $x^2+y^2$.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"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": "Several weights are given, each of which is not heavier than $1 \\mathrm{lb}$. It is known that they cannot be divided into two groups such that the weight of each group is great... | math | {
"ground_truth": "3 \\ \\mathrm{lb}",
"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": "An inverted cone with a base radius of $10 \\mathrm{cm}$ and a height of $15 \\mathrm{cm}$ is full of water. This water is then poured into a cylinder with a base radius of $20 \... | math | {
"ground_truth": "1.25 \\text{ cm}",
"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 $\\sin \\alpha - \\cos \\alpha = -\\frac{1}{5}$, find the value of $\\sin 2\\alpha$.",
"role": "user"
}
] | math | {
"ground_truth": "\\sin 2\\alpha = \\frac{24}{25}",
"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 $a\\ge2$, $b\\ge1$, and $c\\ge0$, and the equations $\\log_a b = c^{2005}$ and $a + b + c = 2005$ hold, determine the number of ordered triples of integers $(a,b,c)$."... | math | {
"ground_truth": "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": "A circular coin \\(A\\) is rolled, without sliding, along the circumference of another stationary circular coin \\(B\\) with radius twice the radius of coin \\(A\\). Let \\(x\\) ... | math | {
"ground_truth": "1080",
"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": "What is the volume, in cubic units, of a cube whose surface area is 864 square units?",
"role": "user"
}
] | math | {
"ground_truth": "1728",
"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 driver travels for 3 hours at a speed of 50 miles per hour. Given the car's gasoline efficiency is 25 miles per gallon, and gasoline currently costs $2.50 per gallon, and the d... | math | {
"ground_truth": "25",
"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": "From the operation of fractions, we know that $\\frac{1}{1\\times2}=\\frac{1}{1}-\\frac{1}{2}$, $\\frac{1}{2\\times3}=\\frac{1}{2}-\\frac{1}{3}$, ..., $\\frac{1}{n(n+1)}=\\frac{1... | math | {
"ground_truth": "\\frac{2015}{2016}",
"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 number of real values of $x$ that satisfy the equation $2^{x^2 - 3x + 2} - 1 = 0$.",
"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": "Crestview's school colors are purple, gold, and silver. The students are designing a flag using four solid-colored horizontal stripes. Using one or more of the school colors, how... | math | {
"ground_truth": "24",
"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 numbers from 1 to 200, inclusive, are placed in a bag and a number is randomly selected from the bag. What is the probability it is not a perfect power (integers that can be ... | math | {
"ground_truth": "\\frac{181}{200}",
"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 \\( \\fbox{2, -1, 0} \\) where \\( \\fbox{a, b, c} = a^b - b^c + c^a \\).",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{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": "For every real number \\( x \\), let \\( \\lfloor x \\rfloor \\) denote the greatest integer less than or equal to \\( x \\). The fractional part of \\( x \\), denoted as \\( \\l... | math | {
"ground_truth": "91",
"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 solid cube has its faces randomly painted either red or blue, with each face independently deciding its color. What is the probability that the cube has at least one blue face ... | math | {
"ground_truth": "\\frac{27}{64}",
"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 $\\oplus(\\oplus(1,3,2), \\oplus(2,1,4), \\oplus(3,4,1))$?",
"role": "user"
}
] | math | {
"ground_truth": "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": "How many three-digit positive integers exist, all of whose digits are 2's, 5's, and/or 7's?",
"role": "user"
}
] | math | {
"ground_truth": "27",
"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": "James is trying to fence a rectangular area containing at least 120 sq. ft while using the least amount of material to build the fence. The length of the rectangular area should ... | 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": "Let $n>1$ be an integer and $S_n$ the set of all permutations $\\pi : \\{1,2,\\cdots,n \\} \\to \\{1,2,\\cdots,n \\}$ where $\\pi$ is bijective function. For every permut... | math | {
"ground_truth": "\\frac{n^2 - 1}{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": "What is the smallest sum of two $3$-digit numbers that can be obtained by placing each of the six digits $1, 2, 3, 7, 8, 9$ in one of the six boxes in this addition problem?\n[as... | math | {
"ground_truth": "417",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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