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": "It is well-known that a quadratic equation has no more than 2 roots. Is it possible for the equation $\\lfloor x^2\\rfloor+px+q=0$ with $p\\neq 0$ to have more than 100 roots... | math | {
"ground_truth": "\\text{We have 119 solutions for the equation } \\lfloor x^2 \\rfloor + 60x + 900 = 0 \\text{ : } x_n = -\\frac{n + 900}{60} \\forall n \\in \\{841, 842, \\ldots, 958, 959\\}",
"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": "Marguerite drove 120 miles in 3 hours. If Sam drove for 4 hours at the same average rate as Marguerite, how many miles did he drive?",
"role": "user"
}
] | math | {
"ground_truth": "160\\textnormal{ miles}",
"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 four-digit number 3003, calculate the total number of different numbers that can be formed by rearranging the four digits.",
"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": "The domain of the function $f(x)=\\frac{\\ln(2x-x^2)}{x-1}$ is .",
"role": "user"
}
] | math | {
"ground_truth": "(0,1)\\cup(1,2)",
"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": "Let $g$ be a function satisfying $g(xy) = g(x)/y$ for all positive real numbers $x$ and $y$. If $g(900) = 5$, what is the value of $g(1000)$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{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": "A region is formed by eight congruent squares, with a total area of 400 square centimeters. The squares are arranged in a configuration with two rows; the first row contains thre... | math | {
"ground_truth": "90\\sqrt{2} \\text{ cm}",
"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 fraction\n\\[\n\\frac{\\left(5^{2022}\\right)^2-\\left(5^{2020}\\right)^2}{\\left(5^{2021}\\right)^2-\\left(5^{2019}\\right)^2}\n\\]\nand determine its simplified va... | math | {
"ground_truth": "C) 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": "Given that the odd function $f(x)$ is monotonically increasing in the interval $(0, +\\infty)$, and $f(2)=0$, then the solution set of the inequality $(x-1)\\cdot f(x)<0$ is.",
... | math | {
"ground_truth": "(-2,0) \\cup (1,2)",
"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 mean weight of the rocks in X is 30 pounds, the mean weight of the rocks in Y is 70 pounds, the mean weight of the rocks in the combined piles X and Y is 50 pounds, and... | math | {
"ground_truth": "70",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The arithmetic mean of four numbers is 10. If one of these numbers is removed, the arithmetic mean of the remaining three increases by 1. If a different number is removed instead... | 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": "$(1)$ Calculate: $\\sqrt{3}\\tan 45^{\\circ}-\\left(2023-\\pi \\right)^{0}+|2\\sqrt{3}-2|+(\\frac{1}{4})^{-1}-\\sqrt{27}$; <br/>$(2)$ Simplify first, then evaluate: $\\frac{{{x^2... | math | {
"ground_truth": "\\frac{4}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The point \\( Q(c,d) \\) in the \\( xy \\)-plane is first rotated counterclockwise by \\( 90^\\circ \\) around the point \\( (3,2) \\) and then reflected about the line \\( y = x... | 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 the universal set $U=\\{\\text{non-negative even numbers not greater than 10}\\}$, $A=\\{0, 2, 4, 6\\}$, $B=\\{x|x\\in A, \\text{ and } x<4\\}$, find the set $\\complement_... | math | {
"ground_truth": "\\{4, 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": "Let $g(x) = \\frac{x + 8}{x}.$ The sequence $(g_n)$ of functions is defined by $g_1 = g$ and\n\\[g_n = g \\circ g_{n - 1}\\]for all $n \\ge 2.$ For example,\n\\[g_2(x) = g(g(x)... | 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": "Circle $C_{1}$: $x^{2}+y^{2}-2mx+m^{2}-4=0$ intersects with circle $C_{2}$: $x^{2}+y^{2}+2x-4my+4m^{2}-8=0$. Determine the range of values for $m$.",
"role": "user"
}
] | math | {
"ground_truth": "\\left(- \\frac{12}{5}, - \\frac{2}{5}\\right) \\cup \\left(\\frac{3}{5}, 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": "If $2p + 5q = 7$ and $5p + 2q = 16$, what is $q$ equal to?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{7}",
"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": "Jessica enjoys vanilla ice cream, and she visits her favorite ice cream shop every day for a week. However, sometimes the shop serves only chocolate ice cream, so each day the sh... | math | {
"ground_truth": "\\frac{945}{16384}",
"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": "$\\left(100-\\left(5050-450\\right)\\right)+\\left(5050-\\left(450-100\\right)\\right) = ?$",
"role": "user"
}
] | 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": "Let $a$ and $b$ be real numbers bigger than $1$ . Find maximal value of $c \\in \\mathbb{R}$ such that $$ \\frac{1}{3+\\log _{a} b}+\\frac{1}{3+\\log _{b} a} \\geq c $$"... | math | {
"ground_truth": "\\frac{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": "Calculate the area of the pentagon with sides of length 18, 25, 30, 28, and 25 units.\n\n[asy]\npair a,b,c,d,e;\na=(0,0);\nb=(28,0);\nc=(28,30);\nd=(6.2,39);\ne=(0,25);\ndraw((0,... | math | {
"ground_truth": "1020",
"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 modulo $7$ remainder of the sum $1 + 2 + 3 + \\ldots + 125 + 126 + 127$.",
"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 $R=gS-4$. When $S=8$, $R=16$. Find the value of $R$ when $S=10$.",
"role": "user"
}
] | math | {
"ground_truth": "21",
"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": "The base of the pyramid \\(TABC\\) is a triangle \\(ABC\\), all sides of which are equal to 3, and the height of the pyramid, equal to \\(\\sqrt{3}\\), coincides with the lateral... | math | {
"ground_truth": "\\frac{11 \\sqrt{3}}{10}",
"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 circle with a radius of 6 is inscribed in a rectangle. The ratio of the length of the rectangle to its width is 3:1. Calculate the area of the rectangle.",
"role": "user"
... | math | {
"ground_truth": "432",
"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 rectangle $ABCD$, $AB = 150$. Let $E$ be the midpoint of $\\overline{AD}$. Let $F$ be a point on $AD$ such that $\\overline{BF}$ is perpendicular to $\\overline{AD}$. Given th... | math | {
"ground_truth": "212",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that there are five departments in a company with reported transactions: Sales: $50$, Marketing: $80$, HR: $30$, Finance: $60$, IT: $40$, and that the HR department actuall... | math | {
"ground_truth": "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": "An equilateral triangle is originally painted black. Each time the triangle is changed, the middle fourth of each black triangle turns white. After five changes, what fractiona... | math | {
"ground_truth": "\\frac{243}{1024}",
"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": "If $x \\in R-\\{-7\\}$ , determine the smallest value of the expression $$ \\frac{2x^2 + 98}{(x + 7)^2} $$",
"role": "user"
}
] | math | {
"ground_truth": "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": "How many pairs of parallel edges are there in a rectangular prism where the length, width, and height are distinct?\nA) 4 \nB) 6 \nC) 8 \nD) 12 \nE) 18",
"role": "user"
... | math | {
"ground_truth": "B) 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": "Round 2748397.542 to the nearest integer.",
"role": "user"
}
] | math | {
"ground_truth": "2748398",
"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": "Stuart has drawn a pair of concentric circles. He draws chords $\\overline{AB}$, $\\overline{BC}, \\ldots$ of the large circle, each tangent to the smaller circle. If $m\\angle A... | math | {
"ground_truth": "3",
"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": "Alex the Kat has written $61$ problems for a math contest, and there are a total of $187$ problems submitted. How many more problems does he need to write (and submit) before... | math | {
"ground_truth": "65",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify the expression $\\dfrac{45}{28} \\cdot \\dfrac{49}{75} \\cdot \\dfrac{100}{63}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{3}",
"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 gigantic sphere has a volume of $972\\pi$ cubic units. A miniature sphere carved from inside this gigantic sphere accounts for $64\\%$ of its volume. Determine the ratio of the... | math | {
"ground_truth": "\\frac{108}{125}",
"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": "On side AC of triangle ABC with a 120-degree angle at vertex B, points D and E are marked such that AD = AB and CE = CB. A perpendicular DF is dropped from point D to line BE. 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": "Find all values of the parameter \\(a\\) for which there exists a number \\(b\\) such that the system\n\n$$\n\\left\\{\\begin{array}{l}\nx = \\frac{6}{a} - |y - a| \\\\\nx^{2} + ... | math | {
"ground_truth": "a \\in \\left(-\\infty, -\\frac{2}{3}\\right] \\cup (0, \\infty)",
"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": "Solve the inequality:\n(1) $\\frac{x-4}{x+3} \\geq 0$;\n(2) $\\frac{x^{2}-6 x+8}{x^{2}+5 x+6} \\leq 0$.",
"role": "user"
}
] | math | {
"ground_truth": "(-3, -2) \\cup [2, 4]",
"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 there exists a permutation \\( a_{1}, a_{2}, \\cdots, a_{n} \\) of \\( 1, 2, \\cdots, n \\) such that \\( k + a_{k} \\) (for \\( k = 1, 2, \\cdots, n \\)) are all perfect squa... | math | {
"ground_truth": "\\{1, 2, 4, 6, 7, 9, 11\\}",
"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 has a cold and must take two blue pills and one orange pill every day for three weeks. An orange pill costs $2 more than a blue pill, and his pills cost a total of $804 for t... | math | {
"ground_truth": "14.10",
"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": "When two dice are rolled simultaneously, the probability of neither showing a $5$ or a $6$ is $\\frac{4}{9}$. What is the probability of at least one die showing a $5$ or a $6$?"... | math | {
"ground_truth": "\\frac{5}{9}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle and a square with equal areas have the same center. What percentage of the square's area is covered by the circle? (Give the answer rounded to the nearest whole percent.... | 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": "At what smallest $n$ is there a convex $n$ -gon for which the sines of all angles are equal and the lengths of all sides are different?",
"role": "user"
}
] | math | {
"ground_truth": "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": "The points $(2, 5), (14, 19)$, and $(6, m)$, where $m$ is an integer, are vertices of a triangle. What is the sum of the values of $m$ for which the area of the triangle is a min... | math | {
"ground_truth": "21",
"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 current time is 6:00 a.m. What time will it be in 1876 minutes?",
"role": "user"
}
] | math | {
"ground_truth": "1\\!:\\!16 \\text{ p.m.}",
"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": "Define a number as special-prime-looking if it is composite but not divisible by $2, 7,$ or $11$. The three smallest special-prime-looking numbers are $15, 21$, and $33$. There a... | math | {
"ground_truth": "(\\mathrm {B}) \\ 478",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The center of a circle has coordinates $(3, -7)$. The circle is reflected about the line $y=-x$. What are the $x,y$ coordinates of the center of the image circle? State the $x$ c... | math | {
"ground_truth": "(7, -3)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\{a_n\\}$ is a geometric sequence, $a_1=2$, and $a_1$, $a_3+1$, $a_4$ form an arithmetic sequence.\n\n(Ⅰ) Find the general formula for the sequence $\\{a_n\\}$.\n\n(... | math | {
"ground_truth": "\\dfrac{n(n+1)}{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": "Determine all prime numbers \\( p \\) for which there exists a unique \\( a \\) in \\( \\{1, \\ldots, p\\} \\) such that \\( a^{3} - 3a + 1 \\) is divisible by \\( p \\).",
"... | 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": "Given a circle passing through the point $\\left(2,1\\right)$ is tangent to both coordinate axes, calculate the distance from the center of the circle to the line $2x-y-3=0$.",
... | math | {
"ground_truth": "\\frac{2\\sqrt{5}}{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 the expression $2-(-3)-4\\times(-5)-6-(-7)-8\\times(-9)+10$, evaluate this expression.",
"role": "user"
}
] | math | {
"ground_truth": "108",
"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": "Multiply and simplify the following expression:\n\n\\[\n\\frac{1-a x}{1+a x} \\cdot \\sqrt{\\frac{1+b x}{1-b x}}\n\\]\n\nwith the condition:\n\n\\[\nx=\\frac{1}{a} \\cdot \\sqrt{... | 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": "In a certain triangle $ABC$ , there are points $K$ and $M$ on sides $AB$ and $AC$ , respectively, such that if $L$ is the intersection of $MB$ and $KC$ , then both ... | math | {
"ground_truth": "\\angle BAC = 45^\\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": "Find set of positive integers divisible with $8$ which sum of digits is $7$ and product is $6$",
"role": "user"
}
] | math | {
"ground_truth": "1312 \\text{ and } 3112",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $a, b, c$ such that $ab + 1$ , $bc + 1$ , and $ca + 1$ are all equal to\nfactorials of some positive integers.\n\nProposed by *Nikola Velov, Mace... | math | {
"ground_truth": "(k! - 1, 1, 1)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "LeRoy, Bernardo, and Clara went on a month-long project and agreed to share the costs equally. Each of them paid for various project expenses. At the end of the project, it turne... | math | {
"ground_truth": "\\textbf{(C)}\\ \\frac{B + C - X - 2L}{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": "Let $k,x,y$ be postive integers. The quotients of $k$ divided by $x^2, y^2$ are $n,n+148$ respectively.( $k$ is divisible by $x^2$ and $y^2$ )\n(a) If $\\gcd(x,y)=1$... | math | {
"ground_truth": "467856",
"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 pairs \\((n, m)\\) such that \\(n > 2, m > 2\\), and there are infinitely many natural numbers \\(k\\) such that \\(k^n + k^2 - 1\\) divides \\(k^m + k - 1\\).",
"ro... | math | {
"ground_truth": "(3, 5)",
"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 sum of two numbers is $R$. Suppose $5$ is added to each number and then each of the resulting numbers is tripled. What is the sum of the final two numbers?",
"role": "use... | math | {
"ground_truth": "3R + 30",
"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 all complex numbers $z$, let \\[f(z) = \\left\\{\n\\begin{array}{cl}\nz^{2}&\\text{ if }z\\text{ is not real}, \\\\\n-z^2 &\\text{ if }z\\text{ is real}.\n\\end{array}\n\\rig... | math | {
"ground_truth": "503521 + 420000i",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the tens digit of $3^{2013}$?",
"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": "Determine the sum of the series $\\dfrac{1}{1\\cdot 4}+ \\dfrac{1}{4\\cdot 7}+ \\dfrac{1}{7\\cdot 10}+ \\cdots + \\dfrac{1}{(3n-2)(3n+1)}=$ \\_\\_\\_\\_\\_\\_\\_\\_",
"role":... | math | {
"ground_truth": "\\dfrac{n}{3n+1}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $s$ be the result when the base and the exponent of $c^d$ are quadrupled, where $c,d>0$. If $s$ equals the product of $c^d$ and $y^d$ where $y>0$, then find $y$.\nA) $64c^3$\... | math | {
"ground_truth": "256c^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 the numbers $a_1,a_2,a_3,a_4,a_5,a_6 \\in \\{-1,0,1 \\}$, find the total count of values of the expression $a_1\\cdot 5^1+a_2\\cdot 5^2+a_3\\cdot 5^3+a_4\\cdot 5^4+a_5\\cdo... | math | {
"ground_truth": "364",
"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": "Fiona joins Abe, Bobby, Charles, Devin, and Edwin in a race. How many different 1st-2nd-3rd-4th place outcomes are possible if there are no ties?",
"role": "user"
}
] | math | {
"ground_truth": "360",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When $777_{10}$ is expressed in this base, it has 4 digits, in the form ABBA, where A and B are two different digits. What base is it?",
"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": "Over all real numbers \\( x \\) and \\( y \\) such that\n\\[ x^3 = 3x + y \\quad \\text{and} \\quad y^3 = 3y + x \\]\ncompute the sum of all possible values of \\( x^2 + y^2 \\).... | math | {
"ground_truth": "15",
"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: $(-1)^{2023}-|1-\\sqrt{3}|+\\sqrt{6} \\times \\sqrt{\\frac{1}{2}}$.",
"role": "user"
}
] | 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": "If $\\sin x + \\sin y = \\frac{33}{65}$ and $\\cos x + \\cos y = \\frac{56}{65}$, then calculate the value of $\\tan x + \\tan y$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{33}{28}",
"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 positive integer $n$ , determine the largest integer $M$ satisfying $$ \\lfloor \\sqrt{a_1}\\rfloor + ... + \\lfloor \\sqrt{a_n} \\rfloor \\ge \\lfloor\\sqrt{ a_1 + ... | math | {
"ground_truth": "\\left\\lfloor \\frac{n^2 - 3n}{3} \\right\\rfloor",
"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": "Four runners start running simultaneously from the same point on a 400-meter circular track and maintain constant speeds of 4.0, 5.0, 6.0, and 7.0 meters per second. Calculate th... | math | {
"ground_truth": "1200",
"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 three-digit number 572 subtracted by another three-digit number formed by rearranging its digits to 275, find the outcome for the units, tens, and hundreds columns.\nA) 2... | math | {
"ground_truth": "The correct answer is D) 297.",
"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": "To just reach the light bulb while standing on a box, calculate the minimum height of the box.",
"role": "user"
}
] | math | {
"ground_truth": "70",
"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": "$\\{\\{\\text{2 3 -1}\\} \\text{ [1 2] } 1\\}$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{23}{18}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the empty set is a proper subset of the set $\\{x|x^2 \\leq a, a \\in \\mathbb{R}\\}$, determine the range of the real number $a$.",
"role": "user"
}
] | math | {
"ground_truth": "[0, +\\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": "The chord \\(AB\\) of the parabola \\(y = x^2\\) intersects the y-axis at point \\(C\\) and is divided by it in the ratio \\(AC : CB = 5 : 2\\). Find the x-coordinates of points ... | math | {
"ground_truth": "\\left(x_{A} = -5 \\sqrt{2}, x_{B} = 2 \\sqrt{2}\\right), \\left(x_{A} = 5 \\sqrt{2}, x_{B} = -2 \\sqrt{2}\\right)",
"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 value $2^{10} - 1$ is divisible by several prime numbers. What is the sum of these prime numbers?",
"role": "user"
}
] | math | {
"ground_truth": "45",
"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 sequence of positive integers is defined by \\(a_{0}=1\\) and \\(a_{n+1}=a_{n}^{2}+1\\) for each \\(n \\geq 0\\). Find \\(\\operatorname{gcd}\\left(a_{999}, a_{2004}\\right)\\)... | math | {
"ground_truth": "677",
"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": "During measurement, due to errors from measuring instruments and human observation, the obtained data can have discrepancies from the true values, providing only approximate valu... | math | {
"ground_truth": "x = \\frac{a_{1} + a_{2} + \\cdots + a_{n}}{n}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $f(x) = x^2$, and $g(x)$ is a polynomial such that $f(g(x)) = 9x^2 - 6x + 1$. Determine all possible polynomials $g(x)$.",
"role": "user"
}
] | math | {
"ground_truth": "g(x) = -3x+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 square sheet of paper $ABCD$ is folded straight in such a way that point $B$ hits to the midpoint of side $CD$ . In what ratio does the fold line divide side $BC$ ?",
... | math | {
"ground_truth": "\\frac{5}{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": "The six-digit number $M=\\overline{abc321}$, where $a, b, c$ are three different numbers, and all are greater than 3. If $M$ is a multiple of 7, what is the smallest value of $M$... | math | {
"ground_truth": "468321",
"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 mayor of a city wishes to establish a transport system with at least one bus line, in which:\n- each line passes exactly three stops,\n- every two different lines have exactl... | math | {
"ground_truth": "s = 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": "Jane and Josh wish to buy a candy. However Jane needs seven more cents to buy the candy, while John needs one more cent. They decide to buy only one candy together, but discover ... | 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": "From a group of 3 male and 1 female students, 2 students are randomly selected to form a team to represent their class in a school competition. What is the probability that the t... | math | {
"ground_truth": "\\dfrac{1}{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 points $A(-4,-3)$ and $B(2,9)$, circle $C$ has $AB$ as its diameter.\n(1) Find the equation of circle $C$;\n(2) Let point $P(0,2)$, then find the equation of line $l_{0}$ w... | 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": "For all positive integers $m>10^{2022}$ , determine the maximum number of real solutions $x>0$ of the equation $mx=\\lfloor x^{11/10}\\rfloor$ .",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The school plans to organize a movie viewing for the students either on January 4th or January 10th. After finalizing the date, the teacher informs the class leader. However, due... | math | {
"ground_truth": "82\\%",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the positive value of \\(x\\) which satisfies the equation:\n\\[\n\\log_3 (x^2 - 3) + \\log_9 (x - 2) + \\log_{\\frac{1}{3}} (x^2 - 3) = 2.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "83",
"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 $\\left(81\\right)^{0.25}\\left(81\\right)^{0.20}$, calculate its value.",
"role": "user"
}
] | math | {
"ground_truth": "6.86",
"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": "Using each of the eight digits $1,3,4,5,6,7,8$ and $9$ exactly once, a three-digit number $A$ , two two-digit numbers $B$ and $C$ , $B<C$ , and a one digit number $D$ ... | 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": "The distance d from the point P(2,5) to the line y = -√3x is (∧frac{2√3+5}{2}).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2\\sqrt{3}+5}{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 number of units in the distance between $(3,-1)$ and $(-4,3)$?",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{65}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all real numbers \\( x \\) for which\n\\[\n\\sqrt{3-x} - \\sqrt{x+1} > \\frac{1}{2}.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "-1 \\leq x < 1- \\frac{\\sqrt{31}}{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": "When the number $3^{210}$ is divided by 17, determine the remainder in the division.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Let $0 \\leq p, q, r, s \\leq 1$. Find the possible values of the expression\n\\[\n\\sqrt{p^2 + (1 - q)^2} + \\sqrt{q^2 + (1 - r)^2} + \\sqrt{r^2 + (1 - s)^2} + \\sqrt{s^2 + (1 -... | math | {
"ground_truth": "[2\\sqrt{2}, 4]",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given two lines $l_1: (a-1)x + y + 3 = 0$ and $l_2: 2x + ay + 1 = 0$, if $l_1 \\parallel l_2$, find the value(s) of $a$.",
"role": "user"
}
] | math | {
"ground_truth": "-1, \\ 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": "If $5p + 3q = 10$ and $3p + 5q = 20$, what is $p$ equal to?",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{5}{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": "Given an obtuse triangle $ABC$ with an obtuse angle at $C$. Points $P$ and $Q$ are marked on its sides $AB$ and $BC$ respectively such that $\\angle ACP = CPQ = 90^\\circ$. Find ... | math | {
"ground_truth": "16",
"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 a list of twelve positive integers of which six are known: $5, 9, 3, 7, 10, 6$. What is the largest possible value of the median of this list of twelve positive integers?",... | math | {
"ground_truth": "6.5",
"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": "What is the greatest positive integer $m$ such that $ n^2(1+n^2-n^4)\\equiv 1\\pmod{2^m} $ for all odd integers $n$ ?",
"role": "user"
}
] | math | {
"ground_truth": "m = 7",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
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