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": "Determine the base prime representation of the natural number $360$.",
"role": "user"
}
] | math | {
"ground_truth": "321",
"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": "Two congruent circles centered at points $A$ and $B$ each pass through the other circle's center. The line containing both $A$ and $B$ is extended to intersect the circles at poi... | math | {
"ground_truth": "\\textbf{(B) } 80",
"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 basket contains a mixture of black pens and red pens, at most $2500$ in total. It is known that, when two pens are selected randomly without replacement, there is a probability... | math | {
"ground_truth": "1275",
"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 positive integer $ n$ is called $ good$ if it can be uniquely written simultaneously as $ a_1\\plus{}a_2\\plus{}...\\plus{}a_k$ and as $ a_1 a_2...a_k$ , where $ a_i$ ... | math | {
"ground_truth": "n = p^2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an arithmetic sequence $\\left\\{a_n\\right\\}$ with the sum of the first $n$ terms denoted as $S_n$, and it is known that $\\frac{S_{25}}{a_{23}}=5$ and $\\frac{S_{45}}{a_... | math | {
"ground_truth": "45",
"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": "Megan has lost Fatima's phone number again. This time, Megan remembers that the first three digits are either 296, 299, or 297. The remaining four digits are 0, 1, 6, 6, but she ... | math | {
"ground_truth": "\\frac{1}{36}",
"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 vectors $\\overrightarrow{a}=(\\sin x,m\\cos x)$ and $\\overrightarrow{b}=(3,-1)$.\n(1) If $\\overrightarrow{a}\\parallel\\overrightarrow{b}$ and $m=1$, find the value of $... | math | {
"ground_truth": "[-2 \\sqrt{3}, \\sqrt{3}]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\(AC\\) and \\(BD\\) are two perpendicular chords in a circle. The chords intersect at \\(E\\), such that \\(BE = 3\\), \\(EC = 2\\), and \\(AE = 6\\). The exact perimeter of th... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a_1$, $a_2$, $a_3$, $d_1$, $d_2$, and $d_3$ be real numbers such that for every real number $x$, we have\n\\[\n x^8 - x^6 + x^4 - x^2 + 1 = (x^2 + a_1 x + d_1)(x^2 + a_2 x ... | 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": "At a sandwich shop, there are five types of bread, seven kinds of meat, and six kinds of cheese. A sandwich is made up of one type of bread, one type of meat, and one type of che... | math | {
"ground_truth": "199",
"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 digits { $0,1,2,...,9$ } . Find the number of numbers of 6 digits which cantain $7$ or $7$ 's digit and they is permulated(For example 137456 and 314756 is one numbers... | math | {
"ground_truth": "2002",
"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 complex plane, the line segment with end-points $-7 + 5i$ and $5 - 9i$ is plotted. Find the complex number corresponding to the mid-point of this line segment.",
"role... | math | {
"ground_truth": "-1 - 2i",
"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 circle C: $(x-3)^2+(y-4)^2=4$, and a line $l_{1}$ passing through the fixed point A (1, 0).\n\n(I) If $l_{1}$ is tangent to circle C, find the equation of $l_{1}$.\n\n(... | math | {
"ground_truth": "The lines for the maximum area are y = x - 1 \\text{ or } y = 7x - 7",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that \\(a\\), \\(b\\), and \\(c\\) are three positive numbers that satisfy the equations \\(abc = 1\\), \\(a + \\frac{1}{c} = 7\\), and \\(b + \\frac{1}{a} = 35\\). Find ... | math | {
"ground_truth": "\\frac{11}{61}",
"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 the first seven terms in the geometric sequence $\\frac15,\\frac1{25},\\frac1{125},\\dots$. Express your answer as a common fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{78124}{312500}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The equation of a parabola is \\(y^2 + 8y + 4x + 5 = 0.\\) Find the vertex of the parabola.",
"role": "user"
}
] | math | {
"ground_truth": "\\left(\\frac{11}{4}, -4\\right)",
"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 in square $ABCE$, $AF=2FE$ and $CD=2DE$, find the ratio of the area of $\\triangle BFD$ to the area of square $ABCE$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{9}",
"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": "50 people, consisting of 30 people who all know each other, and 20 people who know no one, are present at a conference. Determine the number of handshakes that occur among the in... | math | {
"ground_truth": "1170",
"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": "Maria has a choice of 12 different muffins, 10 different kinds of butter, and 8 different kinds of jam. If she wants to make a breakfast set with one muffin, one kind of butter, ... | math | {
"ground_truth": "960",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the function $f(x)$ is defined on $\\mathbb{R}$ and has a period of $4$ as an even function. When $x \\in [2,4]$, $f(x)=|\\log_{4}(x-\\frac{3}{2})|$, then the value of... | 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": "Find the minimum value of the function\n\n$$\nf(x)=x^{2}+(x-2)^{2}+(x-4)^{2}+\\ldots+(x-102)^{2}\n$$\n\nIf you obtain a non-integer number, round the result to the nearest whole ... | math | {
"ground_truth": "46852",
"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 $\\{x\\}$ denote the fractional part of the real number $x$. Given $a=(5 \\sqrt{2}+7)^{2017}$, find the value of $a\\{a\\}$.",
"role": "user"
}
] | 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": "Given the polynomial $z^6 - 12z^5 + Az^4 + Bz^3 + Cz^2 + Dz + 36$ has all roots that are positive integers, determine the value of $B$.",
"role": "user"
}
] | math | {
"ground_truth": "-122",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A certain museum plans to recruit an outstanding volunteer guide. The scores of a volunteer in the written test, trial lecture, and interview are $90$, $94$, and $90$ respectivel... | math | {
"ground_truth": "92",
"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 rabbit initially stands at the position $0$ , and repeatedly jumps on the real line. In each jump, the rabbit can jump to any position corresponds to an integer but it cannot ... | math | {
"ground_truth": "\\{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": "Given triangle $ABC$ with $|AB|=18$, $|AC|=24$, and $m(\\widehat{BAC}) = 150^\\circ$. Points $D$, $E$, $F$ lie on sides $[AB]$, $[AC]$, $[BC]$ respectively, such that $|BD|=6$, $... | math | {
"ground_truth": "96",
"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 school plans to purchase 400 workbooks, with each workbook costing x yuan. The school should pay a total of __ yuan.",
"role": "user"
}
] | math | {
"ground_truth": "400x",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify \n\\[\\frac{\\sin{40^\\circ}+\\sin{80^\\circ}}{\\cos{40^\\circ}+\\cos{80^\\circ}}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{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": "Square $AIME$ has sides of length $10$ units. Isosceles triangle $GEM$ has base $EM$, and the area common to triangle $GEM$ and square $AIME$ is $80$ square units. Find the len... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all triples of natural numbers $(a, b, c)$ for which the number $$ 2^a + 2^b + 2^c + 3 $$ is the square of an integer.",
"role": "user"
}
] | math | {
"ground_truth": "(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": "Solve the following system of equations in real numbers:\r\n\\[ \\begin{cases} \\sqrt{x^2-2x+6}\\cdot \\log_{3}(6-y) =x \\sqrt{y^2-2y+6}\\cdot \\log_{3}(6-z)=y \\sqrt{z^2-2z+6}... | math | {
"ground_truth": "x = y = z \\approx 2.5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The lengths of the parallel sides of a trapezoid are 25 cm and 4 cm, and the lengths of the non-parallel sides are 20 cm and 13 cm. Find the height of the trapezoid.",
"role"... | math | {
"ground_truth": "12",
"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 semicircle is inscribed in an isosceles triangle with base $24$ and height $18$. The diameter of the semicircle is along the base of the triangle. Find the radius of the semici... | math | {
"ground_truth": "\\frac{36\\sqrt{13}}{13}",
"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 which integers $k$ does there exist a function $f: \\mathbb{N} \\rightarrow \\mathbb{Z}$ satisfying $f(2006) = 2007$ and:\n\n$$\nf(xy) = f(x) + f(y) + kf(\\operatorname{PGCD}... | math | {
"ground_truth": "0 \\text{ or } -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": "Two circles are externally tangent at a point. Lines $\\overline{PAB}$ and $\\overline{PA'B'}$ are common external tangents with $A$ and $A'$ on the smaller circle, and $B$ and $... | math | {
"ground_truth": "\\pi \\frac{625 + 200\\sqrt{2}}{49}",
"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 $\\text{lcm}(a,b) = 120$, $\\text{lcm}(a,c) = 450$, and $\\text{lcm}(b,c) = 720$, find the number of ordered triples $(a,b,c)$ of positive integers.",
"role": "use... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A$ equal the number of four-digit odd numbers. Let $B$ equal the number of four-digit multiples of 3. Find $A+B$.",
"role": "user"
}
] | math | {
"ground_truth": "7500",
"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": "Gilda has an initial amount of marbles in a bag, and then gives $30\\%$ of them to her friend Pedro. Next, Gilda gives $40\\%$ of what is left to another friend, Ebony. What perc... | math | {
"ground_truth": "42\\%",
"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 Moe, Loki, and Nick each give Ott a portion of their money, with one-fifth of Moe's money, one-fourth of Loki's money, and one-third of Nick's money being equal to eac... | math | {
"ground_truth": "\\frac{1}{4}",
"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": "In an increasing sequence of four positive integers, the first three terms form an arithmetic progression, the last three terms form a geometric progression, and the first and fo... | math | {
"ground_truth": "129",
"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": "Suppose there are 5 cards, each with a different number, specifically $2, 3, 4, 5, 6$. When these cards are randomly arranged in a row, what is the probability that for each $i(1... | math | {
"ground_truth": "\\frac{2}{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": "The function \\( f(x) \\) is defined as \\( f(x) = \\frac{x-1}{x+1} \\). \nThe equation \\( f(x^2) \\times f(x) = 0.72 \\) has two solutions \\( a \\) and \\( b \\), where \\( a... | math | {
"ground_truth": "134",
"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": "Maya and Naomi travel from their school to a park 8 miles away. Maya, who decides to jog, takes the first 3 miles at an average speed of 5 mph and then walks the remaining part a... | math | {
"ground_truth": "B) 28 mph",
"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 function $f(x)=2\\sin (2x+ \\frac {\\pi}{3})+1$, the smallest positive period of $f(x)$ is ______, and the maximum value of $f(x)$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\[ f(x_1,x_2,x_3) = -2 \\cdot (x_1^3+x_2^3+x_3^3) + 3 \\cdot (x_1^2(x_2+x_3) + x_2^2 \\cdot (x_1+x_3) + x_3^2 \\cdot ( x_1+x_2 ) - 12x_1x_2x_3. \\] For any reals $r,s,t$ ,... | math | {
"ground_truth": "12\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $K$ be the measure of the area bounded by the $x$-axis, the line $x = 10$, and the curve defined by\n\\[f={(x,y)\\quad |\\quad y=x^2 \\text{ when } 0 \\le x \\le 3, y=3x-6 \\... | math | {
"ground_truth": "B) 94.5",
"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": "How many positive integers \\( n \\) satisfy \\( 100 < n^2 < 1000 \\)?",
"role": "user"
}
] | 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": "Calculate the value of $17^2 + 2(17)(5) + 5^2$.",
"role": "user"
}
] | math | {
"ground_truth": "484",
"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 $0 \\leq y_3 \\leq y_2 \\leq y_1 \\leq 1$ and $(1-y_1)^2 + 2(y_1-y_2)^2 + 2(y_2-y_3)^2 + y_3^2 = \\frac{1}{2}$, find $y_1$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{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": "In one of the hotels of the wellness planet Oxys, there are $2019$ saunas. The managers have decided to accommodate $k$ couples for the upcoming long weekend. We know the fol... | math | {
"ground_truth": "2018",
"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 functions $g(x) = 2 - x^2$ and $f(g(x)) = \\frac{2-x^2}{2x^2}$ for $x \\neq 0$. Determine the value of $f(1)$.\nA) $\\frac{1}{2}$\nB) $\\frac{1}{4}$\nC) $\\frac{1}{8... | 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": "The sum of all the positive factors of integer $x$ is 18. If one of the factors is 2, what is the value of $x$?",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "4^2 - 2^3",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the equation of the line that passes through the point (1, 2) and is equidistant from points O(0, 0) and B(3, 1).",
"role": "user"
}
] | math | {
"ground_truth": "3x+y-5=0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given \\( 2^{11} \\times 6^{5} = 4^{x} \\times 3^{y} \\) for some positive integers \\( x \\) and \\( y \\), determine the value of \\( x + y \\).",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each of two boxes contains three chips numbered 1, 2, 3. A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that thei... | math | {
"ground_truth": "\\frac{5}{9}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all triples $(x, y, z)$ of positive integers such that \n\\[x^2 + 4^y = 5^z. \\]\n\n*Proposed by Li4 and ltf0501*",
"role": "user"
}
] | math | {
"ground_truth": "(x, y, z) = (3, 2, 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": "As shown in the diagram, in the square \\(ABCD\\), \\(AB = 2\\). Draw an arc with center \\(C\\) and radius equal to \\(CD\\), and another arc with center \\(B\\) and radius equa... | math | {
"ground_truth": "\\frac{\\pi}{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": "In Ms. Johnson's chemistry class, there are 24 boys, and 30 of her students bring their notebooks to class. If 17 of the students with notebooks are girls, how many boys didn't b... | math | {
"ground_truth": "11",
"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": "Xiaogang played a dart game where he threw more than 11 darts and scored a total of 100 points, with each dart hitting either 8, 9, or 10 points. The number of times he hit 8 poi... | math | {
"ground_truth": "12; 10, 0, 2 \\text{ or } 9, 2, 1 \\text{ or } 8, 4, 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 the sum of $2x^{3}y^{n}$ and $-\\frac{1}{2}x^my^4$ is a monomial, calculate the value of $mn$.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of positive integers $n$ such that a regular polygon with $n$ sides has internal angles with measures equal to an integer number of degrees.",
"role": "us... | math | {
"ground_truth": "22",
"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 vectors $\\overrightarrow{a}=(x, \\sqrt {3})$ and $\\overrightarrow{b}=(x,- \\sqrt {3})$, if $(2 \\overrightarrow{a}+ \\overrightarrow{b}) \\perp \\overrightarrow{b}$, calc... | 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": "A point $X$ exactly $\\sqrt{2}-\\frac{\\sqrt{6}}{3}$ away from the origin is chosen randomly. A point $Y$ less than $4$ away from the origin is chosen randomly. The proba... | math | {
"ground_truth": "34",
"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 $x=-5$ is a solution to the equation $2x+8=\\frac{x}{5}-a$ with respect to $x$, find the value of $a^{2}+2a$.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alexio now has 120 cards numbered from 1 to 120. He places them in a box and randomly picks one card. What is the probability that the number on the card is a multiple of 2, 3, 5... | math | {
"ground_truth": "\\dfrac{104}{120} = \\dfrac{13}{15}",
"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 which pairs of positive integers \\( a \\) and \\( b \\) is the expression \\( a^2 + b^2 - a - b + 1 \\) divisible by \\( ab \\)?",
"role": "user"
}
] | math | {
"ground_truth": "a = 1, b = 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": "A regular polygon has interior angles each measuring \\(150^\\circ\\). Determine how many sides this polygon has.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"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 rectangle $PQRS$, $PQ = 5$ and $QR = 15$. The rectangle is folded so that points $B$ and $D$ coincide, forming the pentagon $PQGHI$. What is the length of segment $GH$? Expres... | math | {
"ground_truth": "15 - 10\\sqrt{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 particle is located on the coordinate plane at $ (5,0)$ . Define a *move* for the particle as a counterclockwise rotation of $ \\pi/4$ radians about the origin followed by a... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that each side of a square $S_1$ with area $16$ is bisected to construct a smaller square $S_2$, and the same process is repeated on $S_2$ to construct an even smaller squa... | math | {
"ground_truth": "4",
"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": "Determine the heaviest object that can be weighed using a set of weights of 2 lb, 4 lb, and 12 lb.\nA) 15 lb\nB) 16 lb\nC) 17 lb\nD) 18 lb",
"role": "user"
}
] | math | {
"ground_truth": "D) 18 lb",
"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": "Four unit circles are placed on a square of side length $2$ , with each circle centered on one of the four corners of the square. Compute the area of the square which is not con... | math | {
"ground_truth": "4 - \\pi",
"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": "Evaluate $81^{-\\frac{1}{4}} - 16^{-\\frac{3}{4}}$. Express your answer as a common fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{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": "How many Friday the 13th can occur in a non-leap year?",
"role": "user"
}
] | 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 the estimated attendance of 50,000 fans in Atlanta and 60,000 fans in Boston, and the actual attendance being within 10% of Anita's estimate and Bob's estimate being within... | math | {
"ground_truth": "22000",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the greatest value of $b$ such that $-b^2 + 8b - 12 \\geq 0$.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A maintenance team needs to replace tiles at the center $C$ of a round patio. They lay a 20-foot plank from $A$ to $B$ and then a 15-foot plank from $D$ to $C$, where $D$ is the ... | math | {
"ground_truth": "325 \\pi \\text{ square feet}",
"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": "Convert $256_{10}$ to base 12. Represent $10$ as $A$, and $11$ as $B$, if necessary.",
"role": "user"
}
] | math | {
"ground_truth": "194_{12}",
"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": "Tony has an old sticky toy spider that very slowly \"crawls\" down a wall after being stuck to the wall. In fact, left untouched, the toy spider crawls down at a rate of one inc... | math | {
"ground_truth": "8",
"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": "When $q = \\sum\\limits_{k=1}^{7} k^2 \\text{ ln }(k+1)$, the number $e^q$ is an integer. Determine the largest power of 3 that is a factor of $e^q$.",
"role": "user"
}
] | math | {
"ground_truth": "3^{29}",
"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": "Suppose $x$, $y$, and $z$ are positive integers such that $x+y+z=2026$, and $x!y!z!=p \\cdot 10^q$, where $p$ and $q$ are integers and $p$ is not divisible by $10$. Find the smal... | math | {
"ground_truth": "505",
"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 ratio of $3x - 2y$ to $x + y$ is $\\frac{4}{5}$, determine the ratio of $x$ to $y$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{14}{11}",
"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 $f(x)=\\sum_{k=2}^{10}(\\lfloor kx \\rfloor -k \\lfloor x \\rfloor)$, where $\\lfloor r \\rfloor$ denotes the greatest integer less than or equal to $r$. Determine the number... | math | {
"ground_truth": "32",
"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 numbers $1, 2, 3, 4, 5, 6, 7, 8, 9$ are randomly placed on the faces of a regular octahedron, with each face containing a unique number. The probability that no two consecuti... | math | {
"ground_truth": "5041",
"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": "Calculation-loving Samson likes to have lunch at the Italian restaurant \"Pablo's.\" On his next visit to the restaurant, Samson was offered to purchase a one-year loyalty card f... | math | {
"ground_truth": "167 \\text{ visits}",
"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": "Define $\\heartsuit(x)$ for a real number $x$ as the average of $x$ and $x^3$. Calculate $\\heartsuit(1) + \\heartsuit(2) + \\heartsuit(4)$.\nA) 15\nB) 25\nC) 35\nD) 40\nE) 45",
... | math | {
"ground_truth": "The final answer is **D) 40**.",
"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": "Compute $\\dbinom{10}{3} - 5$.",
"role": "user"
}
] | math | {
"ground_truth": "115",
"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 a $9$ -digit number be balanced if it has all numerals $1$ to $9$ . Let $S$ be the sequence of the numerals which is constructed by writing all balanced numbers in incr... | math | {
"ground_truth": "q_1, \\cdots, q_9",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The circumference of each of two equal circles with radius \\( R \\) passes through the center of the other. Find the area of the common part of these circles.",
"role": "use... | math | {
"ground_truth": "\\frac{R^2 (4 \\pi - 3 \\sqrt{3})}{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": "Given the hyperbola $\\frac {x^{2}}{4}- \\frac {y^{2}}{12}=1$ whose right focus is $F$, find the range of possible slopes for a line passing through point $F$ that intersects the... | math | {
"ground_truth": "\\left[-\\sqrt{3}, \\sqrt{3}\\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": "Evaluate the expression $-20 + 15 \\times (4^{\\div -1} \\times 2)$.",
"role": "user"
}
] | math | {
"ground_truth": "-12.5",
"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": "Calculate the value of the complex number $i - \\frac{1}{i}$.",
"role": "user"
}
] | math | {
"ground_truth": "2i",
"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": "Positive real numbers $x \\neq 1$ and $y \\neq 1$ satisfy $\\log_3{x} = \\log_y{81}$ and $xy = 243$. What is $(\\log_3{\\tfrac{x}{y}})^2$?\n**A)** 5\n**B)** 7\n**C)** 9\n**D)** 1... | math | {
"ground_truth": "**C)** 9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let x be the number of ounces in Tom's coffee. Let y be the number of ounces in Jerry's coffee. Calculate the number of ounces of coffee Tom and Jerry drink altogether.",
"ro... | math | {
"ground_truth": "36",
"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 base of a right prism $ABC A_{1}B_{1}C_{1}$ is a triangle with $|AB|=|AC|$ and $\\widehat{ABC}=\\alpha$. Additionally, point $D$ is the midpoint of edge $AA_{1}$, $\\widehat{... | math | {
"ground_truth": "4 b^2 \\sin 2 \\beta \\cos^2 \\frac{\\alpha}{2}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the remainder when \\( x^{2023} + 1 \\) is divided by \\( x^{12} - x^9 + x^6 - x^3 + 1 \\).",
"role": "user"
}
] | math | {
"ground_truth": "-x^{15} + 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 sequence of $6$ numbers is formed by starting with two initial numbers. Each subsequent number in the sequence is the product of the two previous numbers. Given that the last t... | math | {
"ground_truth": "\\frac{1}{81}",
"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 celebrate the anniversary of the St. Petersburg Mathematical Olympiads, the mint produced three commemorative coins. One coin was correct, the second coin had two heads, and t... | math | {
"ground_truth": "\\frac{2}{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": "Calculate the simplified value of the sum: $-2^{3} + (-2)^{4} + 2^{2} - 2^{3}$.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
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