data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the estimated cost of constructing a space station on the Moon is $50$ billion dollars and this cost is to be shared equally by half of the $400$ million people in a federatio... | math | {
"ground_truth": "250 \\text{ dollars}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 $M = 36 \\cdot 36 \\cdot 77 \\cdot 330$. Find the ratio of the sum of the odd divisors of $M$ to the sum of the even divisors of $M$.",
"role": "user"
}
] | math | {
"ground_truth": "1 : 62",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$2016$ numbers written on the board: $\\frac{1}{2016}, \\frac{2}{2016}, \\frac{3}{2016}, ..., \\frac{2016}{2016}$ . In one move, it is allowed to choose any two numbers $a$ ... | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 $0<x<\\frac{1}{2}$, find the maximum value of $y=x^{2}(1-2x)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{27}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$4(299)+3(299)+2(299)+298=$",
"role": "user"
}
] | math | {
"ground_truth": "2989",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What must be the value of the coefficient \\(c\\) in \\(P(x) = x^3 + 2x^2 + cx + 8\\), in order for \\(x-3\\) to be a factor of \\(P\\)?",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{53}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $f(x) = x^2 + 1$ for all real numbers $x$, what is the value of $f(3x + 2)$?",
"role": "user"
}
] | math | {
"ground_truth": "9x^2 + 12x + 5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $y = \\displaystyle\\frac{1}{5x+2}$, what is the value of $x$ when $y = 2$?",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{3}{10}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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{pow}(n)\\) is the largest power of the largest prime that divides \\(n\\), find the largest integer \\(m\\) such that \\(6^m\\) divides the product \\( \\pr... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the polynomial\n\\[ b_8 x^8 + b_7 x^7 + b_6 x^6 + \\dots + b_1 x + b_0 = 0 \\]\nwhere all coefficients \\( b_i \\) are integers, and its roots \\( s_1, s_2, \\dots, s_8 ... | math | {
"ground_truth": "\\{1, 1, 1, 1, -1, -1, -1, -1\\}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( m \\) and \\( n \\) are both non-zero real numbers, and satisfy the conditions for the two sets\n$$\n\\begin{array}{l}\nA=\\{z \\mid |z + n \\mathrm{i}| + |z - m \\mathrm{... | math | {
"ground_truth": "(-\\infty, -2]",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define an odd function on $(-\\infty, +\\infty)$, such that when $x > 0$, $f(x) = x^2 + 1$. Find $f(-2) =$ ___.",
"role": "user"
}
] | math | {
"ground_truth": "-5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On September 22, 2020, the Chinese government proposed at the 75th United Nations General Assembly: \"China will increase its national determined contributions, adopt more effect... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Assume a set of points \\( S \\) in the plane has the properties: (i) any three points are not collinear; (ii) the distances between any two points are all distinct. For two poin... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The ratio of cats to dogs at the pet store is 3:4. There are 20 dogs. How many cats are there at the pet store?",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 distance between the points $(1, 2)$ and $(6, 5)$? Express your answer in simplest radical form.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{34}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 cosine of the acute angle of a rhombus if the line through one of its vertices divides the angle in the ratio of $1:3$ and the opposite side in the ratio of $3:5$.",
... | math | {
"ground_truth": "\\frac{7}{18}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sequence $\\left\\{x_{n}\\right\\}$ satisfies $x_{1}=1$, and for any $n \\in \\mathbb{Z}^{+}$, it holds that $x_{n+1}=x_{n}+3 \\sqrt{x_{n}}+\\frac{n}{\\sqrt{x_{n}}}$. Find th... | math | {
"ground_truth": "\\lim_{n \\to \\infty} \\frac{n^2}{x_n} = \\frac{4}{9}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Triangle $DEF$ has side lengths $DE = 15$, $EF = 36$, and $FD = 39$. Rectangle $WXYZ$ has vertex $W$ on $\\overline{DE}$, vertex $X$ on $\\overline{DF}$, and vertices $Y$ and $Z$... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 in the coordinate plane has vertices whose $y$-coordinates are $0$, $3$, $8$, and $11$. Find the area of the square.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1071}{55}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the range of the function $$f(x) = \\frac{1}{(1-5x)^2}~?$$ Express your answer in interval notation.",
"role": "user"
}
] | math | {
"ground_truth": "(0, \\infty)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the limit of the numerical sequence:\n\n$$\n\\lim _{n \\rightarrow \\infty}\\left(\\frac{n-10}{n+1}\\right)^{m+1}\n$$",
"role": "user"
}
] | math | {
"ground_truth": "e^{-33}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Don has $\\frac{3}{4}$ of a gallon of milk in his bottle. He gives $\\frac{1}{2}$ of his milk to Rachel. Afterwards, Rachel's friend Monica drinks $\\frac{1}{3}$ of what Rachel h... | math | {
"ground_truth": "\\frac{1}{8}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 natural numbers \\( y \\) is the number \\( y^2 + 3^y \\) a perfect square?",
"role": "user"
}
] | math | {
"ground_truth": "y=1 \\text{ and } y=3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given two non-coincident planes, alpha ($\\alpha$) and beta ($\\beta$). If 5 points are chosen within plane $\\alpha$, and 4 points are chosen within plane $\\beta$, the maximum ... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a closed bag, there are apples. Three friends tried to lift the bag and guess how many fruits were inside. The first friend guessed that there were 16 apples, the second guess... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function \\( f(x) = x^3 - ax^2 + (a^2 - 2)x + 1 \\), if there exists \\( m > 0 \\) such that \\( f(m) \\leq 0 \\), what is the maximum value of the real number \\( a \\... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The roots of $81x^3 - 162x^2 + 108x - 18 = 0$ are in arithmetic progression. The difference between the largest and smallest roots is?\nA) $\\frac{2}{3}$ \nB) $\\frac{3}{4}$ \n... | math | {
"ground_truth": "\\textbf{(A)}\\ \\frac{2}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 non-zero common difference arithmetic sequence {a<sub>n</sub>}, where a<sub>1</sub> = 1, and a<sub>1</sub>, a<sub>3</sub>, a<sub>9</sub> form a geometric sequence.\n(1) F... | math | {
"ground_truth": "S_{n}=2^{n+1}-2+ \\frac {n(n+1)}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 company operates a machine that prints 800 flyers in 6 minutes. They plan to purchase an additional machine so that together they can complete 800 flyers in 1.5 minutes. Determ... | math | {
"ground_truth": "\\textbf{(B)}\\ \\dfrac{1}{6}+\\dfrac{1}{x}=\\dfrac{1}{1.5}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 set of inequalities about $x$: $$ \\begin{cases} 1 \\leqslant kx^{2} + 2 \\\\ x + k \\leqslant 2 \\end{cases} $$ There is a unique real number solution. Determine the s... | math | {
"ground_truth": "\\{1 + \\sqrt{2}, \\frac{1 - \\sqrt{5}}{2}\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In two weeks three cows eat all the grass on two hectares of land, together with all the grass that regrows there during the two weeks. In four weeks, two cows eat all the grass ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 dog is chasing a rabbit, which has a 50-jump head start. The dog makes 5 jumps in the time the rabbit makes 6 jumps, but 7 of the dog's jumps are equal to 9 of the rabbit's jum... | math | {
"ground_truth": "700",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The average of 15 numbers is 100. If the numbers 80, 90, and 95 are removed from the set of numbers, what is the average of the remaining numbers?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1235}{12}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 \\star b = a^2 + 2ab + b^2$, and defining a new operation $\\diamond$ such that $a \\diamond b = a \\star b - ab$, find the value of $3 \\diamond 7$.",
"role": "user... | math | {
"ground_truth": "79",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 sets of four real numbers $x_1, x_2, x_3, x_4$ such that the sum of any one and the product of the other three is equal to 2.",
"role": "user"
}
] | math | {
"ground_truth": "(1, 1, 1, 1)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 four-digit numbers whose digits add up to $16$ are divisible by $11$?",
"role": "user"
}
] | math | {
"ground_truth": "567",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 ordered pairs \\((2011,2),(2010,3),(2009,4), \\ldots,(1008,1005),(1007,1006)\\) are written from left to right on a blackboard. Every minute, Elizabeth selects a pair of adja... | math | {
"ground_truth": "504510",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that P be a polynomial with each root is real and each coefficient is either $1$ or $-1$, determine the maximum degree of P.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Point \\( P \\) is on the \\( y \\)-axis with \\( y \\)-coordinate greater than 0 and less than 100. A circle is drawn through \\( P, Q(4,4) \\), and \\( O(0,0) \\). How many pos... | math | {
"ground_truth": "66",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $a > 0$ and $b > 0$, if $4a + b = ab$, find the minimum value of $a + b$.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 sum of the six smallest distinct positive integer multiples of 11?",
"role": "user"
}
] | math | {
"ground_truth": "231",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Nicky has a circle. To make his circle look more interesting, he draws a regular 15-gon, 21-gon, and 35-gon such that all vertices of all three polygons lie on the circle. Let $... | math | {
"ground_truth": "510",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an equilateral triangle $(t)$, we draw the medial triangle $\\left(t_{1}\\right)$. In the medial triangle $\\left(t_{1}\\right)$, we again draw the medial triangle $\\left(t_{... | math | {
"ground_truth": "\\frac{4t}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Kelvin the Frog is playing the game of Survival. He starts with two fair coins. Every minute, he flips all his coins one by one, and throws a coin away if it shows tails. The gam... | math | {
"ground_truth": "\\frac{64}{9}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 10-digit positive integers have all 10 digits pairwise distinct and are multiples of 11111?",
"role": "user"
}
] | math | {
"ground_truth": "3456",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle passes through the vertices $Q$ and $E$ of triangle $M Q E$ and intersects its sides $M Q$ and $M E$ at points $B$ and $D$ respectively, which are different from the ver... | math | {
"ground_truth": "BQ : DE = 5 : 19",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the remainder $S$ when $x^{105}$ is divided by $x^2 - 4x + 3$.\nA) $\\frac{3^{105}(x-1) - (x-2)}{2}$\nB) $\\frac{3^{105}(x-1) - (x-1)}{2}$\nC) $\\frac{3^{105}(x-2) - (x... | math | {
"ground_truth": "\\frac{3^{105}(x-1) - (x-2)}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the Cartesian coordinate system, the standard equation of a parabola with the directrix $y=4$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "x^2 = -16y",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 $i^2 = -1$, then compute $(1+2i)^{24} - (1-2i)^{24}$.\nA) -256\nB) -256i\nC) 0\nD) 256\nE) 256i",
"role": "user"
}
] | math | {
"ground_truth": "The correct answer is C) 0.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 2 × 2 grid with a robot placed on the center square, and considering the robot can move left or right without wrap-around for vertical movement, find the probability that... | math | {
"ground_truth": "\\frac{15}{16}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 $n \\in \\mathbb{N}$ , let $P(n)$ denote the product of the digits in $n$ and $S(n)$ denote the sum of the digits in $n$ . Consider the set $A=\\{n \\in \\mathbb{N}: ... | math | {
"ground_truth": "92",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 area of the kombucha in the jar doubles every day. If it takes 17 days to fill the entire jar, calculate the number of days it takes to fill half of the jar.",
"role": "u... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 group of students took a test which consisted of 3 questions. We know that 90% answered the first question correctly, 80% answered the second question correctly, and 70% answer... | math | {
"ground_truth": "40\\%",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the rank of the matrix\n\n$$\nA=\\left(\\begin{array}{rrrrr}\n3 & -1 & 1 & 2 & -8 \\\\\n7 & -1 & 2 & 1 & -12 \\\\\n11 & -1 & 3 & 0 & -16 \\\\\n10 & -2 & 3 & 3 & -20\n\\end{a... | math | {
"ground_truth": "\\text{rank } A = 2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For \\( x, y, z \\in (0,1] \\), find the maximum value of the expression\n\n$$\nA = \\frac{\\sqrt{8 x^{4} + y} + \\sqrt{8 y^{4} + z} + \\sqrt{8 z^{4} + x} - 3}{x + y + z}\n$$",
... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In trapezoid $ABCD$, where $\\overline{AB}\\parallel\\overline{CD}$ and sides $BC=CD=50$, the diagonal $\\overline{AC}$ and $\\overline{BD}$ intersect at point $O$. Point $P$ is ... | math | {
"ground_truth": "**B)** 74",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Construct a right triangle with its legs parallel to the x and y axes and with the medians on its legs lying on the lines y = 3x + 1 and y = mx + 2. Determine the number of value... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute\n\\[\\frac{(11^4+324)(23^4+324)(35^4+324)(47^4+324)(59^4+324)}{(5^4+324)(17^4+324)(29^4+324)(41^4+324)(53^4+324)}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "295.615",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the coefficient of $x^4$ in the expansion of $\\left(\\frac{x^3}{3} - \\frac{3}{x^2}\\right)^{10}$.\nA) 0 \nB) 20 \nC) 30 \nD) -20 \nE) -30",
"role": "user"
}... | math | {
"ground_truth": "\\textbf{(A)}\\ 0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 isosceles right triangle with legs of length $10$ is partitioned into $25$ congruent triangles. If the shaded area consists of $15$ of these smaller triangles, calculate the a... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 is a $n\\times n$ grid with all squares on one diagonal being forbidden. You are allowed to start from any square, and move one step horizontally, vertically or diagonall... | math | {
"ground_truth": "2\\lfloor\\frac{n}{2}\\rfloor - 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 triangle depicted is an equilateral triangle with side length 15 cm. A side of the triangle is the diameter of the circle. Calculate the sum of the areas of the two small sha... | math | {
"ground_truth": "42.75",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 convex polygons $A_1$ and $A_2$ in the same plane, where $A_1$ has $m$ sides and $A_2$ has $m+2$ sides, and any side of $A_1$ intersects with any side of $A_2$ without ... | math | {
"ground_truth": "m^2 + 2m",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 arithmetic progression \\(a_{n}\\) has a non-zero difference, and \\(a_{10}, a_{13}\\), and \\(a_{19}\\) form consecutive terms of some geometric progression. Find the ratio \... | math | {
"ground_truth": "5:11",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the diagram, all empty white triangles should be filled with whole numbers such that the sum of the three numbers in the white neighboring triangles of each gray triangle is d... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the number $52648.2097$, determine the ratio of the value of the place occupied by the digit 6 to the value of the place occupied by the digit 2 in the decimal part.",
... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Circles $\\omega_1$ , $\\omega_2$ , and $\\omega_3$ are centered at $M$ , $N$ , and $O$ , respectively. The points of tangency between $\\omega_2$ and $\\omega_3$ , $... | math | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 $(-3)^7 \\div 3^5 + 2^6 - 4^2$ as an integer.",
"role": "user"
}
] | math | {
"ground_truth": "39",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 $\\triangle ABC$, $A=15^{\\circ}$, express $\\sqrt {3}\\sin A-\\cos (B+C)$ in simplest radical form.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt {2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 $\\mathcal{P}$ be a parabola that passes through the points $(0, 0)$ and $(12, 5)$ . Suppose that the directrix of $\\mathcal{P}$ takes the form $y = b$ . (Recall tha... | math | {
"ground_truth": "7.2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the range of the function $y = 3 + \\cos x$?",
"role": "user"
}
] | math | {
"ground_truth": "[2, 4]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the diagram, \\(AB\\) is a line segment. \\(C\\) is on \\(AB\\) such that \\( \\angle DCE\\) needs to be found. \\(D\\) is a point above \\(C\\) making \\(CD\\) perpendicular ... | math | {
"ground_truth": "32^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Factorization: $3x^{2}-12y^{2}=\\_\\_\\_\\_\\_\\_.$",
"role": "user"
}
] | math | {
"ground_truth": "3\\left(x-2y\\right)\\left(x+2y\\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive integers less than $100$ have an odd number of positive integer divisors?",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Are the vectors \\( \\mathbf{a}, \\mathbf{b}, \\mathbf{c} \\) coplanar?\n\nGiven:\n\\[ \\mathbf{a} = \\{ 3, 1, 0 \\} \\]\n\\[ \\mathbf{b} = \\{ -5, -4, -5 \\} \\]\n\\[ \\mathbf{c... | math | {
"ground_truth": "-18",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Apartment rentals in Greenview run $\\$1.20$ per square foot. Max has determined that he can afford $\\$720$ per month for rent. What is the largest apartment, in square feet, he... | math | {
"ground_truth": "600",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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 maximum number of planes in the space, such there are $ 6$ points, that satisfy to the following conditions:\r**1.**Each plane contains at least $ 4$ of them\r**2.**... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a triangular pyramid \\( S-ABC \\) with a base that is an isosceles right triangle with \\( AB \\) as the hypotenuse, \\( SA = SB = SC = 2 \\), and \\( AB = 2 \\), suppose ... | math | {
"ground_truth": "\\frac{\\sqrt{3}}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a regular polygon with \\( n \\) sides, it has 90 diagonals. What is the value of \\( n \\)?",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The 5 a.m. temperatures for eight consecutive days were $-7^\\circ$, $-4^\\circ$, $-4^\\circ$, $-5^\\circ$, $1^\\circ$, $3^\\circ$, $2^\\circ$, and $4^\\circ$ Celsius. What is th... | math | {
"ground_truth": "-1.25^\\circ \\text{ Celsius}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 8 horses on a track, each named after the number of minutes it takes to complete a lap: Horse 3, Horse 4, Horse 5, Horse 6, Horse 7, Horse 8, Horse 9, and Horse 10. Ini... | math | {
"ground_truth": "\\textbf{(D)}\\ 6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 following:<br/>$(1)$ If $y=\\sqrt{x-2}+\\sqrt{2-x}+3$, find the value of $x-y$;<br/>$(2)$ Simplify first, then find the value: $\\frac{x}{x-2}÷(2+x-\\frac{4}{2-x})$... | math | {
"ground_truth": "\\frac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "1. Given that the line $l$ passing through the point $M(-3,0)$ is intercepted by the circle $x^{2}+(y+2)^{2}=25$ to form a chord of length $8$, what is the equation of line $l$?\... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 all positive integers $k$ for which the equation: $$ \\text{lcm}(m,n)-\\text{gcd}(m,n)=k(m-n) $$ has no solution in integers positive $(m,n)$ with $m\\neq n$ .",
... | math | {
"ground_truth": "k = 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 function $g(x)$ satisfies the equation \\[g(x - y) = g(x)g(y)\\] for all real numbers $x$ and $y$, and additionally, $g(x) \\neq 0$ for any real $x$. Find $g(2)$.",
"role... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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, b, c, \\) and \\( d \\) be real numbers such that \\( a < b < c < d \\), with \\( |a-b| = 3 \\), \\( |b-c| = 4 \\), and \\( |c-d| = 5 \\). What is the sum of all possi... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n{}$ be a positive integer. What is the smallest sum of digits that $5^n + 6^n + 2022^n$ can take?",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a bag, there are 2 red balls, 3 yellow balls, and 4 green balls. These balls are identical except for their colors. The probability of randomly drawing a red or green ball fro... | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 parabola \\\\({{x}^{2}}=2py(p > 0)\\\\) has a focus at \\\\(F\\\\), and its directrix intersects with the hyperbola \\\\(\\dfrac{{{x}^{2}}}{3}-\\dfrac{{{y}^{2}}}{3}=1\\\\) at... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"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 biased coin has a $\\frac{2}{3}$ probability of landing heads and a $\\frac{1}{3}$ probability of landing tails. Calculate the probability that a player wins in game X: Toss th... | math | {
"ground_truth": "\\frac{11}{81}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There is a ten-digit number. From left to right:\n- Its first digit indicates the number of zeros in the ten-digit number.\n- Its second digit indicates the number of ones in the... | math | {
"ground_truth": "6210001000",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The prime factorization of \\( 3600 \\) is \\( 2^4 \\times 3^2 \\times 5^2 \\). How many of its positive integer factors are perfect squares?",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"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: $49^2 - 16^2$",
"role": "user"
}
] | math | {
"ground_truth": "2145",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\log_{10}2 = x$ and $\\log_{10}5 = y$, find $\\log_{8}80$.\nA) $\\frac{x + y}{x}$\nB) $\\frac{4x + y}{3x}$\nC) $\\frac{4x + 3y}{x}$\nD) $\\frac{2x + y}{3x}$",
"role": "u... | math | {
"ground_truth": "\\textbf{(B)}\\ \\frac{4x + y}{3x}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"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 school economics teacher believes that it's extremely important to know the basics of both microeconomics and macroeconomics. Therefore, the teacher has introduced the followin... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $x=-1$ is a solution of the one-variable quadratic equation $x^{2}-2x+a=0$, find the other solution of this equation.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An arc of a circle with radius \\( R \\) contains \\( \\alpha \\) radians. Find the position of its center of gravity. Where is the center of gravity of a semicircle?",
"role... | math | {
"ground_truth": "OZ = \\frac{2R}{\\pi}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The Matini company released a special album with the flags of the $ 12$ countries that compete in the CONCACAM Mathematics Cup. Each postcard envelope has two flags chosen rand... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"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 P and Q be two sets, and define the set P-Q as $\\{x | x \\in P, \\text{ and } x \\notin Q\\}$. If $P = \\{x | \\log_{2}x < 1\\}$ and $Q = \\{x | 3 < 3^{x} < 9\\}$, then what... | math | {
"ground_truth": "\\{x | 0 < x \\leq 1\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
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