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": "Given a mapping \\( f: (x, y) \\to \\left( \\sqrt{ \\frac{1}{xy + 6y^2} }, x^2 + y^3 \\right) \\), find the image of the point (6, -3).",
"role": "user"
}
] | math | {
"ground_truth": "\\left( \\frac{1}{6}, 9 \\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the distance from point $M$ on the parabola $y^{2}=8x$ to the $y$-axis is $3$, what is the distance from point $M$ to the focus $F$ of the parabola?",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When the binary number \\(101110011100_2\\) is divided by 4, what is the remainder (give your answer in base 10)?",
"role": "user"
}
] | math | {
"ground_truth": "0",
"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 wheels are spun, and the resulting numbers from each wheel are added together. Wheel A has five sections with numbers {1, 1, 2, 2, 3}, and Wheel B has six sections with numbe... | 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": "In which of the following equations is $y$ neither directly nor inversely proportional to $x$?\n1. $y = \\frac{x}{3}$\n2. $2xy + 5 = 15$\n3. $y = 3x + 2$\n4. $5x - 4y = 16$\n5. $... | math | {
"ground_truth": "y = 3x + 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": "Let $\\mathcal{P}$ be a regular $2022$ -gon with area $1$ . Find a real number $c$ such that, if points $A$ and $B$ are chosen independently and uniformly at random on ... | math | {
"ground_truth": "\\sqrt{2/\\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": "Compute \\(\\frac{x^8 + 18x^4 + 81}{x^4 + 9}\\) when \\( x = 7 \\).",
"role": "user"
}
] | math | {
"ground_truth": "2410",
"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 \"Christmas tree\" of height 1 is inscribed in the graph of a function that is symmetric with respect to the y-axis. It is known that the \"branches\" of the tree form an angle... | math | {
"ground_truth": "2(1+\\sqrt{2})",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Five distinct points are arranged in space so that the segments connecting them have lengths $a$, $a$, $a$, $a$, $a$, $2a$, $2a$, and $b$. Calculate the ratio of $b$ to $a$.",
... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle with center $O$ is tangent to the coordinate axes and to the hypotenuse of a $45^\\circ$-$45^\\circ$-$90^\\circ$ triangle $ABC$, where $AB=2$. Find the radius $r$ of the... | math | {
"ground_truth": "\\sqrt{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 first four terms of an arithmetic sequence are $p$, $11$, $4p-r$, and $4p+r$. Find the 1005th term of this sequence.",
"role": "user"
}
] | math | {
"ground_truth": "6029",
"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 negation of the proposition \"$\\forall x > 0, x^2 \\neq x$\" is to be expressed.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{Since the negation of a universal proposition is a particular proposition, the negation of the proposition \"$\\forall x > 0, x^2 \\neq x$\" is: }\\quad \\exists x > 0, x^2 = x.",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a sequence $(a_{n})_{n\\geq 1}$ of real numbers it is known that $a_{n}=a_{n-1}+a_{n+2}$ for $n\\geq 2$ .\r\nWhat is the largest number of its consecutive elements that ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number 4 has the property that when divided by \\(q^{2}\\), the remainder is less than \\(q^{2} / 2\\) for any \\(q\\). List all numbers that have this property.",
"role"... | math | {
"ground_truth": "1 \\text{ and } 4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Maria takes an $8,000 loan to renovate her kitchen. The annual interest rate lent by the bank is 10%. She makes no payments for 3 years, but will need to clear the entire owed am... | math | {
"ground_truth": "\\$72.80",
"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 pentagonal prism has 7 faces, 10 vertices, and 15 edges. A new pyramid is to be attached to one of its pentagonal faces. Calculate the sum of the number of exterior faces, vert... | math | {
"ground_truth": "42",
"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 sum of the first $n$ terms of the arithmetic sequence $\\{a\\_n\\}$ is $S\\_n$, and $a\\_6 = S\\_3 = 12$, find the value of $a\\_8$.",
"role": "user"
}
] | math | {
"ground_truth": "16",
"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": "Six painters, all working at the same rate, can finish a job in 1.5 work-days. If only four painters are available, how many work-days will it take them to finish the job, workin... | math | {
"ground_truth": "2\\frac{1}{4} \\text{ work-days}",
"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 domain of the function $f(x) = \\log(4-2x)$ is.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, 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": "The teacher gave each of her $37$ students $36$ pencils in different colors. It turned out that each pair of students received exactly one pencil of the same color. Determine... | math | {
"ground_truth": "666",
"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": "Winnie has 55 cherry lollipops, 134 wintergreen lollipops, 12 grape lollipops, and 265 shrimp cocktail lollipops. She decides to distribute these lollipops equally among her 15 f... | 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": "A parabola $y^2 = 4x$ has a focus at point $F$. A line passing through $F$ intersects the upper part of the parabola at point $A$ and intersects the directrix $l$ at point $B$, w... | math | {
"ground_truth": "4\\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": "Given that the distance from point $P(2,0)$ to one asymptote of the hyperbola $\\frac{{x}^{2}}{{a}^{2}}-\\frac{{y}^{2}}{{b}^{2}}=1 (a > 0, b > 0)$ is $\\sqrt{2}$, find the eccent... | math | {
"ground_truth": "\\sqrt{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": "Two natural numbers are chosen at random; determine the probability that their product is divisible by 3; that the remainder when divided by 3 is 1; that the remainder is 2.",
... | math | {
"ground_truth": "\\frac{5}{9}; \\frac{2}{9}; \\frac{2}{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": "A certain store sells three types of products, A, B, and C. If buying 2 units of A, 3 units of B, and 1 unit of C costs $130, and buying 3 units of A, 5 units of B, and 1 unit of... | math | {
"ground_truth": "55",
"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 computer software retailer has 1200 copies of a new software package to sell. Given that half of them will sell right away at the original price, two-thirds of the remainder wi... | math | {
"ground_truth": "80.90",
"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": "**p1.** Steven has just learned about polynomials and he is struggling with the following problem: expand $(1-2x)^7$ as $a_0 +a_1x+...+a_7x^7$ . Help Steven solve this proble... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $p: \\forall x \\in (0, +\\infty)$, ${x}^{2}-5x \\geq -\\frac{25}{4}$; Let $q$: there exists an even number that is divisible by $3$. \n$(1)$ Write the negation of $p$; \n$... | math | {
"ground_truth": "\\text{Every even number cannot be divided by }3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a circle with center $A(-1,2)$ intersecting with a dynamic line $l$ passing through point $B(-2,0)$, intersecting the circle at points $M$ and $N$, and tangent to the line ... | math | {
"ground_truth": "3x-4y+6=0 \\text{ or } x=-2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If a number line has 40 consecutive integers marked on it and the smallest of these integers is -11, determine the largest integer.",
"role": "user"
}
] | math | {
"ground_truth": "28",
"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": "Factor the expression $3x^2(x-5) + 4x(x-5) + 6(x-5)$.",
"role": "user"
}
] | math | {
"ground_truth": "(3x^2 + 4x + 6)(x-5)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A truck travels $\\frac{b}{4}$ feet every $t$ seconds. There are $3$ feet in a yard. How many yards does the truck travel in $5$ minutes?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{25b}{t}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the expansion of $({2\\sqrt{x}-\\frac{1}{x}})^6$, the constant term is ______.",
"role": "user"
}
] | math | {
"ground_truth": "240",
"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 $i$ is the imaginary unit, the conjugate of the complex number $$z= \\frac {2i}{-1+2i}$$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac {4}{5}+ \\frac {2i}{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that $\\tfrac{5}{4}$ of $16$ apples are worth as much as $10$ mangos. Find the number of mangos worth as much as $\\tfrac{3}{4}$ of $12$ apples.",
"role": "user"
}
... | math | {
"ground_truth": "4.5",
"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": "Let set $A = \\{-1, 0, 1\\}$, and set $B = \\{a + 1, 2a\\}$. If the intersection of sets $A$ and $B$ is $\\{0\\}$, then the value of the real number $a$ is ______________.",
... | math | {
"ground_truth": "a = -1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the area of the parallelogram with vertices at the points (0, 0), (3, 0), (1, 5), and (4, 5).",
"role": "user"
}
] | math | {
"ground_truth": "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": "Drawing randomly from a bag containing red, white, and yellow balls with respective probabilities of $\\dfrac{1}{2}$, $\\dfrac{1}{3}$, and $\\dfrac{1}{6}$, calculate the probabil... | math | {
"ground_truth": "\\dfrac{5}{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": "Pedro Montes notices that the odometer on his motorcycle reads $2332$, a palindrome. After riding for a certain number of hours that day and stopping for a 2-hour maintenance bre... | math | {
"ground_truth": "27.5",
"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": "Let $P(x) = x^2 - 20x - 11$ . If $a$ and $b$ are natural numbers such that $a$ is composite, $\\gcd(a, b) = 1$ , and $P(a) = P(b)$ , compute $ab$ .\n\nNote: $\\gcd(m, ... | math | {
"ground_truth": "99",
"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": "Two right circular cylinders have the same volume. The radius of the second cylinder is $10\\%$ more than the radius of the first. Determine the relationship between the heights ... | math | {
"ground_truth": "\\text{The first height is } 21\\% \\text{ more than the second.}",
"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 sum of the values of $a$ for which the quadratic equation $3x^2 + ax + 6x + 7 = 0$ has exactly one solution for $x$.",
"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": "Let $n \\ge 3$ be an integer. On a circle, there are $n$ points. Each of them is labelled with a real number at most $1$ such that each number is the absolute value of the ... | math | {
"ground_truth": "\\frac{2}{3}n",
"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 line contains the points $(3,7)$, $(5, k)$ and $(11, 15)$. What is the value of $k$?",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A regular 201-sided polygon is inscribed inside a circle with center $C$. Triangles are drawn by connecting any three of the 201 vertices of the polygon. How many of these triang... | math | {
"ground_truth": "338350",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that 3 people are to be selected from 5 girls and 2 boys, if girl A is selected, determine the probability that at least one boy is selected.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A particle is placed on the parabola $y = x^2 - x - 6$ at a point $P$ whose $y$-coordinate is $6$. Find the horizontal distance traveled by the particle, defined as the numerical... | 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": "Find the positive four-digit number that is a multiple of 7 and represents the sum of the cube and square of a certain number.",
"role": "user"
}
] | math | {
"ground_truth": "1386, 1200",
"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 sequence $\\{a_n\\}$ is an arithmetic sequence, where $a_1=f(x+1)$, $a_2=0$, $a_3=f(x-1)$, and $f(x)=x^2-4x+2$. Find the general formula for $a_n$.",
"role": "user"
}
] | math | {
"ground_truth": "2n-4 \\text{ or } 4-2n",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a circle of radius $6$ units, $CD$ and $AB$ are perpendicular diameters. A chord $CH$ cutting $AB$ at $K$ is $10$ units long. The diameter $AB$ is divided into two segments wh... | math | {
"ground_truth": "6 - \\sqrt{11}, 6 + \\sqrt{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": "Given $f(x) = x^2 + ax + b$, satisfying $f(1) = 0$ and $f(2) = 0$, then $f(-1) = \\boxed{6}$.",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the ellipse \\(\\frac{x^{2}}{a^{2}} + \\frac{y^{2}}{b^{2}} = 1\\) with one focus \\(F\\), point \\(P\\) lies on the \\(y\\)-axis. The line \\(PF\\) intersects the ellipse a... | math | {
"ground_truth": "-\\frac{2 a^{2}}{b^{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": "Complex numbers $p, q, r$ form an equilateral triangle with side length 24 in the complex plane. If $|p + q + r| = 48,$ find $|pq + pr + qr|.$",
"role": "user"
}
] | math | {
"ground_truth": "768",
"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 result when the Greatest Common Divisor (GCD) of $7260$ and $540$ is diminished by $12$, then add $5$ to the result.",
"role": "user"
}
] | math | {
"ground_truth": "53",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In right triangle $ABC$, if the acute angle $\\angle A = 50^{\\circ}$, then the other acute angle $\\angle B =$ ____.",
"role": "user"
}
] | math | {
"ground_truth": "40^{\\circ}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The diagonals of a convex quadrilateral form an angle of $45^{\\circ}$. Perpendiculars are drawn from each vertex of the quadrilateral to the lines containing the diagonals that ... | math | {
"ground_truth": "\\frac{1}{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": "Choose a permutation of $ \\{1,2, ..., 20\\}$ at random. Let $m$ be the amount of numbers in the permutation larger than all numbers before it. Find the expected value of $2^... | math | {
"ground_truth": "21",
"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 month with 30 days has the same number of Saturdays and Sundays. How many of the seven days of the week could be the first day of this month?\n**A)** 1 \n**B)** 2 \n**C)** 3 ... | math | {
"ground_truth": "**A)** 1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four unit circles are centered at the vertices of a unit square, one circle at each vertex. What is the area of the region common to all four circles?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\pi}{3} + 1 - \\sqrt{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": "a) Each vertex at the base of a triangle is connected by straight lines to \\( n \\) points located on the opposite side. Into how many parts do these lines divide the triangle?\... | math | {
"ground_truth": "3n^2 + 3n + 1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( x, y, z \\) be relative integers such that for any triangle \\( ABC \\) we have \\( 16 HN^2 = xBC^2 + yCA^2 + zAB^2 \\), where \\( H \\) is the foot of the altitude from ... | 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": "Find all perfect squares $n$ such that if the positive integer $a\\ge 15$ is some divisor $n$ then $a+15$ is a prime power.\n\n*Proposed by Saudi Arabia*",
"role": "u... | math | {
"ground_truth": "1, 4, 9, 16, 49, 64, 196",
"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": "An art exhibition opens at 8:00, but people have already been queuing to enter before that. From the time the first visitor arrives, the number of visitors arriving per minute is... | math | {
"ground_truth": "7:15",
"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": "Given the function $f(x)=3\\ln x-x^{2}+(a-\\frac{1}{2})x$ has a maximum value on the interval $(1,3)$, the range of real number $a$ is ______",
"role": "user"
}
] | math | {
"ground_truth": "(-\\frac{1}{2},\\frac{11}{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": "Gretchen now has ten socks, two of each color: magenta, cyan, black, white, and red. She randomly draws five socks. What is the probability that she ends up with exactly one pair... | math | {
"ground_truth": "\\frac{40}{63}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of the two smallest prime factors of $525$.",
"role": "user"
}
] | 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": "What is the median of the following list of $8160$ numbers?\n\\[1, 2, 3, \\ldots, 4080, 1^2, 2^2, 3^2, \\ldots, 4080^2\\]\nA) 4087\nB) 4088\nC) 4089\nD) 4090",
"role": "user"... | math | {
"ground_truth": "B) 4088",
"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 $A_1B_1C_1$ be a triangle with $A_1B_1 = 16, B_1C_1 = 14,$ and $C_1A_1 = 10$ . Given a positive integer $i$ and a triangle $A_iB_iC_i$ with circumcenter $O_i$ , def... | math | {
"ground_truth": "10800",
"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 $\\sec x - \\tan x = \\frac{5}{2},$ find all possible values of $\\sin x.$",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{21}{29}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the largest integer less than 100 that leaves a remainder of 3 when divided by 8.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=|2x-1|$.\n$(1)$ Solve the inequality $f(x)-f(x+1)\\leqslant 1$ with respect to $x$;\n$(2)$ If the solution set of the inequality $f(x) < m-f(x+1)$ with r... | math | {
"ground_truth": "(2,+\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 2008 congruent circles on a plane such that no two are tangent to each other and each circle intersects at least three other circles. Let $ N$ be the total number of ... | math | {
"ground_truth": "3012",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For an integer $n \\geq 3$ we define the sequence $\\alpha_1, \\alpha_2, \\ldots, \\alpha_k$ as the sequence of exponents in the prime factorization of $n! = p_1^{\\alpha_1}... | math | {
"ground_truth": "3, 6, 10",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Nine teams play a soccer tournament where each team plays every other team exactly once. No ties occur, each match results in a win or a loss with each team having a 50% chance o... | math | {
"ground_truth": "698",
"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": "\\( n \\) is the smallest positive integer that satisfies the following conditions:\n(1) \\( n \\) is a multiple of 75;\n(2) \\( n \\) has exactly 75 positive divisors (including... | math | {
"ground_truth": "75",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a soccer tournament, teams \\( A, B, C, D, E \\) each played exactly once against every other team. For each match, 3 points were awarded for a win, 1 point for a draw, and 0 ... | math | {
"ground_truth": "a = 7, \\, b = 6, \\, c = 4, \\, d = 5, \\, e = 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": "In how many ways can you divide the set of eight numbers $\\{2,3,\\cdots,9\\}$ into $4$ pairs such that no pair of numbers has $\\text{gcd}$ equal to $2$ ?",
"role": "... | math | {
"ground_truth": "36",
"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": "Last year, the cost of a bicycle was $200, a cycling helmet $50, and a pair of cycling gloves $30. This year, the cost of the bicycle increased by $10\\%, the cost of the helmet ... | math | {
"ground_truth": "11.96\\%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the geometric sequence $\\{a_n\\}$, if $a_n > 0$ and $a_3a_7 = 64$, calculate the value of $a_5$.",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S$ be the set of all nonzero real numbers. The function $f : S \\to S$ satisfies the following two properties:\n\n(i) For all $x \\in S,$\n\\[ f \\left( \\frac{1}{x} \\right... | math | {
"ground_truth": "\\frac{3}{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 province is one of the pilot provinces for the high school new curriculum reform. According to the regulations, every student must participate in the academic level test, and a... | math | {
"ground_truth": "0.4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Seth has nine stones: three painted blue, three painted red, and three painted yellow. The blue stones are labeled 1, 2, and 3, as are the red stones and the yellow stones. He bu... | math | {
"ground_truth": "216",
"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 equation of the tangent line to the curve $y=e^{2x+1}$ at its intersection point with the y-axis is.",
"role": "user"
}
] | math | {
"ground_truth": "y=2ex+e",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $a_i \\in \\{-1, 0, 1\\}$ for $0 \\le i \\le 17$, find the number of $18$-tuples $(a_0, a_1, \\dots, a_{17})$ satisfying $a_0 + 2a_1 + 2^2a_2 + \\cdots + 2^{17}a_{17} = 2^{... | 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": "One of the legs of a right triangle is 15 cm, and the radius of the inscribed circle in the triangle is 3 cm. Find the area of the triangle.",
"role": "user"
}
] | math | {
"ground_truth": "60 \\, \\text{cm}^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": "The height of a triangle, which is 2 cm, divides the angle of the triangle in the ratio 2:1, and the base of the triangle into parts, the smaller of which is 1 cm. Find the area ... | math | {
"ground_truth": "\\frac{8}{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": "Out of 1500 people surveyed, $25\\%$ do not enjoy television, and $20\\%$ of the people who do not enjoy television also do not enjoy books. How many people surveyed do not enjoy... | math | {
"ground_truth": "75",
"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 12-digit positive integers have all digits either 1 or 2, and have at least two consecutive digits that are the same?",
"role": "user"
}
] | math | {
"ground_truth": "4094",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integer $n$ , such that for all 35-element-subsets of $M=(1,2,3,...,50)$ ,there exists at least two different elements $a,b$ , satisfing : $a-b=n$ or $... | math | {
"ground_truth": "n \\in [1, 70]",
"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 greatest common divisor of 1337 and 382 is what?",
"role": "user"
}
] | math | {
"ground_truth": "191",
"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": "Square $S_1$ is inscribed inside circle $C_1$ , which is inscribed inside square $S_2$ , which is inscribed inside circle $C_2$ , which is inscribed inside square $S_3$ , w... | math | {
"ground_truth": "2\\sqrt{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": "Person A and Person B start from two locations, A and B respectively, at the same time and move towards each other. Person A walks 70 meters per minute, and Person B walks 60 met... | math | {
"ground_truth": "2080 \\text{ meters}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a positive number $y$, determine the condition that satisfies the inequality $\\sqrt{y} < 3y$.",
"role": "user"
}
] | math | {
"ground_truth": "y > \\frac{1}{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": "A sandwich costs \\$5.00 and a meal plate costs \\$7.00. In how many ways can sandwiches and meal plates be purchased with \\$90.00, without leaving any change?",
"role": "us... | 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": "When a certain biased coin is flipped five times, the probability of getting heads exactly once is not equal to $0$ and is the same as that of getting heads exactly twice. Let ... | math | {
"ground_truth": "283",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the terminal side of the angle $α$ in the second quadrant intersects with the unit circle at point $P(m, \\frac{\\sqrt{3}}{2})$, find the value of $\\tan α$.",
"ro... | math | {
"ground_truth": "-\\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": "On the sides $AB$ and $BC$ of an isosceles triangle $ABC$ with an angle of $44^{\\circ}$ at the vertex, points $M$ and $N$ are taken such that $AM=BN=AC$. Point $X$ on the ray $C... | math | {
"ground_truth": "32^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the distance between the points (0,15,5) and (8,0,-3).",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{353}",
"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 Lorri took a $240 \\mathrm{~km}$ trip to Waterloo, her average speed was $120 \\mathrm{~km} / \\mathrm{h}$ on the way there, and her average speed was $80 \\mathrm{~km} / \... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a positive integer $n$ , we define $\\lambda (n)$ as the number of positive integer solutions of $x^2-y^2=n$ . We say that $n$ is *olympic* if $\\lambda (n) = 2021$ ... | math | {
"ground_truth": "3^{46} \\cdot 5^{42} \\cdot 7",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
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