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": "Evaluate $4 \\otimes (4 \\otimes 4)$, where $x \\otimes y = x^3 + 3xy - y$.",
"role": "user"
}
] | math | {
"ground_truth": "1252",
"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 bug travels from point A to point B on an orthogonal grid consisting of 5 horizontal segments and 5 vertical segments. Calculate the number of different paths the bug can take.... | math | {
"ground_truth": "20",
"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": "Find the smallest positive integer $x$ such that $2^x$ leaves a remainder of $1$ when divided by $5$, $7$, and $31$.",
"role": "user"
}
] | math | {
"ground_truth": "60",
"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 that Theresa's parents have decided to take her to a concert if she spends an average of 12 hours per week helping around the house for 6 weeks, and during the first 5 week... | math | {
"ground_truth": "20",
"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 fruit vendor buys 8 oranges for 15 cents and sells 6 oranges for 18 cents. How many oranges must he sell to make a profit of $150$ cents?\nA) 132 oranges\nB) 133 oranges\nC) 13... | math | {
"ground_truth": "C) 134 oranges",
"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 a cube with side length 6, what is the volume of the tetrahedron formed by any vertex and the three vertices connected to that vertex by edges of the cube?",
"role": "user... | math | {
"ground_truth": "36",
"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-zero vectors $\\overrightarrow {a}$ and $\\overrightarrow {b}$ that satisfy $| \\overrightarrow {a}+ \\overrightarrow {b}|=| \\overrightarrow {a}- \\overrightarrow ... | math | {
"ground_truth": "\\frac{\\pi}{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": "Given that \\(x^2 + \\frac{1}{x^2} = A\\) and \\(x - \\frac{1}{x} = B\\), and now \\(A\\) and \\(B\\) are positive numbers, find the minimum possible value for \\(\\frac{A+1}{B}\... | math | {
"ground_truth": "2\\sqrt{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": "The total surface area of a rectangular solid is $150\\text{ cm}^2$, and the total length of all its edges is $60\\text{ cm}$. Calculate the length in cm of any one of its interi... | math | {
"ground_truth": "5\\sqrt{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": "Regarding the function $f(x)=4\\sin (2x+ \\frac {\\pi}{3}),x\\in\\mathbb{R}$, the following statements are made: \n$(1)$ The initial phase of the function $y=f(x)$ is $\\frac {\... | 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": "Which number is greater, \\(2^{40}\\) or \\(3^{28}\\)?\n\nWhich number is greater, \\(31^{11}\\) or \\(17^{14}\\)?",
"role": "user"
}
] | math | {
"ground_truth": "2^{40} < 3^{28} \\text{ and } 31^{11} < 17^{14}",
"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 volumes of solids formed by the rotation of regions bounded by the graphs of the functions around the y-axis.\n\n$$\ny=\\arcsin \\frac{x}{5}, y=\\arcsin x, y=\\frac... | math | {
"ground_truth": "6 \\pi^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 every $a \\in \\mathbb N$ denote by $M(a)$ the number of elements of the set\n\\[ \\{ b \\in \\mathbb N | a + b \\text{ is a divisor of } ab \\}.\\]\nFind $\\max_{a\\le... | math | {
"ground_truth": "121",
"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 natural numbers $P$ and $P'$ such that $P = P'+10$ and both are divisible by 10 (hence $P$ and $P'$ leave a remainder of 0 when divided by 10). When $P^2 - P'^2$ and $0$ ar... | math | {
"ground_truth": "E) 0, 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": "You have 70 dimes, 30 quarters, and 10 half-dollars. What percent of the value of your money is in quarters?",
"role": "user"
}
] | math | {
"ground_truth": "38.46\\%",
"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 an ellipse $C$: $\\dfrac{x^2}{a^2} + \\dfrac{y^2}{b^2} = 1 (a > b > 0)$ with a focal length of $2$, and point $Q\\left(\\dfrac{a^2}{\\sqrt{a^2 - b^2}}, 0\\right)$ lies on t... | math | {
"ground_truth": "\\sqrt{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": "Find the smallest possible $\\alpha\\in \\mathbb{R}$ such that if $P(x)=ax^2+bx+c$ satisfies $|P(x)|\\leq1 $ for $x\\in [0,1]$ , then we also have $|P'(0)|\\leq \\alpha$... | math | {
"ground_truth": "\\alpha = 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": "Given there are lily pads in a row numbered $0$ to $11$, compute the probability that Fiona the frog reaches pad $10$ without landing on either pad $3$ or pad $6$, where from any... | math | {
"ground_truth": "\\textbf{(A) } \\frac{15}{256}",
"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": "A rectangular box has a total surface area of 130 square inches. The sum of the lengths of all its edges is 56 inches. What is the sum of the lengths in inches of all of its inte... | math | {
"ground_truth": "4\\sqrt{66}",
"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 slant height of a cone is 5, and the radius of its base is 3, calculate its volume.",
"role": "user"
}
] | math | {
"ground_truth": "12\\pi",
"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 complex numbers \\( Z_{1} \\) and \\( Z_{2} \\) satisfy \\( \\left|Z_{1}\\right| = \\left|Z_{1} + Z_{2}\\right| = 3 \\) and \\( \\left|Z_{1} - Z_{2}\\right| = 3 \\sqrt{3} \\)... | math | {
"ground_truth": "4018",
"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 vectors $\\overrightarrow{m}=(\\sqrt{3}\\sin \\omega x,1)$, $\\overrightarrow{n}=({\\cos }^{2}\\omega x+1)$, let the function $f(x)= \\overrightarrow{m}\\cdot \\overrightar... | math | {
"ground_truth": "b\\in(-2, \\frac{\\sqrt{3}-3}{2}]\\cup\\{-\\frac{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": "Given a point \\( P \\) on edge \\( AB \\) of cube \\( ABCD-A_1B_1C_1D_1 \\), find the minimum value of the dihedral angle between planes \\( PDB_1 \\) and \\( ADD_1A_1 \\).",
... | math | {
"ground_truth": "\\arctan\\frac{\\sqrt{2}}{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": "Joy has 30 thin rods, one each of every integer length from 1 cm through 30 cm. She selects rods of lengths 5 cm, 11 cm, and 18 cm to place on a table. Next, she wants to choose ... | math | {
"ground_truth": "**E)** 25",
"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 $f(x)= \\frac {1}{3}x^{3}+ax^{2}+5x+6$ be a monotonic function on the interval $[1,3]$, determine the range of the real number $a$.",
"role": "user"
}
] | math | {
"ground_truth": "(-∞,-3]∪[-\\sqrt{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": "Given the function $y=\\dfrac{\\sqrt {1-x}}{x}$, determine the range of the independent variable $x$.",
"role": "user"
}
] | math | {
"ground_truth": "x\\leqslant 1 \\text{ and } x\\neq 0",
"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": "Given that $a$ and $b$ are positive integers, and $a - b \\sqrt{3} = (2 - \\sqrt{3})^{100}$, find the unit digit of $a \\cdot b$.",
"role": "user"
}
] | 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 a new linear mapping setup, segment $\\overline{AB}$ of length 10 units is mapped to segment $\\overline{A'B'}$ which is 5 units long. If $D$ and $D'$ are the respective midpo... | math | {
"ground_truth": "4.5",
"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": "The number $\\overline{6 x 62 y 4}$ is divisible by 11 and leaves a remainder of 6 when divided by 9. Find the remainder when this number is divided by 13.",
"role": "user"
... | 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": "Given positive real numbers $x_{1}$, $x_{2}$ and the function $f(x)$ satisfying $4^{x}=\\frac {1+f(x)}{1-f(x)}$, and $f(x_{1})+f(x_{2})=1$, determine the minimum value of $f(x_{1... | math | {
"ground_truth": "\\frac{4}{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": "A number $x$ is randomly selected from the interval $(-4,4)$. The probability that the event \"$||x-2|+|x+3||\\geqslant 7$\" occurs is _____.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{8}",
"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 scout troop buys 1500 candy bars at a price of four for $3 dollars. They sell all the candy bars at the price of three for $2 dollars. Calculate their profit, in dollars.",
... | math | {
"ground_truth": "-125",
"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 geometric sequence $\\{a_n\\}$ where the common ratio $q$ is an integer, it is known that $a_1 + a_4 = 18$ and $a_2 + a_3 = 12$. Find the sum of the first 8 terms of this... | math | {
"ground_truth": "510",
"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 the highest power of $2$ that divides $17^5 - 15^5$.\nA) 16\nB) 24\nC) 32\nD) 64",
"role": "user"
}
] | math | {
"ground_truth": "C) 32",
"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": "<u>Set 3</u>**3.1** Annie has $24$ letter tiles in a bag; $8$ C’s, $8$ M’s, and $8$ W’s. She blindly draws tiles from the bag until she has enough to spell “CMWMC.” What ... | math | {
"ground_truth": "\\frac{1}{5}",
"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 geometric sequence with common ratio $q(q > 0)$ and the sum of the first $n$ terms denoted as $S_n$, if $S_2=3a_2+2$ and $S_4=3a_4+2$, calculate the value of $a_1$.",
... | math | {
"ground_truth": "-1",
"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 sides of triangle $DEF$ are in the ratio of $3:4:5$. Segment $EG$ is the angle bisector drawn to the longest side, dividing it into segments $DG$ and $GE$. What is the length... | math | {
"ground_truth": "\\frac{60}{7}",
"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 a modified sequence of squares made of identical square tiles, the edge of each square is two tile lengths longer than the edge of the previous square. How many more tiles doe... | math | {
"ground_truth": "\\text{(D)}\\ 88",
"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 a modified sequence whose $n$th term is defined by $a_n = (-1)^n \\cdot \\lfloor \\frac{3n+1}{2} \\rfloor$. What is the average of the first $150$ terms of this sequence... | math | {
"ground_truth": "-\\frac{1}{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": "Charlie thinks of a number, multiplies it by 3, and then subtracts 4. What number should Emma get after adding 4 to the result and dividing it by 3, given that Charlie initially ... | math | {
"ground_truth": "8",
"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": "Two 12-sided dice, one red and one green, are rolled. What is the probability that the red die shows an even number and the green die shows a number that is a perfect square?",
... | 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": "Let $c$ be a nonnegative integer. Find all infinite sequences of positive integers $\\{a_{n}\\}_{n\\geq 1}$ satisfying the following condition: for all positive integer $n$ ... | math | {
"ground_truth": "a_n = n + (c + 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": "Consider a square with its diagonals and another set of line segments joining the midpoints of opposite sides. Additionally, draw a point at the center of the square and connect ... | math | {
"ground_truth": "40",
"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": "The sequence $\\{c_{n}\\}$ is determined by the following equation. \\[c_{n}=(n+1)\\int_{0}^{1}x^{n}\\cos \\pi x\\ dx\\ (n=1,\\ 2,\\ \\cdots).\\] Let $\\lambda$ be the limit ... | math | {
"ground_truth": "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": "Find the equation of the line that passes through the point P(-1, 2) and is parallel to the line $2x + y - 5 = 0$.",
"role": "user"
}
] | math | {
"ground_truth": "2x + y = 0",
"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": "Determine the values of $m$ for which the quadratic equation $3x^2 + (2m-5)x + 12 = 0$ will have real and equal roots.\nA) 8.5 and 3.5 \nB) 8.5 and -3.5 \nC) 8 and -4 \nD) Onl... | math | {
"ground_truth": "B) 8.5 and -3.5",
"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": "Let $a$ , $b$ , $c$ , $d$ be complex numbers satisfying\n\\begin{align*}\n 5 &= a+b+c+d \n 125 &= (5-a)^4 + (5-b)^4 + (5-c)^4 + (5-d)^4 \n 1205 &= (a+b)^4 + (b+c)^4 + (c+... | math | {
"ground_truth": "70",
"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": "Ken drives to the office in heavy traffic in 30 minutes. On a holiday when there's no traffic, he drives 20 miles per hour faster and gets to the office in 12 minutes. Calculate ... | math | {
"ground_truth": "\\frac{20}{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": "Find all pairs $(x,y)$ of positive real numbers such that $xy$ is an integer and $x+y = \\lfloor x^2 - y^2 \\rfloor$ .",
"role": "user"
}
] | math | {
"ground_truth": "(x, y) = (d, d - 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": "In a triangle ABC, BD is a median where m(∠ABD) = 90°, |AB| = 2, and |AC| = 6. Calculate the length of |BC|.",
"role": "user"
}
] | math | {
"ground_truth": "2\\sqrt{14}",
"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 familiar $3$ -dimensional cube has $6$ $2$ -dimensional faces, $12$ $1$ -dimensional edges, and $8$ $0$ -dimensional vertices. Find the number of $9$ -dimensional ... | math | {
"ground_truth": "1760",
"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 classroom, $65$ students are wearing green shirts, and another $79$ students are wearing red shirts. The $144$ students are grouped into $72$ pairs. In exactly $27$ of these... | math | {
"ground_truth": "34",
"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": "How many 0's are there at the end of the product of $1 \\times 2 \\times 3 \\times 4 \\times \\cdots \\times 2014$?",
"role": "user"
}
] | math | {
"ground_truth": "501",
"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 six bags of marbles have a total of $18, 19, 21, 23, 25$ and $34$ marbles, and one bag contains chipped marbles only, while the other five bags contain no chipped marb... | math | {
"ground_truth": "23",
"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": "Factor the expression $4x(x-5) + 7(x-5) + 12(x-5)$.",
"role": "user"
}
] | math | {
"ground_truth": "(4x + 19)(x-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 there exist a real number $a$ and a positive integer $n$, such that $f\\left(x\\right)=\\cos 2x-a\\sin x$ has exactly $2022$ zeros in the interval $\\left(0,n\\pi \\right)$, t... | 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": "In a right triangle $ABC$ with right angle at $B$, sides $AB=1$, $BC=2$, a right triangle $BCD$ with right angle at $C$ is constructed outwards on the side $\\overline{BC}$ of $A... | math | {
"ground_truth": "\\frac{4}{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": "How many real solutions are there to the equation\n\\[ |||| x|-2|-2|-2|=|||| x|-3|-3|-3| ? \\]",
"role": "user"
}
] | 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": "Find the largest prime divisor of the number represented as $2100210021_3$.",
"role": "user"
}
] | math | {
"ground_truth": "46501",
"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 vectors $\\overrightarrow{m} = (a, -2)$ and $\\overrightarrow{n} = (1, 2-a)$, and that $\\overrightarrow{m}$ is parallel to $\\overrightarrow{n}$, find the value of $a$.",
... | math | {
"ground_truth": "1\\pm\\sqrt{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": "Given lines $x = \\frac{1}{3}y + c$ and $y = \\frac{1}{3}x + d$ intersect at the point $(3, -1)$, calculate the value of $c + d$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{4}{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": "Determine the equation of the tangent line to the curve $y=x^3+x-2$ that is parallel to the line $y=4x-1$.",
"role": "user"
}
] | math | {
"ground_truth": "D: 4x - y = 0 \\quad \\text{or} \\quad 4x - y - 4 = 0",
"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": "Given that circle C passes through points A(0, -6) and B(1, -5), and that the center of the circle lies on line l: $x-y+1=0$, find the standard equation of circle C.",
"role"... | math | {
"ground_truth": "(x + 3)^2 + (y + 2)^2 = 25",
"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": "For any positive real numbers $x_1,\\ x_2,\\ x_3,\\ y_1,\\ y_2,\\ y_3,\\ z_1,\\ z_2,\\ z_3,$ find the maximum value of real number $A$ such that if \\[ M = (x_1^3+x_2^3+x_3^3... | math | {
"ground_truth": "\\frac{9}{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": "A can complete a piece of work in 12 days. B is 50% more efficient than A, and C is twice as efficient as B. Calculate the number of days it takes C to do the same piece of work.... | 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": "Let $PQRS$, $PQVT$, and $PRUT$ be three adjacent square faces of a cube, for which $PT = 10$, and let $O$ be the eighth vertex of the cube. Let $L$, $M$, and $N$, be the points o... | math | {
"ground_truth": "472",
"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 least integer whose square is 75 more than its double?",
"role": "user"
}
] | math | {
"ground_truth": "-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": "In the triangle $ABC$, the angle $\\angle ACB = 120^\\circ$ and $AC + BC = 2$. What are the possible lengths for the side $AB$?",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{3} \\leq AB < 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": "The number of handshakes occur within this gathering among the 40 people is to be determined.",
"role": "user"
}
] | math | {
"ground_truth": "360",
"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 plane \\(Oxy\\), there is a point \\(A\\) whose coordinates \\((x, y)\\) satisfy the equation \\(5a^{2} - 6ax - 2ay + 2x^{2} + 2xy + y^{2} = 0\\), and a circle with center... | math | {
"ground_truth": "(-\\infty, -2) \\cup (-1, 0) \\cup (3, \\infty)",
"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": "There are $N{}$ points marked on the plane. Any three of them form a triangle, the values of the angles of which in are expressed in natural numbers (in degrees). What is the m... | math | {
"ground_truth": "180",
"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 1997th digit in the decimal expansion of the fraction \\(\\frac{1}{7}=0.142857 \\ldots\\)?",
"role": "user"
}
] | math | {
"ground_truth": "5",
"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": "If $f(n) = \\tfrac{1}{4} n(n+1)(n+2)(n+3)$, compute $f(r) - f(r-1)$.",
"role": "user"
}
] | math | {
"ground_truth": "r(r+1)(r+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": "Calculate $\\log_2 64 + \\log_2 4$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "When does this occur? When the clock hands are positioned in such a way that if the distance is taken as the number of minute divisions after XII, the distance traveled by one of... | math | {
"ground_truth": "12 \\text{ hours } 5 \\text{ seconds}",
"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": "If $p$ is a prime positive integer and $x,y$ are positive integers, \nfind , in terms of $p$ , all pairs $(x,y)$ that are solutions of the equation: $p(x-2)=x(y-1)$ . (1... | math | {
"ground_truth": "(11, 10, 11), (14, 7, 7)",
"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": "Find all natural pairs $ (x,y)$ , such that $ x$ and $ y$ are relative prime and satisfy equality: $ 2x^2 \\plus{} 5xy \\plus{} 3y^2 \\equal{} 41x \\plus{} 62y \\plus{} 21$... | math | {
"ground_truth": "(2, 19)",
"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 circle is inscribed in a square of side $m$, then a square is inscribed in that circle, then a circle is inscribed in the latter square, and so on. Determine the sum of the are... | math | {
"ground_truth": "\\frac{\\pi m^2}{2}",
"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": "Mr. Li went to a toy store to buy balls. The money he brought was just enough to buy 60 plastic balls. If he didn't buy plastic balls, he could buy exactly 36 glass balls or 45 w... | math | {
"ground_truth": "45",
"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 how many ways can we fill the cells of a $m\\times n$ board with $+1$ and $-1$ such that the product of numbers on each line and on each column are all equal to $-1$ ?"... | math | {
"ground_truth": "2^{(m-1)(n-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": "Given $k = 2015^{2} + 2^{2015}$, determine the units digit of $k^2 + 2^k$.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"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 \\(\\zeta_1, \\zeta_2,\\) and \\(\\zeta_3\\) be complex numbers such that:\n\\[\n\\zeta_1 + \\zeta_2 + \\zeta_3 = 2, \\quad \\zeta_1^2 + \\zeta_2^2 + \\zeta_3^2 = 8, \\quad \... | math | {
"ground_truth": "219",
"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 single tennis tournament starts with 120 players, with the top 40 players receiving a bye in the first round, leaving 80 players to be paired off into matches. Calculate the to... | math | {
"ground_truth": "120",
"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 a sequence $\\{a_n\\}_{n\\geq 0}$ such that $a_{n+1}=a_n-\\lfloor{\\sqrt{a_n}}\\rfloor\\ (n\\geq 0),\\ a_0\\geq 0$ .\n\n(1) If $a_0=24$ , then find the smallest $n$... | math | {
"ground_truth": "2m - 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": "A four-digit number, if separated by a comma between the hundreds and tens place, can be written as two two-digit numbers (e.g., 3126 → 31,62). If the two two-digit numbers have ... | math | {
"ground_truth": "12",
"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": "Sarah buys $3$ gumballs from a gumball machine that contains $10$ orange, $6$ green, and $9$ yellow gumballs. What is the probability that the first gumball is orange, th... | math | {
"ground_truth": "\\frac{9}{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": "What number can be added to both the numerator and the denominator of $\\frac{4}{7}$ so that the resulting fraction will be equivalent to $\\frac{7}{9}$?",
"role": "user"
}... | math | {
"ground_truth": "6.5",
"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": "Find two-thirds of $\\frac{15}{4}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{2}",
"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": "Derive the formula\n\n$$\nI_{i}^{*}=\\frac{b-a}{n} \\sum_{i=1}^{n}\\left[\\varphi\\left(x_{i}\\right)-g\\left(x_{i}\\right)\\right]+\\int_{a}^{b} g(x) \\mathrm{d} x\n$$\n\nwhere ... | math | {
"ground_truth": "I_{i}^{*} = \\frac{b-a}{n} \\sum_{i=1}^{n} \\left[ \\varphi\\left(x_{i}\\right) - g\\left(x_{i}\\right) \\right] + \\int_{a}^{b} g(x) \\, \\mathrm{d} x",
"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": "Right triangular prism $ABCDEF$ with triangular faces $\\vartriangle ABC$ and $\\vartriangle DEF$ and edges $\\overline{AD}$ , $\\overline{BE}$ , and $\\overline{CF}$ h... | math | {
"ground_truth": "5",
"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 the universal set $U=\\{1,2,3,4,5,6\\}$, set $A=\\{1,2,3,4\\}$, and set $B=\\{1,3,5\\}$, then $C_U(A \\cap B)=$ ?",
"role": "user"
}
] | math | {
"ground_truth": "\\{2,4,5,6\\}",
"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": "Let $g$ be defined by \\[g(x) = \\left\\{\n\\begin{array}{cl}\n3-x & \\text{ if } x \\leq 2, \\\\\n3x-x^2 & \\text{ if } x>2.\n\\end{array}\n\\right.\\]Calculate $g^{-1}(-4)+g^{... | math | {
"ground_truth": "6",
"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 plane has several seats on it, each with its own price, as shown below(attachment). $2n-2$ passengers wish to take this plane, but none of them wants to sit with any other pa... | math | {
"ground_truth": "(n-1)n",
"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 certain year, the price of a commodity rose by $30\\%$ during January, fell by $15\\%$ during February, rose by $10\\%$ during March, and fell by $y\\%$ during April. The pr... | math | {
"ground_truth": "\\textbf{(B)}\\ 14",
"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": "Shift the graph of the function $y=\\sqrt{3}\\sin 2x$ to the right by $\\frac{\\pi}{4}$ units, and then compress the horizontal coordinates of all points on the obtained graph to... | math | {
"ground_truth": "y=-\\sqrt{3} \\cos 4x",
"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 region \\( R \\) in the complex plane is defined by:\n\\[ R = \\{x + iy : -2 \\leq x \\leq 2, -2 \\leq y \\leq 2\\}. \\]\nA complex number \\( z = x + iy \\) is chosen uniforml... | 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 $ABC$ be a triangle with $AB=5$ , $BC=7$ , $CA=8$ , and circumcircle $\\omega$ . Let $P$ be a point inside $ABC$ such that $PA:PB:PC=2:3:6$ . Let rays $\\overrigh... | math | {
"ground_truth": "4082",
"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": "Find all positive integer $n$ , such that $$ \\left[\\frac{n}{2^0}\\right]\\left[\\frac{n}{2^1}\\right]\\ldots\\left[\\frac{n}{2^k}\\right]+2\\cdot 4^{[\\frac{k}{2}]} $$ is a... | math | {
"ground_truth": "n = 2, 4",
"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 the real numbers $1.212$, $1.010010001\\ldots$, $\\frac{\\pi}{2}$, $\\frac{\\sqrt{3}}{2}$, $\\frac{3}{4}$, determine the number of irrational numbers in the set.",
"rol... | 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": "Let \\( n \\) be a positive integer. Each cell of an \\( n \\times n \\) table is colored in one of \\( k \\) colors where every color is used at least once. Two different colors... | math | {
"ground_truth": "k = 2n - 1 \\text{ for } n \\geq 3 \\text{ and } k = 4 \\text{ for } n = 2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
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