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": "Let \\( T \\) be a finite set of positive integers. The greatest integer in \\( T \\) is removed from \\( T \\), and the average value of the integers remaining is \\( 45 \\). If... | math | {
"ground_truth": "C) 50",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the sum of the roots of the equation $3x^2 - 9x + 6 = 0$?",
"role": "user"
}
] | math | {
"ground_truth": "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": "Given the expression $\\frac{3+5+7}{2+4+6} \\times \\frac{1+3+5}{6+8+10}$, calculate the result.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{15}{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": "Triangle $ABC$ is a right triangle with $AC = 8$, $BC = 15$, and right angle at $C$. Point $M$ is the midpoint of $AB$, and $D$ is on the same side of line $AB$ as $C$ such that ... | math | {
"ground_truth": "1052",
"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": "Two integers have a sum of $28$. When two more integers are added, their sum becomes $45$. Finally, when two more integers are added, the sum is $63$. Find the minimum number of ... | math | {
"ground_truth": "1",
"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": "Josh writes the numbers $1,2,3,\\dots,149,150$. He marks out $1$, skips the next two numbers $(2, 3)$, marks out $4$, and continues skipping two and marking out the next number t... | math | {
"ground_truth": "147",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 1002 banana candies and 1002 apple candies in a box. Lara takes two candies from the box without looking at the flavor. If $q$ is the probability that the two candies a... | math | {
"ground_truth": "\\frac{1}{2003}",
"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 $\\triangle ABC$, find the value of $a^{3} \\sin (B-C) + b^{3} \\sin (C-A) + c^{3} \\sin (A-B)$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\{a_n\\}$ is an arithmetic sequence and $a_2 + a_5 + a_8 + a_{11} = 48$, find the value of $a_6 + a_7$.",
"role": "user"
}
] | math | {
"ground_truth": "24",
"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 rectangular plot of land, a man walks in a very peculiar fashion. Labeling the corners $ABCD$ , he starts at $A$ and walks to $C$ . Then, he walks to the midpoint of sid... | math | {
"ground_truth": "793",
"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 *substring* of a number $n$ is a number formed by removing some digits from the beginning and end of $n$ (possibly a different number of digits is removed from each side). ... | math | {
"ground_truth": "576",
"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": "Chewbacca has 25 pieces of cherry gum and 40 pieces of grape gum. Some of the pieces are in complete packs, while others are loose. Each complete pack has exactly \\(y\\) pieces ... | math | {
"ground_truth": "2.5",
"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": "Solve the equation \\( f(f(x)) = x \\), given that \\( f(x) = x^2 + 5x + 1 \\).",
"role": "user"
}
] | math | {
"ground_truth": "-2 \\pm \\sqrt{3}, -3 \\pm \\sqrt{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": "Find $f(2)$ given that $f$ is a real-valued function that satisfies the equation $$ 4f(x)+\\left(\\frac23\\right)(x^2+2)f\\left(x-\\frac2x\\right)=x^3+1. $$",
"role": "u... | math | {
"ground_truth": "\\frac{19}{12}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the sequence $\\{a_n\\}$ have a sum of the first $n$ terms denoted by $S_n$. If $a_1=1$ and $S_n= \\frac{n+2}{3}a_n$, then the general formula for the sequence $\\{a_n\\}$ is... | math | {
"ground_truth": "\\frac{n^2+n}{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": "John has saved up $5373_8$ dollars for a vacation to Japan. A round-trip airline ticket costs $1500_{10}$ dollars. In base ten, how many dollars will he have left for other expen... | math | {
"ground_truth": "1311",
"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 an equilateral triangle with side length $1$ . Points $A_1$ and $A_2$ are chosen on side $BC$ , points $B_1$ and $B_2$ are chosen on side $CA$ , and poi... | 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": "The numbers $p$ and $q$ are prime and satisfy \n\\[\\frac{p}{{p + 1}} + \\frac{{q + 1}}{q} = \\frac{{2n}}{{n + 2}}\\]\nfor some positive integer $n$ . Find all possible valu... | math | {
"ground_truth": "\\{2, 3, 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": "In triangle $ABC$, at $B$ there is a right angle. A point $P$ within the triangle satisfies $PA = 12$, $PB = 8$, and angles $\\angle APB = \\angle BPC = \\angle CPA$. Find the le... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $a$ , $b$ , and $c$ are the roots of the equation $x^3-3x^2+mx+24=0$ , and that $-a$ and $-b$ are the roots of the equation $x^2+nx-6=0$ , determine the valu... | 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": "In $\\triangle ABC$, $A, B, C$ are the three interior angles, and $a, b, c$ are the sides opposite to angles $A, B, C$ respectively. It is given that $2 \\sqrt{2}\\left(\\sin^2 A... | math | {
"ground_truth": "\\frac{3\\sqrt{3}}{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": "Find the number of ordered pairs of positive integers $(a,b)$ such that $a+b=1000$ and neither $a$ nor $b$ has a zero digit.",
"role": "user"
}
] | math | {
"ground_truth": "801",
"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": "Line \\( m \\) has the equation \\( y = 2x + 8 \\). Line \\( n \\) has the equation \\( y = kx - 9 \\). Lines \\( m \\) and \\( n \\) intersect at the point \\((-4, 0)\\). What i... | math | {
"ground_truth": "k = -\\frac{9}{4}",
"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 value of $\\frac{2468 \\times 2468}{2468+2468}$?\nA) 2\nB) 1234\nC) 2468\nD) 4936\nE) 6091024",
"role": "user"
}
] | math | {
"ground_truth": "1234",
"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: $1100 \\div 25 \\times 4 \\div 11 = $",
"role": "user"
}
] | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f\\left(x\\right)=\\sin \\left(ωx+φ\\right)\\left(ω > 0,-\\frac{π}{2}\\leqslant φ < \\frac{π}{2}\\right)$, each point on the graph has its x-coordinate shorte... | math | {
"ground_truth": "\\frac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all real solutions of the system $$ \\begin{cases} x_1 +x_2 +...+x_{2000} = 2000 x_1^4 +x_2^4 +...+x_{2000}^4= x_1^3 +x_2^3 +...+x_{2000}^3\\end{cases} $$",
"role": "... | math | {
"ground_truth": "x_1 = x_2 = \\cdots = x_{2000} = 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 rectangle is said to be inscribed in a parallelogram if its vertices lie one on each side of the parallelogram. On the larger side $AB$ of the parallelogram $ABCD$ , find a... | math | {
"ground_truth": "\\lambda = \\frac{(a+dm)(am+bm-d)}{2am+d(m^{2}-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 a set $\\{4,6,8,12,14,18\\}$, select three different numbers, add two of these numbers, multiply their sum by the third number, and finally subtract the smallest number you... | math | {
"ground_truth": "52",
"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": "Ten points in the plane are given, with no three collinear. Four distinct segments joining pairs of these points are chosen at random, all such segments being equally likely. T... | math | {
"ground_truth": "51345",
"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 \\( a, b, \\) and \\( c \\) are all positive integers, and the parabola \\( y = ax^2 + bx + c \\) intersects the x-axis at two distinct points \\( A \\) and \\( B \\).... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that there are $24$ primes between $3$ and $100$ , inclusive, what is the number of ordered pairs $(p, a)$ with $p$ prime, $3 \\le p < 100$ , and $1 \\le a < p$ ... | math | {
"ground_truth": "48",
"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": "Susan wants to fence a square piece of land with a minimum area of 900 square feet. Inside this land, she also plans to fit a circular garden that should cover at least 100 squar... | math | {
"ground_truth": "30 \\text{ feet}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a regular hexagon $ABCDEF$ with side length $10$ feet. A circle is drawn passing through vertices $A$ and $F$ and is tangent to side $CD$. Find the radius of the circle in ... | 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": "Grandma gave Bryce, Carter, and April some raisins. Bryce received 10 more raisins than Carter, and Carter received one-third the number of raisins Bryce received. April received... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate \\(3^{18} \\div 27^2\\) and multiply the result by 7. Write your answer as an integer.",
"role": "user"
}
] | math | {
"ground_truth": "3720087",
"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 the derivative of the function $f(x)$ is $f′(x)$, and it satisfies $f(x)=2xf′(1)+\\ln x$, calculate the value of $f′(1)$.",
"role": "user"
}
] | 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": "A rectangle \\( R \\) has side lengths \\( a \\) and \\( b \\), where \\( a < b \\). To obtain a rectangle with side lengths \\( x \\) and \\( y \\) (where \\( x < a \\) and \\( ... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the circle $x^2+y^2+2kx+2y+2=0$ ($k>0$) does not intersect with the coordinate axes, determine the range of the real number $k$.",
"role": "user"
}
] | math | {
"ground_truth": "1<k<\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $d$ is a digit, find the number of values of $d$ for which $2.0d05 > 2.015$.",
"role": "user"
}
] | 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": "In the Cartesian coordinate system $xoy$, the curve $C_{1}$ is defined by $\\begin{cases} x=t\\cos\\alpha \\\\ y=t\\sin\\alpha \\end{cases}$ (where $t$ is a parameter, $t{\\neq }... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $104$ is divided into three parts which are proportional to $2, \\frac{2}{3}, \\frac{1}{3}$, find the value of the smallest part.",
"role": "user"
}
] | math | {
"ground_truth": "11.56",
"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 an arithmetic sequence $\\{a_n\\}$, where $a_4 = 7$ and $a_5 + a_7 = 26$, find the sum of the first 8 terms, $S_8 = \\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | math | {
"ground_truth": "68",
"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 collection of pennies, nickels, dimes, and quarters with a total value of $\\$1.02$, having at least one coin of each type, determine the minimum number of dimes in the c... | math | {
"ground_truth": "1",
"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": "Given the function $f(x)=a^{x-1}$ ($a > 0$ and $a \\neq 1$), \n(1) If the graph of the function $y=f(x)$ passes through the point $P(3,4)$, find the value of $a$; \n(2) If $f(\... | math | {
"ground_truth": "\\text{When } a > 1, f(\\lg \\frac {1}{100}) > f(-2.1); \\text{ when } 0 < a < 1, f(\\lg \\frac {1}{100}) < f(-2.1).",
"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": "Compute the value of $y$ such that \n\\[\n\\left(1 + \\frac{1}{3} + \\frac{1}{9} + \\frac{1}{27} + \\cdots\\right) \\left(1 - \\frac{1}{3} + \\frac{1}{9} - \\frac{1}{27} + \\cdot... | math | {
"ground_truth": "9",
"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 the sequence $ \\{a_n\\}_{n\\geq 1}$ be defined by $ a_1 \\equal{} 20$ , $ a_2 \\equal{} 30$ and $ a_{n \\plus{} 2} \\equal{} 3a_{n \\plus{} 1} \\minus{} a_n$ for all ... | math | {
"ground_truth": "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 that $|\\vec{a}|=4$ and $\\vec{b}$ is in the opposite direction to $\\vec{a}$ with $|\\vec{b}|=2$, find the scalar $k$ such that $\\vec{a} = k \\vec{b}$.",
"role": "use... | math | {
"ground_truth": "-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": "Four coplanar circles are placed as shown. What is the maximum number of points on the circles that a line passing through all four circles can touch?\n\n[asy]\nimport graph;\ndr... | 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": "$2\\sin 75^{\\circ}\\cos 15^{\\circ}-1=$ \\_\\_\\_\\_\\_\\_ .",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{3}}{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 the sets $A=\\{0,3,4\\}$ and $B=\\{-1,0,2,3\\}$, then $A \\cap B=$ ______.",
"role": "user"
}
] | math | {
"ground_truth": "\\{0,3\\}",
"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 vectors $\\overrightarrow{a} = (2, -3, 1)$, $\\overrightarrow{b} = (2, 0, 3)$, and $\\overrightarrow{c} = (0, 2, 2)$, find the dot product of $\\overrightarrow{a}$ with the... | 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": "In a right triangle XYZ, where angle XYZ is right, find $\\tan X$ if the lengths of side XY is 40 and the hypotenuse YZ is 41.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{40}",
"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": "Three standard 6-sided dice are tossed. What is the probability that the sum of the numbers shown on the dice is a prime number? Express your answer as a common fraction.",
"... | math | {
"ground_truth": "\\frac{73}{216}",
"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": "How many primes between $2$ and $2^{30}$ are $1$ more than a multiple of $2017$ ? If $C$ is the correct answer and $A$ is your answer, then your score will be rounded ... | math | {
"ground_truth": "25560",
"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 blackboard contains 68 pairs of nonzero integers. Suppose that for each positive integer $k$ at most one of the pairs $(k, k)$ and $(-k, -k)$ is written on the blackboard. A ... | math | {
"ground_truth": "43",
"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": "In the quadrilateral \\(ABCD\\), it is given that \\(\\cos \\angle BAD = \\frac{3}{4}\\), \\(\\angle BAC = \\angle DAC\\), \\(AD < AB\\), and \\(AB = 5\\), \\(AC = BD = \\sqrt{14... | math | {
"ground_truth": "\\lambda + \\mu = \\frac{7}{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": "For a positive integer $n$ , let $d_n$ be the units digit of $1 + 2 + \\dots + n$ . Find the remainder when\n\\[\\sum_{n=1}^{2017} d_n\\]\nis divided by $1000$ .",
"role... | math | {
"ground_truth": "69",
"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": "Marisela is putting on a juggling show! She starts with $1$ ball, tossing it once per second. Lawrence tosses her another ball every five seconds, and she always tosses each ba... | math | {
"ground_truth": "390",
"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 diagram shows a circle with radius 1 that rolls without slipping around the inside of a square with sides of length 5.\n\nThe circle rolls once around the square, returning t... | 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": "Given $x>0$, $y>0$, and $\\frac{2}{x} + \\frac{1}{y} = 1$, if $x+2y > m^2 - 2m$ always holds, determine the range of the real number $m$.",
"role": "user"
}
] | math | {
"ground_truth": "(-2,4)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Adam has a single stack of $3 \\cdot 2^n$ rocks, where $n$ is a nonnegative integer. Each move, Adam can either split an existing stack into two new stacks whose sizes differ... | math | {
"ground_truth": "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": "A circle centered at $O$ is circumscribed around $\\triangle ABC$. The central angles are $\\angle AOC = 140^\\circ$ and $\\angle AOB = 160^\\circ$. Calculate the measure of $\\a... | math | {
"ground_truth": "30^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence $\\{a\\_n\\}$ with its first $n$ terms sum $S\\_n$, and it satisfies $S\\_n = 2 - a\\_n$ for $n = 1, 2, 3, ...$.\n\n1. Find the general term formula for the sequ... | math | {
"ground_truth": "3 - \\frac{1}{2^{n-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": "Petya and Vasya simultaneously set off on scooters towards each other. There is a bridge exactly in the middle between them. The road from Petya to the bridge is paved, while the... | 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": "Determine the minimum possible value of the sum\n\\[\n\\frac{a}{3b} + \\frac{b}{6c} + \\frac{c}{9a} + \\frac{a^2b}{18bc}\n\\]\nwhere $a, b,$ and $c$ are positive real numbers.",
... | math | {
"ground_truth": "\\frac{4}{9}",
"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": "At the entrance to an amusement park, they sell children's and adult tickets. One children's ticket costs 600 rubles. Alexander bought 2 children's and 3 adult tickets, while Ann... | math | {
"ground_truth": "3600",
"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": "Let $O$ be the origin. There exists a scalar $k$ such that for any points $A,$ $B,$ $C,$ and $D$ where\n\\[2 \\overrightarrow{OA} + 3 \\overrightarrow{OB} - 4 \\overrightarrow{OC... | 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": "Given the universal set $ U = \\{1, 2, 3, 4, 5\\} $ and the set $ A = \\{2, 3, 4\\} $, find the complement of $ A $ with respect to $ U $, denoted as $ \\complement_U A $.",
... | math | {
"ground_truth": "\\complement_U A = \\{1, 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 that the first term of the sequence is zero, and the sequence of differences is: \\(2, 4, -1, 0, -5, -3, 3\\). Construct a diagram. How can you determine the last term of t... | math | {
"ground_truth": "0",
"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 $n$ is a four-digit positive integer and is the product of three distinct prime factors $x$, $y$ and $10y+x$, where $x$ and $y$ are each less than 10. What is the larg... | math | {
"ground_truth": "1533",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the integer $n,$ $0 \\le n \\le 180,$ such that $\\cos n^\\circ = \\cos 1534^\\circ.$",
"role": "user"
}
] | math | {
"ground_truth": "154",
"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 percent of square $EFGH$ is shaded? All angles in the diagram are right angles. [asy]\nimport graph;\ndefaultpen(linewidth(0.7));\n\nxaxis(0,6,Ticks(1.0,NoZero));\nyaxis(0,6... | math | {
"ground_truth": "61.11\\%",
"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": "Jar #1 contains five red marbles, three blue marbles, and one green marble.\nJar #2 contains five blue marbles, three green marbles, and one red marble.\nJar #3 contains five gre... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many of the fifteen hexominoes shown below have at least one line of reflectional symmetry or one point of rotational symmetry?\n[asy] unitsize(5mm); defaultpen(linewidth(1pt... | math | {
"ground_truth": "C) 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": "A factory plans to produce two types of student desks and chairs, type A and type B, for a disaster-stricken school, aiming to accommodate 1250 students with a total of 500 sets.... | math | {
"ground_truth": "56500",
"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": "Fred and George play a game, as follows. Initially, $x = 1$ . Each turn, they pick $r \\in \\{3,5,8,9\\}$ uniformly at random and multiply $x$ by $r$ . If $x+1$ is a mult... | math | {
"ground_truth": "\\frac{25}{46}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ways are there to partition $7$ students into the groups of $2$ or $3$ ?",
"role": "user"
}
] | math | {
"ground_truth": "105",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ k$ be a positive integer. Find all polynomials\r\n\r\n\\[ P(x) \\equal{} a_0 \\plus{} a_1 x \\plus{} \\cdots \\plus{} a_n x^n,\\]\r\n\r\nwhere the $ a_i$ are real, whic... | math | {
"ground_truth": "P(x) = 0",
"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 $x$ and $y$ are positive real numbers satisfying the equation $\\frac{1}{2x+y} + \\frac{4}{2x+3y} = 1$, find the minimum value of $x + y$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{9}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sequence $\\{a\\_n\\}$ that satisfies the condition: when $n \\geqslant 2$ and $n \\in \\mathbb{N}^+$, we have $a\\_n + a\\_{n-1} = (-1)^n \\times 3$. Calculate the sum... | math | {
"ground_truth": "300",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the arithmetic sequence $\\{a_n\\}$, $a_2=12$, $a_n=-20$, and the common difference $d=-2$. Find the value of $n$.",
"role": "user"
}
] | math | {
"ground_truth": "18",
"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 you and eight friends want to raise $2400 for a new community project, and you plan to split the amount equally among all contributors, calculate the amount each of you nee... | math | {
"ground_truth": "266",
"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 parabola $y=-5\\left(x+2\\right)^{2}-6$, find the coordinates of its vertex.",
"role": "user"
}
] | math | {
"ground_truth": "(-2,-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": "Find all functions $f: \\mathbb{R} \\to \\mathbb{R}$ that have a continuous second derivative and for which the equality $f(7x+1)=49f(x)$ holds for all $x \\in \\mathbb{R}$ ... | math | {
"ground_truth": "f(x) = b\\left(x + \\frac{1}{6}\\right)^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": "Given the set $\\{0,1, 2,..., 2014\\}$, find the number of integers such that $\\binom{2014}{x} \\ge \\binom{2014}{999}$.",
"role": "user"
}
] | math | {
"ground_truth": "17",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\triangle ABC$ be a right triangle at $A$ with circumcircle $\\omega$. The tangents to $\\omega$ at $B$ and $C$ intersect at $T$. Let $X$ and $Y$ be the projections of $T$ ... | math | {
"ground_truth": "987.5",
"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": "In normal circumstances, the size of machine parts manufactured by workers follows a normal distribution $N(\\mu, \\sigma^2)$. In a normal experiment, when 1000 parts are taken, ... | 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": "If the value of the polynomial $2x^2 - x$ equals $1$, then the value of $4x^4 - 4x^3 + 3x^2 - x - 1$ equals ____.",
"role": "user"
}
] | 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": "Let $f(x)= \\frac{ax+b}{cx+d}$ where $a$, $b$, $c$, and $d$ are nonzero real numbers. The function has the properties $f(5)=5$, $f(50)=50$ and $f(f(x))=x$ for all values except $... | math | {
"ground_truth": "27.5",
"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 the set $A=\\{x|ax^{2}-2ax+1 \\lt 0\\}=\\varnothing$, then the range of real number $a$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "[0,1)",
"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": "In a chess tournament, two students from the 7th grade and some number of students from the 8th grade participated. The two 7th graders scored a total of 8 points, and each of th... | math | {
"ground_truth": "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": "Let the arithmetic sequence \\(\\{a_n\\}\\) have a common difference \\(d\\), with \\(d \\neq 0\\). The sequence \\(\\{b_n\\}\\) is a geometric sequence with a common ratio \\(q\... | math | {
"ground_truth": "n = 2^{(m+1)/2} - 1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are $n$ students standing in line positions $1$ to $n$ . While the teacher looks away, some students change their positions. When the teacher looks back, they are stan... | math | {
"ground_truth": "\\left\\lfloor \\frac{n^2}{2} \\right\\rfloor",
"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": "There is a calculator with digits from 0 to 9 and two operation signs. Initially, the display shows the number 0. You can press any keys. The calculator executes actions in the s... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cylindrical tank is one-third full of a solution. The solution is made up of alcohol and water in a ratio of 1:5. If the tank has a height of 9 feet and a diameter of 3 feet, w... | math | {
"ground_truth": "3.53 \\text{ cubic feet}",
"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 solution to the linear equation in one variable $(2m-6)x^{|\\!m|-2}=m^{2}$ is .",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{3}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A researcher in a botanical garden documented the heights of 5 sequential trees. The height of each tree either increases by 5 meters or decreases by 3 meters compared to the pre... | math | {
"ground_truth": "20.4",
"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": "Two circles are externally tangent at a point. The first circle has a radius of 2 and is centered at point $C$, while the second circle has a radius of 5 and is centered at point... | math | {
"ground_truth": "\\frac{5}{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": "Given a rectangle \\(ABCD\\). A line passing through vertex \\(A\\) and point \\(K\\) on side \\(BC\\) divides the entire rectangle into two parts, one of which has an area 5 tim... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
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