data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Analyzing the intersection of $y = x^3 - 6x + 2$ and $y = m$ where $-10 < m < 10$, define $L(m)$ as the smallest $x$ coordinate of their intersection points. Calculate the functi... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( x = 12 \\) and \\( y = -6 \\), calculate the value of \\( \\frac{3x + y}{x - y} \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{3}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of the expression $1 - \\frac{1}{1 + \\sqrt{2}} + \\frac{1}{1 - \\sqrt{2}}$.\nA) $1 - 2\\sqrt{2}$\nB) $1 + \\sqrt{2}$\nC) $-\\sqrt{2}$\nD) $1 - 2\\sqrt{3}$",
... | math | {
"ground_truth": "1 - 2\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $SP_1P_2P_3EP_4P_5$ be a heptagon. A frog starts jumping at vertex $S$. From any vertex of the heptagon except $E$, the frog may jump to either of the two adjacent vertices. ... | math | {
"ground_truth": "351",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a semipro basketball league has teams with 15 players each and each player must receive a minimum salary of $20,000, and the total of all players' salaries for each te... | math | {
"ground_truth": "220,000",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An ATM password at Fred's Bank consists of four digits from $0$ to $9$. No password may begin with the sequence \"123\", and if a password begins with \"123\", the fourth digit c... | math | {
"ground_truth": "9992",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Five judges score a gymnast. If the highest score is removed, the average score is 9 points. If the lowest score is removed, the average score is 9.2 points. What is the differen... | math | {
"ground_truth": "0.8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\{a_n\\}$ is a geometric sequence, $a_4+a_7=2$, and $a_5a_6=-8$, find the value of $a_1+a_{10}$.",
"role": "user"
}
] | math | {
"ground_truth": "-7",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jori has 3 gallons of distilled water and uses 11/4 gallons in a science experiment. What fraction of a gallon does she have left?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the smallest integer $j$ such that it is possible to fill the fields of the table $10\\times 10$ with numbers from $1$ to $100$ so that every $10$ consecutive... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively. It is given that $b\\cos C=(2a-c)\\cos B$. \n(Ⅰ) Find angle $B$;... | math | {
"ground_truth": "5+ \\sqrt {7}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose a function $h(x)$ is defined on the domain $[-10, 6]$. Define a new function $p(x)$ by $$p(x) = h(-3x + 1).$$ What is the domain of $p(x)$? Express your answer in interva... | math | {
"ground_truth": "[-5/3, 11/3]",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a positive integer $n$ , we say an $n$ -*transposition* is a bijection $\\sigma: \\{1,2, \\dots , n\\} \\rightarrow \\{1,2, \\dots , n\\}$ such that there exist exactly t... | math | {
"ground_truth": "197",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When valves A, B, and C are opened together, it takes 12 minutes to fill the entire pool; when valves B, C, and D are opened together, it takes 15 minutes to fill the entire pool... | math | {
"ground_truth": "10 \\text{ minutes}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function $f(x) = x^2 - 2(1-a)x + 2$ is decreasing on $(-\\infty, 4]$. Determine the range of the real number $a$.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, -3]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given two tangents to a circle are drawn from a point A. The points of contact B and C divide the circle into arcs with lengths in the ratio 3:5. What is the degree measure of ∠B... | math | {
"ground_truth": "67.5^\\circ",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a line passes through the intersection of the lines \\(3x + 2y - 5 = 0\\) and \\(2x + 3y - 5 = 0\\), and has an intercept of -5 on the y-axis, what is the equation of ... | math | {
"ground_truth": "6x - y - 5 = 0",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle and on the sides we draw, externally, the squares $BADE, CBFG$ and $ACHI$ . Determine the greatest positive real constant $k$ such that, for any tr... | math | {
"ground_truth": "k = 4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each of the spots in a $8\\times 8$ chessboard is occupied by either a black or white “horse”. At most how many black horses can be on the chessboard so that none of the horses... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle $ABC$ , $\\angle ABC$ is obtuse. Point $D$ lies on side $AC$ such that $\\angle ABD$ is right, and point $E$ lies on side $AC$ between $A$ and $D$ s... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a$ and $b$ be the roots of the equation $x^2 - mx + 3 = 0.$ Suppose that $a + \\frac{1}{b}$ and $b + \\frac{1}{a}$ are the roots of the equation $x^2 - px + q = 0.$ What is ... | math | {
"ground_truth": "\\frac{16}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A triangle $\\vartriangle ABC$ has $\\angle B = 90^o$ . A circle is tangent to $AB$ at $B$ and also tangent to $AC$ . Another circle is tangent to the first circle as we... | math | {
"ground_truth": "\\frac{\\sqrt{3}}{6}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A set contains five numbers. The ten pairwise sums of distinct elements of the set, in no particular order, are $210$, $350$, $305$, $255$, $x$, $y$, $400$, $345$, $380$, and $z$... | math | {
"ground_truth": "3690",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an arithmetic sequence $\\{a_{n}\\}$ with $a_{1}=2$, common difference $d\\neq 0$, and $a_{1}$, $a_{2}$, $a_{5}$ form a geometric sequence, find $d$.",
"role": "user"
... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an isosceles right-angled triangle, the sum of the squares of the three side lengths is 1452. What is the length of the hypotenuse?",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{726}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the $\\emph{positive}$ real number(s) $x$ such that $\\frac{1}{3}(4x^2 - 3) = (x^2 - 75x - 15)(x^2 + 40x + 8)$.",
"role": "user"
}
] | math | {
"ground_truth": "x = \\frac{75 + \\sqrt{5677}}{2} \\quad \\text{or} \\quad x = \\frac{-40 + \\sqrt{1572}}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For a given point $P$ on the curve $x^2 - y - \\ln x = 0$, what is the minimum distance from point $P$ to the line $y = x - 2$?",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If ${e}^{x+1}-\\frac{lnx+2k}{x}-k≥0$ always holds for any $x \\gt 0$, then the range of real number $k$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, 1]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two wheels are spun and the numbers that come up are added. The first wheel has 5 sections, 3 of which are even; the second wheel has 4 sections, 2 of which are even. Determine t... | math | {
"ground_truth": "\\text{(C)}\\ \\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle, and let $P$ be a point on side $BC$ such that $\\frac{BP}{PC}=\\frac{1}{2}$ . If $\\measuredangle ABC$ $=$ $45^{\\circ}$ and $\\measuredang... | math | {
"ground_truth": "75^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If Sarah is leading a class of 35 students, and each time Sarah waves her hands a prime number of students sit down, determine the greatest possible number of students that could... | math | {
"ground_truth": "31",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine how many integer Fahrenheit temperatures between 50 and 2000 inclusive, when converted to Celsius (rounded to the nearest integer), converted back to Fahrenheit, and ro... | math | {
"ground_truth": "1091",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that \\( A = [-2, 4) \\) and \\( B = \\{ x \\mid x^2 - ax - 4 \\leq 0 \\} \\), if \\( B \\subseteq A \\), determine the range of values for the real number \\( a \\).",
... | math | {
"ground_truth": "[0, 3)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The \"World Population Prospects 2022\" report by the United Nations states that by the end of 2022, the global population will reach 8,000,000,000 people. Express the number 8,0... | math | {
"ground_truth": "8 \\times 10^{9}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the line \\( y = \\sqrt{3}x + b \\) intersect the parabola \\( y^2 = 2px \\) (where \\( p > 0 \\)) at points \\( A \\) and \\( B \\). The circle passing through \\( A \\) and... | math | {
"ground_truth": "60^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The graphs of $3y + 2x - 6 = 0$ and $4y + bx + 8 = 0$ are perpendicular. Solve for $b.$",
"role": "user"
}
] | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an alley of width $w$, a ladder of length $l = 10 \\text{ meters}$ leans against two opposite walls. At one wall the top part of the ladder reaches a height of $4 \\text{ mete... | math | {
"ground_truth": "\\text{D) }5(\\sqrt{3} + 1) \\text{ meters}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Cyclic pentagon $ ABCDE$ has a right angle $ \\angle{ABC} \\equal{} 90^{\\circ}$ and side lengths $ AB \\equal{} 15$ and $ BC \\equal{} 20$ . Supposing that $ AB \\equal{... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many pairs of positive integers \\((a, b)\\) with \\(ab \\leq 100\\) satisfy the equation\n\\[\n\\frac{a+b^{-1}}{a^{-1}+b} = 9?\n\\]\nA) 1\nB) 2\nC) 3\nD) 4\nE) 5",
"role... | math | {
"ground_truth": "\\text{(C) } 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A capacitor with capacitance \\( C \\) charged to a voltage \\( U_0 \\) is connected through a resistor with resistance \\( R \\) to an uncharged capacitor with capacitance \\( 4... | math | {
"ground_truth": "Q = \\frac{2}{5} C U_0^2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For $n$ measured in degrees, let $T(n) = \\cos^2(30^\\circ -n) - \\cos(30^\\circ -n)\\cos(30^\\circ +n) +\\cos^2(30^\\circ +n)$ . Evaluate $$ 4\\sum^{30}_{n=1} n \\cdot T(... | math | {
"ground_truth": "1395",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the digits in the set $\\{1, 3, 4, 5, 6, 9\\}$, count the number of even integers between 300 and 800 whose digits are all different.",
"role": "user"
}
] | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The value range of the function $y=\\sin^2x+\\sin x-1$ is what value range?",
"role": "user"
}
] | math | {
"ground_truth": "\\left[- \\dfrac{5}{4},1\\right]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ be a natural number. The finite sequence $\\alpha$ of positive integer terms, there are $n$ different numbers ( $\\alpha$ can have repeated terms). Moreover, if fr... | math | {
"ground_truth": "3k^2 + 5k + 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When \\( x = -2 \\), evaluate the value of \\( (x + 1)^{3} \\).",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Choose one of the three conditions: ①$ac=\\sqrt{3}$, ②$c\\sin A=3$, ③$c=\\sqrt{3}b$, and supplement it in the following question. If the triangle in the question exists, find the... | math | {
"ground_truth": "2\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Positive integers $a$, $b$, $c$, and $d$ are randomly and independently selected with replacement from the set $\\{1, 2, 3,\\dots, 100\\}$. What is the probability that $abcd + a... | math | {
"ground_truth": "\\text{E) }\\frac{43}{100}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "From among $4^{1/4}, 5^{1/5}, 16^{1/16}, 25^{1/25}$, determine the greatest and the next to the greatest values.\nA) $4^{1/4}, 5^{1/5}$\nB) $5^{1/5}, 16^{1/16}$\nC) $16^{1/16}, 2... | math | {
"ground_truth": "\\textbf{A) } 4^{1/4}, 5^{1/5}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\cos \\left( \\frac{5\\pi}{12}-\\theta \\right)= \\frac{1}{3}$, find the value of $\\sin \\left( \\frac{\\pi}{12}+\\theta \\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In coordinate space, a particle starts at the point $(1,2,2)$ and ends at the point $(-2,-2,-1),$ moving along the line connecting these two points. During its journey, the parti... | math | {
"ground_truth": "143",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For any real numbers \\(a_{1}, a_{2}, \\cdots, a_{2016}\\), find the range of values of\n$$\n\\frac{7+23 \\sum_{1 \\leqslant i<j \\leqslant 2} \\sin ^{2}\\left(a_{i}-a_{j}\\right... | math | {
"ground_truth": "\\left[ \\frac{1}{6963841}, \\frac{3338497}{3480193} \\right]",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the numbers 7 and 9, find the smallest prime number dividing the sum $7^{15} + 9^{17}$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$S$ is natural, and $S=d_{1}>d_2>...>d_{1000000}=1$ are all divisors of $S$ . What minimal number of divisors can have $d_{250}$ ?",
"role": "user"
}
] | math | {
"ground_truth": "4000",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the ratio of the legs of a right triangle is 1:2, determine the ratio of the corresponding segments of the hypotenuse made by a perpendicular upon it from the vertex.",
"r... | math | {
"ground_truth": "1:4",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the parabola $C: y^2 = 2px (p > 0)$ with a focus point $F$, let $M(x_0, 2\\sqrt{2})$ be a point on parabola $C$. A circle centered at $M$ with a radius $|MF|$ intersects th... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "At Pine Grove Middle School, there are 300 students where the ratio of boys to girls is 3:2. Meanwhile, Maple Town Middle School has 240 students with a ratio of boys to girls of... | math | {
"ground_truth": "\\dfrac{7}{18}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A magician has $300$ cards with numbers from $1$ to $300$ written on them, each number on exactly one card. The magician then lays these cards on a $3 \\times 100$ rectan... | math | {
"ground_truth": "k = 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "To guard an oil platform located at sea, it is necessary to distribute around it 5 radars, each covering a circular area with a radius of $r=13$ km. Determine the maximum distanc... | math | {
"ground_truth": "\\frac{12}{\\sin 36^\\circ} ; \\frac{240 \\pi}{\\tan 36^\\circ}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the polynomial $C_{10}^{1}(x-1) + C_{10}^{2}(x-1)^2 + C_{10}^{3}(x-1)^3 + \\ldots + C_{10}^{10}(x-1)^{10}$, find the coefficient of the $x^3$ term.",
"role": "user"
}
] | math | {
"ground_truth": "C_{10}^{3} + C_{10}^{4}C_{4}^{1} + C_{10}^{5}C_{5}^{2} + \\ldots + C_{10}^{10}C_{10}^{7}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Denote $\\mathbb{Z}_{>0}=\\{1,2,3,...\\}$ the set of all positive integers. Determine all functions $f:\\mathbb{Z}_{>0}\\rightarrow \\mathbb{Z}_{>0}$ such that, for each posi... | math | {
"ground_truth": "f(n) = n^3",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the graph showing the price of five gallons of gasoline during the first ten months of the year, calculate the percent by which the highest price is more than the lowest pr... | math | {
"ground_truth": "70\\%",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given any point $P$ on the curve $y={x}^{3}- \\sqrt{3}x+ \\frac{3}{5}$, let $\\alpha$ be the angle of inclination of the tangent line at point $P$. Determine the range of values ... | math | {
"ground_truth": "[0^{\\circ}, 90^{\\circ}] \\cup [120^{\\circ}, 180^{\\circ})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the 13th of any particular month falls on a Friday, we call it Friday the 13th. It is known that Friday the 13th occurs at least once every calendar year. If the longest inter... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a,$ $b,$ and $t$ be real numbers such that $a + b = t$ and $a - b = s.$ Find, in terms of $t$ and $s,$ the minimum value of $a^2 + b^2$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{t^2 + s^2}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The pairs of values of $x$ and $y$ that are the common solutions of the equations $y=(x+1)^2$ and $xy+y=1$ are what?",
"role": "user"
}
] | math | {
"ground_truth": "1 \\text{ real and 2 imaginary pairs}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the sum of the six smallest distinct positive integer multiples of 12?",
"role": "user"
}
] | math | {
"ground_truth": "252",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A ballpoint pen costs 10 rubles, a gel pen costs 30 rubles, and a fountain pen costs 60 rubles. What is the maximum number of ballpoint pens that can be bought under the conditio... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence $\\{a_n\\}$ whose sum of the first $n$ terms is $S_n = 3^n - 1$, calculate the value of $a_1a_2 + a_2a_3 + \\cdots + a_na_{n+1}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{3}{2}\\left(9^n - 1\\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Arrange five volunteers $A$, $B$, $C$, $D$, $E$ to serve in two welfare homes, $A$ and $B$ are arranged in different welfare homes, the probability is ______.",
"role": "user... | math | {
"ground_truth": "\\frac{8}{15}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of distinct points in the $xy$-plane where the graphs of $(x+2y-8)(3x-y+6)=0$ and $(2x-3y+2)(4x+y-16)=0$ intersect.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $(1+2i)=a+bi(a,b∈R,i)$ is the imaginary unit, find the value of $a+b$.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\operatorname{cif}(x)$ denote the sum of the digits of the number $x$ in the decimal system. Put $a_1=1997^{1996^{1997}}$ , and $a_{n+1}=\\operatorname{cif}(a_n)$ fo... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\triangle ABC$ with $AB=AC$ and $BC=14$ be inscribed in a circle $\\omega$ . Let $D$ be the point on ray $BC$ such that $CD=6$ . Let the intersection of $AD$ ... | math | {
"ground_truth": "105",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of three numbers is $120$. The ratio of the first to the second is $\\frac{3}{4}$, and the ratio of the second to the third is $\\frac{5}{8}$. Find the second number.\n**... | math | {
"ground_truth": "\\textbf{(B)}\\ \\frac{2400}{67}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $\\sqrt[3]{27} \\cdot \\sqrt[4]{81} \\cdot \\sqrt{9}$ and express it as a positive integer.",
"role": "user"
}
] | math | {
"ground_truth": "27",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the Cartesian coordinate system $xOy$, given circle $C_1: x^2+y^2-6x+4y+9=0$, and circle $C_2: (x+m)^2+(y+m+5)^2=2m^2+8m+10$ ($m \\in \\mathbb{R}$, and $m \\neq -3$).\n\n(I) I... | math | {
"ground_truth": "(-1, 0)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle of radius $r$ has chords $\\overline{AB}$ of length $12$ and $\\overline{CD}$ of length $9$. When $\\overline{AB}$ and $\\overline{CD}$ are extended through $B$ and $C$,... | math | {
"ground_truth": "200",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A $39$ -tuple of real numbers $(x_1,x_2,\\ldots x_{39})$ satisfies\n\\[2\\sum_{i=1}^{39} \\sin(x_i) = \\sum_{i=1}^{39} \\cos(x_i) = -34.\\] \nThe ratio between the maximum of ... | math | {
"ground_truth": "37",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We are given a triangle $ABC$ . Points $D$ and $E$ on the line $AB$ are such that $AD=AC$ and $BE=BC$ , with the arrangment of points $D - A - B - E$ . The circumscrib... | math | {
"ground_truth": "60^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Bob is making partitions of $10$ , but he hates even numbers, so he splits $10$ up in a special way. He starts with $10$ , and at each step he takes every even number in the ... | math | {
"ground_truth": "902",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that \\( 3 + \\triangle = 5 \\) and \\( \\triangle + \\square = 7 \\), calculate the value of \\( \\triangle + \\triangle + \\triangle + \\square + \\square \\).",
"rol... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $α$ and $β$ are in $(0, \\frac{π}{2})$, and $\\cos α= \\frac{5}{13}$, $\\sin (α-β)= \\frac{4}{5}$, then $\\sin β=$ \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{16}{65}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\mathcal{P}$ be a parabola defined by the equation $y = -x^2$. Let $V_1$ and $F_1$ be its vertex and focus, respectively. Let $A$ and $B$ be points on $\\mathcal{P}$ so tha... | math | {
"ground_truth": "\\frac{7}{8}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the number of complex numbers $z$ such that $|z| = 1$ and\n\\[\\left| \\frac{z^2}{\\overline{z}^2} + \\frac{\\overline{z}^2}{z^2} \\right| = 1.\\]",
"role": "user"
... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all real roots of the quartic \\( x^4 - (2N + 1)x^2 - x + N^2 + N - 1 = 0 \\) correct to 4 decimal places, where \\( N = 10^{10} \\).",
"role": "user"
}
] | math | {
"ground_truth": "99999.9984 \\text{ and } 100000.0016",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Olga Ivanovna, the homeroom teacher of class 5B, is organizing a \"Mathematical Ballet\". She wants to arrange the boys and girls so that exactly 2 boys are at a distance of 5 me... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle XYZ$, medians $\\overline{XM}$ and $\\overline{YN}$ intersect at right angles. If $XM = 15$ and $YN = 20$, calculate the length of side $YZ$.",
"role": "user"
... | math | {
"ground_truth": "\\frac{20\\sqrt{13}}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $A:B:C = 3:2:5$, what is the value of $(5A + 3B) \\div (3C - 2A)$? Express your answer as a common fraction.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{7}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let p and q be any two odd numbers, with q less than p. Determine the largest integer which divides all possible numbers of the form p^2 - 3q^2.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A polynomial $p(x)$ is called semi-balanced if it has integer coefficients and $p(50) = 50$. If $p(x)$ is a semi-balanced polynomial, what is the maximum number of integer soluti... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive integer $n$ for which one can select $n$ distinct real numbers such that each of them is equal to the sum of some two other selected numbers.\n\n*P... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jimmy finds that 7 oranges weigh the same as 5 apples, and that 10 pears weigh the same as 6 apples. If Jimmy has 49 oranges, how many apples and how many pears would equal the w... | math | {
"ground_truth": "58",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the sides of the rectangle if the perimeter $k$ is given, and the ratio of its area to the area of the square over its diagonal $(\\mu)$. For example, $k=8 \\mathrm{~cm... | math | {
"ground_truth": "a_1 = 3 \\ \\text{cm}, \\quad b_1 = 1 \\ \\text{cm}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A deck of $ 2n\\plus{}1$ cards consists of a joker and, for each number between 1 and $ n$ inclusive, two cards marked with that number. The $ 2n\\plus{}1$ cards are placed... | math | {
"ground_truth": "n = 3, 4, 7, 8",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice and Bob play a game with a basketball. On each turn, if Alice has the ball, there is a 2/3 chance that she will toss it to Bob and a 1/3 chance that she will keep the ball.... | math | {
"ground_truth": "\\frac{5}{9}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the equation of the line that passes through the vertex of the parabola $y = x^2 - 4x + 4$ and is perpendicular to the line represented by $\\frac{x}{4} + \\frac{y}{3} = 1$.... | math | {
"ground_truth": "y = \\frac{4}{3}x - \\frac{8}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many different prime numbers are factors of $M$ if\n\n$\\log_2 ( \\log_5 ( \\log_7 (\\log_ {11} M))) = 9?$\nA) 1 \nB) 2 \nC) 3 \nD) 4 \nE) 7",
"role": "user"
}
] | math | {
"ground_truth": "A) 1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the points (2, y1) and (-2, y2) lie on the graph of the quadratic equation y = 2x^2 + bx + c, and y1 - y2 = 12, determine the value of b.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a_{1}, a_{2}, a_{3}, \\cdots$ be an increasing sequence of nonnegative integers such that every nonnegative integer can be expressed uniquely in the form $a_{i}+2a_{j}+4a... | math | {
"ground_truth": "1227096648",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine how many perfect squares less than 20,000 can be expressed as the difference of squares of two consecutive even numbers.",
"role": "user"
}
] | math | {
"ground_truth": "35",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
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