data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "\nCalculate the definite integral:\n\n$$\n\\int_{0}^{4} e^{\\sqrt{(4-x) /(4+x)}} \\cdot \\frac{d x}{(4+x) \\sqrt{16-x^{2}}}\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}(e-1)"
} | {
"split": "train",
"index": 35649,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In this Number Wall, you add the numbers next to each other and write the sum in the block directly above the two numbers. Which number will be in the block labeled '$m$'? [asy]\ndraw((0,0)--(8,0)--(8,2)--(0,2)--cycle);\ndraw((2,0)--(2,2));\ndraw((4,0)--(4,2));\ndraw((6,0)--(6,... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 35650,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Semicircles $POQ$ and $ROS$ pass through the center $O$. What is the ratio of the combined areas of the two semicircles to the area of circle $O$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 35651,
"solution": "1. **Identify the radii of the semicircles and the circle**: \n - Assume the radius of each semicircle $POQ$ and $ROS$ is $r$. Since these semicircles pass through the center $O$ of the circle, and each semicircle's diameter is a chord of the circle that passes t... |
deepscaler | [
{
"role": "user",
"content": "What fraction of the area of an isosceles trapezoid $KLMN (KL \\parallel MN)$ is the area of triangle $ABC$, where $A$ is the midpoint of base $KL$, $B$ is the midpoint of base $MN$, and $C$ is the midpoint of leg $KN$? Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 35652,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "You want to paint some edges of a regular dodecahedron red so that each face has an even number of painted edges (which can be zero). Determine from How many ways this coloration can be done.\n\nNote: A regular dodecahedron has twelve pentagonal faces and in each vertex concur ... | math | {
"style": "rule",
"ground_truth": "2048"
} | {
"split": "train",
"index": 35653,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. Angles $A$, $B$, $C$ form an arithmetic sequence, $c - a = 1$, and $b = \\sqrt{7}$.\n\n(I) Find the area $S$ of $\\triangle ABC$.\n\n(II) Find the value of $\\sin\\left(2C + \\frac{\... | math | {
"style": "rule",
"ground_truth": "\\frac{3\\sqrt{6} - 13\\sqrt{2}}{28}"
} | {
"split": "train",
"index": 35654,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two circles with centers \\( M \\) and \\( N \\), lying on the side \\( AB \\) of triangle \\( ABC \\), are tangent to each other and intersect the sides \\( AC \\) and \\( BC \\) at points \\( A, P \\) and \\( B, Q \\) respectively. Additionally, \\( AM = PM = 2 \\) and \\( BN... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 35655,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Convert $110_{(5)}$ to binary. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11110_{(2)}"
} | {
"split": "train",
"index": 35656,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "King Qi and Tian Ji are competing in a horse race. Tian Ji's top horse is better than King Qi's middle horse, worse than King Qi's top horse; Tian Ji's middle horse is better than King Qi's bottom horse, worse than King Qi's middle horse; Tian Ji's bottom horse is worse than Ki... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 35657,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ has a right angle at $B$. Point $D$ is the foot of the altitude from $B$, $AD=3$, and $DC=4$. What is the area of $\\triangle ABC$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7\\sqrt{3}"
} | {
"split": "train",
"index": 35658,
"solution": "1. **Identify the relationship between segments in the triangle**: Given that $ABC$ is a right triangle with the right angle at $B$, and $D$ is the foot of the altitude from $B$ to $AC$, we know that $AD = 3$ and $DC = 4$. \n\n2. **Use the geometric property of rig... |
deepscaler | [
{
"role": "user",
"content": "6 books of different types are to be divided into 3 groups, one group containing 4 books and the other two groups containing 1 book each. Calculate the number of different ways this can be done. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 35659,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Chords $\\overline{A B}$ and $\\overline{C D}$ of circle $\\omega$ intersect at $E$ such that $A E=8, B E=2, C D=10$, and $\\angle A E C=90^{\\circ}$. Let $R$ be a rectangle inside $\\omega$ with sides parallel to $\\overline{A B}$ and $\\overline{C D}$, such that no point in t... | math | {
"style": "rule",
"ground_truth": "26+6 \\sqrt{17}"
} | {
"split": "train",
"index": 35660,
"solution": "By power of a point, $(C E)(E D)=(A E)(E B)=16$, and $C E+E D=C D=$ 10. Thus $C E, E D$ are 2, 8. Without loss of generality, assume $C E=8$ and $D E=2$. Assume our circle is centered at the origin, with points $A=(-3,5), B=(-3,-5), C=(5,-3)$, $D=(-5,-3)$, and the ... |
deepscaler | [
{
"role": "user",
"content": "If $\\sqrt[3]{0.3}\\approx 0.6694$ and $\\sqrt[3]{3}\\approx 1.442$, then $\\sqrt[3]{300}\\approx$____. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6.694"
} | {
"split": "train",
"index": 35661,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the expression $\\frac{\\sqrt{3}\\tan 12^\\circ - 3}{\\sin 12^\\circ (4\\cos^2 12^\\circ - 2)}=\\_\\_\\_\\_\\_\\_\\_\\_.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4\\sqrt{3}"
} | {
"split": "train",
"index": 35662,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Daniel worked for 50 hours per week for 10 weeks during the summer, earning \\$6000. If he wishes to earn an additional \\$8000 during the school year which lasts for 40 weeks, how many fewer hours per week must he work compared to the summer if he receives the same hourly wage... | math | {
"style": "rule",
"ground_truth": "33.33"
} | {
"split": "train",
"index": 35663,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $\\angle A$ is a right angle, and $\\sin B$ is given as $\\frac{3}{5}$. Calculate $\\cos C$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 35664,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "To calculate $31^2$, Emily mentally figures the value $30^2$ and adds 61. Emily subtracts a number from $30^2$ to calculate $29^2$. What number does she subtract? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "59"
} | {
"split": "train",
"index": 35665,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An eight-digit integer is formed by repeating a positive four-digit integer. For example, 25,632,563 or 60,786,078 are integers of this form. What is the greatest common divisor of all eight-digit integers of this form? Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "10001"
} | {
"split": "train",
"index": 35666,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At a university dinner, there are 2017 mathematicians who each order two distinct entrées, with no two mathematicians ordering the same pair of entrées. The cost of each entrée is equal to the number of mathematicians who ordered it, and the university pays for each mathematici... | math | {
"style": "rule",
"ground_truth": "127009"
} | {
"split": "train",
"index": 35667,
"solution": "\nTo determine the maximum total amount the university could have paid, we can model the problem using graph theory. Consider a graph \\( G \\) with 2017 edges, where each edge represents a pair of distinct entrées ordered by a mathematician. The cost of each entré... |
deepscaler | [
{
"role": "user",
"content": "To enhance students' physical fitness, our school has set up sports interest classes for seventh graders. Among them, the basketball interest class has $x$ students, the number of students in the soccer interest class is $2$ less than twice the number of students in the basketb... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 35668,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What time is it 2017 minutes after 20:17? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "05:54"
} | {
"split": "train",
"index": 35669,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Several oranges (not necessarily of equal mass) were picked from a tree. On weighing them, it turned out that the mass of any three oranges taken together is less than 5% of the total mass of the remaining oranges. What is the minimum number of oranges that could have been pick... | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 35670,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain interest group conducted a survey on the reading of classic literature by people of different age groups in a certain region. The relevant data is shown in the table below:\n\n| Age Interval | $[0,10)$ | $[10,15)$ | $[15,20)$ | $[20,25)$ | $[25,30)$ |\n|--------------... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 35671,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer $x$ that, when multiplied by $450$, results in a product that is a multiple of $800$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 35672,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Fred the Four-Dimensional Fluffy Sheep is walking in 4 -dimensional space. He starts at the origin. Each minute, he walks from his current position $\\left(a_{1}, a_{2}, a_{3}, a_{4}\\right)$ to some position $\\left(x_{1}, x_{2}, x_{3}, x_{4}\\right)$ with integer coordinates ... | math | {
"style": "rule",
"ground_truth": "\\binom{40}{10}\\binom{40}{20}^{3}"
} | {
"split": "train",
"index": 35673,
"solution": "The possible moves correspond to the vectors $\\pm\\langle 2,0,0,0\\rangle, \\pm\\langle 1,1,1,-1\\rangle$, and their permutations. It's not hard to see that these vectors form the vertices of a 4-dimensional hypercube, which motivates the change of coordinates $$\... |
deepscaler | [
{
"role": "user",
"content": "Find the integer $n$, $0 \\le n \\le 6$, such that \\[n \\equiv 100000 \\pmod{7}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 35674,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A merchant purchases a gadget for $30$ less $15\\%$. He aims to sell the gadget at a gain of $25\\%$ on his cost after allowing a $10\\%$ discount on his marked price. At what price, in dollars, should the gadget be marked? Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "35.42"
} | {
"split": "train",
"index": 35675,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that tetrahedron $ABCD$ is inscribed in sphere $O$, and $AD$ is the diameter of sphere $O$. If triangles $\\triangle ABC$ and $\\triangle BCD$ are equilateral triangles with side length 1, what is the volume of tetrahedron $ABCD$? Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{12}"
} | {
"split": "train",
"index": 35676,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\theta \\in \\left[\\dfrac{\\pi}{4}, \\dfrac{\\pi}{2}\\right]$ and $\\sin 2\\theta = \\dfrac{3\\sqrt{7}}{8}$, find the value of $\\sin \\theta$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{3}{4}"
} | {
"split": "train",
"index": 35677,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest integer $n$ such that $\\sqrt{n+99}-\\sqrt{n}<1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2402"
} | {
"split": "train",
"index": 35678,
"solution": "This is equivalent to $$\\begin{aligned} \\sqrt{n+99} & <\\sqrt{n}+1 \\\\ n+99 & <n+1+2 \\sqrt{n} \\\\ 49 & <\\sqrt{n} \\end{aligned}$$ So the smallest integer $n$ with this property is $49^{2}+1=2402$."
} |
deepscaler | [
{
"role": "user",
"content": "In \\\\(\\triangle ABC\\\\), let the sides opposite to angles \\\\(A\\\\), \\\\(B\\\\), and \\\\(C\\\\) be \\\\(a\\\\), \\\\(b\\\\), and \\\\(c\\\\) respectively. Let vector \\\\( \\overrightarrow{m}=(\\cos A+ \\sqrt {2},\\sin A)\\\\) and vector \\\\( \\overrightarrow{n}=(-\\si... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 35679,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a magic square, the numbers in each row, the numbers in each column, and the numbers on each diagonal have the same sum. In the magic square shown, what is the value of $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2.2"
} | {
"split": "train",
"index": 35680,
"solution": "Using the second row, we see that the sum of the numbers in each row, column and diagonal must be $3.6 + 3 + 2.4 = 9$. Since the sum of the numbers in the first column must be 9, then the bottom left number must be $9 - 2.3 - 3.6 = 9 - 5.9 = 3.1$. Since the sum of ... |
deepscaler | [
{
"role": "user",
"content": "Find all pairs $(x,y)$ of nonnegative integers that satisfy \\[x^3y+x+y=xy+2xy^2.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(0, 0), (1, 1), (2, 2)"
} | {
"split": "train",
"index": 35681,
"solution": "\nWe need to find all pairs \\((x, y)\\) of nonnegative integers that satisfy the equation:\n\n\\[\nx^3 y + x + y = xy + 2xy^2\n\\]\n\nLet's start by simplifying the given equation. We rewrite the equation as follows:\n\n\\[\nx^3 y + x + y = xy + 2xy^2\n\\]\n\nRear... |
deepscaler | [
{
"role": "user",
"content": "For every positive integer $k$ , let $\\mathbf{T}_k = (k(k+1), 0)$ , and define $\\mathcal{H}_k$ as the homothety centered at $\\mathbf{T}_k$ with ratio $\\tfrac{1}{2}$ if $k$ is odd and $\\tfrac{2}{3}$ is $k$ is even. Suppose $P = (x,y)$ is a point such that ... | math | {
"style": "rule",
"ground_truth": "256"
} | {
"split": "train",
"index": 35682,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $(2x-1)^{2015} = a_{0} + a_{1}x + a_{2}x^{2} + \\ldots + a_{2015}x^{2015}$ ($x \\in \\mathbb{R}$), evaluate the expression $\\frac {1}{2}+ \\frac {a_{2}}{2^{2}a_{1}}+ \\frac {a_{3}}{2^{3}a_{1}}+\\ldots+ \\frac {a_{2015}}{2^{2015}a_{1}}$. Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "\\frac {1}{4030}"
} | {
"split": "train",
"index": 35683,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Fix a sequence $ a_1,a_2,a_3,... $ of integers satisfying the following condition:for all prime numbers $ p $ and all positive integers $ k $ , we have $ a_{pk+1}=pa_k-3a_p+13 $ .Determine all possible values of $ a_{2013} $ . Let's think step by step and put only the fi... | math | {
"style": "rule",
"ground_truth": "2016"
} | {
"split": "train",
"index": 35684,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an extended game, each of 6 players, including Hugo, rolls a standard 8-sided die. The winner is the one who rolls the highest number. In the case of a tie for the highest roll, the tied players will re-roll until a single winner emerges. What is the probability that Hugo's ... | math | {
"style": "rule",
"ground_truth": "\\frac{8856}{32768}"
} | {
"split": "train",
"index": 35685,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sequence $\\{a_{n}\\}$ where ${a}_{1}=\\frac{1}{2}$, ${a}_{4}=\\frac{1}{8}$, and $a_{n+1}a_{n}+a_{n-1}a_{n}=2a_{n+1}a_{n-1}$ for $n\\geqslant 2$, find the value of $T_{2024}$, where $T_{n}$ is the sum of the first $n$ terms of the sequence $\\{b_{n}\\}$ and $b_{n}=a_{... | math | {
"style": "rule",
"ground_truth": "\\frac{506}{2025}"
} | {
"split": "train",
"index": 35686,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The numbers from 1 to 9 are divided into three groups of three numbers, and then the numbers in each group are multiplied. $A$ is the largest of the three products. What is the smallest possible value of $A$? Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 35687,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest prime factor of 99? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 35688,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $f(\\alpha)= \\frac {\\sin (\\pi-\\alpha)\\cos (2\\pi-\\alpha)\\tan (-\\alpha+ \\frac {3\\pi}{2})}{\\cot (-\\alpha-\\pi)\\sin (-\\pi-\\alpha)}$. \n$(1)$ Simplify $f(\\alpha)$; \n$(2)$ If $\\alpha$ is an angle in the third quadrant, and $\\cos (\\alpha- \\frac {3\\pi}{2}... | math | {
"style": "rule",
"ground_truth": "\\frac {2 \\sqrt {6}}{5}"
} | {
"split": "train",
"index": 35689,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The distance between two parallel lines $x-y=1$ and $2x-2y+3=0$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5\\sqrt{2}}{4}"
} | {
"split": "train",
"index": 35690,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given five letters a, b, c, d, and e arranged in a row, find the number of arrangements where both a and b are not adjacent to c. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 35691,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the area of a trapezoid, whose diagonals are 7 and 8, and whose bases are 3 and 6. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4 : 3"
} | {
"split": "train",
"index": 35692,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\sin\\theta + \\cos\\theta = \\frac{1}{5}$, with $\\theta \\in (0,\\pi)$,\n1. Find the value of $\\tan\\theta$;\n2. Find the value of $\\frac{1+\\sin 2\\theta + \\cos 2\\theta}{1+\\sin 2\\theta - \\cos 2\\theta}$. Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "-\\frac{3}{4}"
} | {
"split": "train",
"index": 35693,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a point $P = (a,a^2)$ in the coordinate plane, let $l(P)$ denote the line passing through $P$ with slope $2a$. Consider the set of triangles with vertices of the form $P_1 = (a_1, a_1^2), P_2 = (a_2, a_2^2), P_3 = (a_3, a_3^2)$, such that the intersection of the lines $l(P_... | math | {
"style": "rule",
"ground_truth": "y = -\\frac{1}{4}"
} | {
"split": "train",
"index": 35694,
"solution": "\nLet \\( P_1 = (a_1, a_1^2) \\), \\( P_2 = (a_2, a_2^2) \\), and \\( P_3 = (a_3, a_3^2) \\) be points in the coordinate plane. The lines \\( l(P_1) \\), \\( l(P_2) \\), and \\( l(P_3) \\) have equations with slopes equal to \\( 2a_1 \\), \\( 2a_2 \\), and \\( 2a_3... |
deepscaler | [
{
"role": "user",
"content": "Given $| \\mathbf{e} |=1$, and it satisfies $|\\mathbf{a} + \\mathbf{e}|=|\\mathbf{a} - 2\\mathbf{e}|$, then the projection of vector $\\mathbf{a}$ in the direction of $\\mathbf{e}$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 35695,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $AC = 13$, $BC = 14$, and $AB=15$. Points $M$ and $D$ lie on $AC$ with $AM=MC$ and $\\angle ABD = \\angle DBC$. Points $N$ and $E$ lie on $AB$ with $AN=NB$ and $\\angle ACE = \\angle ECB$. Let $P$ be the point, other than $A$, of intersection of the circumcir... | math | {
"style": "rule",
"ground_truth": "218"
} | {
"split": "train",
"index": 35696,
"solution": "This problem can be solved with barycentric coordinates. Let triangle $ABC$ be the reference triangle with $A=(1,0,0)$, $B=(0,1,0)$, and $C=(0,0,1)$. Thus, $N=(1:1:0)$ and $M=(1:0:1)$. Using the Angle Bisector Theorem, we can deduce that $D=(14:0:15)$ and $(14:13:0... |
deepscaler | [
{
"role": "user",
"content": "Given a $4 \\times 4$ square grid, where each unit square is painted white or black with equal probability and then rotated $180\\,^{\\circ}$ clockwise, calculate the probability that the grid becomes entirely black after this operation. Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{65536}"
} | {
"split": "train",
"index": 35697,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Sam drove $96$ miles in $90$ minutes. His average speed during the first $30$ minutes was $60$ mph (miles per hour), and his average speed during the second $30$ minutes was $65$ mph. What was his average speed, in mph, during the last $30$ minutes? Let's think step by step and... | math | {
"style": "rule",
"ground_truth": "67"
} | {
"split": "train",
"index": 35698,
"solution": "1. **Identify the total distance and total time**: Sam drove a total of $96$ miles in $90$ minutes. To convert minutes to hours, we divide by $60$: \n \\[\n 90 \\text{ minutes} = \\frac{90}{60} \\text{ hours} = 1.5 \\text{ hours}\n \\]\n\n2. **Calculate the o... |
deepscaler | [
{
"role": "user",
"content": "Find the sum of $432_7$, $54_7$, and $6_7$ in base $7$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "525_7"
} | {
"split": "train",
"index": 35699,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a triangle $\\triangle ABC$ with angles $A$, $B$, $C$ and their respective opposite sides $a$, $b$, $c$, and $\\frac{a}{b}=\\frac{1+\\cos A}{\\cos C}$.\n(1) Find angle $A$;\n(2) If $a=1$, find the maximum area $S$ of $\\triangle ABC$. Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 35700,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"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$ and $\\omega$ be $E$ . Given that $AE=7$ , find $AC^2$ .\n\n*Proposed by Ephram Chun and Euhan ... | math | {
"style": "rule",
"ground_truth": "105"
} | {
"split": "train",
"index": 35701,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A factory produces a certain product for the Brazilian Olympic Games with an annual fixed cost of 2.5 million yuan. For every $x$ thousand units produced, an additional cost of $C(x)$ (in ten thousand yuan) is incurred. When the annual production is less than 80 thousand units,... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 35702,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The base radius of a circular television tower is 15 meters. Now, it is planned to plant a 5-meter-wide ring-shaped lawn around it. \n(1) How many square meters of lawn are needed? \n(2) If each square meter of lawn costs 500 yuan, how much money is needed to plant this lawn ... | math | {
"style": "rule",
"ground_truth": "274750"
} | {
"split": "train",
"index": 35703,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest integer $n$ satisfying the following conditions:\n(i) $n^2$ can be expressed as the difference of two consecutive cubes;\n(ii) $2n + 79$ is a perfect square.\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "181"
} | {
"split": "train",
"index": 35704,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 15 girls in a class of 27 students. The ratio of boys to girls in this class is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4:5"
} | {
"split": "train",
"index": 35705,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Any six points are taken inside or on a rectangle with dimensions $2 \\times 1$. Let $b$ be the smallest possible number with the property that it is always possible to select one pair of points from these six such that the distance between them is equal to or less than $b$. De... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{5}}{2}"
} | {
"split": "train",
"index": 35706,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The ratio $\\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}$ is closest to which whole number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 35707,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three male students and two female students stand in a row. The total number of arrangements where the female students do not stand at the ends is given by what total count. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 35708,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of all numbers in the following square matrix?\n$$\n\\begin{array}{l}\n1, 2, 3, \\ldots, 98, 99, 100 \\\\\n2, 3, 4, \\ldots, 99, 100, 101 \\\\\n3, 4, 5, \\ldots, 100, 101, 102 \\\\\n\\ldots \\\\\n100, 101, 102, \\ldots, 197, 198, 199\n\\end{array}\n$$ Let's thin... | math | {
"style": "rule",
"ground_truth": "1000000"
} | {
"split": "train",
"index": 35709,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Arrange 7 staff members to be on duty from May 1st to May 7th. Each person works for one day, among them, person A and person B are not scheduled on May 1st and 2nd. The total number of different arrangements is $\\boxed{\\text{\\_\\_\\_\\_\\_\\_\\_\\_}}$. Let's think step by s... | math | {
"style": "rule",
"ground_truth": "2400"
} | {
"split": "train",
"index": 35710,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For the infinite series $1-\\frac12-\\frac14+\\frac18-\\frac{1}{16}-\\frac{1}{32}+\\frac{1}{64}-\\frac{1}{128}-\\cdots$ let $S$ be the (limiting) sum. Then $S$ equals: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{7}"
} | {
"split": "train",
"index": 35711,
"solution": "To solve for the sum $S$ of the series $1-\\frac12-\\frac14+\\frac18-\\frac{1}{16}-\\frac{1}{32}+\\frac{1}{64}-\\frac{1}{128}-\\cdots$, we first observe the pattern in the series. The series can be grouped into terms of three as follows:\n\\[\nS = \\left(1 - \\frac... |
deepscaler | [
{
"role": "user",
"content": "A line through the points $(2, -9)$ and $(j, 17)$ is parallel to the line $2x + 3y = 21$. What is the value of $j$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-37"
} | {
"split": "train",
"index": 35712,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points $A$, $B$, and $C$ lie in that order along a straight path where the distance from $A$ to $C$ is $1800$ meters. Ina runs twice as fast as Eve, and Paul runs twice as fast as Ina. The three runners start running at the same time with Ina starting at $A$ and running toward ... | math | {
"style": "rule",
"ground_truth": "800"
} | {
"split": "train",
"index": 35713,
"solution": "Let $x$ be the distance from $A$ to $B$. Then the distance from $B$ to $C$ is $1800-x$. Since Eve is the slowest, we can call her speed $v$, so that Ina's speed is $2v$ and Paul's speed is $4v$.\n For Paul and Eve to meet, they must cover a total distance of $1800-... |
deepscaler | [
{
"role": "user",
"content": "Calculate the area of an isosceles triangle if the length of its altitude, drawn to one of the equal sides, is $12 \\mathrm{~cm}$, and the length of the base is $15 \\mathrm{~cm}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 35714,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\sqrt{2 + \\frac{2}{3}} = 2\\sqrt{\\frac{2}{3}}, \\sqrt{3 + \\frac{3}{8}} = 3\\sqrt{\\frac{3}{8}}, \\sqrt{4 + \\frac{4}{15}} = 4\\sqrt{\\frac{4}{15}}\\ldots$, if $\\sqrt{6 + \\frac{a}{b}} = 6\\sqrt{\\frac{a}{b}}$ (where $a,b$ are real numbers), please deduce $a = \\_\\_... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 35715,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Francesca uses 100 grams of lemon juice, 100 grams of sugar, and 400 grams of water to make lemonade. There are 25 calories in 100 grams of lemon juice and 386 calories in 100 grams of sugar. Water contains no calories. How many calories are in 200 grams of her lemonade? Let... | math | {
"style": "rule",
"ground_truth": "137"
} | {
"split": "train",
"index": 35716,
"solution": "1. **Calculate the total weight of the lemonade**: \n Francesca uses 100 grams of lemon juice, 100 grams of sugar, and 400 grams of water. The total weight of the lemonade is:\n \\[\n 100 \\text{ grams (lemon juice)} + 100 \\text{ grams (sugar)} + 400 \\text{... |
deepscaler | [
{
"role": "user",
"content": "In an arcade game, the \"monster\" is the shaded sector of a circle of radius $1$ cm, as shown in the figure. The missing piece (the mouth) has central angle $60^\\circ$. What is the perimeter of the monster in cm? Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{3}\\pi + 2"
} | {
"split": "train",
"index": 35717,
"solution": "1. **Identify the components of the perimeter**: The perimeter of the monster consists of two parts:\n - The arc of the circle that is not part of the mouth.\n - The two radii that form the mouth of the monster.\n\n2. **Calculate the length of the radii**: Each... |
deepscaler | [
{
"role": "user",
"content": "Liliane has $50\\%$ more soda than Jacqueline, and Alice has $25\\%$ more soda than Jacqueline. What is the relationship between the amounts of soda that Liliane and Alice have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20\\%"
} | {
"split": "train",
"index": 35718,
"solution": "Let's denote the amount of soda Jacqueline has as $J$. According to the problem, Liliane has $50\\%$ more soda than Jacqueline, and Alice has $25\\%$ more soda than Jacqueline. We can express the amounts of soda Liliane and Alice have in terms of $J$.\n\n1. **Calcu... |
deepscaler | [
{
"role": "user",
"content": "Color the vertices of a quadrilateral pyramid so that the endpoints of each edge are different colors. If there are only 5 colors available, what is the total number of distinct coloring methods? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "420"
} | {
"split": "train",
"index": 35719,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many even numbers are greater than 202 and less than 405? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "101"
} | {
"split": "train",
"index": 35720,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a trapezoid \\(ABCD\\) with bases \\(AB\\) and \\(CD\\), and angles \\(\\angle C = 30^\\circ\\) and \\(\\angle D = 80^\\circ\\). Find \\(\\angle ACB\\), given that \\(DB\\) is the bisector of \\(\\angle D\\). Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 35721,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(x)=(x^2+3x+2)^{\\cos(\\pi x)}$. Find the sum of all positive integers $n$ for which \\[\\left |\\sum_{k=1}^n\\log_{10}f(k)\\right|=1.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 35722,
"solution": "Note that $\\cos(\\pi x)$ is $-1$ when $x$ is odd and $1$ when $x$ is even. Also note that $x^2+3x+2=(x+1)(x+2)$ for all $x$. Therefore \\[\\log_{10}f(x)=\\log_{10}(x+1)+\\log_{10}(x+2)\\ \\ \\ \\text{if }x \\text{ is even}\\] \\[\\log_{10}f(x)=-\\log_{10}(x+1)-\\l... |
deepscaler | [
{
"role": "user",
"content": "Points $A = (3,9)$, $B = (1,1)$, $C = (5,3)$, and $D=(a,b)$ lie in the first quadrant and are the vertices of quadrilateral $ABCD$. The quadrilateral formed by joining the midpoints of $\\overline{AB}$, $\\overline{BC}$, $\\overline{CD}$, and $\\overline{DA}$ is a square. What ... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 35723,
"solution": "1. **Identify the midpoints of sides of the quadrilateral**: \n - The midpoint of $\\overline{AB}$ is calculated as:\n \\[\n \\left(\\frac{3+1}{2}, \\frac{9+1}{2}\\right) = (2, 5)\n \\]\n - The midpoint of $\\overline{BC}$ is calculated as:\n \\... |
deepscaler | [
{
"role": "user",
"content": "Calculate $101 \\times 102^{2} - 101 \\times 98^{2}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "80800"
} | {
"split": "train",
"index": 35724,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A regular octagon is inscribed in a circle and another regular octagon is circumscribed about the same circle. What is the ratio of the area of the larger octagon to the area of the smaller octagon? Express your answer as a common fraction. Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "4 - 2\\sqrt{2}"
} | {
"split": "train",
"index": 35725,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A group of 101 Dalmathians participate in an election, where they each vote independently on either candidate \\(A\\) or \\(B\\) with equal probability. If \\(X\\) Dalmathians voted for the winning candidate, the expected value of \\(X^{2}\\) can be expressed as \\(\\frac{a}{b}... | math | {
"style": "rule",
"ground_truth": "51"
} | {
"split": "train",
"index": 35726,
"solution": "Claim: with 101 replaced with \\(2k+1\\), the expectation of \\(X^{2}\\) is \\(\\frac{\\binom{2k}{k}}{2^{2k+1}}(2k+1)^{2}+\\frac{(2k+1)(2k+2)}{4}\\). The answer is this value taken modulo 103, which can be calculated by noting that the integers modulo 103 form a fi... |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1(a>b>0)$ with left and right foci $F_{1}(-c,0)$ and $F_{2}(c,0)$ respectively, and a point $P$ on the ellipse (different from the left and right vertices), the radius of the inscribed circle of $\\triangle PF_{1}F_{2}... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{5}"
} | {
"split": "train",
"index": 35727,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $f(x)=x^{3}+3ax^{2}+bx+a^{2}$ has an extremum of $0$ at $x=-1$, find $a-b=\\_\\_\\_\\_\\_\\_\\_\\_$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-7"
} | {
"split": "train",
"index": 35728,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve the inequality\n\\[|x - 1| + |x + 2| < 5.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(-3,2)"
} | {
"split": "train",
"index": 35729,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three distinct numbers are selected simultaneously and at random from the set $\\{1, 2, 3, 4, 5, 6, 7, 8, 9\\}$. What is the probability that the smallest positive difference between any two of those numbers is $3$ or greater? Express your answer as a common fraction. Let's thi... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{14}"
} | {
"split": "train",
"index": 35730,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We have an equilateral triangle with circumradius $1$ . We extend its sides. Determine the point $P$ inside the triangle such that the total lengths of the sides (extended), which lies inside the circle with center $P$ and radius $1$ , is maximum.\n(The total distance of ... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{3}"
} | {
"split": "train",
"index": 35731,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The graph of \\[y^4 - 4x^4 = 2y^2 - 1\\]is the union of the graphs of two different conic sections. Which two types of conic sections are they?\n\n(Write your answer as a list, with \"C\" for circle, \"E\" for ellipse, \"H\" for hyperbola, and \"P\" for parabola. For example, \... | math | {
"style": "rule",
"ground_truth": "\\text{H, E}"
} | {
"split": "train",
"index": 35732,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the sum of the solutions of the equation $-32x^2 + 84x + 135=0$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{21}{8}"
} | {
"split": "train",
"index": 35733,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Using the Horner's method (also known as Qin Jiushao's algorithm), calculate the value of the polynomial \\\\(f(x)=12+35x-8x^{2}+79x^{3}+6x^{4}+5x^{5}+3x^{6}\\\\) when \\\\(x=-4\\\\), and determine the value of \\\\(V_{3}\\\\). Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "-57"
} | {
"split": "train",
"index": 35734,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The even throws belong to B. Bons. Therefore, Bons wins only when the total number of throws, including the last successful one, is even. The probability of rolling a six is $\\frac{1}{6}$. The probability of the opposite event is $\\frac{5}{6}$. Hence, the probability that the... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{11}"
} | {
"split": "train",
"index": 35735,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Randomly select a number $x$ in the interval $[-1, 1]$. The probability that the value of $\\cos \\frac{\\pi x}{2}$ falls between 0 and $\\frac{1}{2}$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 35736,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\frac{\\cos 2\\alpha}{\\sqrt{2}\\sin\\left(\\alpha+\\frac{\\pi}{4}\\right)}=\\frac{\\sqrt{5}}{2}$, find the value of $\\tan\\alpha+\\frac{1}{\\tan\\alpha}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-8"
} | {
"split": "train",
"index": 35737,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the set $\\{1, a, \\frac{b}{a}\\} = \\{0, a^2, a+b\\}$, find the value of $a^{2015} + b^{2016}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 35738,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An equilateral pentagon $AMNPQ$ is inscribed in triangle $ABC$ such that $M\\in\\overline{AB}$ , $Q\\in\\overline{AC}$ , and $N,P\\in\\overline{BC}$ .\n \nSuppose that $ABC$ is an equilateral triangle of side length $2$ , and that $AMNPQ$ has a line of symmetry per... | math | {
"style": "rule",
"ground_truth": "5073"
} | {
"split": "train",
"index": 35739,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the length of the segment tangent from the point $(1,1)$ to the circle that passes through the points $(4,5),$ $(7,9),$ and $(6,14).$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5\\sqrt{2}"
} | {
"split": "train",
"index": 35740,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the sum of the sequence $2 - 6 + 10 - 14 + 18 - \\cdots - 98 + 102$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-52"
} | {
"split": "train",
"index": 35741,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest real constant $\\alpha$ such that for all positive integers $n$ and real numbers $0=y_{0}<$ $y_{1}<\\cdots<y_{n}$, the following inequality holds: $\\alpha \\sum_{k=1}^{n} \\frac{(k+1)^{3 / 2}}{\\sqrt{y_{k}^{2}-y_{k-1}^{2}}} \\geq \\sum_{k=1}^{n} \\frac{k^{2}+... | math | {
"style": "rule",
"ground_truth": "\\frac{16 \\sqrt{2}}{9}"
} | {
"split": "train",
"index": 35742,
"solution": "We first prove the following lemma: Lemma. For positive reals $a, b, c, d$, the inequality $\\frac{a^{3 / 2}}{c^{1 / 2}}+\\frac{b^{3 / 2}}{d^{1 / 2}} \\geq \\frac{(a+b)^{3 / 2}}{(c+d)^{1 / 2}}$ holds. Proof. Apply Hölder's inequality in the form $\\left(\\frac{a^{3... |
deepscaler | [
{
"role": "user",
"content": "A box of 25 chocolate candies costs $\\$6$. How many dollars does it cost to buy 600 chocolate candies? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 35743,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given circle $M$: $(x+1)^{2}+y^{2}=1$, and circle $N$: $(x-1)^{2}+y^{2}=9$, a moving circle $P$ is externally tangent to circle $M$ and internally tangent to circle $N$. The trajectory of the center of circle $P$ is curve $C$.\n$(1)$ Find the equation of $C$.\n$(2)$ Let $l$ be ... | math | {
"style": "rule",
"ground_truth": "\\dfrac {18}{7}"
} | {
"split": "train",
"index": 35744,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the distance between the foci of the hyperbola $x^2 - 6x - 4y^2 - 8y = 27.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4 \\sqrt{10}"
} | {
"split": "train",
"index": 35745,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rare genetic disorder is present in one out of every 1000 people in a certain community, and it typically shows no outward symptoms. There is a specialized blood test to detect this disorder. For individuals who have this disorder, the test consistently yields a positive resu... | math | {
"style": "rule",
"ground_truth": "0.019"
} | {
"split": "train",
"index": 35746,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jennifer wants to enclose her rectangular vegetable garden using 160 feet of fencing. She has decided that one side of the garden should be exactly 30 feet long. What is the maximum area that she can enclose, assuming the sides of the rectangle are natural numbers? Let's think ... | math | {
"style": "rule",
"ground_truth": "1500"
} | {
"split": "train",
"index": 35747,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the largest integer $x$ for which $4^{27} + 4^{1010} + 4^{x}$ is a perfect square. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1992"
} | {
"split": "train",
"index": 35748,
"solution": ""
} |
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