data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Adva is a regular tetrahedron with side length \\( s \\), and there are three spheres associated with it. The first sphere passes through the vertices of the tetrahedron, the second intersects the midpoints of the edges, and the third is inscribed such that it touches the faces... | math | {
"style": "rule",
"ground_truth": "9:3:1"
} | {
"split": "train",
"index": 37249,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A right triangle \\(ABC\\) is inscribed in a circle. A chord \\(CM\\) is drawn from the vertex \\(C\\) of the right angle, intersecting the hypotenuse at point \\(K\\). Find the area of triangle \\(ABM\\) if \\(AK : AB = 1 : 4\\), \\(BC = \\sqrt{2}\\), and \\(AC = 2\\). Let's t... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{19} \\sqrt{2}"
} | {
"split": "train",
"index": 37250,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In trapezoid \\(ABCD\\), the angles \\(A\\) and \\(D\\) at the base \\(AD\\) are \\(60^{\\circ}\\) and \\(30^{\\circ}\\) respectively. Point \\(N\\) lies on the base \\(BC\\) such that \\(BN : NC = 2\\). Point \\(M\\) lies on the base \\(AD\\), the line \\(MN\\) is perpendicula... | math | {
"style": "rule",
"ground_truth": "3:4"
} | {
"split": "train",
"index": 37251,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ted's grandfather used his treadmill on 3 days this week. He went 2 miles each day. On Monday he jogged at a speed of 5 miles per hour. He walked at the rate of 3 miles per hour on Wednesday and at 4 miles per hour on Friday. If Grandfather had always walked at 4 miles per hour... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 37252,
"solution": "1. **Calculate the time spent on each day using the formula $d = rt$, where $d$ is distance, $r$ is rate, and $t$ is time.**\n - **Monday:** The rate is $5$ mph and the distance is $2$ miles. \n \\[\n t = \\frac{d}{r} = \\frac{2}{5} \\text{ hours}\n \... |
deepscaler | [
{
"role": "user",
"content": "In a race on the same distance, two cars and a motorcycle participated. The second car took 1 minute longer to cover the entire distance than the first car. The first car moved 4 times faster than the motorcycle. What portion of the distance per minute did the second car cover ... | math | {
"style": "rule",
"ground_truth": "2/3"
} | {
"split": "train",
"index": 37253,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the volume of the tetrahedron with vertices at points \\( A_{1}, A_{2}, A_{3}, A_{4} \\) and its height dropped from the vertex \\( A_{4} \\) to the face \\( A_{1} A_{2} A_{3} \\).\n\n\\( A_{1}(-2, -1, -1) \\)\n\n\\( A_{2}(0, 3, 2) \\)\n\n\\( A_{3}(3, 1, -4) \\)\n\n\\... | math | {
"style": "rule",
"ground_truth": "\\frac{140}{\\sqrt{1021}}"
} | {
"split": "train",
"index": 37254,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $h(x)$, with terms in order of decreasing degree, if \\[3x^4+2x-1+h(x)=5x^2-6x-1.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3x^4+5x^2-8x"
} | {
"split": "train",
"index": 37255,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that triangle \\( ABC \\) has all side lengths as positive integers, \\(\\angle A = 2 \\angle B\\), and \\(CA = 9\\), what is the minimum possible value of \\( BC \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 37256,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a blackboard, it's written the following expression $ 1-2-2^2-2^3-2^4-2^5-2^6-2^7-2^8-2^9-2^{10}$ We put parenthesis by different ways and then we calculate the result. For example: $ 1-2-\\left(2^2-2^3\\right)-2^4-\\left(2^5-2^6-2^7\\right)-2^8-\\left( 2^9-2^{10}\\right)= 4... | math | {
"style": "rule",
"ground_truth": "1024"
} | {
"split": "train",
"index": 37257,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A collection of 8 cubes consists of one cube with edge-length $k$ for each integer $k, 1 \\le k \\le 8.$ A tower is to be built using all 8 cubes according to the rules:\nAny cube may be the bottom cube in the tower.\nThe cube immediately on top of a cube with edge-length $k$ m... | math | {
"style": "rule",
"ground_truth": "458"
} | {
"split": "train",
"index": 37258,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve the following system of equations:\n$$x+\\frac{1}{x^3}=2y,\\quad y+\\frac{1}{y^3}=2z,\\quad z+\\frac{1}{z^3}=2w,\\quad w+\\frac{1}{w^3}=2x.$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(1, 1, 1, 1) \\text{ and } (-1, -1, -1, -1)"
} | {
"split": "train",
"index": 37259,
"solution": "\nTo solve the given system of equations:\n\n\\[\nx + \\frac{1}{x^3} = 2y, \\quad y + \\frac{1}{y^3} = 2z, \\quad z + \\frac{1}{z^3} = 2w, \\quad w + \\frac{1}{w^3} = 2x,\n\\]\n\nwe will analyze the conditions for possible solutions step-by-step. \n\n### Step 1: An... |
deepscaler | [
{
"role": "user",
"content": "In the subtraction shown, $K, L, M$, and $N$ are digits. What is the value of $K+L+M+N$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 37260,
"solution": "We work from right to left as we would if doing this calculation by hand. In the units column, we have $L-1$ giving 1. Thus, $L=2$. (There is no borrowing required.) In the tens column, we have $3-N$ giving 5. Since 5 is larger than 3, we must borrow from the hundr... |
deepscaler | [
{
"role": "user",
"content": "Twelve tiles numbered $1$ through $12$ are turned face down. One tile is turned up at random, and an eight-sided die (numbered 1 to 8) is rolled. What is the probability that the product of the numbers on the tile and the die will be a square?\nA) $\\frac{1}{12}$\nB) $\\frac{1}... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 37261,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 7 students participating in 5 sports events. Students A and B cannot participate in the same event. Each event must have participants, and each student can only participate in one event. How many different arrangements satisfy these conditions? (Answer in numbers) Let... | math | {
"style": "rule",
"ground_truth": "15000"
} | {
"split": "train",
"index": 37262,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( m \\) and \\( n \\) be positive integers such that \\( m > n \\). If the last three digits of \\( 2012^m \\) and \\( 2012^n \\) are identical, find the smallest possible value of \\( m+n \\). Let's think step by step and put only the final answer within \\boxed{}."
}
... | math | {
"style": "rule",
"ground_truth": "104"
} | {
"split": "train",
"index": 37263,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Majka examined multi-digit numbers in which odd and even digits alternate regularly. Those that start with an odd digit, she called \"funny,\" and those that start with an even digit, she called \"cheerful\" (for example, the number 32387 is funny, the number 4529 is cheerful).... | math | {
"style": "rule",
"ground_truth": "635040"
} | {
"split": "train",
"index": 37264,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate \\[\\left|\\left(2 + 2i\\right)^6 + 3\\right|\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "515"
} | {
"split": "train",
"index": 37265,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A line contains the points $(-1, 6)$, $(6, k)$ and $(20, 3)$. What is the value of $k$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 37266,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the product of $1101_2 \\cdot 111_2$. Express your answer in base 2. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1000111_2"
} | {
"split": "train",
"index": 37267,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A line $l$ is tangent to the circle $x^{2}+y^{2}=1$ and the sum of its intercepts on the two coordinate axes is equal to $\\sqrt{3}$. Find the area of the triangle formed by line $l$ and the two coordinate axes. Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"split": "train",
"index": 37268,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Vertex $E$ of equilateral $\\triangle ABE$ is in the interior of square $ABCD$, and $F$ is the point of intersection of diagonal $BD$ and line segment $AE$. If length $AB$ is $\\sqrt{1+\\sqrt{3}}$ then the area of $\\triangle ABF$ is Let's think step by step and put only the fi... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 37269,
"solution": "1. **Positioning the Square and Triangle on the Coordinate Plane**:\n Place square $ABCD$ on the coordinate plane with $A$ at the origin $(0,0)$, $B$ at $(\\sqrt{1+\\sqrt{3}}, 0)$, $C$ at $(\\sqrt{1+\\sqrt{3}}, \\sqrt{1+\\sqrt{3}})$, and $D$ at $(0, \\sqrt{1+\\sq... |
deepscaler | [
{
"role": "user",
"content": "Snow White entered a room where 30 chairs were arranged around a circular table. Some of the chairs were occupied by dwarfs. It turned out that Snow White could not sit in such a way that there was no one next to her. What is the minimum number of dwarfs that could have been at... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 37270,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find a monic polynomial of degree $4,$ in $x,$ with rational coefficients such that $\\sqrt{2} +\\sqrt{3}$ is a root of the polynomial. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x^4-10x^2+1"
} | {
"split": "train",
"index": 37271,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Badgers play the Cougars in a series of seven basketball games. Each team has an equal chance of winning each game. What is the probability that the Badgers will win at least four games? Express your answer as a common fraction. Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 37272,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jane starts to make a list, in increasing order, of the positive integers that have a first digit of 2. She writes $2, 20, 21, 22, \\ldots$ and wants to find the three-digit number formed by the 998th, 999th, and 1000th digits. Help her determine what those digits are. Let's th... | math | {
"style": "rule",
"ground_truth": "216"
} | {
"split": "train",
"index": 37273,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\triangle ABC$ be an acute scalene triangle with circumcircle $\\omega$. The tangents to $\\omega$ at $B$ and $C$ intersect at $T$. Let $X$ and $Y$ be the projections of $T$ onto lines $AB$ and $AC$, respectively. Suppose $BT = CT = 16$, $BC = 22$, and $TX^2 + TY^2 + XY^2... | math | {
"style": "rule",
"ground_truth": "717"
} | {
"split": "train",
"index": 37274,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $8^{-1} \\equiv 85 \\pmod{97}$, find $64^{-1} \\pmod{97}$, as a residue modulo 97. (Give an answer between 0 and 96, inclusive.) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "47"
} | {
"split": "train",
"index": 37275,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "During a year when Valentine's Day, February 14, falls on a Tuesday, what day of the week is Cinco de Mayo (May 5) and how many days are between February 14 and May 5 inclusively? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"split": "train",
"index": 37276,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A school wishes to understand the psychological state of learning among its senior students and adopts a systematic sampling method to select 40 students out of 800 for a test. The students are randomly assigned numbers from 1 to 800 and then grouped. In the first group, number... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 37277,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Convert the point $(6,2 \\sqrt{3})$ in rectangular coordinates to polar coordinates. Enter your answer in the form $(r,\\theta),$ where $r > 0$ and $0 \\le \\theta < 2 \\pi.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left( 4 \\sqrt{3}, \\frac{\\pi}{6} \\right)"
} | {
"split": "train",
"index": 37278,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest value of $x$ that satisfies the equation $|x-5|=12$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 37279,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x, y, z$ be positive real numbers such that $x + 2y + 3z = 1$. Find the maximum value of $x^2 y^2 z$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{16807}"
} | {
"split": "train",
"index": 37280,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate:<br/>$(1)-4\\times 9$;<br/>$(2)10-14-\\left(-5\\right)$;<br/>$(3)-3×(-\\frac{1}{3})^3$;<br/>$(4)-56+(-8)×(\\frac{1}{8})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-57"
} | {
"split": "train",
"index": 37281,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the value of $x$ such that $\\sqrt{x - 2} = 8$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "66"
} | {
"split": "train",
"index": 37282,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the odd function $f(x)$ and the even function $g(x)$ defined on $\\mathbb{R}$ satisfy $f(x) + g(x) = a^x - a^{-x} + 2$, and $g(2) = a$, find the value of $f(2)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{15}{4}"
} | {
"split": "train",
"index": 37283,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A B C D$ be a convex quadrilateral so that all of its sides and diagonals have integer lengths. Given that $\\angle A B C=\\angle A D C=90^{\\circ}, A B=B D$, and $C D=41$, find the length of $B C$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "580"
} | {
"split": "train",
"index": 37284,
"solution": "Let the midpoint of $A C$ be $O$ which is the center of the circumcircle of $A B C D . A D C$ is a right triangle with a leg of length 41 , and $41^{2}=A C^{2}-A D^{2}=(A C-A D)(A C+A D)$. As $A C, A D$ are integers and 41 is prime, we must have $A C=840, A D=841$.... |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)= \\sqrt {3}|\\cos \\frac {π}{2}x|(x≥0)$, the highest points of the graph from left to right are consecutively labeled as P₁, P₃, P₅, …, and the intersection points of the function y=f(x) with the x-axis from left to right are consecutively labeled as P₂... | math | {
"style": "rule",
"ground_truth": "\\frac {2}{3}"
} | {
"split": "train",
"index": 37285,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the square of 1023 without a calculator. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1046529"
} | {
"split": "train",
"index": 37286,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An oreo shop sells $5$ different flavors of oreos and $3$ different flavors of milk. Alpha and Beta decide to purhcase some oreos. Since Alpha is picky, he will not order more than 1 of the same flavor. To be just as weird, Beta will only order oreos, but she will be willing to... | math | {
"style": "rule",
"ground_truth": "351"
} | {
"split": "train",
"index": 37287,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $sin2θ=-\\frac{1}{3}$, if $\\frac{π}{4}＜θ＜\\frac{3π}{4}$, then $\\tan \\theta =$____. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3-2\\sqrt{2}"
} | {
"split": "train",
"index": 37288,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define the operation: \\(a \\quad b = \\frac{a \\times b}{a + b}\\). Calculate the result of the expression \\(\\frac{20102010 \\cdot 2010 \\cdots 2010 \\cdot 201 \\text{ C}}{\\text{ 9 \" \"}}\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "201"
} | {
"split": "train",
"index": 37289,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the sequence \\(\\left\\{a_{n}\\right\\}\\) defined by \\(a_{0}=\\frac{1}{2}\\) and \\(a_{n+1}=a_{n}+\\frac{a_{n}^{2}}{2023}\\) for \\(n = 0, 1, \\ldots\\). Find the integer \\(k\\) such that \\(a_{k} < 1 < a_{k+1}\\). Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "2023"
} | {
"split": "train",
"index": 37290,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The third quartile of the data $13$, $11$, $12$, $15$, $16$, $18$, $21$, $17$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17.5"
} | {
"split": "train",
"index": 37291,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": " $(HUN 6)$ Find the positions of three points $A,B,C$ on the boundary of a unit cube such that $min\\{AB,AC,BC\\}$ is the greatest possible. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 37292,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The second and fourth terms of a geometric sequence are 2 and 6. Which of the following is a possible first term? Type the letter of the correct option.\n\nA. $-\\sqrt{3}$\n\nB. $-\\frac{2\\sqrt{3}}{3}$\n\nC. $-\\frac{\\sqrt{3}}{3}$\n\nD. $\\sqrt{3}$\n\nE. $3$ Let's think step... | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 37293,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $R^+$ be the set of positive real numbers. Determine all functions $f:R^+$ $\\rightarrow$ $R^+$ such that for all positive real numbers $x$ and $y:$\n $$f(x+f(xy))+y=f(x)f(y)+1$$\n\n[i]Ukraine Let's think step by step and put only the final answer within \\boxed{}... | math | {
"style": "rule",
"ground_truth": "f(x) = x + 1"
} | {
"split": "train",
"index": 37294,
"solution": "\nLet \\( R^+ \\) be the set of positive real numbers. We need to determine all functions \\( f: R^+ \\rightarrow R^+ \\) such that for all positive real numbers \\( x \\) and \\( y \\), the following equation holds:\n\\[\nf(x + f(xy)) + y = f(x)f(y) + 1\n\\]\n\n##... |
deepscaler | [
{
"role": "user",
"content": "Find the smallest exact square with last digit not $0$ , such that after deleting its last two digits we shall obtain another exact square. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "121"
} | {
"split": "train",
"index": 37295,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathbf{a} = \\begin{pmatrix} 7 \\\\ -4 \\\\ -4 \\end{pmatrix}$ and $\\mathbf{c} = \\begin{pmatrix} -2 \\\\ -1 \\\\ 2 \\end{pmatrix}.$ Find the vector $\\mathbf{b}$ such that $\\mathbf{a},$ $\\mathbf{b},$ and $\\mathbf{c}$ are collinear, and $\\mathbf{b}$ bisects the ang... | math | {
"style": "rule",
"ground_truth": "\\begin{pmatrix} 1/4 \\\\ -7/4 \\\\ 1/2 \\end{pmatrix}"
} | {
"split": "train",
"index": 37296,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many unique five-digit numbers greater than 20000, using the digits 1, 2, 3, 4, and 5 without repetition, can be formed such that the hundreds place is not the digit 3? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "78"
} | {
"split": "train",
"index": 37297,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $x, y, z$ are real numbers such that $x=y+z+2$, $y=z+x+1$, and $z=x+y+4$. Compute $x+y+z$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-7"
} | {
"split": "train",
"index": 37298,
"solution": "Adding all three equations gives $$x+y+z=2(x+y+z)+7$$ from which we find that $x+y+z=-7$."
} |
deepscaler | [
{
"role": "user",
"content": "Given that $AC$ and $CE$ are two diagonals of a regular hexagon $ABCDEF$, and points $M$ and $N$ divide $AC$ and $CE$ internally such that $\\frac{AM}{AC}=\\frac{CN}{CE}=r$. If points $B$, $M$, and $N$ are collinear, find the value of $r$. Let's think step by step and put only ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{\\sqrt{3}}"
} | {
"split": "train",
"index": 37299,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest possible area, in square units, of a right triangle with two sides measuring $4$ units and $5$ units? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 37300,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Anh traveled 75 miles on the interstate and 15 miles on a mountain pass. The speed on the interstate was four times the speed on the mountain pass. If Anh spent 45 minutes driving on the mountain pass, determine the total time of his journey in minutes. Let's think step by step... | math | {
"style": "rule",
"ground_truth": "101.25"
} | {
"split": "train",
"index": 37301,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve for $X$ if $\\sqrt[4]{X^5} = 32\\sqrt[16]{32}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16\\sqrt[4]{2}"
} | {
"split": "train",
"index": 37302,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively, where $C$ is an obtuse angle. Given $\\cos(A + B - C) = \\frac{1}{4}$, $a = 2$, and $\\frac{\\sin(B + A)}{\\sin A} = 2$.\n\n(1) Find the value of $\\cos C$;\n\n(2) Find the ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{6}"
} | {
"split": "train",
"index": 37303,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain coin is weighted such that the chance of flipping heads is $\\frac{1}{3}$ and the chance of flipping tails is $\\frac{2}{3}$. Suppose that we win $\\$3$ if we flip a heads on a coin toss, but lose $\\$2$ if we flip tails. What is the expected value, in dollars, of o... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{3}"
} | {
"split": "train",
"index": 37304,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Select 5 people from 3 orthopedic doctors, 4 neurosurgeons, and 5 internists to form an earthquake relief medical team. The number of ways to select such that there is at least one doctor from each specialty is (answer in digits). Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "590"
} | {
"split": "train",
"index": 37305,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a math interest class, the teacher gave a problem for everyone to discuss: \"Given real numbers $a$, $b$, $c$ not all equal to zero satisfying $a+b+c=0$, find the maximum value of $\\frac{|a+2b+3c|}{\\sqrt{{a}^{2}+{b}^{2}+{c}^{2}}}.\"$ Jia quickly offered his opinion: Isn't ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 37306,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When \\(0 < x < \\frac{\\pi}{2}\\), the value of the function \\(y = \\tan 3x \\cdot \\cot^3 x\\) cannot take numbers within the open interval \\((a, b)\\). Find the value of \\(a + b\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "34"
} | {
"split": "train",
"index": 37307,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive integers less than 200 are divisible by 2, 3 and 5? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 37308,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the positive integer $n\\,$ for which \\[\\lfloor\\log_2{1}\\rfloor+\\lfloor\\log_2{2}\\rfloor+\\lfloor\\log_2{3}\\rfloor+\\cdots+\\lfloor\\log_2{n}\\rfloor=1994\\] (For real $x\\,$, $\\lfloor x\\rfloor\\,$ is the greatest integer $\\le x.\\,$) Let's think step by step and... | math | {
"style": "rule",
"ground_truth": "312"
} | {
"split": "train",
"index": 37309,
"solution": "Note that if $2^x \\le a<2^{x+1}$ for some $x\\in\\mathbb{Z}$, then $\\lfloor\\log_2{a}\\rfloor=\\log_2{2^{x}}=x$.\n Thus, there are $2^{x+1}-2^{x}=2^{x}$ integers $a$ such that $\\lfloor\\log_2{a}\\rfloor=x$. So the sum of $\\lfloor\\log_2{a}\\rfloor$ for all such... |
deepscaler | [
{
"role": "user",
"content": "An isosceles triangle has its vertex at $(0,5)$ and a base between points $(3,5)$ and $(13,5)$. The two equal sides are each 10 units long. If the third vertex (top vertex) is in the first quadrant, what is the y-coordinate? Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "5 + 5\\sqrt{3}"
} | {
"split": "train",
"index": 37310,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the wavelength of each light quantum is approximately $688$ nanometers and $1$ nanometer is equal to $0.000000001$ meters, express the wavelength of each light quantum in scientific notation. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "6.88\\times 10^{-7}"
} | {
"split": "train",
"index": 37311,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the natural numbers $1,2,3,\\ldots,10,11,12$, divide them into two groups such that the quotient of the product of all numbers in the first group by the product of all numbers in the second group is an integer and takes on the smallest possible value. What is this quotien... | math | {
"style": "rule",
"ground_truth": "231"
} | {
"split": "train",
"index": 37312,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$ ($a > 0$, $b > 0$) with its right focus at point $F$, and a point $P$ on the left branch of the hyperbola. Also given is that $PF$ is tangent to the circle $x^2 + y^2 = a^2$ at point $M$, where $M$ is precisely the m... | math | {
"style": "rule",
"ground_truth": "\\sqrt{5}"
} | {
"split": "train",
"index": 37313,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A seafood wholesaler purchased 1000 kg of crucian carp at a price of 10 yuan/kg and cultured them in a lake (assuming that the weight of each crucian carp remains unchanged during the culture period). According to market estimates, the market price of crucian carp after lake cu... | math | {
"style": "rule",
"ground_truth": "6000"
} | {
"split": "train",
"index": 37314,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the probability that four randomly chosen vertices of a cube form a tetrahedron (triangular pyramid). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{29}{35}"
} | {
"split": "train",
"index": 37315,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nGroup the set of positive odd numbers $\\{1, 3, 5, \\cdots\\}$ in increasing order such that the $n$-th group has $(2n-1)$ odd numbers:\n\\[\n\\{1\\}, \\quad \\{3, 5, 7\\}, \\quad \\{9, 11, 13, 15, 17\\}, \\cdots\n\\]\n(first group)(second group)(third group)\n\nDetermine whi... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 37316,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Attempt to obtain one billion (1,000,000,000) by multiplying two integers, each of which contains no zeros. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "512 * 1953125"
} | {
"split": "train",
"index": 37317,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve for $x$: $0.05x - 0.09(25 - x) = 5.4$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "54.6428571"
} | {
"split": "train",
"index": 37318,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sealed bottle, which contains water, has been constructed by attaching a cylinder of radius \\(1 \\mathrm{~cm}\\) to a cylinder of radius \\(3 \\mathrm{~cm}\\). When the bottle is right side up, the height of the water inside is \\(20 \\mathrm{~cm}\\). When the bottle is upsi... | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 37319,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The numerator of a fraction is $6x + 1$, then denominator is $7 - 4x$, and $x$ can have any value between $-2$ and $2$, both included. The values of $x$ for which the numerator is greater than the denominator are: Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5} < x \\le 2"
} | {
"split": "train",
"index": 37320,
"solution": "We are given a fraction with the numerator $6x + 1$ and the denominator $7 - 4x$. We need to find the values of $x$ for which the numerator is greater than the denominator. This can be set up as an inequality:\n\\[ 6x + 1 > 7 - 4x. \\]\n\n1. **Isolate $x$:**\n \\... |
deepscaler | [
{
"role": "user",
"content": "Thirty identical toothpicks were used to create the figure below. There are over 25 triangles in the figure. What is the fewest number of toothpicks that could be removed so that no triangles remain?\n\n[asy]\ndraw((0,0)--(8,0), linewidth(1));\ndraw(2dir(60)--(2dir(60)+(6,0)), ... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 37321,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the minimum possible value of the sum\n\\[\n\\frac{a}{3b} + \\frac{b}{6c} + \\frac{c}{9a},\n\\]\nwhere \\(a, b, c\\) are positive real numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3 \\cdot \\frac{1}{\\sqrt[3]{162}}"
} | {
"split": "train",
"index": 37322,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the length of the diagonal of a square with side length $50\\sqrt{2}$ cm? Express your answer in simplest form. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 37323,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( A B C D \\) be a quadrilateral and \\( P \\) the intersection of \\( (A C) \\) and \\( (B D) \\). Assume that \\( \\widehat{C A D} = 50^\\circ \\), \\( \\widehat{B A C} = 70^\\circ \\), \\( \\widehat{D C A} = 40^\\circ \\), and \\( \\widehat{A C B} = 20^\\circ \\). Calc... | math | {
"style": "rule",
"ground_truth": "70"
} | {
"split": "train",
"index": 37324,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Timur and Alexander are counting the trees growing around the house. Both move in the same direction, but they start counting from different trees. What is the number of trees growing around the house if the tree that Timur called the 12th, Alexander counted as $33-m$, and the ... | math | {
"style": "rule",
"ground_truth": "76"
} | {
"split": "train",
"index": 37325,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A straight line joins the points $(-1,1)$ and $(3,9)$. Its $x$-intercept is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{3}{2}"
} | {
"split": "train",
"index": 37326,
"solution": "1. **Identify the coordinates of the given points and calculate the slope ($m$) of the line.**\n The points given are $(-1,1)$ and $(3,9)$. The slope formula is:\n \\[\n m = \\frac{\\Delta y}{\\Delta x} = \\frac{y_2 - y_1}{x_2 - x_1} = \\frac{9 - 1}{3 - (-1)}... |
deepscaler | [
{
"role": "user",
"content": "Find the volume of a regular triangular pyramid where the planar angle at the apex is $90^{\\circ}$ and the side of the base is 3 cm. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9\\sqrt{2}}{8}"
} | {
"split": "train",
"index": 37327,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle \\(ABC\\), \\(AB = 13\\) and \\(BC = 15\\). On side \\(AC\\), point \\(D\\) is chosen such that \\(AD = 5\\) and \\(CD = 9\\). The angle bisector of the angle supplementary to \\(\\angle A\\) intersects line \\(BD\\) at point \\(E\\). Find \\(DE\\). Let's think step... | math | {
"style": "rule",
"ground_truth": "7.5"
} | {
"split": "train",
"index": 37328,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The real numbers $c, b, a$ form an arithmetic sequence with $a \\geq b \\geq c \\geq 0$. The quadratic $ax^2+bx+c$ has exactly one root. What is this root? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2-\\sqrt{3}"
} | {
"split": "train",
"index": 37329,
"solution": "\nGiven that $a, b, c$ form an arithmetic sequence and $a \\geq b \\geq c \\geq 0$, we can express $b$ and $c$ in terms of $a$ and a common difference $d$:\n\\[ b = a - d, \\quad c = a - 2d. \\]\n\nThe quadratic equation is $ax^2 + bx + c = 0$. Since it has exactly... |
deepscaler | [
{
"role": "user",
"content": "Let \\( a \\) and \\( b \\) be real numbers, and consider the function \\( f(x) = x^{3} + a x^{2} + b x \\). If there exist three real numbers \\( x_{1}, x_{2}, x_{3} \\) such that \\( x_{1} + 1 \\leqslant x_{2} \\leqslant x_{3} - 1 \\), and \\( f(x_{1}) = f(x_{2}) = f(x_{3}) \... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 37330,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that Luis wants to arrange his sticker collection in rows with exactly 4 stickers in each row, and he has 29 stickers initially, find the minimum number of additional stickers Luis must purchase so that the total number of stickers can be exactly split into 5 equal groups... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 37331,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a committee composed of eight women and two men. When they meet, they sit in a row---the women in indistinguishable rocking chairs and the men on indistinguishable stools. How many distinct ways are there for me to arrange the eight chairs and two stools for a meeting... | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 37332,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABCD$ be a square and $P$ be a point on the shorter arc $AB$ of the circumcircle of the square. Which values can the expression $\\frac{AP+BP}{CP+DP}$ take? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2} - 1"
} | {
"split": "train",
"index": 37333,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nWe want to set up an electric bell. The location of the bell is at a distance of $30 \\mathrm{~m}$ from the ringing spot. The internal resistance of the bell is 2 ohms. We plan to use 2 Leclanché cells connected in series, each with an electromotive force of 1.5 Volts and an ... | math | {
"style": "rule",
"ground_truth": "0.63"
} | {
"split": "train",
"index": 37334,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For rational numbers $x$, $y$, $a$, $t$, if $|x-a|+|y-a|=t$, then $x$ and $y$ are said to have a \"beautiful association number\" of $t$ with respect to $a$. For example, $|2-1|+|3-1|=3$, then the \"beautiful association number\" of $2$ and $3$ with respect to $1$ is $3$. <br/>... | math | {
"style": "rule",
"ground_truth": "2001000"
} | {
"split": "train",
"index": 37335,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On the game show $\\text{\\emph{Wheel of Fraction}}$, you see the following spinner. Given that each region is the same area, what is the probability that you will earn exactly $\\$1700$ in your first three spins? Express your answer as a common fraction. [asy]\nimport olympiad... | math | {
"style": "rule",
"ground_truth": "\\frac{6}{125}"
} | {
"split": "train",
"index": 37336,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Bulls are playing the Heat in the NBA finals. To win the championship, a team needs to secure 4 victories before the opponent does. If the Heat win each game with a probability of $\\frac{3}{4}$ and there are no ties, what is the probability that the Bulls will win the NBA ... | math | {
"style": "rule",
"ground_truth": "\\frac{540}{16384}"
} | {
"split": "train",
"index": 37337,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and all but 4 are blue. How many marbles are in the jar? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 37338,
"solution": "Let's denote the number of red marbles as $r$, green marbles as $g$, and blue marbles as $b$. According to the problem, we have the following equations based on the information given:\n\n1. All but 6 marbles are red, so the number of non-red marbles (green and blue... |
deepscaler | [
{
"role": "user",
"content": "The height of an isosceles trapezoid is \\( h \\). The upper base of the trapezoid is viewed from the midpoint of the lower base at an angle of \\( 2\\alpha \\), and the lower base is viewed from the midpoint of the upper base at an angle of \\( 2\\beta \\). Find the area of th... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 37339,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\Delta ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and it is given that $\\sqrt{3}a\\cos C=(2b-\\sqrt{3}c)\\cos A$\n\n(Ⅰ) Find the magnitude of angle $A$;\n\n(Ⅱ) If $a=2$, find the maximum area of $\\Delta ABC$. Let's think step... | math | {
"style": "rule",
"ground_truth": "2+ \\sqrt{3}"
} | {
"split": "train",
"index": 37340,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $C$: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 (a > b > 0)$, where the upper vertex of $C$ is $A$, and the two foci are $F_{1}$ and $F_{2}$, with an eccentricity of $\\frac{1}{2}$. A line passing through $F_{1}$ and perpendicular to $AF_{2}$ intersects $C$ at po... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 37341,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the inequality $x^{2}+ax+1 \\geqslant 0$ holds for all $x \\in (0, \\frac{1}{2}]$, find the minimum value of $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{5}{2}"
} | {
"split": "train",
"index": 37342,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many ordered pairs $(S, T)$ of subsets of $\\{1,2,3,4,5,6,7,8,9,10\\}$ are there whose union contains exactly three elements? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3240"
} | {
"split": "train",
"index": 37343,
"solution": "Let the three elements in the union be $a, b$, and $c$. We know that $a$ can be only in $S$, only in $T$, or both, so there are 3 possibilities for placing it. (Recall that $S=\\{a\\}, T=\\{b, c\\}$ is different from $S=\\{b, c\\}, T=\\{a\\}$ because $S$ and $T$ ar... |
deepscaler | [
{
"role": "user",
"content": "Divide the numbers 1 through 10 into three groups such that the difference between any two numbers within the same group does not appear in that group. If one of the groups is {2, 5, 9}, then the sum of all the numbers in the group that contains 10 is $\\qquad$. Let's think ste... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 37344,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many distinct arrangements of the letters in the word \"basics\" are there, specifically those beginning with a vowel? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "120"
} | {
"split": "train",
"index": 37345,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "This was a highly dangerous car rally. It began with a small and very narrow bridge, where one out of five cars would fall into the water. Then followed a terrifying sharp turn, where three out of ten cars would go off the road. Next, there was a dark and winding tunnel where o... | math | {
"style": "rule",
"ground_truth": "69.76"
} | {
"split": "train",
"index": 37346,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A high school math team received 5 college students for a teaching internship, who are about to graduate. They need to be assigned to three freshman classes: 1, 2, and 3, with at least one and at most two interns per class. Calculate the number of different allocation schemes. ... | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 37347,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of games won by five softball teams are displayed in the graph. However, the names of the teams are missing. The following clues provide information about the teams:\n\n1. The Tigers won more games than the Eagles.\n\n2. The Patriots won more games than the Cubs, but... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 37348,
"solution": ""
} |
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