data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Given triangle $\\triangle ABC$ with sides $a$, $b$, $c$ opposite to angles $A$, $B$, $C$ respectively. If $\\overrightarrow{BC} \\cdot \\overrightarrow{BA} + 2\\overrightarrow{AC} \\cdot \\overrightarrow{AB} = \\overrightarrow{CA} \\cdot \\overrightarrow{CB}$. <br/>$(1)$ Find ... | math | {
"style": "rule",
"ground_truth": "\\frac{3\\sqrt{2} - \\sqrt{10}}{8}"
} | {
"split": "train",
"index": 29349,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A real number $a$ is chosen randomly and uniformly from the interval $[-20, 18]$. Find the probability that the roots of the polynomial\n\\[x^4 + 2ax^3 + (2a - 2)x^2 + (-4a + 3)x - 2\\]are all real. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{18}{19}"
} | {
"split": "train",
"index": 29350,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system, it is known that the terminal side of an angle $\\alpha$ with the origin as the vertex and the non-negative half-axis of the $x$-axis as the initial side passes through the point $(-3,-4)$. \n$(1)$ Find the value of $\\frac{sin\\alpha}{tan\\... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 29351,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=x^2+x+b\\ (b\\in\\mathbb{R})$ with a value range of $[0,+\\infty)$, the solution to the equation $f(x) < c$ is $m+8$. Determine the value of $c$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 29352,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle \\( \\triangle ABC \\), \\(E\\) and \\(F\\) are the midpoints of \\(AC\\) and \\(AB\\) respectively, and \\( AB = \\frac{2}{3} AC \\). If \\( \\frac{BE}{CF} < t \\) always holds, then the minimum value of \\( t \\) is ______. Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{8}"
} | {
"split": "train",
"index": 29353,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A building contractor needs to pay his $108$ workers $\\$ 200 $ each. He is carrying $ 122 $ one hundred dollar bills and $ 188 $ fifty dollar bills. Only $ 45 $ workers get paid with two $ \\ $100$ bills. Find the number of workers who get paid with four $\\$ 50$ bills. L... | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 29354,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an arithmetic sequence $\\{a_n\\}$ where $a_1=1$ and $a_n=70$ (for $n\\geq3$), find all possible values of $n$ if the common difference is a natural number. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "70"
} | {
"split": "train",
"index": 29355,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the area bounded by the graph of $y = \\arcsin(\\cos x)$ and the $x$-axis on the interval $0 \\le x \\le 2\\pi.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi^2}{4}"
} | {
"split": "train",
"index": 29356,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The six-digit number $M=\\overline{abc321}$, where $a, b, c$ are three different numbers, and all are greater than 3. If $M$ is a multiple of 7, what is the smallest value of $M$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "468321"
} | {
"split": "train",
"index": 29357,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the greatest constant $N,$ so that\n\\[\\frac{a^2 + b^2 + ab}{c^2} > N\\]whenever $a,$ $b,$ and $c$ are the sides of a triangle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 29358,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are four more girls than boys in Ms. Raub's class of $28$ students. What is the ratio of number of girls to the number of boys in her class? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4 : 3"
} | {
"split": "train",
"index": 29359,
"solution": "1. **Define Variables:**\n Let $g$ be the number of girls in Ms. Raub's class. Since there are four more girls than boys, the number of boys, $b$, can be expressed as $b = g - 4$.\n\n2. **Set Up the Equation:**\n The total number of students in the class is giv... |
deepscaler | [
{
"role": "user",
"content": "Given a triangle $\\triangle ABC$ with its three interior angles $A$, $B$, and $C$ satisfying: $$A+C=2B, \\frac {1}{\\cos A}+ \\frac {1}{\\cos C}=- \\frac { \\sqrt {2}}{\\cos B}$$, find the value of $$\\cos \\frac {A-C}{2}$$. Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "\\frac { \\sqrt {2}}{2}"
} | {
"split": "train",
"index": 29360,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $a > 0$, $b > 0$, and $4a - b \\geq 2$, find the maximum value of $\\frac{1}{a} - \\frac{1}{b}$. 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": 29361,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $m$ is an integer and $0<3m<27$, what is the sum of all possible integer values of $m$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 29362,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "To survive the coming Cambridge winter, Chim Tu doesn't wear one T-shirt, but instead wears up to FOUR T-shirts, all in different colors. An outfit consists of three or more T-shirts, put on one on top of the other in some order, such that two outfits are distinct if the sets o... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 29363,
"solution": "We note that there are 4 choices for Chim Tu's innermost T-shirt, 3 choices for the next, and 2 choices for the next. At this point, he has exactly 1 T-shirt left, and 2 choices: either he puts that one on as well or he discards it. Thus, he has a total of $4 \\tim... |
deepscaler | [
{
"role": "user",
"content": "The areas of three of the faces of a right, rectangular prism are $24 \\hspace{.6mm} \\mathrm{cm}^2$, $32 \\hspace{.6mm} \\mathrm{cm}^2$, and $48 \\hspace{.6mm} \\mathrm{cm}^2$. What is the volume of the prism, in cubic centimeters? Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "192"
} | {
"split": "train",
"index": 29364,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "ABCD is a square with side of unit length. Points E and F are taken respectively on sides AB and AD so that AE = AF and the quadrilateral CDFE has maximum area. In square units this maximum area is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{8}"
} | {
"split": "train",
"index": 29365,
"solution": "1. **Define the problem setup**: Let $ABCD$ be a square with side length 1. Points $E$ and $F$ are on sides $AB$ and $AD$ respectively such that $AE = AF = x$. We need to maximize the area of quadrilateral $CDFE$.\n\n2. **Express the area of $CDFE$**: Consider drop... |
deepscaler | [
{
"role": "user",
"content": "Let $m$ be the smallest integer whose cube root is of the form $n+s$, where $n$ is a positive integer and $s$ is a positive real number less than $1/500$. Find $n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 29366,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify $$\\frac{13!}{11! + 3 \\cdot 9!}$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{17160}{113}"
} | {
"split": "train",
"index": 29367,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have?\n[asy] draw((0,0)--(3,0)--(3,3)--(0,3)--cycle); draw((3,0)--(5,2)--(5,5)--(2,5)--(0,3)); draw((3,3)--(5,5)); draw((2,0)--(3,1.8)--(4,1)--cycle,linewidth(... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 29368,
"solution": "1. **Identify the original structure**: The original figure is a rectangular prism, which has 8 vertices and 12 edges.\n\n2. **Understand the modification**: Each corner (vertex) of the prism is cut off. The cut at each vertex is such that it does not intersect any... |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer that can be written in the form $2002m + 44444n$, where $m$ and $n$ are integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 29369,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Among 5 table tennis players, there are 2 veteran players and 3 new players. Now, 3 players are to be selected to form a team and arranged in positions 1, 2, and 3 to participate in a team competition. The arrangement must include at least 1 veteran player, and among players 1 ... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 29370,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an experiment, a certain constant \\( c \\) is measured to be 2.43865 with an error range of \\(\\pm 0.00312\\). The experimenter wants to publish the value of \\( c \\), with each digit being significant. This means that regardless of how large \\( c \\) is, the announced v... | math | {
"style": "rule",
"ground_truth": "2.44"
} | {
"split": "train",
"index": 29371,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(x\\) and \\(y\\) be positive real numbers such that\n\\[\n\\frac{1}{x + 1} + \\frac{1}{y + 1} = \\frac{1}{2}.\n\\]\nFind the minimum value of \\(x + 3y.\\) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4 + 4 \\sqrt{3}"
} | {
"split": "train",
"index": 29372,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each of two wheels contains numbers from 1 to 8. When the wheels are spun, a number is selected from each wheel. Find the probability that the sum of the two selected numbers is divisible by 4. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 29373,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the base-$10$ logarithms of the divisors of $6^n$ is $540$. What is $n$?\nA) 9\nB) 10\nC) 11\nD) 12\nE) 13 Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 29374,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two circles are centered at the origin, as shown. The point $P(8,6)$ is on the larger circle and the point $S(0,k)$ is on the smaller circle. If $QR=3$, what is the value of $k$?\n\n[asy]\nunitsize(0.2 cm);\n\ndefaultpen(linewidth(.7pt)+fontsize(10pt));\ndotfactor=4;\ndraw(Ci... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 29375,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify first, then evaluate: $1-\\frac{a-b}{a+2b}÷\\frac{a^2-b^2}{a^2+4ab+4b^2}$. Given that $a=2\\sin 60^{\\circ}-3\\tan 45^{\\circ}$ and $b=3$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\sqrt{3}"
} | {
"split": "train",
"index": 29376,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For positive integers $a, b, a \\uparrow \\uparrow b$ is defined as follows: $a \\uparrow \\uparrow 1=a$, and $a \\uparrow \\uparrow b=a^{a \\uparrow \\uparrow(b-1)}$ if $b>1$. Find the smallest positive integer $n$ for which there exists a positive integer $a$ such that $a \\u... | math | {
"style": "rule",
"ground_truth": "283"
} | {
"split": "train",
"index": 29377,
"solution": "We see that the smallest such $n$ must be a prime power, because if two numbers are distinct mod $n$, they must be distinct mod at least one of the prime powers that divide $n$. For $k \\geq 2$, if $a \\uparrow \\uparrow k$ and $a \\uparrow \\uparrow(k+1)$ are dist... |
deepscaler | [
{
"role": "user",
"content": "Given a function $f(x)=\\log _{a}\\left(\\sqrt {x^{2}+1}+x\\right)+\\dfrac{1}{a^{x}-1}+\\dfrac{3}{2}$, where $a > 0$ and $a \\neq 1$. If $f\\left(\\log _{3}b\\right)=5$ for $b > 0$ and $b \\neq 1$, find the value of $f\\left(\\log _{\\frac{1}{3}}b\\right)$. Let's think step by ... | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 29378,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The physical education teacher lined up the class so that everyone was facing him. There are 12 people to the right of Kolya, 20 people to the left of Sasha, and 8 people to the right of Sasha. How many people are to the left of Kolya? Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 29379,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the value of $$\\sum_{a=1}^{\\infty} \\sum_{b=1}^{\\infty} \\sum_{c=1}^{\\infty} \\frac{a b(3 a+c)}{4^{a+b+c}(a+b)(b+c)(c+a)}$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{54}"
} | {
"split": "train",
"index": 29380,
"solution": "Let $S$ denote the given sum. By summing over all six permutations of the variables $a, b, c$ we obtain $$\\begin{aligned} 6 S & =\\sum_{a=1}^{\\infty} \\sum_{b=1}^{\\infty} \\sum_{c=1}^{\\infty} \\frac{3\\left(a^{2} b+a^{2} c+b^{2} a+b^{2} c+c^{2} a+c^{2} b\\right... |
deepscaler | [
{
"role": "user",
"content": "Along the southern shore of a boundless sea stretches an archipelago of an infinite number of islands. The islands are connected by an endless chain of bridges, and each island is connected by a bridge to the shore. In the event of a strong earthquake, each bridge independently... | math | {
"style": "rule",
"ground_truth": "2/3"
} | {
"split": "train",
"index": 29381,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If 600 were expressed as a sum of at least two distinct powers of 2, what would be the least possible sum of the exponents of these powers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 29382,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a point $P^{}_{}$ on a triangular piece of paper $ABC,\\,$ consider the creases that are formed in the paper when $A, B,\\,$ and $C\\,$ are folded onto $P.\\,$ Let us call $P_{}^{}$ a fold point of $\\triangle ABC\\,$ if these creases, which number three unless $P^{}_{}$ ... | math | {
"style": "rule",
"ground_truth": "597"
} | {
"split": "train",
"index": 29383,
"solution": "Let $O_{AB}$ be the intersection of the perpendicular bisectors (in other words, the intersections of the creases) of $\\overline{PA}$ and $\\overline{PB}$, and so forth. Then $O_{AB}, O_{BC}, O_{CA}$ are, respectively, the circumcenters of $\\triangle PAB, PBC, PC... |
deepscaler | [
{
"role": "user",
"content": "G.H. Hardy once went to visit Srinivasa Ramanujan in the hospital, and he started the conversation with: \"I came here in taxi-cab number 1729. That number seems dull to me, which I hope isn't a bad omen.\" \"Nonsense,\" said Ramanujan. \"The number isn't dull at all. It's quit... | math | {
"style": "rule",
"ground_truth": "251"
} | {
"split": "train",
"index": 29384,
"solution": "Let this smallest positive integer be represented as $a^{3} + b^{3} + c^{3} = d^{3} + e^{3} + f^{3}$. By inspection, a solution is not possible with the first 4 cubes. We prove that it is impossible to write the same number as two different sums of the first 5 cube... |
deepscaler | [
{
"role": "user",
"content": "Find the greatest real $k$ such that, for every tetrahedron $ABCD$ of volume $V$ , the product of areas of faces $ABC,ABD$ and $ACD$ is at least $kV^2$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9/2"
} | {
"split": "train",
"index": 29385,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many perfect squares less than 20,000 can be represented as the difference of squares of two integers that differ by 2? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "70"
} | {
"split": "train",
"index": 29386,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The first four terms in an arithmetic sequence are $x + y, x - y, xy,$ and $x/y,$ in that order. What is the fifth term? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{123}{40}"
} | {
"split": "train",
"index": 29387,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $T$ be the set of ordered triples $(x,y,z)$ of real numbers where\n\\[\\log_{10}(2x+2y) = z \\text{ and } \\log_{10}(x^{2}+2y^{2}) = z+2.\\]\nFind constants $c$ and $d$ such that for all $(x,y,z) \\in T$, the expression $x^{3} + y^{3}$ equals $c \\cdot 10^{3z} + d \\cdot 10... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{16}"
} | {
"split": "train",
"index": 29388,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the maximum value of $\\frac{(3^t - 5t)t}{9^t}$ for real values of $t$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{20}"
} | {
"split": "train",
"index": 29389,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The expression $a^3-a^{-3}$ equals: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left(a-\\frac{1}{a}\\right)\\left(a^2+1+\\frac{1}{a^2}\\right)"
} | {
"split": "train",
"index": 29390,
"solution": "1. **Identify the form of the expression**: We are given the expression $a^3 - a^{-3}$ and need to simplify it. We recognize that this expression can be rewritten using the difference of cubes formula.\n\n2. **Recall the difference of cubes formula**: The formula f... |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, point $F$ divides side $AC$ in the ratio $1:2$. Let $E$ be the point of intersection of side $BC$ and $AG$ where $G$ is the midpoints of $BF$. The point $E$ divides side $BC$ in the ratio Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "1/3"
} | {
"split": "train",
"index": 29391,
"solution": "1. **Assigning Masses Based on Given Ratios:**\n - Since point $F$ divides side $AC$ in the ratio $1:2$, we assign a mass of $2$ to point $A$ and a mass of $1$ to point $C$. The total mass at point $F$ is the sum of the masses at $A$ and $C$, which is $2 + 1 = 3$... |
deepscaler | [
{
"role": "user",
"content": "Compute\n\\[\n\\left( 1 - \\sin \\frac {\\pi}{8} \\right) \\left( 1 - \\sin \\frac {3\\pi}{8} \\right) \\left( 1 - \\sin \\frac {5\\pi}{8} \\right) \\left( 1 - \\sin \\frac {7\\pi}{8} \\right).\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 29392,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A point $(x,y)$ is randomly picked from inside the rectangle with vertices $(0,0)$, $(6,0)$, $(6,2)$, and $(0,2)$. What is the probability that $x^2 < y$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{18}"
} | {
"split": "train",
"index": 29393,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of ways to pave a $1 \\times 10$ block with tiles of sizes $1 \\times 1, 1 \\times 2$ and $1 \\times 4$, assuming tiles of the same size are indistinguishable. It is not necessary to use all the three kinds of tiles. Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "169"
} | {
"split": "train",
"index": 29394,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For $n > 1$ , let $a_n$ be the number of zeroes that $n!$ ends with when written in base $n$ . Find the maximum value of $\\frac{a_n}{n}$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1/2"
} | {
"split": "train",
"index": 29395,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $(xOy)$, with the origin as the pole and the positive semi-axis of $x$ as the polar axis, establish a polar coordinate system using the same unit of length. The parametric equations of line $l$ are given by $\\begin{cases}x=2+t \\\\ y=1+t\\end... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 29396,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $S$ is a series of real numbers between $2$ and $8$ inclusive, and that for any two elements $y > x$ in $S,$ $$ 98y - 102x - xy \\ge 4. $$ What is the maximum possible size for the set $S?$ Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 29397,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two distinct numbers a and b are chosen randomly from the set $\\{3, 3^2, 3^3, ..., 3^{20}\\}$. What is the probability that $\\mathrm{log}_a b$ is an integer?\nA) $\\frac{12}{19}$\nB) $\\frac{1}{4}$\nC) $\\frac{24}{95}$\nD) $\\frac{1}{5}$ Let's think step by step and put only ... | math | {
"style": "rule",
"ground_truth": "\\frac{24}{95}"
} | {
"split": "train",
"index": 29398,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The area of triangle \\(ABC\\) is 1. Let \\(A_1\\), \\(B_1\\), and \\(C_1\\) be the midpoints of the sides \\(BC\\), \\(CA\\), and \\(AB\\) respectively. Points \\(K\\), \\(L\\), and \\(M\\) are taken on segments \\(AB_1\\), \\(CA_1\\), and \\(BC_1\\) respectively. What is the ... | math | {
"style": "rule",
"ground_truth": "1/8"
} | {
"split": "train",
"index": 29399,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Call an integer $n$ oddly powerful if there exist positive integers $a$ and $b$, where $b>1$, $b$ is odd, and $a^b = n$. How many oddly powerful integers are less than $2010$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 29400,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x$ satisfies $x^2 + 3x + \\frac{3}x + \\frac{1}{x^2} = 26$ and $x$ can be written as $a + \\sqrt{b}$ where $a$ and $b$ are positive integers, then find $a + b$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 29401,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=2\\ln x - ax^2 + 3$, \n(1) Discuss the monotonicity of the function $y=f(x)$; \n(2) If there exist real numbers $m, n \\in [1, 5]$ such that $f(m)=f(n)$ holds when $n-m \\geq 2$, find the maximum value of the real number $a$. Let's think step by step ... | math | {
"style": "rule",
"ground_truth": "\\frac{\\ln 3}{4}"
} | {
"split": "train",
"index": 29402,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $| \\overrightarrow{a}|=2$, $\\overrightarrow{e}$ is a unit vector, and the angle between $\\overrightarrow{a}$ and $\\overrightarrow{e}$ is $\\dfrac {\\pi}{3}$, find the projection of $\\overrightarrow{a}+ \\overrightarrow{e}$ on $\\overrightarrow{a}- \\overrightarr... | math | {
"style": "rule",
"ground_truth": "\\sqrt {3}"
} | {
"split": "train",
"index": 29403,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the parameter equation of line $l$ and the equation of circle $C$ in the polar coordinate system, find the rectangular coordinate equation of circle $C$ and the minimum value of $\\frac{1}{|PA|} + \\frac{1}{|PB|}$, where $P(1, 2)$ and $A$, $B$ are the intersection points ... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{7}}{7}"
} | {
"split": "train",
"index": 29404,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $xOy$, the parametric equation of line $l$ is\n$$\n\\begin{cases}\nx = -1 + \\frac {\\sqrt {2}}{2}t \\\\\ny = 1 + \\frac {\\sqrt {2}}{2}t\n\\end{cases}\n(t \\text{ is the parameter}),\n$$\nand the equation of circle $C$ is $(x-2)^{2} + (y-1)^{... | math | {
"style": "rule",
"ground_truth": "\\frac{3\\sqrt{10}}{10}"
} | {
"split": "train",
"index": 29405,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest number, all of whose digits are 1 or 2, and whose digits add up to $10$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "111111112"
} | {
"split": "train",
"index": 29406,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the terminal side of angle $\\alpha$ passes through point P $\\left(\\frac{4}{5}, -\\frac{3}{5}\\right)$.\n\n(1) Find the value of $\\sin\\alpha$.\n\n(2) Calculate the value of $\\frac{\\sin\\left(\\frac{\\pi}{2}-\\alpha\\right)}{\\sin(\\alpha +\\pi)} \\cdot \\frac{\... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{4}"
} | {
"split": "train",
"index": 29407,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A,B,C$ be angles of an acute triangle with \\begin{align*} \\cos^2 A + \\cos^2 B + 2 \\sin A \\sin B \\cos C &= \\frac{15}{8} \\text{ and} \\\\ \\cos^2 B + \\cos^2 C + 2 \\sin B \\sin C \\cos A &= \\frac{14}{9} \\end{align*} There are positive integers $p$, $q$, $r$, and $... | math | {
"style": "rule",
"ground_truth": "222"
} | {
"split": "train",
"index": 29408,
"solution": "According to LOC $a^2+b^2-2ab\\cos{\\angle{c}}=c^2$, we can write it into $\\sin^2{\\angle{A}}+\\sin^2{\\angle{B}}-2\\sin{\\angle{A}}\\sin{\\angle{B}}\\cos{\\angle{C}}=\\sin^2{\\angle{C}}$. $\\sin^2{\\angle{A}}+\\sin^2{\\angle{B}}-2\\sin{\\angle{A}}\\sin{\\angle{B}... |
deepscaler | [
{
"role": "user",
"content": "When three standard dice are tossed, the numbers $x, y, z$ are obtained. Find the probability that $xyz = 72$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{24}"
} | {
"split": "train",
"index": 29409,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Fill in the 3x3 grid with 9 different natural numbers such that for each row, the sum of the first two numbers equals the third number, and for each column, the sum of the top two numbers equals the bottom number. What is the smallest possible value for the number in the bottom... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 29410,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a triangle with sides 6 cm, 10 cm, and 12 cm, an inscribed circle is tangent to the two longer sides. Find the perimeter of the resulting triangle formed by the tangent line and the two longer sides. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 29411,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "180 grams of 920 purity gold was alloyed with 100 grams of 752 purity gold. What is the purity of the resulting alloy? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "860"
} | {
"split": "train",
"index": 29412,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $\\frac{1}{2}\\cos 2A = \\cos^2 A - \\cos A$.\n(I) Find the measure of angle $A$;\n(II) If $a=3$, $\\sin B = 2\\sin C$, find the area of $\\triangle ABC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 29413,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given Orvin goes to a store with just enough money to buy 40 balloons, and the store has a special promotion: for every balloon bought at full price, a second one can be bought at 1/2 off. Find the maximum number of balloons Orvin can buy. Let's think step by step and put only ... | math | {
"style": "rule",
"ground_truth": "52"
} | {
"split": "train",
"index": 29414,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house number. She tells him, \"My house number has two digits, and exactly three of the following four statements about it are true.\" \n(1) It is prime.\n(2) It is even... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 29415,
"solution": "1. **Analyze the given statements**: Isabella's house number is a two-digit number, and exactly three out of the four statements about it are true:\n - (1) It is prime.\n - (2) It is even.\n - (3) It is divisible by 7.\n - (4) One of its digits is 9.\n\n2. ... |
deepscaler | [
{
"role": "user",
"content": "Mom asks Xiao Ming to boil water and make tea for guests. Washing the kettle takes 1 minute, boiling water takes 15 minutes, washing the teapot takes 1 minute, washing the teacups takes 1 minute, and getting the tea leaves takes 2 minutes. Xiao Ming estimates that it will take ... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 29416,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The perimeter of a rectangle is 48. What is the largest possible area of the rectangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 29417,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a,$ $b,$ $c,$ $d,$ $e,$ $f,$ $g,$ and $h$ be real numbers such that $abcd = 4$ and $efgh = 9.$ Find the minimum value of\n\\[(ae)^2 + (bf)^2 + (cg)^2 + (dh)^2.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 29418,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose $\\triangle ABC$ is a triangle where $AB = 36, AC = 36$, and $\\angle B = 60^\\circ$. A point $P$ is considered a fold point if the creases formed when vertices $A, B,$ and $C$ are folded onto point $P$ do not intersect inside $\\triangle ABC$. Find the area of the set ... | math | {
"style": "rule",
"ground_truth": "381"
} | {
"split": "train",
"index": 29419,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "One of the following four-digit numbers is not divisible by 4: 3544, 3554, 3564, 3572, 3576. What is the product of the units digit and the tens digit of that number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 29420,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all solutions to $aabb=n^4-6n^3$ , where $a$ and $b$ are non-zero digits, and $n$ is an integer. ( $a$ and $b$ are not necessarily distinct.) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6655"
} | {
"split": "train",
"index": 29421,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the area bounded by the graph of $y = \\arccos(\\cos x)$ and the $x$-axis on the interval $0 \\leq x \\leq 2\\pi$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\pi^2"
} | {
"split": "train",
"index": 29422,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nCalculate the volume of the tetrahedron with vertices at points $A_{1}, A_{2}, A_{3}, A_{4}$ and its height dropped from vertex $A_{4}$ onto the face $A_{1} A_{2} A_{3}$.\n\n$A_{1}(1, 1, 2)$\n\n$A_{2}(-1, 1, 3)$\n\n$A_{3}(2, -2, 4)$\n\n$A_{4}(-1, 0, -2)$ Let's think step by s... | math | {
"style": "rule",
"ground_truth": "\\sqrt{\\frac{35}{2}}"
} | {
"split": "train",
"index": 29423,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $60\\%$ of the high school students like ice skating, $50\\%$ like skiing, and $70\\%$ like either ice skating or skiing, calculate the probability that a randomly selected student who likes skiing also likes ice skating. Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "0.8"
} | {
"split": "train",
"index": 29424,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABC$ be an equilateral triangle . Let point $D$ lie on side $AB,E$ lie on side $AC, D_1$ and $E_1$ lie on side BC such that $AB=DB+BD_1$ and $AC=CE+CE_1$ . Calculate the smallest angle between the lines $DE_1$ and $ED_1$ . Let's think step by step and put... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 29425,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points $P$ and $Q$ are on a circle of radius $7$ and $PQ = 8$. Point $R$ is the midpoint of the minor arc $PQ$. Calculate the length of the line segment $PR$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{98 - 14\\sqrt{33}}"
} | {
"split": "train",
"index": 29426,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of permutations $x_1, x_2, x_3, x_4, x_5$ of numbers $1, 2, 3, 4, 5$ such that the sum of five products \\[x_1x_2x_3 + x_2x_3x_4 + x_3x_4x_5 + x_4x_5x_1 + x_5x_1x_2\\] is divisible by $3$. Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "80"
} | {
"split": "train",
"index": 29427,
"solution": "Since $3$ is one of the numbers, a product with a $3$ in it is automatically divisible by $3,$ so WLOG $x_3=3,$ we will multiply by $5$ afterward since any of $x_1, x_2, \\ldots, x_5$ would be $3,$ after some cancelation we see that now all we need to find is the n... |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the set of positive integers $N$ with the property that the last four digits of $N$ are $2020,$ and when the last four digits are removed, the result is a divisor of $N.$ For example, $42,020$ is in $S$ because $4$ is a divisor of $42,020.$ Find the sum of all the di... | math | {
"style": "rule",
"ground_truth": "93"
} | {
"split": "train",
"index": 29428,
"solution": "We note that any number in $S$ can be expressed as $a(10,000) + 2,020$ for some integer $a$. The problem requires that $a$ divides this number, and since we know $a$ divides $a(10,000)$, we need that $a$ divides 2020. Each number contributes the sum of the digits o... |
deepscaler | [
{
"role": "user",
"content": "Three cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is an Ace, the second card is a diamond, and the third card is a Jack? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{650}"
} | {
"split": "train",
"index": 29429,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the direction vector of line $l$ is $\\overrightarrow{d}=(1,\\sqrt{3})$, then the inclination angle of line $l$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{3}"
} | {
"split": "train",
"index": 29430,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be the least positive integer greater than $1000$ for which\n\\[\\gcd(63, n+120) =21\\quad \\text{and} \\quad \\gcd(n+63, 120)=60.\\]What is the sum of the digits of $n$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 29431,
"solution": "1. **Understanding the Problem:**\n We need to find the smallest integer $n > 1000$ such that:\n - $\\gcd(63, n+120) = 21$\n - $\\gcd(n+63, 120) = 60$\n\n2. **Using the Euclidean Algorithm:**\n - For $\\gcd(63, n+120) = 21$, we have:\n \\[\n \\gcd(6... |
deepscaler | [
{
"role": "user",
"content": "Call a number prime-looking if it is composite but not divisible by $2, 3,$ or $5.$ The three smallest prime-looking numbers are $49, 77$, and $91$. There are $168$ prime numbers less than $1000$. How many prime-looking numbers are there less than $1000$? Let's think step by st... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 29432,
"solution": "1. **Identify the total number of integers less than 1000**: \n There are 999 integers from 1 to 999.\n\n2. **Calculate the number of prime numbers less than 1000**:\n It is given that there are 168 prime numbers less than 1000.\n\n3. **Exclude the primes 2, 3,... |
deepscaler | [
{
"role": "user",
"content": "Find the distance between the midpoints of the non-parallel sides of different bases of a regular triangular prism, each of whose edges is 2. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{5}"
} | {
"split": "train",
"index": 29433,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of the expression $\\frac {x^2-x-6}{x-3}$ for $x=2$? 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": "4"
} | {
"split": "train",
"index": 29434,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\alpha\\geq 1$ be a real number. Define the set $$ A(\\alpha)=\\{\\lfloor \\alpha\\rfloor,\\lfloor 2\\alpha\\rfloor, \\lfloor 3\\alpha\\rfloor,\\dots\\} $$ Suppose that all the positive integers that **does not belong** to the $A(\\alpha)$ are exactly the positive i... | math | {
"style": "rule",
"ground_truth": "\\frac{2021}{2020}"
} | {
"split": "train",
"index": 29435,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a horizontal plane, touching each other, there lie 4 spheres with a radius of \\( 24-12\\sqrt{2} \\), and their centers form a square. On top above the center of the square, a fifth sphere of the same radius is placed over the four spheres. Find the distance from its highest... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 29436,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = \\cos x \\cdot \\sin\\left(\\frac{\\pi}{6} - x\\right)$, \n(1) Find the interval where $f(x)$ is monotonically decreasing; \n(2) In $\\triangle ABC$, the sides opposite angles A, B, and C are denoted as $a$, $b$, and $c$ respectively. If $f(C) = -\\... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{3}"
} | {
"split": "train",
"index": 29437,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jamar bought some pencils costing more than a penny each at the school bookstore and paid $1.43$. Sharona bought some of the same pencils and paid $1.87$. How many more pencils did Sharona buy than Jamar? Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 29438,
"solution": "1. **Calculate the difference in money spent by Sharona and Jamar:**\n \\[\n 1.87 - 1.43 = 0.44\n \\]\n This means Sharona spent $\\$0.44$ more than Jamar.\n\n2. **Determine the possible number of extra pencils Sharona bought:**\n Since the difference in ... |
deepscaler | [
{
"role": "user",
"content": "Given that point \\( P \\) moves on the circle \\( C: x^{2}+(y+2)^{2}=\\frac{1}{4} \\), and point \\( Q \\) moves on the curve \\( y=a x^{2} \\) (where \\( a > 0 \\) and \\( -1 \\leq x \\leq 2 \\)), if the maximum value of \\(|PQ|\\) is \\(\\frac{9}{2}\\), then find \\( a \\). ... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3} - 1}{2}"
} | {
"split": "train",
"index": 29439,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the numbers 300, 2020, and 10001 is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12321"
} | {
"split": "train",
"index": 29440,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The formula which expresses the relationship between $x$ and $y$ as shown in the accompanying table is:\n\\[\\begin{tabular}[t]{|c|c|c|c|c|c|}\\hline x&0&1&2&3&4\\\\\\hline y&100&90&70&40&0\\\\\\hline\\end{tabular}\\] Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "y=100-5x-5x^{2}"
} | {
"split": "train",
"index": 29441,
"solution": "To find the correct formula that expresses the relationship between $x$ and $y$, we will substitute the given points into each of the proposed formulas and check which one satisfies all the points.\n\n#### Step 1: Test the point $(0, 100)$\n- **Option A:** $y = 100... |
deepscaler | [
{
"role": "user",
"content": "Petya and Vasya competed in a 60-meter race. When Petya finished, Vasya was 9 meters behind him. In the second race, Petya stood exactly 9 meters behind Vasya at the starting point. Who finished first in the second race and by how many meters did he lead his opponent? (Assume t... | math | {
"style": "rule",
"ground_truth": "1.35"
} | {
"split": "train",
"index": 29442,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest real number $c$ such that \\[x_1^2 + x_2^2 + \\dots + x_{101}^2 \\geq cM^2\\]whenever $x_1,x_2,\\ldots,x_{101}$ are real numbers such that $x_1+x_2+\\cdots+x_{101}=0$ and $M$ is the median of $x_1,x_2,\\ldots,x_{101}.$ Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "\\tfrac{5151}{50}"
} | {
"split": "train",
"index": 29443,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A company conducts quality checks on a batch of products using systematic sampling. From 100 products, 5 are to be sampled for testing. The products are randomly numbered and divided into 5 groups: Group 1 contains numbers 1–20, Group 2 contains numbers 21–40, and so on up to G... | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 29444,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The area of the large square \\(ABCD\\) in the diagram is 1, and the other points are the midpoints of the sides.\n\nQuestion: What is the area of the shaded triangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{32}"
} | {
"split": "train",
"index": 29445,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a high school's \"Campus Microfilm Festival\" event, the school will evaluate the films from two aspects: \"viewing numbers\" and \"expert ratings\". If a film A is higher than film B in at least one of these aspects, then film A is considered not inferior to film B. It is k... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 29446,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An isosceles right triangle is removed from each corner of a square piece of paper, as shown, to create a rectangle. If $AB = 12$ units, what is the combined area of the four removed triangles, in square units? [asy]\nunitsize(5mm);\ndefaultpen(linewidth(.7pt)+fontsize(8pt));\n... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 29447,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What are the last $2$ digits of the number $2018^{2018}$ when written in base $7$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "44"
} | {
"split": "train",
"index": 29448,
"solution": ""
} |
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