data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "For each positive integer $1 \\leq m \\leq 10$, Krit chooses an integer $0 \\leq a_{m}<m$ uniformly at random. Let $p$ be the probability that there exists an integer $n$ for which $n \\equiv a_{m}(\\bmod m)$ for all $m$. If $p$ can be written as $\\frac{a}{b}$ for relatively p... | math | {
"style": "rule",
"ground_truth": "1540"
} | {
"split": "train",
"index": 8000,
"solution": "Tuples of valid $a_{m}$ correspond with residues $\\bmod \\operatorname{lcm}(1,2, \\ldots, 10)$, so the answer is $$\\frac{\\operatorname{lcm}(1,2, \\ldots, 10)}{10!}=\\frac{2^{3} \\cdot 3^{2} \\cdot 5 \\cdot 7}{2^{8} \\cdot 3^{4} \\cdot 5^{2} \\cdot 7}=\\frac{1}{14... |
deepscaler | [
{
"role": "user",
"content": "Positive integers $a$, $b$, and $c$ are randomly and independently selected with replacement from the set $\\{1, 2, 3,\\dots, 2010\\}$. What is the probability that $abc + ab + a$ is divisible by $3$? Let's think step by step and put only the final answer within \\boxed{}."
}... | math | {
"style": "rule",
"ground_truth": "\\frac{13}{27}"
} | {
"split": "train",
"index": 8001,
"solution": "1. **Understanding the Problem:**\n We need to find the probability that the expression $abc + ab + a$ is divisible by $3$ when $a$, $b$, and $c$ are chosen randomly from the set $\\{1, 2, 3, \\dots, 2010\\}$.\n\n2. **Divisibility Analysis:**\n We can simplify t... |
deepscaler | [
{
"role": "user",
"content": "Determine the number of revolutions a wheel, with a fixed center and with an outside diameter of 8 feet, would require to cause a point on the rim to travel one mile. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{660}{\\pi}"
} | {
"split": "train",
"index": 8002,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define a \"digitized number\" as a ten-digit number $a_0a_1\\ldots a_9$ such that for $k=0,1,\\ldots, 9$ , $a_k$ is equal to the number of times the digit $k$ occurs in the number. Find the sum of all digitized numbers. Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "6210001000"
} | {
"split": "train",
"index": 8003,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the function $f(x)$ satisfies $f(x+y)=f(x)+f(y)$ for any $x, y \\in \\mathbb{R}$, and $f(x) < 0$ when $x > 0$, with $f(1)=-2$.\n1. Determine the parity (odd or even) of the function $f(x)$.\n2. When $x \\in [-3, 3]$, does the function $f(x)$ have an extreme value (ma... | math | {
"style": "rule",
"ground_truth": "-6"
} | {
"split": "train",
"index": 8004,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The students in Mr. Neatkin's class took a penmanship test. Two-thirds of the boys and $\\frac{3}{4}$ of the girls passed the test, and an equal number of boys and girls passed the test. What is the minimum possible number of students in the class? Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 8005,
"solution": "1. **Define Variables:**\n Let $b$ represent the number of boys and $g$ represent the number of girls in Mr. Neatkin's class.\n\n2. **Set Up the Equation:**\n According to the problem, two-thirds of the boys and three-fourths of the girls passed the test, and th... |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $(xOy)$, the parametric equations of curve $C_{1}$ are given by $\\begin{cases}x=2t-1 \\\\ y=-4t-2\\end{cases}$ $(t$ is the parameter$)$, and in the polar coordinate system with the coordinate origin $O$ as the pole and the positive half of th... | math | {
"style": "rule",
"ground_truth": "\\frac{3 \\sqrt{5}}{10}"
} | {
"split": "train",
"index": 8006,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the remainder when $2x^2-17x+47$ is divided by $x-5$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 8007,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Eleven girls are standing around a circle. A ball is thrown clockwise around the circle. The first girl, Ami, starts with the ball, skips the next three girls and throws to the fifth girl, who then skips the next three girls and throws the ball to the ninth girl. If the throwin... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 8008,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On the side \\( AD \\) of the rhombus \\( ABCD \\), a point \\( M \\) is taken such that \\( MD = 0.3 \\, AD \\) and \\( BM = MC = 11 \\). Find the area of triangle \\( BCM \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20\\sqrt{6}"
} | {
"split": "train",
"index": 8009,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Inside a pentagon, 1000 points were marked and the pentagon was divided into triangles such that each of the marked points became a vertex of at least one of them. What is the minimum number of triangles that could be formed? Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "1003"
} | {
"split": "train",
"index": 8010,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Five students, labeled as A, B, C, D, and E, are standing in a row to participate in a literary performance. If student A does not stand at either end, calculate the number of different arrangements where students C and D are adjacent. Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 8011,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The circumference of a particular circle is 18 cm. In square centimeters, what is the area of the circle? Express your answer as a common fraction in terms of $\\pi$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{81}{\\pi}"
} | {
"split": "train",
"index": 8012,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many positive integers $n \\le 1000$ is$\\left\\lfloor \\dfrac{998}{n} \\right\\rfloor+\\left\\lfloor \\dfrac{999}{n} \\right\\rfloor+\\left\\lfloor \\dfrac{1000}{n}\\right \\rfloor$not divisible by $3$? Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 8013,
"solution": "We are tasked with finding how many positive integers \\( n \\leq 1000 \\) make the expression\n\\[\n\\left\\lfloor \\frac{998}{n} \\right\\rfloor + \\left\\lfloor \\frac{999}{n} \\right\\rfloor + \\left\\lfloor \\frac{1000}{n} \\right\\rfloor\n\\]\nnot divisible by... |
deepscaler | [
{
"role": "user",
"content": "Given real numbers $a$ and $b$ satisfying $a^{2}-4\\ln a-b=0$, find the minimum value of $\\left(a-c\\right)^{2}+\\left(b+2c\\right)^{2}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9}{5}"
} | {
"split": "train",
"index": 8014,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "With all angles measured in degrees, the product $\\prod_{k=1}^{45} \\csc^2(2k-1)^\\circ=m^n$, where $m$ and $n$ are integers greater than 1. Find $m+n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "91"
} | {
"split": "train",
"index": 8015,
"solution": "Let $p=\\sin1\\sin3\\sin5...\\sin89$\n\\[p=\\sqrt{\\sin1\\sin3\\sin5...\\sin177\\sin179}\\]\n\\[=\\sqrt{\\frac{\\sin1\\sin2\\sin3\\sin4...\\sin177\\sin178\\sin179}{\\sin2\\sin4\\sin6\\sin8...\\sin176\\sin178}}\\]\n\\[=\\sqrt{\\frac{\\sin1\\sin2\\sin3\\sin4...\\sin17... |
deepscaler | [
{
"role": "user",
"content": "On an east-west shipping lane are ten ships sailing individually. The first five from the west are sailing eastwards while the other five ships are sailing westwards. They sail at the same constant speed at all times. Whenever two ships meet, each turns around and sails in t... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 8016,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "You would like to provide airline service to the 10 cities in the nation of Schizophrenia, by instituting a certain number of two-way routes between cities. Unfortunately, the government is about to divide Schizophrenia into two warring countries of five cities each, and you do... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 8017,
"solution": "Each city $C$ must be directly connected to at least 6 other cities, since otherwise the government could put $C$ in one country and all its connecting cities in the other country, and there would be no way out of $C$. This means that we have 6 routes for each of 10... |
deepscaler | [
{
"role": "user",
"content": "Consider a trapezoidal field where it's planted uniformly with wheat. The trapezoid has the following measurements: side $AB$ is 150 m, base $AD$ (the longest side) is 300 m, and the other base $BC$ is 150 m. The angle at $A$ is $75^\\circ$, and the angle at $B$ is $105^\\circ$... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 8018,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the ordered pair $(x,y)$ if\n\n\\begin{align*}\nx+y&=(5-x)+(5-y),\\\\\nx-y&=(x-1)+(y-1).\n\\end{align*} Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(4,1)"
} | {
"split": "train",
"index": 8019,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A positive integer is said to be \"nefelibata\" if, upon taking its last digit and placing it as the first digit, keeping the order of all the remaining digits intact (for example, 312 -> 231), the resulting number is exactly double the original number. Find the smallest possib... | math | {
"style": "rule",
"ground_truth": "105263157894736842"
} | {
"split": "train",
"index": 8020,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\na) Find all the divisors of the number 572 based on its prime factorization.\n\nb) How many divisors does the number \\(572 a^{3} b c\\) have if:\n\n I. \\(a, b\\), and \\(c\\) are prime numbers greater than 20 and different from each other? \n\n II. \\(a = 31\\), \\(b = ... | math | {
"style": "rule",
"ground_truth": "384"
} | {
"split": "train",
"index": 8021,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From $A$ to $B$ it is 999 km. Along the road, there are kilometer markers with distances written to $A$ and to $B$:\n\n$0|999,1|998, \\ldots, 999|0$.\n\nHow many of these markers have only two different digits? Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 8022,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The yearly changes in the population census of a city for five consecutive years are, respectively, 20% increase, 10% increase, 30% decrease, 20% decrease, and 10% increase. Calculate the net change over these five years, to the nearest percent. Let's think step by step and put... | math | {
"style": "rule",
"ground_truth": "-19\\%"
} | {
"split": "train",
"index": 8023,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The area of the ground plane of a truncated cone $K$ is four times as large as the surface of the top surface. A sphere $B$ is circumscribed in $K$ , that is to say that $B$ touches both the top surface and the base and the sides. Calculate ratio volume $B :$ Volume $... | math | {
"style": "rule",
"ground_truth": "9/14"
} | {
"split": "train",
"index": 8024,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A game board is constructed by shading two of the regions formed by the altitudes of an equilateral triangle as shown. What is the probability that the tip of the spinner will come to rest in a shaded region? Express your answer as a common fraction. [asy]\nimport olympiad; siz... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 8025,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Bank of Oslo issues two types of coin: aluminum (denoted A) and bronze (denoted B). Marianne has $n$ aluminum coins and $n$ bronze coins arranged in a row in some arbitrary initial order. A chain is any subsequence of consecutive coins of the same type. Given a fixed positi... | math | {
"style": "rule",
"ground_truth": "{n \\leq k \\leq \\lceil \\tfrac32n \\rceil}"
} | {
"split": "train",
"index": 8026,
"solution": "\nGiven the problem, Marianne has $n$ aluminum coins and $n$ bronze coins arranged in a row in some arbitrary initial order. We want to find pairs \\((n, k)\\) for a fixed positive integer $k \\leq 2n$ such that as Gilberty performs his operation, at some point, the... |
deepscaler | [
{
"role": "user",
"content": "In the game of projective set, each card contains some nonempty subset of six distinguishable dots. A projective set deck consists of one card for each of the 63 possible nonempty subsets of dots. How many collections of five cards have an even number of each dot? The order in ... | math | {
"style": "rule",
"ground_truth": "109368"
} | {
"split": "train",
"index": 8027,
"solution": "We'll first count sets of cards where the order does matter. Suppose we choose the first four cards. Then there is exactly one card that can make each dot appear twice. However, this card could be empty or it could be one of the cards we've already chosen, so we hav... |
deepscaler | [
{
"role": "user",
"content": "How many foonies are in a stack that has a volume of $50 \\mathrm{~cm}^{3}$, given that each foonie has a volume of $2.5 \\mathrm{~cm}^{3}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 8028,
"solution": "Since the face of a foonie has area $5 \\mathrm{~cm}^{2}$ and its thickness is 0.5 cm, then the volume of one foonie is $5 \\times 0.5=2.5 \\mathrm{~cm}^{3}$. If a stack of foonies has a volume of $50 \\mathrm{~cm}^{3}$ and each foonie has a volume of $2.5 \\mathrm{... |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive $a$ such that $a$ is a multiple of $4$ and $a$ is a multiple of $14.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 8029,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $[x]$ is the greatest integer less than or equal to $x$, then $\\sum_{N=1}^{1024}\\left[\\log _{2} N\\right]$ equals Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8204"
} | {
"split": "train",
"index": 8030,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many non-empty subsets \\( S \\) of \\( \\{1, 2, 3, \\ldots, 12\\} \\) have the following two properties?\n1. No two consecutive integers belong to \\( S \\).\n2. If \\( S \\) contains \\( k \\) elements, then \\( S \\) contains no number less than \\( k \\). Let's think st... | math | {
"style": "rule",
"ground_truth": "128"
} | {
"split": "train",
"index": 8031,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the right triangle $ABC$, $AC=12$, $BC=5$, and angle $C$ is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{10}{3}"
} | {
"split": "train",
"index": 8032,
"solution": "1. **Identify the triangle and its properties**: \n In the right triangle $ABC$, with $AC=12$, $BC=5$, and angle $C$ being a right angle, we can use the Pythagorean theorem to find $AB$:\n \\[\n AB = \\sqrt{AC^2 + BC^2} = \\sqrt{12^2 + 5^2} = \\sqrt{144 + 25} ... |
deepscaler | [
{
"role": "user",
"content": "One dimension of a cube is increased by $1$, another is decreased by $1$, and the third is left unchanged. The volume of the new rectangular solid is $5$ less than that of the cube. What was the volume of the cube? Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "125"
} | {
"split": "train",
"index": 8033,
"solution": "1. **Define the dimensions and volume of the original cube:**\n Let the edge length of the original cube be $a$. Therefore, the volume of the cube is given by:\n \\[\n V_{\\text{cube}} = a^3\n \\]\n\n2. **Define the dimensions and volume of the new rectangul... |
deepscaler | [
{
"role": "user",
"content": "For $0 \\leq p \\leq 1/2$, let $X_1, X_2, \\dots$ be independent random variables such that \\[ X_i = \\begin{cases} 1 & \\mbox{with probability $p$,} \\\\ -1 & \\mbox{with probability $p$,} \\\\ 0 & \\mbox{with probability $1-2p$,} \\end{cases} \\] for all $i \\geq 1$. Given a... | math | {
"style": "rule",
"ground_truth": "p \\leq 1/4"
} | {
"split": "train",
"index": 8034,
"solution": "The answer is $p \\leq 1/4$. We first show that $p >1/4$ does not satisfy the desired condition. For $p>1/3$, $P(0,1) = 1-2p < p = P(1,1)$. For $p=1/3$, it is easily calculated (or follows from the next calculation) that $P(0,1,2) = 1/9 < 2/9 = P(1,1,2)$. Now suppos... |
deepscaler | [
{
"role": "user",
"content": "Tom's graduating class has 288 students. At the graduation ceremony, the students will sit in rows with the same number of students in each row. If there must be at least 10 rows and at least 15 students in each row, then there can be $x$ students in each row. What is the sum o... | math | {
"style": "rule",
"ground_truth": "58"
} | {
"split": "train",
"index": 8035,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of positive integers less than 1000000 that are divisible by some perfect cube greater than 1. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "168089"
} | {
"split": "train",
"index": 8036,
"solution": "Using the following code, we get the answer (denoted by the variable ans): ans $=0$ for $n$ in xrange $(1,1000000)$ : ``` divisible_by_cube = True for i in xrange(2,101): if n%(i*i*i)==0: divisible_by_cube = False break if divisible_by_cube: ans = ans + 1 print ans ... |
deepscaler | [
{
"role": "user",
"content": "Given that the polynomial $x^2 - kx + 24$ has only positive integer roots, find the average of all distinct possibilities for $k$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 8037,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "During breaks, schoolchildren played table tennis. Any two schoolchildren played no more than one game against each other. At the end of the week, it turned out that Petya played half, Kolya - a third, and Vasya - one fifth of the total number of games played during the week. W... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 8038,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the remainder when 53! is divided by 59. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 8039,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The measures of the interior angles of a convex polygon of $n$ sides are in arithmetic progression. If the common difference is $5^{\\circ}$ and the largest angle is $160^{\\circ}$, then $n$ equals: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 8040,
"solution": "1. **Identify the formula for the sum of interior angles of a polygon**: The sum of the interior angles of a polygon with $n$ sides is given by the formula:\n \\[\n S = 180^\\circ (n-2)\n \\]\n\n2. **Set up the arithmetic sequence**: Given that the angles are ... |
deepscaler | [
{
"role": "user",
"content": "Find the minimum value of\n\\[x^2 + 8x + \\frac{64}{x^3}\\]for $x > 0.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 8041,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Twenty five of King Arthur's knights are seated at their customary round table. Three of them are chosen - all choices being equally likely - and are sent off to slay a troublesome dragon. Let $P$ be the probability that at least two of the three had been sitting next to each o... | math | {
"style": "rule",
"ground_truth": "57"
} | {
"split": "train",
"index": 8042,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Among the two-digit numbers less than 20, the largest prime number is ____, and the largest composite number is ____. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 8043,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given four points $O,\\ A,\\ B,\\ C$ on a plane such that $OA=4,\\ OB=3,\\ OC=2,\\ \\overrightarrow{OB}\\cdot \\overrightarrow{OC}=3.$ Find the maximum area of $\\triangle{ABC}$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{7} + \\frac{3\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 8044,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest two-digit integer $n$ such that switching its digits and then adding 3 results in $2n$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 8045,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Stan has a stack of 100 blocks and starts with a score of 0, and plays a game in which he iterates the following two-step procedure: (a) Stan picks a stack of blocks and splits it into 2 smaller stacks each with a positive number of blocks, say $a$ and $b$. (The order in which ... | math | {
"style": "rule",
"ground_truth": "4950"
} | {
"split": "train",
"index": 8046,
"solution": "Let $E(n)$ be the expected value of the score for an $n$-block game. It suffices to show that the score is invariant regardless of how the game is played. We proceed by induction. We have $E(1)=0$ and $E(2)=1$. We require that $E(n)=E(n-k)+E(k)+(n-k) k$ for all $k$.... |
deepscaler | [
{
"role": "user",
"content": "The maximum point of the function $f(x)=\\frac{1}{3}x^3+\\frac{1}{2}x^2-2x+3$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 8047,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the multiplicative inverse of $201$ modulo $299$. Express your answer as an integer from $0$ to $298$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "180"
} | {
"split": "train",
"index": 8048,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In hexagon $ABCDEF$, $AC$ and $CE$ are two diagonals. Points $M$ and $N$ divide $AC$ and $CE$ internally such that $\\frac{AM}{AC}=\\frac{CN}{CE}=r$. Given that points $B$, $M$, and $N$ are collinear, find $r$. Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 8049,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x=-2016$. What is the value of $|| |x|-x|-|x||-x$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4032"
} | {
"split": "train",
"index": 8050,
"solution": "1. **Substitute the value of \\( x \\)**:\n Given \\( x = -2016 \\), we substitute this into the expression:\n \\[\n \\Bigg\\vert\\Big\\vert |x|-x\\Big\\vert-|x|\\Bigg\\vert-x\n \\]\n\n2. **Simplify \\( |x| \\) and \\( -x \\)**:\n Since \\( x \\) is negati... |
deepscaler | [
{
"role": "user",
"content": "A circular paper with a radius of 6 inches has a section removed to form a \\(240^\\circ\\) sector. This sector is then used to form a right circular cone by bringing the two radii together. Find the circumference of the base of the cone in terms of \\(\\pi\\). Let's think step... | math | {
"style": "rule",
"ground_truth": "8\\pi"
} | {
"split": "train",
"index": 8051,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $99^3 + 3(99^2) + 3(99) + 1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1,\\!000,\\!000"
} | {
"split": "train",
"index": 8052,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find a natural number of the form \\( n = 2^{x} 3^{y} 5^{z} \\), knowing that half of this number has 30 fewer divisors, a third has 35 fewer divisors, and a fifth has 42 fewer divisors than the number itself. Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "2^6 * 3^5 * 5^4"
} | {
"split": "train",
"index": 8053,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$\\triangle PQR$ is similar to $\\triangle XYZ$. What is the number of centimeters in the length of $\\overline{YZ}$? Express your answer as a decimal to the nearest tenth.\n\n[asy]\ndraw((0,0)--(10,-2)--(8,6)--cycle);\nlabel(\"10cm\",(6,3),NW);\nlabel(\"7cm\",(10.2,2.5),NE);\n... | math | {
"style": "rule",
"ground_truth": "5.7"
} | {
"split": "train",
"index": 8054,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At a robot racing competition, a certain number of mechanisms were presented. The robots were paired to race the same distance. The protocol recorded the differences in the finishing times between the winner and the loser in each of the races. All the differences were distinct:... | math | {
"style": "rule",
"ground_truth": "63"
} | {
"split": "train",
"index": 8055,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the arithmetic sequence $\\{a_n\\}$, $a_{10} < 0$, $a_{11} > 0$ and $a_{11} > |a_{10}|$. If the sum of the first $n$ terms of $\\{a_n\\}$, denoted as $S_n$, is less than $0$, the maximum value of $n$ is ____. Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 8056,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of permutations \\((b_1, b_2, b_3, b_4, b_5, b_6)\\) of \\((1,2,3,4,5,6)\\) such that\n\\[\n\\frac{b_1 + 6}{2} \\cdot \\frac{b_2 + 5}{2} \\cdot \\frac{b_3 + 4}{2} \\cdot \\frac{b_4 + 3}{2} \\cdot \\frac{b_5 + 2}{2} \\cdot \\frac{b_6 + 1}{2} > 6!.\n\\] Let's thin... | math | {
"style": "rule",
"ground_truth": "719"
} | {
"split": "train",
"index": 8057,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of $1+2+4+8+16+ \\cdots + 1024$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2047"
} | {
"split": "train",
"index": 8058,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A running track is the ring formed by two concentric circles. If the circumferences of the two circles differ by $10\\pi $ feet, how wide is the track in feet?\n\n[asy]size(100); path g=scale(2)*unitcircle;\nfilldraw(unitcircle^^g,evenodd+grey,black);\n[/asy] Let's think step b... | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 8059,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the paper triangle whose vertices are $(0,0), (34,0),$ and $(16,24).$ The vertices of its midpoint triangle are the midpoints of its sides. A triangular pyramid is formed by folding the triangle along the sides of its midpoint triangle. What is the volume of this pyram... | math | {
"style": "rule",
"ground_truth": "408"
} | {
"split": "train",
"index": 8060,
"solution": "The formed tetrahedron has pairwise parallel planar and oppositely equal length ($4\\sqrt{13},15,17$) edges and can be inscribed in a parallelepiped (rectangular box) with the six tetrahedral edges as non-intersecting diagonals of the box faces. Let the edge lengths... |
deepscaler | [
{
"role": "user",
"content": "The brakes of a car allow it to stay stationary on an inclined asphalt surface with a base angle not exceeding $30^{\\circ}$. Determine the minimum braking distance of this car when traveling at a speed of $30 \\, \\text{m/s}$ on a flat horizontal road with the same surface. Th... | math | {
"style": "rule",
"ground_truth": "78"
} | {
"split": "train",
"index": 8061,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Throw a fair die, and let event $A$ be that the number facing up is even, and event $B$ be that the number facing up is greater than $2$ and less than or equal to $5$. Then, the probability of the complement of event $B$ is ____, and the probability of event $A \\cup B$ is $P(A... | math | {
"style": "rule",
"ground_truth": "\\dfrac{5}{6}"
} | {
"split": "train",
"index": 8062,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest sum of six consecutive prime numbers that is divisible by 5. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 8063,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two right circular cones with vertices facing down as shown in the figure below contain the same amount of liquid. The radii of the tops of the liquid surfaces are $3$ cm and $6$ cm. Into each cone is dropped a spherical marble of radius $1$ cm, which sinks to the bottom and is... | math | {
"style": "rule",
"ground_truth": "4:1"
} | {
"split": "train",
"index": 8064,
"solution": "\n#### Initial Scenario\nLet the heights of the narrow cone and the wide cone be \\( h_1 \\) and \\( h_2 \\), respectively. The volumes of the cones before the marble is dropped are given by:\n\\[\n\\text{Volume of Narrow Cone} = \\frac{1}{3}\\pi(3)^2h_1 = 3\\pi h_1... |
deepscaler | [
{
"role": "user",
"content": "A bar graph shows the number of hamburgers sold by a fast food chain each season. However, the bar indicating the number sold during the winter is covered by a smudge. If exactly $25\\%$ of the chain's hamburgers are sold in the fall, how many million hamburgers are sold in t... | math | {
"style": "rule",
"ground_truth": "2.5"
} | {
"split": "train",
"index": 8065,
"solution": "1. **Identify the total sales in terms of the fall sales**: We are given that the sales in the fall account for exactly $25\\%$ of the total sales. This implies that the fall sales are $\\frac{1}{4}$ of the total sales. Let $T$ represent the total number of hamburge... |
deepscaler | [
{
"role": "user",
"content": "Call a triangle nice if the plane can be tiled using congruent copies of this triangle so that any two triangles that share an edge (or part of an edge) are reflections of each other via the shared edge. How many dissimilar nice triangles are there? Let's think step by step and... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 8066,
"solution": "The triangles are 60-60-60, 45-45-90, 30-60-90, and 30-30-120. We make two observations. - By reflecting \"around\" the same point, any angle of the triangle must be an integer divisor of $360^{\\circ}$. - if any angle is an odd divisor of $360^{\\circ}$, i.e equals... |
deepscaler | [
{
"role": "user",
"content": "In a two-day problem-solving tournament, Alpha and Gamma both attempted questions worth a total of 600 points. Alpha scored 210 points out of 350 points on the first day, and 150 points out of 250 points on the second day. Gamma, who did not attempt 350 points on the first day,... | math | {
"style": "rule",
"ground_truth": "\\frac{359}{600}"
} | {
"split": "train",
"index": 8067,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the maximum number of bishops that can be placed on an $8 \\times 8$ chessboard such that at most three bishops lie on any diagonal? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "38"
} | {
"split": "train",
"index": 8068,
"solution": "If the chessboard is colored black and white as usual, then any diagonal is a solid color, so we may consider bishops on black and white squares separately. In one direction, the lengths of the black diagonals are $2,4,6,8,6,4$, and 2 . Each of these can have at mos... |
deepscaler | [
{
"role": "user",
"content": "Given that $0 < a < \\pi, \\tan a=-2$,\n\n(1) Find the value of $\\cos a$;\n\n(2) Find the value of $2\\sin^{2}a - \\sin a \\cos a + \\cos^{2}a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{11}{5}"
} | {
"split": "train",
"index": 8069,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of six-digit palindromes. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "900"
} | {
"split": "train",
"index": 8070,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the multiplicative inverse of $185$ modulo $341$. Express your answer as an integer from $0$ to $340$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "74466"
} | {
"split": "train",
"index": 8071,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the point \\( A(0,1) \\) and the curve \\( C: y = \\log_a x \\) which always passes through point \\( B \\), if \\( P \\) is a moving point on the curve \\( C \\) and the minimum value of \\( \\overrightarrow{AB} \\cdot \\overrightarrow{AP} \\) is 2, then the real number ... | math | {
"style": "rule",
"ground_truth": "e"
} | {
"split": "train",
"index": 8072,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose $p(x)$ is a monic cubic polynomial with real coefficients such that $p(3-2i)=0$ and $p(0)=-52$.\n\nDetermine $p(x)$ (in expanded form). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x^3-10x^2+37x-52"
} | {
"split": "train",
"index": 8073,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow {OA} = (2, -3)$, $\\overrightarrow {OB} = (-5, 4)$, $\\overrightarrow {OC} = (1-\\lambda, 3\\lambda+2)$:\n1. If $\\triangle ABC$ is a right-angled triangle and $\\angle B$ is the right angle, find the value of the real number $\\lambda$.\n2. If p... | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 8074,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an isosceles triangle \\(ABC\\) (\\(AC = BC\\)), an incircle with radius 3 is inscribed. A line \\(l\\) is tangent to this incircle and is parallel to the side \\(AC\\). The distance from point \\(B\\) to the line \\(l\\) is 3. Find the distance between the points where the ... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{3}"
} | {
"split": "train",
"index": 8075,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Liu and Li, each with one child, go to the park together to play. After buying tickets, they line up to enter the park. For safety reasons, the first and last positions must be occupied by fathers, and the two children must stand together. The number of ways for these 6 people ... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 8076,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a geometric sequence $\\{a_n\\}$ with positive terms, the sum of the first $n$ terms is $S_n$. If $-3$, $S_5$, and $S_{10}$ form an arithmetic sequence, calculate the minimum value of $S_{15} - S_{10}$. Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 8077,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Smith family has 4 sons and 3 daughters. In how many ways can they be seated in a row of 7 chairs such that at least 2 boys are next to each other? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4896"
} | {
"split": "train",
"index": 8078,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In rectangle $ABCD$, $P$ is a point on $BC$ so that $\\angle APD=90^{\\circ}$. $TS$ is perpendicular to $BC$ with $BP=PT$, as shown. $PD$ intersects $TS$ at $Q$. Point $R$ is on $CD$ such that $RA$ passes through $Q$. In $\\triangle PQA$, $PA=20$, $AQ=25$ and $QP=15$. [asy]\... | math | {
"style": "rule",
"ground_truth": "12,9"
} | {
"split": "train",
"index": 8079,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Eight teams participated in a football tournament, and each team played exactly once against each other team. If a match was drawn then both teams received 1 point; if not then the winner of the match was awarded 3 points and the loser received no points. At the end of the tour... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 8080,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let us consider a set $S = \\{ a_1 < a_2 < \\ldots < a_{2004}\\}$ , satisfying the following properties: $f(a_i) < 2003$ and $f(a_i) = f(a_j) \\quad \\forall i, j$ from $\\{1, 2,\\ldots , 2004\\}$ , where $f(a_i)$ denotes number of elements which are relatively prime wi... | math | {
"style": "rule",
"ground_truth": "1003"
} | {
"split": "train",
"index": 8081,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The line with equation $y = 3x + 5$ is translated 2 units to the right. What is the equation of the resulting line? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "y = 3x - 1"
} | {
"split": "train",
"index": 8082,
"solution": "The line with equation $y = 3x + 5$ has slope 3 and $y$-intercept 5. Since the line has $y$-intercept 5, it passes through $(0, 5)$. When the line is translated 2 units to the right, its slope does not change and the new line passes through $(2, 5)$. A line with slo... |
deepscaler | [
{
"role": "user",
"content": "By what common fraction does $0.\\overline{06}$ exceed $0.06$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{1650}"
} | {
"split": "train",
"index": 8083,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Below is the graph of $y = a \\sin (bx + c) + d$ for some positive constants $a,$ $b,$ $c,$ and $d.$ Find $a.$\n\n[asy]import TrigMacros;\n\nsize(400);\n\nreal f(real x)\n{\n\treturn 2*sin(3*x + pi) + 1;\n}\n\ndraw(graph(f,-3*pi,3*pi,n=700,join=operator ..),red);\ntrig_axes(-3... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 8084,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A square in the coordinate plane has vertices whose $y$-coordinates are $0$, $1$, $4$, and $5$. What is the area of the square? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 8085,
"solution": "1. **Identify the vertices and their coordinates**: \n Given that the $y$-coordinates of the vertices of the square are $0$, $1$, $4$, and $5$, we can assume the vertices are $A=(0,0)$, $B=(x_1,1)$, $C=(x_2,5)$, and $D=(x_3,4)$ after a suitable translation.\n\n2. ... |
deepscaler | [
{
"role": "user",
"content": "A person's age at the time of their death was one 31st of their birth year. How old was this person in 1930? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 8086,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( f \\) be a function on \\([0,1]\\) satisfying:\n1. \\( f(0) = 0, f(1) = 1 \\).\n2. For all \\( x, y \\in [0, 1] \\), with \\( x \\leq y \\), \\( f\\left(\\frac{x+y}{2}\\right) = (1-a) f(x) + a f(y) \\), where \\( a \\) is a real number and \\( 0 \\leq a \\leq 1 \\). Fin... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{7}"
} | {
"split": "train",
"index": 8087,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Distribute five students, namely A, B, C, D, and E, to Peking University, Tsinghua University, and Renmin University of China for recommendation, with the condition that each university gets at least one student and student A cannot be recommended to Peking University. How many... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 8088,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Hui is an avid reader. She bought a copy of the best seller Math is Beautiful. On the first day, Hui read $1/5$ of the pages plus $12$ more, and on the second day she read $1/4$ of the remaining pages plus $15$ pages. On the third day she read $1/3$ of the remaining pages plus ... | math | {
"style": "rule",
"ground_truth": "240"
} | {
"split": "train",
"index": 8089,
"solution": "Let $x$ be the total number of pages in the book.\n\n1. **Reading on the first day:**\n Hui reads $\\frac{1}{5}x + 12$ pages. The remaining pages are:\n \\[\n x - \\left(\\frac{1}{5}x + 12\\right) = \\frac{4}{5}x - 12\n \\]\n\n2. **Reading on the second day:... |
deepscaler | [
{
"role": "user",
"content": "Three friends are driving cars on a road in the same direction. At a certain moment, they are positioned relative to each other as follows: Andrews is at a certain distance behind Brooks, and Carter is at a distance twice the distance from Andrews to Brooks, ahead of Brooks. Ea... | math | {
"style": "rule",
"ground_truth": "6.666666666666667"
} | {
"split": "train",
"index": 8090,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Quadrilateral $ABCD$ satisfies $\\angle ABC = \\angle ACD = 90^{\\circ}, AC=20,$ and $CD=30.$ Diagonals $\\overline{AC}$ and $\\overline{BD}$ intersect at point $E,$ and $AE=5.$ What is the area of quadrilateral $ABCD?$ Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "360"
} | {
"split": "train",
"index": 8091,
"solution": "1. **Assign Variables and Use Pythagorean Theorem in $\\triangle ABC$**:\n Let $AB = x$ and $BC = y$. Since $\\angle ABC = 90^\\circ$, by the Pythagorean theorem, we have:\n \\[\n x^2 + y^2 = AC^2 = 20^2 = 400.\n \\]\n\n2. **Calculate $DE$ and Area of $\\tri... |
deepscaler | [
{
"role": "user",
"content": "Let \\( g(x) = x^2 - 4x \\). How many distinct real numbers \\( c \\) satisfy \\( g(g(g(g(c)))) = 2 \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 8092,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the spring round of the 2000 City Tournament, high school students in country $N$ were presented with six problems. Each problem was solved by exactly 1000 students, and no two students solved all six problems together. What is the smallest possible number of high school stu... | math | {
"style": "rule",
"ground_truth": "2000"
} | {
"split": "train",
"index": 8093,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse? Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 8094,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many numbers are in the list $ -33, -28, -23, \\ldots, 52, 57?$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 8095,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A regular dodecagon \\(Q_1 Q_2 \\dotsb Q_{12}\\) is drawn in the coordinate plane with \\(Q_1\\) at \\((1,0)\\) and \\(Q_7\\) at \\((3,0)\\). If \\(Q_n\\) is the point \\((x_n,y_n),\\) compute the numerical value of the product\n\\[(x_1 + y_1 i)(x_2 + y_2 i)(x_3 + y_3 i) \\dots... | math | {
"style": "rule",
"ground_truth": "4095"
} | {
"split": "train",
"index": 8096,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the asymptote equation of the hyperbola $y^{2}+\\frac{x^2}{m}=1$ is $y=\\pm \\frac{\\sqrt{3}}{3}x$, find the value of $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 8097,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the product of the solutions of the equation $-21 = -x^2 + 4x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-21"
} | {
"split": "train",
"index": 8098,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = A\\sin(x + \\varphi)$ ($A > 0$, $0 < \\varphi < \\pi$) has a maximum value of 1, and its graph passes through point M ($\\frac{\\pi}{3}$, $\\frac{1}{2}$), then $f(\\frac{3\\pi}{4})$ = \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "-\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 8099,
"solution": ""
} |
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