data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Let $f(x)$ have a derivative, and satisfy $\\lim_{\\Delta x \\to 0} \\frac{f(1)-f(1-2\\Delta x)}{2\\Delta x}=-1$. Find the slope of the tangent line at point $(1,f(1))$ on the curve $y=f(x)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 2700,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A standard domino game consists of 28 tiles. Each tile is made up of two integers ranging from 0 to 6, inclusive. All possible combinations $(a, b)$, where $a \\leq b$, are listed exactly once. Note that tile $(4,2)$ is listed as tile $(2,4)$, because $2 \\leq 4$. Excluding the... | math | {
"style": "rule",
"ground_truth": "\\frac{13}{2}"
} | {
"split": "train",
"index": 2701,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four circles of radius 1 are externally tangent to each other and internally tangent to a larger circle. What is the radius of the large circle? Express your answer as a common fraction in simplest radical form. Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "1 + \\sqrt{2}"
} | {
"split": "train",
"index": 2702,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain scenic area has two attractions that require tickets for visiting. The three ticket purchase options presented at the ticket office are as follows: \nOption 1: Visit attraction A only, $30$ yuan per person; \nOption 2: Visit attraction B only, $50$ yuan per person; ... | math | {
"style": "rule",
"ground_truth": "188.1"
} | {
"split": "train",
"index": 2703,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a different factor tree, each value is also the product of the two values below it, unless the value is a prime number. Determine the value of $X$ for this factor tree:\n\n[asy]\ndraw((-1,-.3)--(0,0)--(1,-.3),linewidth(1));\ndraw((-2,-1.3)--(-1.5,-.8)--(-1,-1.3),linewidth(1)... | math | {
"style": "rule",
"ground_truth": "4620"
} | {
"split": "train",
"index": 2704,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A gymnastics team consists of 48 members. To form a square formation, they need to add at least ____ people or remove at least ____ people. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 2705,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A list of five positive integers has all of the following properties:\n\n$\\bullet$ The only integer in the list that occurs more than once is $8,$\n\n$\\bullet$ its median is $9,$ and\n\n$\\bullet$ its average (mean) is $10.$\n\nWhat is the largest possible integer that cou... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 2706,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A man asks: \"How old are you, my son?\"\n\nTo this question, I answered:\n\n\"If my father were seven times as old as I was eight years ago, then one quarter of my father's current age would surely be fourteen years now. Please calculate from this how many years weigh upon my ... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 2707,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Tianfu Greenway is a popular check-in spot for the people of Chengdu. According to statistics, there is a linear relationship between the number of tourists on the Tianfu Greenway, denoted as $x$ (in units of 10,000 people), and the economic income of the surrounding busine... | math | {
"style": "rule",
"ground_truth": "88"
} | {
"split": "train",
"index": 2708,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)= \\frac{x}{4} + \\frac{a}{x} - \\ln x - \\frac{3}{2}$, where $a \\in \\mathbb{R}$, and the curve $y=f(x)$ has a tangent at the point $(1,f(1))$ which is perpendicular to the line $y=\\frac{1}{2}x$. \n(i) Find the value of $a$; \n(ii) Determine the int... | math | {
"style": "rule",
"ground_truth": "-\\ln 5"
} | {
"split": "train",
"index": 2709,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For positive integers $N$ and $k$, define $N$ to be $k$-nice if there exists a positive integer $a$ such that $a^{k}$ has exactly $N$ positive divisors. Find the number of positive integers less than $1000$ that are neither $7$-nice nor $8$-nice.\n Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "749"
} | {
"split": "train",
"index": 2710,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\sin \\left(x+ \\frac {\\pi}{3}\\right)= \\frac {1}{3}$, then the value of $\\sin \\left( \\frac {5\\pi}{3}-x\\right)-\\cos \\left(2x- \\frac {\\pi}{3}\\right)$ is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {4}{9}"
} | {
"split": "train",
"index": 2711,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many 10-digit positive integers have all digits either 1 or 2, and have two consecutive 1's?\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "880"
} | {
"split": "train",
"index": 2712,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rotating disc is divided into five equal sectors labeled $A$, $B$, $C$, $D$, and $E$. The probability of the marker stopping on sector $A$ is $\\frac{1}{5}$, the probability of it stopping in $B$ is $\\frac{1}{5}$, and the probability of it stopping in sector $C$ is equal to ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"split": "train",
"index": 2713,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathbf{a} = \\begin{pmatrix} 3 \\\\ 4 \\\\ 0 \\end{pmatrix}$ and $\\mathbf{b} = \\begin{pmatrix} -1 \\\\ 1 \\\\ -1 \\end{pmatrix}.$ Find the unit vector $\\mathbf{v}$ so that $\\mathbf{b}$ bisects the angle between $\\mathbf{a}$ and $\\mathbf{v}.$ Let's think step by st... | math | {
"style": "rule",
"ground_truth": "\\begin{pmatrix} -11/15 \\\\ -2/3 \\\\ -2/15 \\end{pmatrix}"
} | {
"split": "train",
"index": 2714,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three distinct diameters are drawn on a unit circle such that chords are drawn as shown. If the length of one chord is \\(\\sqrt{2}\\) units and the other two chords are of equal lengths, what is the common length of these chords? Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2-\\sqrt{2}}"
} | {
"split": "train",
"index": 2715,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the geometric sequence $\\{a_n\\}$, $(a_1 \\cdot a_2 \\cdot a_3 = 27)$, $(a_2 + a_4 = 30)$, $(q > 0)$\n\nFind:\n$(1)$ $a_1$ and the common ratio $q$;\n\n$(2)$ The sum of the first $6$ terms $(S_6)$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "364"
} | {
"split": "train",
"index": 2716,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two spheres are inscribed in a dihedral angle in such a way that they touch each other. The radius of one sphere is 1.5 times the radius of the other, and the line connecting the centers of the spheres forms an angle of $30^{\\circ}$ with the edge of the dihedral angle. Find th... | math | {
"style": "rule",
"ground_truth": "0.5"
} | {
"split": "train",
"index": 2717,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a chessboard, $n$ white rooks and $n$ black rooks are arranged such that rooks of different colors do not attack each other. Find the maximum possible value of $n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 2718,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\tan \\alpha = -\\frac{4}{3}$, then the value of $\\sin^2\\alpha + 2\\sin \\alpha \\cos \\alpha$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{8}{25}"
} | {
"split": "train",
"index": 2719,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nA phone number \\( d_{1} d_{2} d_{3}-d_{4} d_{5} d_{6} d_{7} \\) is called \"legal\" if the number \\( d_{1} d_{2} d_{3} \\) is equal to \\( d_{4} d_{5} d_{6} \\) or to \\( d_{5} d_{6} d_{7} \\). For example, \\( 234-2347 \\) is a legal phone number. Assume each \\( d_{i} \\)... | math | {
"style": "rule",
"ground_truth": "19990"
} | {
"split": "train",
"index": 2720,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\{1, a, \\frac{b}{a}\\} = \\{0, a^{2}, a+b\\}$, find the value of $a^{2009} + b^{2009}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 2721,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all integers satisfying the equation $ 2^x\\cdot(4\\minus{}x)\\equal{}2x\\plus{}4$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0, 1, 2"
} | {
"split": "train",
"index": 2722,
"solution": "\nTo solve the equation \\(2^x \\cdot (4 - x) = 2x + 4\\) for integer values of \\(x\\), we will analyze the equation step-by-step.\n\n### Step 1: Simplification and Possible Inspection\n\nFirst, it's often useful to inspect possible simple integer solutions that mi... |
deepscaler | [
{
"role": "user",
"content": "6 boys and 4 girls are each assigned as attendants to 5 different buses, with 2 attendants per bus. Assuming that boys and girls are separated, and the buses are distinguishable, how many ways can the assignments be made? Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "5400"
} | {
"split": "train",
"index": 2723,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A new train goes $20\\%$ farther than an older train in the same amount of time. During the time it takes the older train to go 200 miles, how many miles can the newer train complete? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "240"
} | {
"split": "train",
"index": 2724,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Among all proper fractions whose numerator and denominator are two-digit numbers, find the smallest fraction that is greater than \\(\\frac{4}{9}\\). Provide the numerator of this fraction in your answer. Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "41"
} | {
"split": "train",
"index": 2725,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Elective 4-4: Coordinate System and Parametric Equations\n\nGiven the parametric equations of curve \\\\(C\\\\) as \\\\(\\begin{cases}x=2\\cos \\left(\\theta\\right) \\\\ y= \\sqrt{3}\\sin \\left(\\theta\\right)\\end{cases} \\\\), in the same plane Cartesian coordinate system, ... | math | {
"style": "rule",
"ground_truth": "\\dfrac{3\\sqrt{3}}{5}"
} | {
"split": "train",
"index": 2726,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many numbers from $1$ to $150$ are not perfect squares or perfect cubes? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "135"
} | {
"split": "train",
"index": 2727,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many of the 512 smallest positive integers written in base 8 use 5 or 6 (or both) as a digit? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "296"
} | {
"split": "train",
"index": 2728,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x=3$, $y=2x$, and $z=3y$, what is the value of $z$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 2729,
"solution": "Since $x=3$ and $y=2x$, then $y=2 \\cdot 3=6$. Since $y=6$ and $z=3y$, then $z=3 \\cdot 6=18$."
} |
deepscaler | [
{
"role": "user",
"content": "In the geometric sequence $\\{a_n\\}$, if $a_5 + a_6 + a_7 + a_8 = \\frac{15}{8}$ and $a_6a_7 = -\\frac{9}{8}$, then find the value of $\\frac{1}{a_5} + \\frac{1}{a_6} + \\frac{1}{a_7} + \\frac{1}{a_8}$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "-\\frac{5}{3}"
} | {
"split": "train",
"index": 2730,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a finite sequence \\(P = \\left(p_{1}, p_{2}, \\cdots, p_{n}\\right)\\), the Caesar sum (named after a mathematician Caesar) is defined as \\(\\frac{s_{1}+s_{2}+\\cdots+s_{n}}{n}\\), where \\(s_{k} = p_{1} + p_{2} + \\cdots + p_{k}\\) for \\(1 \\leq k \\leq n\\). If a seque... | math | {
"style": "rule",
"ground_truth": "991"
} | {
"split": "train",
"index": 2731,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Nine positive integers $a_1,a_2,...,a_9$ have their last $2$ -digit part equal to $11,12,13,14,15,16,17,18$ and $19$ respectively. Find the last $2$ -digit part of the sum of their squares. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "85"
} | {
"split": "train",
"index": 2732,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A recipe that makes $5$ servings of hot chocolate requires $2$ squares of chocolate, $\\frac{1}{4}$ cup sugar, $1$ cup water and $4$ cups milk. Jordan has $5$ squares of chocolate, $2$ cups of sugar, lots of water, and $7$ cups of milk. If he maintains the same ratio of ingredi... | math | {
"style": "rule",
"ground_truth": "8 \\frac{3}{4}"
} | {
"split": "train",
"index": 2733,
"solution": "To determine the maximum number of servings Jordan can make, we need to calculate the number of servings each ingredient can produce and then find the minimum of these values, as this will be the limiting factor.\n\n1. **Chocolate**: \n - The recipe requires $2$ s... |
deepscaler | [
{
"role": "user",
"content": "For any positive integer $a, \\sigma(a)$ denotes the sum of the positive integer divisors of $a$. Let $n$ be the least positive integer such that $\\sigma(a^n)-1$ is divisible by $2021$ for all positive integers $a$. Find the sum of the prime factors in the prime factorization ... | math | {
"style": "rule",
"ground_truth": "125"
} | {
"split": "train",
"index": 2734,
"solution": "Since the problem works for all positive integers $a$, let's plug in $a=2$ and see what we get. Since $\\sigma({2^n}) = 2^{n+1}-1,$ we have $2^{n+1} \\equiv 2 \\pmod{2021}.$ Simplifying using CRT and Fermat's Little Theorem, we get that $2^n \\equiv 0 \\pmod{42}$ an... |
deepscaler | [
{
"role": "user",
"content": "The values of $k$ for which the equation $2x^2-kx+x+8=0$ will have real and equal roots are: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9 and -7"
} | {
"split": "train",
"index": 2735,
"solution": "To find the values of $k$ for which the quadratic equation $2x^2 - kx + x + 8 = 0$ has real and equal roots, we first simplify the equation:\n\\[ 2x^2 - kx + x + 8 = 0 \\]\n\\[ 2x^2 + (1-k)x + 8 = 0 \\]\n\nFor a quadratic equation $ax^2 + bx + c = 0$, the condition ... |
deepscaler | [
{
"role": "user",
"content": "To $m$ ounces of a $m\\%$ solution of acid, $x$ ounces of water are added to yield a $(m-10)\\%$ solution. If $m>25$, then $x$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{10m}{m-10}"
} | {
"split": "train",
"index": 2736,
"solution": "To solve this problem, we start by analyzing the initial and final conditions of the solution.\n\n1. **Initial Condition:**\n - The initial solution has $m$ ounces of a $m\\%$ solution of acid.\n - This means that the amount of pure acid in the solution is $\\fr... |
deepscaler | [
{
"role": "user",
"content": "What is the largest $5$ digit integer congruent to $17 \\pmod{26}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "99997"
} | {
"split": "train",
"index": 2737,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a function f(x) defined on ℝ that satisfies f(x-2)=f(-2-x), and when x ≥ -2, f(x)=2^x-3. If the function f(x) has a zero point in the interval (k,k+1) (k ∈ ℤ), determine the value of k. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-6"
} | {
"split": "train",
"index": 2738,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\lg 2=0.3010$ and $\\lg 3=0.4771$, at which decimal place does the first non-zero digit of $\\left(\\frac{6}{25}\\right)^{100}$ occur?\n(Shanghai Middle School Mathematics Competition, 1984) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "62"
} | {
"split": "train",
"index": 2739,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the quadratic equation $2x^{2}-1=6x$, the coefficient of the quadratic term is ______, the coefficient of the linear term is ______, and the constant term is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 2740,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nSasha and Misha are playing a game: they take turns naming a number from 1 to 213 (Misha goes first, and the numbers must be different). Then each counts the number of different rectangles with integer sides whose perimeter equals the named number. The one with the greater nu... | math | {
"style": "rule",
"ground_truth": "212"
} | {
"split": "train",
"index": 2741,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given Professor Chen has ten different language books, including two Arabic, four German, and four Spanish books, arranged on the shelf so that the Arabic books are together, the Spanish books are together, and two of the German books are treated as indistinguishable, calculate... | math | {
"style": "rule",
"ground_truth": "576"
} | {
"split": "train",
"index": 2742,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest common factor of 32 and 48? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 2743,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a sequence $\\{a_n\\}$ whose sum of the first $n$ terms is $S_n$, $a_1=15$, and it satisfies $\\frac{a_{n+1}}{2n-3} = \\frac{a_n}{2n-5}+1$, knowing $n$, $m\\in\\mathbb{N}$, and $n > m$, find the minimum value of $S_n - S_m$. Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "-14"
} | {
"split": "train",
"index": 2744,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Point $G$ is placed on side $AD$ of square $WXYZ$. At $Z$, a perpendicular is drawn to $ZG$, meeting $WY$ extended at $H$. The area of square $WXYZ$ is $144$ square inches, and the area of $\\triangle ZGH$ is $72$ square inches. Determine the length of segment $WH$.\nA) $6\\sqr... | math | {
"style": "rule",
"ground_truth": "12\\sqrt{2}"
} | {
"split": "train",
"index": 2745,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ten tiles numbered $1$ through $10$ are turned face down. One tile is turned up at random, and a die is rolled. What is the probability that the product of the numbers on the tile and the die will be a square? Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{60}"
} | {
"split": "train",
"index": 2746,
"solution": "To solve this problem, we need to determine the total number of outcomes and the number of favorable outcomes where the product of the numbers on the tile and the die is a perfect square.\n\n1. **Total Outcomes**: \n - There are 10 tiles, each with a number from 1... |
deepscaler | [
{
"role": "user",
"content": "Given the vectors $\\overrightarrow {a}$ = (1, x) and $\\overrightarrow {b}$ = (2x+3, -x) in the plane, where x ∈ R, they are parallel to each other. Find the magnitude of $\\overrightarrow {a}$ - 2$\\overrightarrow {b}$. Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{5}"
} | {
"split": "train",
"index": 2747,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A square is inscribed in a circle. The number of inches in the perimeter of the square equals the number of square inches in the area of the circumscribed circle. What is the radius, in inches, of the circle? Express your answer in terms of pi. Let's think step by step and put ... | math | {
"style": "rule",
"ground_truth": "\\frac{4\\sqrt{2}}{\\pi}"
} | {
"split": "train",
"index": 2748,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the remainder when $1 + 2 + 3 + 4 + \\dots + 9 + 10$ is divided by 8? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 2749,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a trapezoid, the lengths of the bases are 5 and 15, and the lengths of the diagonals are 12 and 16. Find the area of the trapezoid. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 2750,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If a die is rolled, event \\( A = \\{1, 2, 3\\} \\) consists of rolling one of the faces 1, 2, or 3. Similarly, event \\( B = \\{1, 2, 4\\} \\) consists of rolling one of the faces 1, 2, or 4.\n\nThe die is rolled 10 times. It is known that event \\( A \\) occurred exactly 6 ti... | math | {
"style": "rule",
"ground_truth": "\\frac{16}{3}"
} | {
"split": "train",
"index": 2751,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Gretchen has ten socks, two of each color: red, blue, green, yellow, and purple. She randomly draws six socks. What is the probability that she ends up with exactly two pairs, each of a different color? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{7}"
} | {
"split": "train",
"index": 2752,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The numbers \\(a, b, c, d\\) belong to the interval \\([-8.5, 8.5]\\). Find the maximum value of the expression \\(a + 2b + c + 2d - ab - bc - cd - da\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "306"
} | {
"split": "train",
"index": 2753,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the simplest method to solve the system of equations using substitution $$\\begin{cases} x=2y\\textcircled{1} \\\\ 2x-y=5\\textcircled{2} \\end{cases}$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "y = \\frac{5}{3}"
} | {
"split": "train",
"index": 2754,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an arc length of 50cm and the central angle corresponding to the arc is 200°, (1) find the radius of the circle containing this arc, (2) find the area of the sector formed by this arc and the radius. Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "\\frac{1125}{\\pi}"
} | {
"split": "train",
"index": 2755,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle passes through the midpoints of the hypotenuse $AB$ and the leg $BC$ of the right triangle $ABC$ and touches the leg $AC$. In what ratio does the point of tangency divide the leg $AC$?\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1 : 3"
} | {
"split": "train",
"index": 2756,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The graph of $y = \\frac{p(x)}{q(x)}$ is shown, where $p(x)$ and $q(x)$ are quadratic polynomials. The horizontal asymptote is $y = 2$, and the vertical asymptote is $x = -3$. There is a hole in the graph at $x=4$. \n\nFind $\\frac{p(5)}{q(5)}$ if the graph passes through $(2,0... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 2757,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The numbers \\( a, b, c, d \\) belong to the interval \\([-5, 5]\\). Find the maximum value of the expression \\( a + 2b + c + 2d - ab - bc - cd - da \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "110"
} | {
"split": "train",
"index": 2758,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that in the expansion of $\\left(1+x\\right)^{n}$, the coefficient of $x^{3}$ is the largest, then the sum of the coefficients of $\\left(1+x\\right)^{n}$ is ____. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 2759,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, medians $\\overline{AM}$ and $\\overline{BN}$ are perpendicular. If $AM = 15$ and $BN = 20$, find the length of side $AB$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{50}{3}"
} | {
"split": "train",
"index": 2760,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\(a\\), \\(b\\), and \\(c\\) are positive numbers with \\(ab = 24\\sqrt[3]{3}\\), \\(ac = 40\\sqrt[3]{3}\\), and \\(bc = 15\\sqrt[3]{3}\\), find the value of \\(abc\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "120\\sqrt{3}"
} | {
"split": "train",
"index": 2761,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the domain of the function $f(x)$ is $R$, $f(2x+2)$ is an even function, $f(x+1)$ is an odd function, and when $x\\in [0,1]$, $f(x)=ax+b$. If $f(4)=1$, find the value of $\\sum_{i=1}^3f(i+\\frac{1}{2})$. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2}"
} | {
"split": "train",
"index": 2762,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The distance on the map is 3.6 cm, and the actual distance is 1.2 mm. What is the scale of this map? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "30:1"
} | {
"split": "train",
"index": 2763,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides corresponding to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $a=2$, $b=3$, $\\cos B= \\frac{1}{3}$.\n(1) Find the value of side $c$;\n(2) Find the value of $\\cos (A-C)$. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "\\frac{23}{27}"
} | {
"split": "train",
"index": 2764,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In parallelogram \\(ABCD\\), point \\(P\\) is taken on side \\(BC\\) such that \\(3PB = 2PC\\), and point \\(Q\\) is taken on side \\(CD\\) such that \\(4CQ = 5QD\\). Find the ratio of the area of triangle \\(APQ\\) to the area of triangle \\(PQC\\). Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "37/15"
} | {
"split": "train",
"index": 2765,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Xiaopang arranges the 50 integers from 1 to 50 in ascending order without any spaces in between. Then, he inserts a \"+\" sign between each pair of adjacent digits, resulting in an addition expression: \\(1+2+3+4+5+6+7+8+9+1+0+1+1+\\cdots+4+9+5+0\\). Please calculate the sum of... | math | {
"style": "rule",
"ground_truth": "330"
} | {
"split": "train",
"index": 2766,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(ABCD\\) be a convex quadrilateral with \\(\\angle ABC = 90^\\circ\\), \\(\\angle BAD = \\angle ADC = 80^\\circ\\). Let \\(M\\) and \\(N\\) be points on \\([AD]\\) and \\([BC]\\) such that \\(\\angle CDN = \\angle ABM = 20^\\circ\\). Finally, assume \\(MD = AB\\). What is... | math | {
"style": "rule",
"ground_truth": "70"
} | {
"split": "train",
"index": 2767,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $f(x) = 3-\\!\\sqrt{x}$ and $g(x) = 5x +2x^2$, what is $f(g(-5))$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 2768,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": " $A$ and $B$ are on a circle of radius $20$ centered at $C$ , and $\\angle ACB = 60^\\circ$ . $D$ is chosen so that $D$ is also on the circle, $\\angle ACD = 160^\\circ$ , and $\\angle DCB = 100^\\circ$ . Let $E$ be the intersection of lines $AC$ and $BD$ . Wh... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 2769,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "It is now between 10:00 and 11:00 o'clock, and six minutes from now, the minute hand of a watch will be exactly opposite the place where the hour hand was three minutes ago. What is the exact time now? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "10:15"
} | {
"split": "train",
"index": 2770,
"solution": "To solve this problem, we need to determine the positions of the hour and minute hands at specific times relative to each other.\n\n1. **Understanding the problem**: \n - Let $t$ be the current time in minutes after 10:00. \n - The minute hand moves at a rate of... |
deepscaler | [
{
"role": "user",
"content": "A power locomotive's hourly electricity consumption cost is directly proportional to the cube of its speed. It is known that when the speed is $20$ km/h, the hourly electricity consumption cost is $40$ yuan. Other costs amount to $400$ yuan per hour. The maximum speed of the lo... | math | {
"style": "rule",
"ground_truth": "20 \\sqrt[3]{5}"
} | {
"split": "train",
"index": 2771,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four points are randomly chosen from the vertices of a regular 12-sided polygon. Find the probability that the four chosen points form a rectangle (including square). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1/33"
} | {
"split": "train",
"index": 2772,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The operation $\\nabla$ is defined by $a \\nabla b=4 a+b$. What is the value of $(5 \\nabla 2) \\nabla 2$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 2773,
"solution": "Using the definition, $(5 \\nabla 2) \\nabla 2=(4 \\times 5+2) \\nabla 2=22 \\nabla 2=4 \\times 22+2=90$."
} |
deepscaler | [
{
"role": "user",
"content": "Given that points A and B lie on the graph of y = \\frac{1}{x} in the first quadrant, ∠OAB = 90°, and AO = AB, find the area of the isosceles right triangle ∆OAB. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{5}}{2}"
} | {
"split": "train",
"index": 2774,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive integers $n$ between 1 and 2011 make the equation $(1+i)^{2n} = 2^n i$ hold true, where $i$ is the imaginary unit? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "503"
} | {
"split": "train",
"index": 2775,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the arithmetic sequence $\\{a_n\\}$, it is given that $a_1 > 0$, $a_{2012} + a_{2013} > 0$, and $a_{2012} \\cdot a_{2013} < 0$, calculate the largest natural number n that satisfies S_n > 0. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4024"
} | {
"split": "train",
"index": 2776,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Freshmen go for a long walk in the suburbs after the start of school. They arrive at point \\( A \\) 6 minutes later than the originally planned time of 10:10, and they arrive at point \\( C \\) 6 minutes earlier than the originally planned time of 13:10. There is exactly one p... | math | {
"style": "rule",
"ground_truth": "11:40"
} | {
"split": "train",
"index": 2777,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $(x, y)$ be a pair of real numbers satisfying $$56x+33y=\\frac{-y}{x^{2}+y^{2}}, \\quad \\text { and } \\quad 33x-56y=\\frac{x}{x^{2}+y^{2}}$$ Determine the value of $|x|+|y|$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{11}{65}"
} | {
"split": "train",
"index": 2778,
"solution": "Observe that $$\\frac{1}{x+yi}=\\frac{x-yi}{x^{2}+y^{2}}=33x-56y+(56x+33y)i=(33+56i)(x+yi)$$ So $$(x+yi)^{2}=\\frac{1}{33+56i}=\\frac{1}{(7+4i)^{2}}=\\left(\\frac{7-4i}{65}\\right)^{2}$$ It follows that $(x, y)= \\pm\\left(\\frac{7}{65},-\\frac{4}{65}\\right)$."
} |
deepscaler | [
{
"role": "user",
"content": "Given an arithmetic sequence $\\{a_{n}\\}$ with the sum of the first $n$ terms as $S_{n}$, and a positive geometric sequence $\\{b_{n}\\}$ with the sum of the first $n$ terms as $T_{n}$, where $a_{1}=2$, $b_{1}=1$, and $b_{3}=3+a_{2}$. <br/>$(1)$ If $b_{2}=-2a_{4}$, find the ge... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 2779,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathcal{H}$ be the unit hypercube of dimension 4 with a vertex at $(x, y, z, w)$ for each choice of $x, y, z, w \\in \\{0,1\\}$. A bug starts at the vertex $(0,0,0,0)$. In how many ways can the bug move to $(1,1,1,1)$ by taking exactly 4 steps along the edges of $\\mathc... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 2780,
"solution": "You may think of this as sequentially adding 1 to each coordinate of $(0,0,0,0)$. There are 4 ways to choose the first coordinate, 3 ways to choose the second, and 2 ways to choose the third. The product is 24."
} |
deepscaler | [
{
"role": "user",
"content": "Find the ratio of the volume of the cone to the volume of the cylinder. Express your answer as a common fraction.\n\n[asy]\nimport solids; size(150); import three; defaultpen(linewidth(0.8)); currentprojection = orthographic(5,0,3);\nrevolution c = cylinder((0,0,0), 1, 3);\nrev... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 2781,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What percentage of students did not receive a muffin, given that 38\\% of students received a muffin? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "62\\%"
} | {
"split": "train",
"index": 2782,
"solution": "Since $38\\%$ of students received a muffin, then $100\\% - 38\\% = 62\\%$ of students did not receive a muffin."
} |
deepscaler | [
{
"role": "user",
"content": "In quadrilateral $ABCD$ with diagonals $AC$ and $BD$, intersecting at $O$, suppose $BO=5$, $OD = 7$, $AO=9$, $OC=4$, and $AB=7$. The length of $AD$ is:\n**A)** $15$\n**B)** $\\sqrt{210}$\n**C)** $14$\n**D)** $\\sqrt{220}$\n**E)** $13$ Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "\\sqrt{210}"
} | {
"split": "train",
"index": 2783,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A$ be the set of all real numbers $a$ that satisfy $\\left(a-2\\right)x^{2}+2\\left(a-2\\right)x-4 \\lt 0$ for any $x\\in R$. Let $B$ be the set of all real numbers $x$ that satisfy $\\left(a-2\\right)x^{2}+2\\left(a-2\\right)x-4 \\lt 0$ for any $a\\in \\left[-2,2\\right]$... | math | {
"style": "rule",
"ground_truth": "\\{-1\\}"
} | {
"split": "train",
"index": 2784,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a point $p$ and a line segment $l$, let $d(p, l)$ be the distance between them. Let $A, B$, and $C$ be points in the plane such that $A B=6, B C=8, A C=10$. What is the area of the region in the $(x, y)$-plane formed by the ordered pairs $(x, y)$ such that there exists a ... | math | {
"style": "rule",
"ground_truth": "\\frac{288}{5}"
} | {
"split": "train",
"index": 2785,
"solution": "Place $A B C$ in the coordinate plane so that $A=(0,6), B=(0,0), C=(8,0)$. Consider a point $P=(a, b)$ inside triangle $A B C$. Clearly, $d(P, A B)=a, d(P, B C)=b$. Now, we see that the area of triangle $A B C$ is $\\frac{6 \\cdot 8}{2}=24$, but may also be computed... |
deepscaler | [
{
"role": "user",
"content": "Let $z$ be a nonreal complex number such that $|z| = 1.$ Find the real part of $\\frac{1}{1 - z}.$ 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": 2786,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\sqrt{3}\\cos (\\frac{\\pi }{2}+x)\\bullet \\cos x+\\sin^{2}x$, where $x\\in R$.\n(I) Find the interval where $f(x)$ is monotonically increasing.\n(II) In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. If $... | math | {
"style": "rule",
"ground_truth": "\\frac{3+\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 2787,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the numbers $1$, $2$, $3$, $4$, $5$, randomly select $3$ numbers (with repetition allowed) to form a three-digit number, find the probability that the sum of its digits equals $12$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{2}{25}"
} | {
"split": "train",
"index": 2788,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The probability of an event occurring in each of 900 independent trials is 0.5. Find the probability that the relative frequency of the event will deviate from its probability by no more than 0.02. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.7698"
} | {
"split": "train",
"index": 2789,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the arithmetic sequence $\\{a_n\\}$ satisfy: the common difference $d\\in \\mathbb{N}^*$, $a_n\\in \\mathbb{N}^*$, and any two terms' sum in $\\{a_n\\}$ is also a term in the sequence. If $a_1=3^5$, then the sum of all possible values of $d$ is . Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "364"
} | {
"split": "train",
"index": 2790,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A positive integer $N$ has base-eleven representation $\\underline{a}\\kern 0.1em\\underline{b}\\kern 0.1em\\underline{c}$ and base-eight representation $\\underline1\\kern 0.1em\\underline{b}\\kern 0.1em\\underline{c}\\kern 0.1em\\underline{a},$ where $a,b,$ and $c$ represent ... | math | {
"style": "rule",
"ground_truth": "621"
} | {
"split": "train",
"index": 2791,
"solution": "From the given information, $121a+11b+c=512+64b+8c+a \\implies 120a=512+53b+7c$. Since $a$, $b$, and $c$ have to be positive, $a \\geq 5$. Since we need to minimize the value of $n$, we want to minimize $a$, so we have $a = 5$. Then we know $88=53b+7c$, and we can s... |
deepscaler | [
{
"role": "user",
"content": "Given a triangle $ABC$ with sides opposite angles $A$, $B$, $C$ denoted by $a$, $b$, $c$ respectively, and with $b = 3$, $c = 2$, and the area $S_{\\triangle ABC} = \\frac{3\\sqrt{3}}{2}$:\n1. Determine the value of angle $A$;\n2. When angle $A$ is obtuse, find the height from ... | math | {
"style": "rule",
"ground_truth": "\\frac{3\\sqrt{57}}{19}"
} | {
"split": "train",
"index": 2792,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABCD$ be a parallelogram. Extend $\\overline{DA}$ through $A$ to a point $P,$ and let $\\overline{PC}$ meet $\\overline{AB}$ at $Q$ and $\\overline{DB}$ at $R.$ Given that $PQ = 735$ and $QR = 112,$ find $RC.$ Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "308"
} | {
"split": "train",
"index": 2793,
"solution": "We have $\\triangle BRQ\\sim \\triangle DRC$ so $\\frac{112}{RC} = \\frac{BR}{DR}$. We also have $\\triangle BRC \\sim \\triangle DRP$ so $\\frac{ RC}{847} = \\frac {BR}{DR}$. Equating the two results gives $\\frac{112}{RC} = \\frac{ RC}{847}$ and so $RC^2=112*847$ ... |
deepscaler | [
{
"role": "user",
"content": "Suppose $a$ is a real number such that $\\sin(\\pi \\cdot \\cos a) = \\cos(\\pi \\cdot \\sin a)$ . Evaluate $35 \\sin^2(2a) + 84 \\cos^2(4a)$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 2794,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\cos (\\alpha - \\pi) = -\\frac{5}{13}$, and $\\alpha$ is an angle in the fourth quadrant, find the value of $\\sin (-2\\pi + \\alpha)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{12}{13}"
} | {
"split": "train",
"index": 2795,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the length of the arc of a sector is $\\pi$ and the radius is 3, the radian measure of the central angle of the sector is ______, and the area of the sector is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3\\pi}{2}"
} | {
"split": "train",
"index": 2796,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $y=a^{2x}+2a^{x}-1 (a > 0$ and $a \\neq 1)$, find the value of $a$ when the maximum value of the function is $14$ for the domain $-1 \\leq x \\leq 1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 2797,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A number is composed of 6 millions, 3 tens of thousands, and 4 thousands. This number is written as ____, and when rewritten in terms of \"ten thousands\" as the unit, it becomes ____ ten thousands. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "603.4"
} | {
"split": "train",
"index": 2798,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $3p+4q=8$ and $4p+3q=13$, what is $q$ equal to? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 2799,
"solution": ""
} |
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