data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Points $P$ and $Q$ are 3 units apart. A circle centered at $P$ with a radius of $\\sqrt{3}$ units intersects a circle centered at $Q$ with a radius of 3 units at points $A$ and $B$. Find the area of quadrilateral APBQ. Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "\\frac{3 \\sqrt{11}}{2}"
} | {
"split": "train",
"index": 34049,
"solution": "The area is twice the area of triangle $A P Q$, which is isosceles with side lengths $3,3, \\sqrt{3}$. By Pythagoras, the altitude to the base has length $\\sqrt{3^{2}-(\\sqrt{3} / 2)^{2}}=\\sqrt{33} / 2$, so the triangle has area $\\frac{\\sqrt{99}}{4}$. Double th... |
deepscaler | [
{
"role": "user",
"content": "Before the soccer match between the \"North\" and \"South\" teams, five predictions were made:\n\na) There will be no draw;\n\nb) \"South\" will concede goals;\n\nc) \"North\" will win;\n\nd) \"North\" will not lose;\n\ne) Exactly 3 goals will be scored in the match.\n\nAfter t... | math | {
"style": "rule",
"ground_truth": "2-1"
} | {
"split": "train",
"index": 34050,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that Fox wants to ensure he has 20 coins left after crossing the bridge four times, and paying a $50$-coin toll each time, determine the number of coins that Fox had at the beginning. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 34051,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Identical matches of length 1 are used to arrange the following pattern. If \\( c \\) denotes the total length of matches used, find \\( c \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "700"
} | {
"split": "train",
"index": 34052,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Cut a 12cm long thin iron wire into three segments with lengths a, b, and c, \n(1) Find the maximum volume of the rectangular solid with lengths a, b, and c as its dimensions; \n(2) If these three segments each form an equilateral triangle, find the minimum sum of the areas o... | math | {
"style": "rule",
"ground_truth": "\\frac {4 \\sqrt {3}}{3}"
} | {
"split": "train",
"index": 34053,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the sum of the first $n$ terms of the sequence ${a_n}$ is $S_n$, and $S_n + \\frac{1}{3}a_n = 1 (n \\in \\mathbb{N}^*)$.\n(I) Find the general term formula of the sequence ${a_n}$;\n(II) Let $b_n = \\log_4(1 - S_{n+1}) (n \\in \\mathbb{N}^*)$, $T_n = \\frac{1}{b_1b_2... | math | {
"style": "rule",
"ground_truth": "2014"
} | {
"split": "train",
"index": 34054,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\cos(\\frac{1}{2}x-\\frac{π}{3})$, the graph is shifted to the right by $φ(0＜φ＜\\frac{π}{2})$ units to obtain the graph of the function $g(x)$, and $g(x)+g(-x)=0$. Determine the value of $g(2φ+\\frac{π}{6})$. Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{6}+\\sqrt{2}}{4}"
} | {
"split": "train",
"index": 34055,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $f(n) = n^2 + n + 17$, what is the value of $f(11)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "149"
} | {
"split": "train",
"index": 34056,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum\n$$\n\\frac{1}{1 \\times 2 \\times 3}+\\frac{1}{2 \\times 3 \\times 4}+\\frac{1}{3 \\times 4 \\times 5}+\\cdots+\\frac{1}{100 \\times 101 \\times 102}\n$$\ncan be expressed as $\\frac{a}{b}$, a fraction in its simplest form. Find $a+b$. Let's think step by step and put ... | math | {
"style": "rule",
"ground_truth": "12877"
} | {
"split": "train",
"index": 34057,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of terms in the expansion of $[(a+3b)^{2}(a-3b)^{2}]^{2}$ when simplified is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 34058,
"solution": "1. **Simplify the given expression**: \n Start by applying the property of exponents to the expression $[(a+3b)^2(a-3b)^2]^2$:\n \\[\n [(a+3b)^2(a-3b)^2]^2 = [(a+3b)(a-3b)]^4\n \\]\n This simplification uses the property that $(x^m)^n = x^{mn}$ and the fa... |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $C$ with one focus at $F_{1}(2,0)$ and the corresponding directrix $x=8$, and eccentricity $e=\\frac{1}{2}$.\n\n$(1)$ Find the equation of the ellipse $C$;\n\n$(2)$ Find the length of the chord cut from the ellipse $C$ by a line passing through the other focus ... | math | {
"style": "rule",
"ground_truth": "\\frac{48}{7}"
} | {
"split": "train",
"index": 34059,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC,$ if median $\\overline{AD}$ makes an angle of $45^\\circ$ with side $\\overline{BC},$ then find the value of $|\\cot B - \\cot C|.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 34060,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function f(x) = 2/(x+1) for a positive number x, calculate the sum of f(100) + f(99) + f(98) + ... + f(2) + f(1) + f(1/2) + ... + f(1/98) + f(1/99) + f(1/100). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "199"
} | {
"split": "train",
"index": 34061,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $r$ and $s$ are the roots of $x^2-px+q=0$, then $r^2+s^2$ equals: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "p^2-2q"
} | {
"split": "train",
"index": 34062,
"solution": "1. **Identify the relationship between roots and coefficients**: Given the quadratic equation $x^2 - px + q = 0$, by Vieta's formulas, we know:\n - The sum of the roots $r+s = p$.\n - The product of the roots $rs = q$.\n\n2. **Express $r^2 + s^2$ using the sum ... |
deepscaler | [
{
"role": "user",
"content": "The states of Sunshine and Prairie have adopted new license plate configurations. Sunshine license plates are formatted \"LDDLDL\" where L denotes a letter and D denotes a digit. Prairie license plates are formatted \"LDDLDD\". Assuming all 10 digits and 26 letters are equally ... | math | {
"style": "rule",
"ground_truth": "10816000"
} | {
"split": "train",
"index": 34063,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A line $l$ in the coordinate plane has the equation $2x - 3y + 30 = 0$. This line is rotated $90^\\circ$ counterclockwise about the point $(15,10)$ to obtain line $k'$. Find the $x$-coordinate of the $x$-intercept of $k'$. Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "\\frac{65}{3}"
} | {
"split": "train",
"index": 34064,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the parabola $C:y^{2}=8x$ with focus $F$ and directrix $l$. $P$ is a point on $l$ and the line $(PF)$ intersects the parabola $C$ at points $M$ and $N$. If $\\overrightarrow{{PF}}=3\\overrightarrow{{MF}}$, find the length of the segment $MN$. Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "\\frac{32}{3}"
} | {
"split": "train",
"index": 34065,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Several sets of prime numbers, such as $\\{7,83,421,659\\}$ use each of the nine nonzero digits exactly once. What is the smallest possible sum such a set of primes could have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "207"
} | {
"split": "train",
"index": 34066,
"solution": "1. **Identify the constraints on the digits of prime numbers**: \n - Prime numbers greater than 2 are odd, so they cannot end in an even digit (0, 2, 4, 6, 8).\n - Additionally, a prime number cannot end in 5 unless it is 5 itself, because any other number endi... |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the sum of all positive integers $n$ such that $\\frac{3}{5}$ of the positive divisors of $n$ are multiples of $6$ and $n$ has no prime divisors greater than $3$ . Compute $\\frac{S}{36}$ . Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "2345"
} | {
"split": "train",
"index": 34067,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Barry has three sisters. The average age of the three sisters is 27. The average age of Barry and his three sisters is 28. What is Barry's age? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 34068,
"solution": "Since the average age of the three sisters is 27, then the sum of their ages is $3 \times 27=81$. When Barry is included the average age of the four people is 28, so the sum of the ages of the four people is $4 \times 28=112$. Barry's age is the difference between ... |
deepscaler | [
{
"role": "user",
"content": "The average of a set of distinct primes is 27. What is the largest prime that can be in this set? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "139"
} | {
"split": "train",
"index": 34069,
"solution": "Denote the set of these primes by $A$ and the number of elements in $A$ by n. There are 9 primes smaller than 27, namely $2,3,5,7,11,13,17,19$ and 23. Since 27 is odd and all primes except 2 are odd, $2 \\notin A$. Thus the largest prime $p$ is at most $27 \\cdot 9... |
deepscaler | [
{
"role": "user",
"content": "Find the focus of the the parabola $y = x^2.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left( 0, \\frac{1}{4} \\right)"
} | {
"split": "train",
"index": 34070,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Football tickets are normally priced at $15 each. After buying 5 tickets, any additional tickets are sold at a discounted price of $12 each. If Jane has $150, what is the maximum number of tickets she can buy? Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 34071,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From six balls numbered respectively $1$, $2$, $3$, $4$, $5$, $6$, which are all of the same size, three balls are randomly drawn. Find the probability that exactly two of the balls have consecutive numbers. Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "\\dfrac{3}{5}"
} | {
"split": "train",
"index": 34072,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In how many ways can the numbers $1,2, \\ldots, 2002$ be placed at the vertices of a regular 2002-gon so that no two adjacent numbers differ by more than 2? (Rotations and reflections are considered distinct.) Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "4004"
} | {
"split": "train",
"index": 34073,
"solution": "4004. There are 2002 possible positions for the 1. The two numbers adjacent to the 1 must be 2 and 3; there are two possible ways of placing these. The positions of these numbers uniquely determine the rest: for example, if 3 lies clockwise from 1, then the number ... |
deepscaler | [
{
"role": "user",
"content": "There are $n$ students in the math club. When grouped in 4s, there is one incomplete group. When grouped in 3s, there are 3 more complete groups than with 4s, and one incomplete group. When grouped in 2s, there are 5 more complete groups than with 3s, and one incomplete group. ... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 34074,
"solution": "Suppose that, when the $n$ students are put in groups of 2, there are $g$ complete groups and 1 incomplete group. Since the students are being put in groups of 2, an incomplete group must have exactly 1 student in it. Therefore, $n=2g+1$. Since the number of comple... |
deepscaler | [
{
"role": "user",
"content": "The construction rule of the sequence $\\{a_{n}\\}$ is as follows: $a_{1}=1$, if $a_{n}-2$ is a natural number and has not appeared before, then use the recursive formula $a_{n+1}=a_{n}-2$. Otherwise, use the recursive formula $a_{n+1}=3a_{n}$, then $a_{6}=$ _____. Let's think ... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 34075,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(p\\) be the answer to this question. If a point is chosen uniformly at random from the square bounded by \\(x=0, x=1, y=0\\), and \\(y=1\\), what is the probability that at least one of its coordinates is greater than \\(p\\)? Let's think step by step and put only the fi... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{5}-1}{2}"
} | {
"split": "train",
"index": 34076,
"solution": "The probability that a randomly chosen point has both coordinates less than \\(p\\) is \\(p^{2}\\), so the probability that at least one of its coordinates is greater than \\(p\\) is \\(1-p^{2}\\). Since \\(p\\) is the answer to this question, we have \\(1-p^{2}=p\... |
deepscaler | [
{
"role": "user",
"content": "Find the sum of $10_{10} + 23_{10}$, first by converting each number to base 3, performing the addition in base 3, and then converting the result back to base 10. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "33"
} | {
"split": "train",
"index": 34077,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A parabola with equation $y=x^2+bx+c$ passes through the points $(-1,-11)$ and $(3,17)$. What is $c$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-7"
} | {
"split": "train",
"index": 34078,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest 3-digit base 8 positive integer that is divisible by 5? (Express your answer in base 8.) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "776_8"
} | {
"split": "train",
"index": 34079,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $(a_1,b_1),$ $(a_2,b_2),$ $\\dots,$ $(a_{100},b_{100})$ are distinct ordered pairs of nonnegative integers. Let $N$ denote the number of pairs of integers $(i,j)$ satisfying $1\\leq i<j\\leq 100$ and $|a_ib_j-a_jb_i|=1$. Determine the largest possible value of $N$ ... | math | {
"style": "rule",
"ground_truth": "197"
} | {
"split": "train",
"index": 34080,
"solution": "\nTo determine the largest possible value of \\( N \\) over all possible choices of 100 distinct ordered pairs of nonnegative integers \\((a_i, b_i)\\), we analyze pairs \\((i, j)\\) such that \\(1 \\leq i < j \\leq 100\\) and \\(|a_i b_j - a_j b_i| = 1\\).\n\nThis... |
deepscaler | [
{
"role": "user",
"content": "Let $(x_1,y_1),$ $(x_2,y_2),$ $\\dots,$ $(x_n,y_n)$ be the solutions to\n\\begin{align*}\n|x - 3| &= |y - 9|, \\\\\n|x - 9| &= 2|y - 3|.\n\\end{align*}Find $x_1 + y_1 + x_2 + y_2 + \\dots + x_n + y_n.$ Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "-4"
} | {
"split": "train",
"index": 34081,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ S $ be the set of all sides and diagonals of a regular hexagon. A pair of elements of $ S $ are selected at random without replacement. What is the probability that the two chosen segments have the same length? Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "\\frac{17}{35}"
} | {
"split": "train",
"index": 34082,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a tournament there are six teams that play each other twice. A team earns $3$ points for a win, $1$ point for a draw, and $0$ points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the gre... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 34083,
"solution": "1. **Understanding the Tournament Setup**: In this tournament, there are six teams, and each team plays every other team twice. This results in a total of $\\binom{6}{2} \\times 2 = 15 \\times 2 = 30$ games played in the tournament.\n\n2. **Scoring System**: Each t... |
deepscaler | [
{
"role": "user",
"content": "Find $k$ if\n\\[(\\sin \\alpha + \\csc \\alpha)^2 + (\\cos \\alpha + \\sec \\alpha)^2 = k + \\tan^2 \\alpha + \\cot^2 \\alpha.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 34084,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of natural numbers from 1 to 1992 that are multiples of 3, but not multiples of 2 or 5, is\n\n(Ninth \"Jinyun Cup\" Middle School Mathematics Invitational Competition, 1992) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "266"
} | {
"split": "train",
"index": 34085,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cube has eight vertices (corners) and twelve edges. A segment, such as $x$, which joins two vertices not joined by an edge is called a diagonal. Segment $y$ is also a diagonal. How many diagonals does a cube have? [asy]\n/* AMC8 1998 #17 Problem */\npair A=(0,48), B=(0,0), C=... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 34086,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sequence of positive integers $a_1,a_2,\\ldots $ is such that for each $m$ and $n$ the following holds: if $m$ is a divisor of $n$ and $m<n$ , then $a_m$ is a divisor of $a_n$ and $a_m<a_n$ . Find the least possible value of $a_{2000}$ . Let's think step by s... | math | {
"style": "rule",
"ground_truth": "128"
} | {
"split": "train",
"index": 34087,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the USA, dates are written as: month number, then day number, and year. In Europe, the format is day number, then month number, and year. How many days in a year are there whose dates cannot be interpreted unambiguously without knowing which format is being used? Let's think... | math | {
"style": "rule",
"ground_truth": "132"
} | {
"split": "train",
"index": 34088,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a = \\pi/2008$. Find the smallest positive integer $n$ such that\\[2[\\cos(a)\\sin(a) + \\cos(4a)\\sin(2a) + \\cos(9a)\\sin(3a) + \\cdots + \\cos(n^2a)\\sin(na)]\\]is an integer.\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "251"
} | {
"split": "train",
"index": 34089,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Cory made a complete list of the prime numbers between 1 and 25. What is the sum of the smallest prime number and the largest prime number on his list? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 34090,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many ordered pairs of positive integers $(M,N)$ satisfy the equation $\\frac{M}{6}=\\frac{6}{N}?$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 34091,
"solution": "1. **Start with the given equation and cross-multiply:**\n \\[\n \\frac{M}{6} = \\frac{6}{N} \\implies M \\cdot N = 36\n \\]\n\n2. **Factorize 36 into pairs of positive integers:**\n \\[\n 36 = 1 \\cdot 36, \\quad 2 \\cdot 18, \\quad 3 \\cdot 12, \\quad 4... |
deepscaler | [
{
"role": "user",
"content": "A workshop produces products of types $A$ and $B$. Producing one unit of product $A$ requires 10 kg of steel and 23 kg of non-ferrous metals, while producing one unit of product $B$ requires 70 kg of steel and 40 kg of non-ferrous metals. The profit from selling one unit of pro... | math | {
"style": "rule",
"ground_truth": "2180"
} | {
"split": "train",
"index": 34092,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "(1) Let the function $f(x)=|x+2|+|x-a|$. If the inequality $f(x) \\geqslant 3$ always holds for $x$ in $\\mathbb{R}$, find the range of the real number $a$.\n\n(2) Given positive numbers $x$, $y$, $z$ satisfying $x+2y+3z=1$, find the minimum value of $\\frac{3}{x}+\\frac{2}{y}+... | math | {
"style": "rule",
"ground_truth": "16+8\\sqrt{3}"
} | {
"split": "train",
"index": 34093,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The angles of quadrilateral $ABCD$ satisfy $\\angle A = 2\\angle B =\n3\\angle C = 4\\angle D$. What is the degree measure of $\\angle A$, rounded to the nearest whole number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "173"
} | {
"split": "train",
"index": 34094,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the ratio of the area of a square inscribed in a semicircle with radius $r$ to the area of a square inscribed in a circle with radius $r$? Express your answer as a common fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{2}{5}"
} | {
"split": "train",
"index": 34095,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a, b, c, x$ be reals with $(a+b)(b+c)(c+a) \\neq 0$ that satisfy $$\\frac{a^{2}}{a+b}=\\frac{a^{2}}{a+c}+20, \\quad \\frac{b^{2}}{b+c}=\\frac{b^{2}}{b+a}+14, \\quad \\text { and } \\quad \\frac{c^{2}}{c+a}=\\frac{c^{2}}{c+b}+x$$ Compute $x$. Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "-34"
} | {
"split": "train",
"index": 34096,
"solution": "Note that $$\\begin{aligned} \\frac{a^{2}}{a+b}+\\frac{b^{2}}{b+c}+\\frac{c^{2}}{c+a}-\\frac{a^{2}}{c+a}-\\frac{b^{2}}{a+b}-\\frac{c^{2}}{b+c} & =\\frac{a^{2}-b^{2}}{a+b}+\\frac{b^{2}-c^{2}}{b+c}+\\frac{c^{2}-a^{2}}{c+a} \\\\ & =(a-b)+(b-c)+(c-a) \\\\ & =0 \\end{al... |
deepscaler | [
{
"role": "user",
"content": "Theo's watch is 10 minutes slow, but he believes it is 5 minutes fast. Leo's watch is 5 minutes fast, but he believes it is 10 minutes slow. At the same moment, each of them looks at his own watch. Theo thinks it is 12:00. What time does Leo think it is?\n\nA) 11:30 \nB) 11:45... | math | {
"style": "rule",
"ground_truth": "12:30"
} | {
"split": "train",
"index": 34097,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Xiaoming forgot how to write $egg$ and only remembered there were three letters $e$, $g$, $g$. He randomly wrote one of them. Calculate the probability that he wrote it correctly. 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": 34098,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given parallelogram $ABCD$ with $E$ the midpoint of diagonal $BD$. Point $E$ is connected to a point $F$ in $DA$ so that $DF=\\frac{1}{3}DA$. What is the ratio of the area of $\\triangle DFE$ to the area of quadrilateral $ABEF$? Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "1/5"
} | {
"split": "train",
"index": 34099,
"solution": "1. **Assumption of Coordinates**: Assume $ABCD$ is a unit square for simplicity, with coordinates $A(0, 0)$, $B(0, 1)$, $C(1, 1)$, and $D(1, 0)$. \n\n2. **Locating Point $E$**: Since $E$ is the midpoint of diagonal $BD$, we find $E$ by averaging the coordinates of ... |
deepscaler | [
{
"role": "user",
"content": "What is the total number of digits used when the first 1500 positive odd integers are written? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5445"
} | {
"split": "train",
"index": 34100,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sequence of even counting numbers starting from $0$, find the sum of the first $1500$ terms. Then, given the sequence of odd counting numbers, find the sum of the first $1500$ terms, and calculate their difference. Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "1500"
} | {
"split": "train",
"index": 34101,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 700 cards in a box, in six colors: red, orange, yellow, green, blue, and white. The ratio of the number of red, orange, and yellow cards is $1: 3: 4$, and the ratio of the number of green, blue, and white cards is $3:1:6$. Given that there are 50 more yellow cards tha... | math | {
"style": "rule",
"ground_truth": "312"
} | {
"split": "train",
"index": 34102,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The product underwent a price reduction from 25 yuan to 16 yuan. Calculate the average percentage reduction for each price reduction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20\\%"
} | {
"split": "train",
"index": 34103,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of six consecutive positive integers is 2013. What is the largest of these six integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "338"
} | {
"split": "train",
"index": 34104,
"solution": "Let the six consecutive integers be $n, n+1, n+2, n+3, n+4, n+5$. The sum of these integers can be expressed as:\n\\[\nn + (n+1) + (n+2) + (n+3) + (n+4) + (n+5) = 6n + 15\n\\]\nWe are given that this sum equals 2013:\n\\[\n6n + 15 = 2013\n\\]\nTo solve for $n$, we ... |
deepscaler | [
{
"role": "user",
"content": "Find the number of real solutions to the equation\n\\[\\frac{1}{x - 1} + \\frac{2}{x - 2} + \\frac{3}{x - 3} + \\dots + \\frac{120}{x - 120} = x.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "121"
} | {
"split": "train",
"index": 34105,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A thin diverging lens with an optical power of $D_{p} = -6$ diopters is illuminated by a beam of light with a diameter $d_{1} = 10$ cm. On a screen positioned parallel to the lens, a light spot with a diameter $d_{2} = 20$ cm is observed. After replacing the thin diverging lens... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 34106,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $Y$ be as in problem 14. Find the maximum $Z$ such that three circles of radius $\\sqrt{Z}$ can simultaneously fit inside an equilateral triangle of area $Y$ without overlapping each other. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10 \\sqrt{3}-15"
} | {
"split": "train",
"index": 34107,
"solution": "We first find that, in problem 15, each of the circles of radius $\\sqrt{Z}$ is the incircle of a $30^{\\circ}-60^{\\circ}-90^{\\circ}$ triangle formed by cutting the equilateral one in half. The equilateral triangle itself has sidelength $\\frac{2 \\sqrt{Y}}{\\sqr... |
deepscaler | [
{
"role": "user",
"content": "In the arithmetic sequence $\\{a\\_n\\}$, $a_{66} < 0$, $a_{67} > 0$, and $a_{67} > |a_{66}|$. $S_{n}$ denotes the sum of the first $n$ terms of the sequence. Find the smallest value of $n$ such that $S_{n} > 0$. Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "132"
} | {
"split": "train",
"index": 34108,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a segment of length $2$ with endpoints $A$ and $B$ sliding respectively on the $x$-axis and $y$-axis, the midpoint $M$ of segment $AB$ traces curve $C$. \n(Ⅰ) Find the equation of curve $C$; \n(Ⅱ) Point $P(x,y)$ is a moving point on curve $C$, find the range of values f... | math | {
"style": "rule",
"ground_truth": "t=\\lambda= \\frac {3}{2}"
} | {
"split": "train",
"index": 34109,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "While hiking in a valley, a hiker first walks 15 miles north, then 8 miles east, then 9 miles south, and finally 2 miles east. How far is the hiker from the starting point after completing these movements? Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{34}"
} | {
"split": "train",
"index": 34110,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Identical regular pentagons are arranged in a ring. Each of the regular pentagons has a perimeter of 65. The regular polygon formed as the inner boundary of the ring has a perimeter of \\( P \\). What is the value of \\( P \\)? Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "130"
} | {
"split": "train",
"index": 34111,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many of the natural numbers from 1 to 1000, inclusive, contain the digit 5 at least once? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "270"
} | {
"split": "train",
"index": 34112,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jo, Blair, and Parker take turns counting from 1, increasing by one more than the last number said by the previous person. What is the $100^{\\text{th}}$ number said? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 34113,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Tom adds up all the even integers from 2 to 600, inclusive. Lara adds up all the integers from 1 to 200, inclusive. What is Tom's sum divided by Lara's sum? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4.5"
} | {
"split": "train",
"index": 34114,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a selection of $2$ algebra questions and $3$ geometry questions, one question is randomly selected each time without replacement. Let $A=$\"selecting an algebra question first\" and $B=$\"selecting a geometry question second\". Find $P\\left(AB\\right)=\\_\\_\\_\\_\\_\\_$ an... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 34115,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An obtuse triangle with positive area has side lengths 10, 17, and \\(x\\). If \\(x\\) is an integer, what is the sum of all possible values of \\(x\\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "224"
} | {
"split": "train",
"index": 34116,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $a=2 \\int_{-3}^{3} (x+|x|) \\, dx$, determine the total number of terms in the expansion of $(\\sqrt{x} - \\frac{1}{\\sqrt[3]{x}})^a$ where the power of $x$ is not an integer. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 34117,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A team won $40$ of its first $50$ games. How many of the remaining $40$ games must this team win so it will have won exactly $70 \\%$ of its games for the season? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 34118,
"solution": "1. **Identify the total number of games and the desired win percentage**: The team plays a total of $50 + 40 = 90$ games in the season and aims to win 70% of these games. \n\n2. **Convert the percentage to a fraction**: The fraction corresponding to 70% is $\\frac{... |
deepscaler | [
{
"role": "user",
"content": "Given that a class selects 4 athletes from 5 male and 4 female track and field athletes to participate in the competition, where the selection must include both male and female athletes, and at least one of the male athlete A or female athlete B must be selected, calculate the ... | math | {
"style": "rule",
"ground_truth": "86"
} | {
"split": "train",
"index": 34119,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two cells in a \\(20 \\times 20\\) board are adjacent if they have a common edge (a cell is not considered adjacent to itself). What is the maximum number of cells that can be marked in a \\(20 \\times 20\\) board such that every cell is adjacent to at most one marked cell? Let... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 34120,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A bag contains 3 red balls, 2 black balls, and 1 white ball. All 6 balls are identical in every aspect except for color and are well mixed. Balls are randomly drawn from the bag.\n(1) With replacement, find the probability of drawing exactly 1 red ball in 2 consecutive draws;\n... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 34121,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram below, angle $ABC$ is a right angle. Point $D$ is on $\\overline{BC}$, and $\\overline{AD}$ bisects angle $CAB$. Points $E$ and $F$ are on $\\overline{AB}$ and $\\overline{AC}$, respectively, so that $AE=3$ and $AF=10$. Given that $EB=9$ and $FC=27$, find the int... | math | {
"style": "rule",
"ground_truth": "148"
} | {
"split": "train",
"index": 34122,
"solution": "By the Pythagorean Theorem, $BC=35$. By the Angle Bisector Theorem $BD = 60/7$ and $DC = 185/7$. We can find the coordinates of F, and use that the find the equation of line EF. Then, we can find the coordinates of G. Triangle $ADC = 1110/7$ and we can find the are... |
deepscaler | [
{
"role": "user",
"content": "What is the sum of all values of $x$ for which $\\sqrt{(x+3)^{2}} = 7$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-6"
} | {
"split": "train",
"index": 34123,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Circles $P$, $Q$, and $R$ are externally tangent to each other and internally tangent to circle $S$. Circles $Q$ and $R$ are congruent. Circle $P$ has radius 2 and passes through the center of $S$. What is the radius of circle $Q$? Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "\\frac{16}{9}"
} | {
"split": "train",
"index": 34124,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given two circles $x^2+y^2=a^2$ and $x^2+y^2+ay-6=0$ have a common chord with a length of $2\\sqrt{3}$, find the value of $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 34125,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine how many integer values of $n$ between 1 and 180 inclusive ensure that the decimal representation of $\\frac{n}{180}$ terminates. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 34126,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the expanded country of Mathlandia, all automobile license plates have five symbols. The first two must be vowels (A, E, I, O, U), the next two must be different non-vowels among the 21 non-vowels in the alphabet, and the fifth must be a digit (0 through 9). Determine the pr... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{105,000}"
} | {
"split": "train",
"index": 34127,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a plane, 100 points are marked. It turns out that 40 marked points lie on each of two different lines \\( a \\) and \\( b \\). What is the maximum number of marked points that can lie on a line that does not coincide with \\( a \\) or \\( b \\)? Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 34128,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $x^3y = k$ for a positive constant $k$, find the percentage decrease in $y$ when $x$ increases by $20\\%$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "42.13\\%"
} | {
"split": "train",
"index": 34129,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jessica works at a bakery, and every day she makes 30 pie crusts that each use up $\\frac16$ cup of flour. One day, she decides that she instead wants to make 20 larger pie crusts using the same total amount of flour. How many cups of flour will go into each of the new crusts? ... | math | {
"style": "rule",
"ground_truth": "\\frac14"
} | {
"split": "train",
"index": 34130,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the set\n$$\nT=\\left\\{n \\mid n=5^{a}+5^{b}, 0 \\leqslant a \\leqslant b \\leqslant 30, a, b \\in \\mathbf{Z}\\right\\},\n$$\nif a number is randomly selected from set $T$, what is the probability that the number is a multiple of 9? Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "5/31"
} | {
"split": "train",
"index": 34131,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of ways $66$ identical coins can be separated into three nonempty piles so that there are fewer coins in the first pile than in the second pile and fewer coins in the second pile than in the third pile. Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "331"
} | {
"split": "train",
"index": 34132,
"solution": "Suppose we have $1$ coin in the first pile. Then $(1, 2, 63), (1, 3, 62), \\ldots, (1, 32, 33)$ all work for a total of $31$ piles. Suppose we have $2$ coins in the first pile, then $(2, 3, 61), (2, 4, 60), \\ldots, (2, 31, 33)$ all work, for a total of $29$. Conti... |
deepscaler | [
{
"role": "user",
"content": "Four prime numbers are randomly selected without replacement from the first ten prime numbers. What is the probability that the sum of the four selected numbers is odd? Express your answer as a common fraction. Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{5}"
} | {
"split": "train",
"index": 34133,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many integers are there between 0 and \\( 10^5 \\) having the digit sum equal to 8? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "495"
} | {
"split": "train",
"index": 34134,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A tangent line is drawn from a point on the line $y=x$ to the circle $(x-4)^2 + (y+2)^2 = 1$. Find the minimum length of the tangent line. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{17}"
} | {
"split": "train",
"index": 34135,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the hyperbola $C$: $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$ ($a > 0, b > 0$) with asymptotic equations $y = \\pm \\sqrt{3}x$, and $O$ as the origin, the point $M(\\sqrt{5}, \\sqrt{3})$ lies on the hyperbola.\n\n$(1)$ Find the equation of the hyperbola $C$.\n\n$(2)$ If a ... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 34136,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given real numbers $a$ and $b$ satisfying $ab=1$, and $a>b\\geq \\frac{2}{3}$, the maximum value of $\\frac{a-b}{a^{2}+b^{2}}$ is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{30}{97}"
} | {
"split": "train",
"index": 34137,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The graph of \\[\\sqrt{(x-1)^2+(y+2)^2} - \\sqrt{(x-5)^2+(y+2)^2} = 3\\]consists of one branch of a hyperbola. Compute the positive value for the slope of an asymptote of the hyperbola. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt7}{3}"
} | {
"split": "train",
"index": 34138,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find (in terms of $n \\geq 1$) the number of terms with odd coefficients after expanding the product: $\\prod_{1 \\leq i<j \\leq n}\\left(x_{i}+x_{j}\\right)$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "n!"
} | {
"split": "train",
"index": 34139,
"solution": "Note that if we take $(\\bmod 2)$, we get that $\\prod_{1 \\leq i<j \\leq n}\\left(x_{i}+x_{j}\\right) \\equiv \\prod_{1 \\leq i<j \\leq n}\\left(x_{j}-x_{i}\\right)=\\operatorname{det}(M)$ where $M$ is the matrix with $M_{ij}=x_{i}^{j-1}$. This is called a Vanderm... |
deepscaler | [
{
"role": "user",
"content": "Two cards are dealt from a standard deck of 52 cards. What is the probability that the first card dealt is a $\\heartsuit$ and the second card dealt is a $\\clubsuit$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{13}{204}"
} | {
"split": "train",
"index": 34140,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an ant crawling inside an equilateral triangle with side length $4$, calculate the probability that the distance from the ant to all three vertices of the triangle is more than $1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1- \\dfrac { \\sqrt {3}\\pi}{24}"
} | {
"split": "train",
"index": 34141,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We draw 6 circles of equal radius on the surface of a unit sphere such that the circles do not intersect. What is the maximum possible radius of these circles?\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 34142,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The population of a city increases annually by $1 / 50$ of the current number of inhabitants. In how many years will the population triple? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "55"
} | {
"split": "train",
"index": 34143,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For any integer $k\\geq 1$, let $p(k)$ be the smallest prime which does not divide $k.$ Define the integer function $X(k)$ to be the product of all primes less than $p(k)$ if $p(k)>2$, and $X(k)=1$ if $p(k)=2.$ Let $\\{x_n\\}$ be the sequence defined by $x_0=1$, and $x_{n+1}X(x... | math | {
"style": "rule",
"ground_truth": "149"
} | {
"split": "train",
"index": 34144,
"solution": "We go through the terms and look for a pattern. We find that\n$x_0 = 1$ $x_8 = 7$\n$x_1 = 2$ $x_9 = 14$\n$x_2 = 3$ $x_{10} = 21$\n$x_3 = 6$ $x_{11} = 42$\n$x_4 = 5$ $x_{12} = 35$\n$x_5 = 10$ $x_{13} = 70$\n$x_6 = 15$ $x_{14} = 105$\n$x_7 = 30$ $x_{15} = 210$\n Comm... |
deepscaler | [
{
"role": "user",
"content": "Elective 4-4: Coordinate System and Parametric Equations\n\nIn the Cartesian coordinate system $xOy$, the parametric equation of line $l_1$ is $\\begin{cases} x=2+t \\\\ y=kt \\end{cases}$ ($t$ is the parameter), and the parametric equation of line $l_2$ is $\\begin{cases} x=-2... | math | {
"style": "rule",
"ground_truth": "\\sqrt{5}"
} | {
"split": "train",
"index": 34145,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "During the night shift, four duty personnel ate a whole barrel of pickles. If Assistant Mur ate half as much, one-tenth of the barrel would remain. If Lab Technician Trott ate half as much, one-eighth of the barrel would remain. If Intern Glupp ate half as much, one-quarter of ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{40}"
} | {
"split": "train",
"index": 34146,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given points $P(\\sqrt{3}, 1)$, $Q(\\cos x, \\sin x)$, and $O$ as the origin of coordinates, the function $f(x) = \\overrightarrow{OP} \\cdot \\overrightarrow{QP}$\n\n(Ⅰ) Find the smallest positive period of the function $f(x)$;\n\n(Ⅱ) If $A$ is an internal angle of $\\triangle... | math | {
"style": "rule",
"ground_truth": "3 + 2\\sqrt{3}"
} | {
"split": "train",
"index": 34147,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Tom's favorite number is between $100$ and $150$. It is a multiple of $13$, but not a multiple of $3$. The sum of its digits is a multiple of $4$. What is Tom's favorite number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "143"
} | {
"split": "train",
"index": 34148,
"solution": ""
} |
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