data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "What is the smallest prime divisor of $5^{23} + 7^{17}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 1800,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Every morning when Tim wakes up, he groggily searches around his sock drawer and picks two socks randomly. If he has 10 gray-bottomed socks and 8 white-bottomed socks in his drawer, what is the probability that he picks a matching pair? Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "\\frac{73}{153}"
} | {
"split": "train",
"index": 1801,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Five friends sat in a movie theater in a row containing $5$ seats, numbered $1$ to $5$ from left to right. (The directions \"left\" and \"right\" are from the point of view of the people as they sit in the seats.) During the movie Ada went to the lobby to get some popcorn. When... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 1802,
"solution": "To solve this problem, we need to analyze the movements of each friend and determine the original seating arrangement based on the given movements.\n\n1. **Initial Setup**: There are 5 seats, and each friend occupies one seat. Ada leaves, creating one empty seat.\n\... |
deepscaler | [
{
"role": "user",
"content": "Find the volume of the region in space defined by\n\\[|x - y + z| + |x - y - z| \\le 10\\]and $x, y, z \\ge 0$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "125"
} | {
"split": "train",
"index": 1803,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Last summer $30\\%$ of the birds living on Town Lake were geese, $25\\%$ were swans, $10\\%$ were herons, and $35\\%$ were ducks. What percent of the birds that were not swans were geese? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 1804,
"solution": "1. **Assume Total Number of Birds**: Let's assume there are 100 birds in total on Town Lake. This assumption simplifies calculations because all percentages can be directly treated as numbers.\n\n2. **Calculate Number of Each Type of Bird**:\n - Geese: $30\\%$ of ... |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate plane $xOy$, the equation of the ellipse $C$ is $\\frac{x^{2}}{9}+\\frac{y^{2}}{10}=1$. Let $F$ be the upper focus of $C$, $A$ be the right vertex of $C$, and $P$ be a moving point on $C$ located in the first quadrant. Find the maximum value of the a... | math | {
"style": "rule",
"ground_truth": "\\frac{3 \\sqrt{11}}{2}"
} | {
"split": "train",
"index": 1805,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calvin has a bag containing 50 red balls, 50 blue balls, and 30 yellow balls. Given that after pulling out 65 balls at random (without replacement), he has pulled out 5 more red balls than blue balls, what is the probability that the next ball he pulls out is red? Let's think s... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{26}"
} | {
"split": "train",
"index": 1806,
"solution": "Solution 1. The only information this gives us about the number of yellow balls left is that it is even. A bijection shows that the probability that there are $k$ yellow balls left is equal to the probability that there are $30-k$ yellow balls left (flip the colors ... |
deepscaler | [
{
"role": "user",
"content": "A point $P$ lies at the center of square $A B C D$. A sequence of points $\\left\\{P_{n}\\right\\}$ is determined by $P_{0}=P$, and given point $P_{i}$, point $P_{i+1}$ is obtained by reflecting $P_{i}$ over one of the four lines $A B, B C, C D, D A$, chosen uniformly at random... | math | {
"style": "rule",
"ground_truth": "\\frac{1225}{16384}"
} | {
"split": "train",
"index": 1807,
"solution": "Solution 1. WLOG, $A B$ and $C D$ are horizontal line segments and $B C$ and $D A$ are vertical. Then observe that we can consider the reflections over vertical lines separately from those over horizontal lines, as each reflection over a vertical line moves $P_{i}$ ... |
deepscaler | [
{
"role": "user",
"content": "It is known that the variance of each of the given independent random variables does not exceed 4. Determine the number of such variables for which the probability that the deviation of the arithmetic mean of the random variable from the arithmetic mean of their mathematical ex... | math | {
"style": "rule",
"ground_truth": "6400"
} | {
"split": "train",
"index": 1808,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A pentagon is drawn by placing an isosceles right triangle on top of a square as pictured. What percent of the area of the pentagon is the area of the right triangle?\n\n[asy]\nsize(50);\ndraw((0,0)--(0,-1)--(1,-1)--(1,0)--(0,0)--(.5,.5)--(1,0));\n[/asy] Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "20\\%"
} | {
"split": "train",
"index": 1809,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Using only the digits $2,3$ and $9$ , how many six-digit numbers can be formed which are divisible by $6$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"split": "train",
"index": 1810,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define $x\\otimes y=x^3-y$. What is $h\\otimes (h\\otimes h)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "h"
} | {
"split": "train",
"index": 1811,
"solution": "1. **Define the operation $\\otimes$:** Given $x \\otimes y = x^3 - y$.\n\n2. **Calculate $h \\otimes h$:** Using the definition, substitute $x = h$ and $y = h$:\n \\[\n h \\otimes h = h^3 - h.\n \\]\n\n3. **Calculate $h \\otimes (h \\otimes h)$:** Now, substi... |
deepscaler | [
{
"role": "user",
"content": "In a batch of 100 products, there are 98 qualified products and 2 defective ones. During product inspection, 3 products are randomly selected from the 100 products. \n(1) How many different ways are there to select the 3 products? \n(2) How many ways are there to select exact... | math | {
"style": "rule",
"ground_truth": "9604"
} | {
"split": "train",
"index": 1812,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Add $49.213$ to $27.569$, and round your answer to the nearest whole number. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "77"
} | {
"split": "train",
"index": 1813,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $P$ be a point not on line $XZ$ and $Q$ a point on line $XZ$ such that $PQ \\perp XZ.$ Meanwhile, $R$ is a point on line $PZ$ such that $SR \\perp PZ.$ If $SR = 5,$ $PQ = 6,$ and $XZ = 7,$ then what is the length of $PZ?$ Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "8.4"
} | {
"split": "train",
"index": 1814,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest positive integer that must divide the sum of the first ten terms of any arithmetic sequence whose terms are positive integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 1815,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\sqrt{3\\sqrt{s-3}} = \\sqrt[4]{9 - s}$, then find $s$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3.6"
} | {
"split": "train",
"index": 1816,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose there exists a convex $n$-gon such that each of its angle measures, in degrees, is an odd prime number. Compute the difference between the largest and smallest possible values of $n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "356"
} | {
"split": "train",
"index": 1817,
"solution": "We can't have $n=3$ since the sum of the angles must be $180^{\\circ}$ but the sum of three odd numbers is odd. On the other hand, for $n=4$ we can take a quadrilateral with angle measures $83^{\\circ}, 83^{\\circ}, 97^{\\circ}, 97^{\\circ}$. The largest possible va... |
deepscaler | [
{
"role": "user",
"content": "Compute the volumes of the solids obtained by rotating the regions bounded by the graphs of the functions about the y-axis.\n\n$$\ny=x^{3}, \\quad y=x\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4\\pi}{15}"
} | {
"split": "train",
"index": 1818,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A = \\left\\{a_{1}, a_{2}, \\cdots, a_{n}\\right\\}$ be a set of numbers, and let the arithmetic mean of all elements in $A$ be denoted by $P(A)\\left(P(A)=\\frac{a_{1}+a_{2}+\\cdots+a_{n}}{n}\\right)$. If $B$ is a non-empty subset of $A$ such that $P(B) = P(A)$, then $B$ ... | math | {
"style": "rule",
"ground_truth": "51"
} | {
"split": "train",
"index": 1819,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define\n\\[A = \\frac{1}{1^2} + \\frac{1}{5^2} - \\frac{1}{7^2} - \\frac{1}{11^2} + \\frac{1}{13^2} + \\frac{1}{17^2} - \\dotsb,\\]which omits all terms of the form $\\frac{1}{n^2}$ where $n$ is an odd multiple of 3, and\n\\[B = \\frac{1}{3^2} - \\frac{1}{9^2} + \\frac{1}{15^2}... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 1820,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate: $(-2)^{2}+\\sqrt{(-3)^{2}}-\\sqrt[3]{27}+|\\sqrt{3}-2|$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6 - \\sqrt{3}"
} | {
"split": "train",
"index": 1821,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "All positive integers whose digits add up to 14 are listed in increasing order. What is the eleventh number in that list? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "194"
} | {
"split": "train",
"index": 1822,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the two functions $f(x)=x^2+1$ and $g(x)=2x-1$, find $f(g(5))$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "82"
} | {
"split": "train",
"index": 1823,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the intended number is multiplied by 6, then 382 is added to the product, the result is the largest three-digit number written with two identical even digits and one odd digit. Find the intended number. Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "101"
} | {
"split": "train",
"index": 1824,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x,$ $y,$ and $z$ be three positive real numbers whose sum is 1. If no one of these numbers is more than twice any other, then find the minimum value of the product $xyz.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{32}"
} | {
"split": "train",
"index": 1825,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Dad says he is exactly 35 years old, not counting weekends. How old is he really? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "49"
} | {
"split": "train",
"index": 1826,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Distribute 3 male and 2 female freshmen, a total of 5 students, into two classes, Class A and Class B, with each class receiving no fewer than 2 students, and Class A must have at least 1 female student. The number of different distribution schemes is ______. Let's think step b... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 1827,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $xoy$, the parametric equation of line $l$ is $\\begin{cases}x= \\frac{ \\sqrt{2}}{2}t \\\\ y=3+ \\frac{ \\sqrt{2}}{2}t\\end{cases} (t$ is the parameter$)$, in the polar coordinate system with $O$ as the pole and the positive half-axis of $x$ ... | math | {
"style": "rule",
"ground_truth": "\\frac{2 \\sqrt{5}}{3}"
} | {
"split": "train",
"index": 1828,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ron has eight sticks, each having an integer length. He observes that he cannot form a triangle using any three of these sticks as side lengths. The shortest possible length of the longest of the eight sticks is: Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 1829,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The squares of a $3 \\times 3$ grid are filled with positive integers such that 1 is the label of the upperleftmost square, 2009 is the label of the lower-rightmost square, and the label of each square divides the one directly to the right of it and the one directly below it. H... | math | {
"style": "rule",
"ground_truth": "2448"
} | {
"split": "train",
"index": 1830,
"solution": "We factor 2009 as $7^{2} \\cdot 41$ and place the 41 's and the 7 's in the squares separately. The number of ways to fill the grid with 1's and 41 's so that the divisibility property is satisfied is equal to the number of nondecreasing sequences $a_{1}, a_{2}, a_{... |
deepscaler | [
{
"role": "user",
"content": "In a box, there are 2 one-cent coins, 4 five-cent coins, and 6 ten-cent coins. Six coins are drawn in sequence without replacement, and each coin has an equal probability of being selected. What is the probability that the total value of the drawn coins is at least 50 cents? Le... | math | {
"style": "rule",
"ground_truth": "\\frac{127}{924}"
} | {
"split": "train",
"index": 1831,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all real values of $x$ which satisfy\n\\[\\frac{1}{x + 1} + \\frac{6}{x + 5} \\ge 1.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(-5,-2] \\cup (-1,3]"
} | {
"split": "train",
"index": 1832,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=|2x-9|-|x-5|$.<br/>$(1)$ Find the solution set of the inequality $f(x)\\geqslant 2x-1$;<br/>$(2)$ The minimum value of the function $y=f(x)+3|x-5|$ is $m$. For positive real numbers $a$ and $b$ satisfying $\\frac{1}{a}+\\frac{3}{b}=m$, find the minimum ... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 1833,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a certain city, the rules for selecting license plate numbers online are as follows: The last five characters of the plate must include two English letters (with the letters \"I\" and \"O\" not allowed), and the last character must be a number. How many possible combinations... | math | {
"style": "rule",
"ground_truth": "3456000"
} | {
"split": "train",
"index": 1834,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In convex quadrilateral $ABCD$, $AB=8$, $BC=4$, $CD=DA=10$, and $\\angle CDA=60^\\circ$. If the area of $ABCD$ can be written in the form $\\sqrt{a}+b\\sqrt{c}$ where $a$ and $c$ have no perfect square factors (greater than 1), what is $a+b+c$? Let's think step by step and put... | math | {
"style": "rule",
"ground_truth": "259"
} | {
"split": "train",
"index": 1835,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABC$ be a triangle with incenter $I$ and $AB = 1400$ , $AC = 1800$ , $BC = 2014$ . The circle centered at $I$ passing through $A$ intersects line $BC$ at two points $X$ and $Y$ . Compute the length $XY$ .\n\n*Proposed by Evan Chen* Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "1186"
} | {
"split": "train",
"index": 1836,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that point $P$ is a moving point on the curve $y= \\frac {3-e^{x}}{e^{x}+1}$, find the minimum value of the slant angle $\\alpha$ of the tangent line at point $P$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3\\pi}{4}"
} | {
"split": "train",
"index": 1837,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Among the four-digit numbers formed by the digits 0, 1, 2, ..., 9 without repetition, determine the number of cases where the absolute difference between the units digit and the hundreds digit equals 8. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "210"
} | {
"split": "train",
"index": 1838,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Vera has a set of weights, each of which has a distinct mass and weighs an integer number of grams. It is known that the lightest weight in the set weighs 71 times less than the sum of the weights of all other weights in the set. It is also known that the two lightest weights t... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 1839,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the set $E = \\{5, 6, 7, 8, 9\\}$ . For any partition ${A, B}$ of $E$ , with both $A$ and $B$ non-empty, consider the number obtained by adding the product of elements of $A$ to the product of elements of $B$ . Let $N$ be the largest prime number amonh the... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 1840,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all triples $(x; y; p)$ of two non-negative integers $x, y$ and a prime number p such that $ p^x-y^p=1 $ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(0, 0, 2), (1, 1, 2), (2, 2, 3)"
} | {
"split": "train",
"index": 1841,
"solution": "\nThe problem requires us to find all triples \\((x, y, p)\\) consisting of two non-negative integers \\(x\\) and \\(y\\), and a prime number \\(p\\), such that:\n\n\\[\np^x - y^p = 1\n\\]\n\nTo solve this problem, we'll analyze it case by case, beginning with small... |
deepscaler | [
{
"role": "user",
"content": "Find all positive integers \\( n > 1 \\) such that any of its positive divisors greater than 1 has the form \\( a^r + 1 \\), where \\( a \\) is a positive integer and \\( r \\) is a positive integer greater than 1. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 1842,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "One endpoint of a line segment is $(4,3)$ and its midpoint is $(2,9)$. What is the sum of the coordinates of the other endpoint? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 1843,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rachel and Brian are playing a game on a grid with 1 row of 2011 squares. Initially, there is one white checker in each of the first two squares from the left, and one black checker in the third square from the left. At each stage, Rachel can choose to either run or fight. If R... | math | {
"style": "rule",
"ground_truth": "2009"
} | {
"split": "train",
"index": 1844,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A batch of tablets from four different brands was delivered to a computer store. Among them, Lenovo, Samsung, and Huawei tablets made up less than a third of the total, with Samsung tablets being 6 more than Lenovo tablets. All remaining tablets are Apple iPads, and there are t... | math | {
"style": "rule",
"ground_truth": "94"
} | {
"split": "train",
"index": 1845,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Justine has two fair dice, one with sides labeled $1,2,\\ldots, m$ and one with sides labeled $1,2,\\ldots, n.$ She rolls both dice once. If $\\tfrac{3}{20}$ is the probability that at least one of the numbers showing is at most 3, find the sum of all distinct possible va... | math | {
"style": "rule",
"ground_truth": "996"
} | {
"split": "train",
"index": 1846,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of positive divisors of 2002. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 1847,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three spheres with radii $11$, $13$, and $19$ are mutually externally tangent. A plane intersects the spheres in three congruent circles centered at $A$, $B$, and $C$, respectively, and the centers of the spheres all lie on the same side of this plane. Suppose that $AB^2 = 560$... | math | {
"style": "rule",
"ground_truth": "756"
} | {
"split": "train",
"index": 1848,
"solution": "Let the distance between the center of the sphere to the center of those circular intersections as $a,b,c$ separately. $a-11,b-13,c-19$. According to the problem, we have $a^2-11^2=b^2-13^2=c^2-19^2;(11+13)^2-(b-a)^2=560$. After solving we have $b-a=4$, plug this ba... |
deepscaler | [
{
"role": "user",
"content": "Given plane vectors $\\overrightarrow{a}=(-1,2)$ and $\\overrightarrow{b}=(1,-4)$. \n$(1)$ If $4\\overrightarrow{a}+\\overrightarrow{b}$ is perpendicular to $k\\overrightarrow{a}-\\overrightarrow{b}$, find the value of the real number $k$. \n$(2)$ If $\\theta$ is the angle be... | math | {
"style": "rule",
"ground_truth": "-\\frac{3}{4}"
} | {
"split": "train",
"index": 1849,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A regular hexagon is inscribed in an equilateral triangle. If the hexagon has an area of 12, what is the area of the equilateral triangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 1850,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many ways are there to arrange the letters of the word $\\text{ZOO}_1\\text{M}_1\\text{O}_2\\text{M}_2\\text{O}_3$, in which the three O's and the two M's are considered distinct? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5040"
} | {
"split": "train",
"index": 1851,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose $\\cos R = \\frac{4}{9}$ in the diagram below. What is $QS$?\n\n\n\n[asy]\n\npair Q,R,S;\n\nS = (0,0);\n\nQ = (sqrt(65),0);\n\nR = (sqrt(65),-4);\n\ndraw(S--Q--R--S);\n\ndraw(rightanglemark(S,Q,R,13));\n\nlabel(\"$S$\",S,NW);\n\nlabel(\"$Q$\",Q,NE);\n\nlabel(\"$R$\",R,... | math | {
"style": "rule",
"ground_truth": "\\sqrt{65}"
} | {
"split": "train",
"index": 1852,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $x^{2}-5x-2006=0$, evaluate the algebraic expression $\\dfrac {(x-2)^{3}-(x-1)^{2}+1}{x-2}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2010"
} | {
"split": "train",
"index": 1853,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate $$\\sin \\left(1998^{\\circ}+237^{\\circ}\\right) \\sin \\left(1998^{\\circ}-1653^{\\circ}\\right)$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{4}"
} | {
"split": "train",
"index": 1854,
"solution": "We have \\(\\sin \\left(1998^{\\circ}+237^{\\circ}\\right) \\sin \\left(1998^{\\circ}-1653^{\\circ}\\right)=\\sin \\left(2235^{\\circ}\\right) \\sin \\left(345^{\\circ}\\right)=\\sin \\left(75^{\\circ}\\right) \\sin \\left(-15^{\\circ}\\right)=-\\sin \\left(75^{\\ci... |
deepscaler | [
{
"role": "user",
"content": "Let $[x]$ denote the greatest integer not exceeding $x$, for example, $[3.14] = 3$. Then, find the value of $\\left[\\frac{2017 \\times 3}{11}\\right] + \\left[\\frac{2017 \\times 4}{11}\\right] + \\left[\\frac{2017 \\times 5}{11}\\right] + \\left[\\frac{2017 \\times 6}{11}\\ri... | math | {
"style": "rule",
"ground_truth": "6048"
} | {
"split": "train",
"index": 1855,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "John wants to find all the five-letter words that begin and end with the same letter. How many combinations of letters satisfy this property? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "456976"
} | {
"split": "train",
"index": 1856,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a geometric sequence with positive terms $\\{a_n\\}$ and a common ratio of $2$, if $a_ma_n=4a_2^2$, then the minimum value of $\\frac{2}{m}+ \\frac{1}{2n}$ equals \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 1857,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of degrees in the measure of angle $x$.\n\n[asy]\nimport markers;\nsize (5cm,5cm);\npair A,B,C,D,F,H;\n\nA=(0,0);\nB=(5,0);\nC=(9,0);\nD=(3.8,7);\n\nF=(2.3,7.2);\nH=(5.3,7.2);\n\ndraw((4.2,6.1){up}..{right}(5.3,7.2));\ndraw((3.6,6.1){up}..{left}(2.3,7.2));\n\ndr... | math | {
"style": "rule",
"ground_truth": "82^\\circ"
} | {
"split": "train",
"index": 1858,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain brand specialty store is preparing to hold a promotional event during New Year's Day. Based on market research, the store decides to select 4 different models of products from 2 different models of washing machines, 2 different models of televisions, and 3 different m... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 1859,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rectangle $ABCD$ has $AB=6$ and $BC=3$. Point $M$ is chosen on side $AB$ so that $\\angle AMD=\\angle CMD$. What is the degree measure of $\\angle AMD$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "75"
} | {
"split": "train",
"index": 1860,
"solution": "1. **Identify the Given Information**: \n - Rectangle $ABCD$ has sides $AB = 6$ and $BC = 3$.\n - Point $M$ is on side $AB$ such that $\\angle AMD = \\angle CMD$.\n\n2. **Analyze the Angles**:\n - Since $AB \\parallel CD$ (as $ABCD$ is a rectangle), by the Alt... |
deepscaler | [
{
"role": "user",
"content": "Objects $A$ and $B$ move simultaneously in the coordinate plane via a sequence of steps, each of length one. Object $A$ starts at $(0,0)$ and each of its steps is either right or up, both equally likely. Object $B$ starts at $(5,7)$ and each of its steps is either left or down,... | math | {
"style": "rule",
"ground_truth": "0.20"
} | {
"split": "train",
"index": 1861,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that f(x) = |log₃x|, if a and b satisfy f(a - 1) = f(2b - 1), and a ≠ 2b, then the minimum value of a + b is ___. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2} + \\sqrt{2}"
} | {
"split": "train",
"index": 1862,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Create three-digit numbers without repeating digits using the numbers 0, 1, 2, 3, 4, 5: \n(1) How many of them have a ones digit smaller than the tens digit? \n(2) How many of them are divisible by 5? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 1863,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the real numbers $a, x, y$ that satisfy the equation:\n$$\nx \\sqrt{a(x-a)}+y \\sqrt{a(y-a)}=\\sqrt{|\\lg (x-a)-\\lg (a-y)|},\n$$\n\nfind the value of the algebraic expression $\\frac{3 x^{2}+x y-y^{2}}{x^{2}-x y+y^{2}}$. Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 1864,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a sequence $\\{a_{n}\\}$ with the sum of the first $n$ terms denoted as $S_{n}$, $a_{1}=3$, $\\frac{{S}_{n+1}}{{S}_{n}}=\\frac{{3}^{n+1}-1}{{3}^{n}-1}$, $n\\in N^{*}$. \n$(1)$ Find $S_{2}$, $S_{3}$, and the general formula for $\\{a_{n}\\}$; \n$(2)$ Let $b_n=\\frac{a_{n... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{32}"
} | {
"split": "train",
"index": 1865,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Helena needs to save 40 files onto disks, each with 1.44 MB space. 5 of the files take up 1.2 MB, 15 of the files take up 0.6 MB, and the rest take up 0.3 MB. Determine the smallest number of disks needed to store all 40 files. Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 1866,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the reflection of $\\begin{pmatrix} 0 \\\\ 4 \\end{pmatrix}$ over the vector $\\begin{pmatrix} 1 \\\\ 3 \\end{pmatrix}.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\begin{pmatrix} 12/5 \\\\ 16/5 \\end{pmatrix}"
} | {
"split": "train",
"index": 1867,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$2\\left(1-\\frac{1}{2}\\right) + 3\\left(1-\\frac{1}{3}\\right) + 4\\left(1-\\frac{1}{4}\\right) + \\cdots + 10\\left(1-\\frac{1}{10}\\right)=$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 1868,
"solution": "1. **Identify the General Term**: \n Each term in the sequence is of the form $n\\left(1-\\frac{1}{n}\\right)$ for $n$ ranging from $2$ to $10$. Simplifying the expression inside the parentheses:\n \\[\n 1 - \\frac{1}{n} = \\frac{n-1}{n}\n \\]\n Multiplyi... |
deepscaler | [
{
"role": "user",
"content": "A high school basketball team has 16 players, including a set of twins named Bob and Bill, and another set of twins named Tom and Tim. How many ways can we choose 5 starters if no more than one player from each set of twins can be chosen? Let's think step by step and put only t... | math | {
"style": "rule",
"ground_truth": "3652"
} | {
"split": "train",
"index": 1869,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": " $DEB$ is a chord of a circle such that $DE=3$ and $EB=5$ . Let $O$ be the centre of the circle. Join $OE$ and extend $OE$ to cut the circle at $C$ . (See diagram). Given $EC=1$ , find the radius of the circle.\n\n[asy]\nsize(6cm);\n\npair O = (0,0), B = dir(110), D... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 1870,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $6a^2 + 5a + 4 = 3,$ then what is the smallest possible value of $2a + 1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 1871,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The product of two 2-digit numbers is $4536$. What is the smaller of the two numbers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "54"
} | {
"split": "train",
"index": 1872,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( a > b \\), the quadratic inequality \\( ax^{2}+2x+b \\geqslant 0 \\) holds for all real numbers \\( x \\), and there exists \\( x_{0} \\in \\mathbb{R} \\) such that \\( ax_{0}^{2}+2x_{0}+b=0 \\) is satisfied. Find the minimum value of \\( 2a^{2}+b^{2} \\). Let's think... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}"
} | {
"split": "train",
"index": 1873,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For the power of $n$ of natural numbers $m$ greater than or equal to 2, the following decomposition formula exists:\n\n$2^2 = 1 + 3$, $3^2 = 1 + 3 + 5$, $4^2 = 1 + 3 + 5 + 7 \\ldots$\n\n$2^3 = 3 + 5$, $3^3 = 7 + 9 + 11 \\ldots$\n\n$2^4 = 7 + 9 \\ldots$\n\nBased on this pattern,... | math | {
"style": "rule",
"ground_truth": "125"
} | {
"split": "train",
"index": 1874,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A group of $10$ students from Class 9(1) of a certain school are doing \"pull-up\" training. The number of times they have done it is recorded in the table below. Find the median of the number of times these $10$ students have done.\n\n| Times | $4$ | $5$ | $6$ | $7$ | $8$ |\n|... | math | {
"style": "rule",
"ground_truth": "5.5"
} | {
"split": "train",
"index": 1875,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(a\\), \\(b\\), \\(c\\), and \\(d\\) be positive integers with \\(a < 3b\\), \\(b < 4c\\), and \\(c < 5d\\). If \\(d < 80\\), find the largest possible value for \\(a\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4724"
} | {
"split": "train",
"index": 1876,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a modified function $C' = \\frac{2en}{R + 2nr}$, where $e = 4$, $R = 6$, and $r = 3$. Determine the behavior of $C'$ as $n$ increases from a positive starting point. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{3}"
} | {
"split": "train",
"index": 1877,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Julia's garden has a 3:7 ratio of tulips to daisies. She currently has 35 daisies. She plans to add 30 more daisies and wants to plant additional tulips to maintain the original ratio. How many tulips will she have after this addition? Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 1878,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(x) = 2a^{x} - 2a^{-x}$ where $a > 0$ and $a \\neq 1$. <br/> $(1)$ Discuss the monotonicity of the function $f(x)$; <br/> $(2)$ If $f(1) = 3$, and $g(x) = a^{2x} + a^{-2x} - 2f(x)$, $x \\in [0,3]$, find the minimum value of $g(x)$. Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 1879,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The lengths of the three sides of a triangle are \\( 10 \\), \\( y+5 \\), and \\( 3y-2 \\). The perimeter of the triangle is \\( 50 \\). What is the length of the longest side of the triangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25.75"
} | {
"split": "train",
"index": 1880,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a tetrahedron \\(ABCD\\), \\(\\angle ADB = \\angle BDC = \\angle CDA = 60^\\circ\\). The areas of \\(\\triangle ADB\\), \\(\\triangle BDC\\), and \\(\\triangle CDA\\) are \\(\\frac{\\sqrt{3}}{2}\\), \\(2\\), and \\(1\\) respectively. What is the volume of the tetrahedron? Le... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{6}}{9}"
} | {
"split": "train",
"index": 1881,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a 4x4 grid with points that are equally spaced horizontally and vertically, where the distance between two neighboring points is 1 unit. Two triangles are formed: Triangle A connects points at (0,0), (3,2), and (2,3), while Triangle B connects points at (0,3), (3,3), a... | math | {
"style": "rule",
"ground_truth": "0.5"
} | {
"split": "train",
"index": 1882,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the product of all possible real values for $k$ such that the system of equations $$ x^2+y^2= 80 $$ $$ x^2+y^2= k+2x-8y $$ has exactly one real solution $(x,y)$ .\n\n*Proposed by Nathan Xiong* Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "960"
} | {
"split": "train",
"index": 1883,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a point P(3, 2) outside the circle $x^2+y^2-2x-2y+1=0$, find the cosine of the angle between the two tangents drawn from this point to the circle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 1884,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Fibonacci sequence starts with two 1s, and each term afterwards is the sum of its two predecessors. Determine the last digit to appear in the units position of a number in the Fibonacci sequence when considered modulo 12. Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 1885,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\log _{3}(9x) \\cdot \\log _{3}(3x)$, where $\\frac {1}{9}\\leqslant x\\leqslant 9$.\n(I) If $m=\\log _{3}x$, find the range of $m$;\n(II) Find the maximum and minimum values of $f(x)$, and provide the corresponding $x$ values. Let's think step by step... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 1886,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the inequality $x\\ln x - kx > 3$, which holds true for any $x > 1$, determine the maximum value of the integer $k$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 1887,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $C$ be the graph of $xy = 1$, and denote by $C^*$ the reflection of $C$ in the line $y = 2x$. Let the equation of $C^*$ be written in the form\n\\[12x^2 + bxy + cy^2 + d = 0.\\]\n Find the product $bc$. Let's think step by step and put only the final answer within \\boxed{}... | math | {
"style": "rule",
"ground_truth": "84"
} | {
"split": "train",
"index": 1888,
"solution": "Find some simple points on the graph of C, reflect them and note down the new coordinates, and plug 'em into the given equation. After some plugging and chugging and solving the system of equations that follow, we get that $b = -7$ and $c = -12$, so $bc = 84$. The a... |
deepscaler | [
{
"role": "user",
"content": "John earned scores of 92, 85, and 91 on his first three physics examinations. If John receives a score of 95 on his fourth exam, then by how much will his average increase? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1.42"
} | {
"split": "train",
"index": 1889,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A permutation of \\{1,2, \\ldots, 7\\} is chosen uniformly at random. A partition of the permutation into contiguous blocks is correct if, when each block is sorted independently, the entire permutation becomes sorted. For example, the permutation $(3,4,2,1,6,5,7)$ can be parti... | math | {
"style": "rule",
"ground_truth": "\\frac{151}{105}"
} | {
"split": "train",
"index": 1890,
"solution": "Let $\\sigma$ be a permutation on \\{1, \\ldots, n\\}. Call $m \\in\\{1, \\ldots, n\\}$ a breakpoint of $\\sigma$ if $\\{\\sigma(1), \\ldots, \\sigma(m)\\}=$ $\\{1, \\ldots, m\\}$. Notice that the maximum partition is into $k$ blocks, where $k$ is the number of brea... |
deepscaler | [
{
"role": "user",
"content": "Joe now randomly chooses with equal probabilities either an apple, an orange, a banana, a pear, or a grape to eat for each of his three meals a day, and this goes on for two consecutive days. What is the probability that over these two days, Joe will eat at least two different ... | math | {
"style": "rule",
"ground_truth": "\\frac{15620}{15625}"
} | {
"split": "train",
"index": 1891,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Every day at noon, a scheduled ship departs from Moscow to Astrakhan and from Astrakhan to Moscow. The ship traveling from Moscow takes exactly four days to reach Astrakhan, then stays there for two days, and at noon two days after its arrival in Astrakhan, it departs back to M... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 1892,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many integers between $1500$ and $2500$ have the property that their units digit is the sum of the other digits?\n**A)** $76$ \n**B)** $81$ \n**C)** $85$ \n**D)** $91$ \n**E)** $96$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"split": "train",
"index": 1893,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A number is the product of four prime numbers. What is this number if the sum of the squares of the four prime numbers is 476? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1989"
} | {
"split": "train",
"index": 1894,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two lines have the same non-zero $y$-intercept. The first line has a slope of 10 and an $x$-intercept of $(s, 0)$. The second line has a slope of 6 and an $x$-intercept of $(t, 0)$. What is the ratio of $s $ to $t$? Express your answer as a common fraction. Let's think step by ... | math | {
"style": "rule",
"ground_truth": "\\frac 35"
} | {
"split": "train",
"index": 1895,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $a$, $b$, $c$ form an arithmetic sequence in triangle $ABC$, $\\angle B=30^{\\circ}$, and the area of $\\triangle ABC$ is $\\frac{1}{2}$, determine the value of $b$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3+ \\sqrt{3}}{3}"
} | {
"split": "train",
"index": 1896,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many ordered pairs $(m,n)$ of positive integers, with $m \\ge n$, have the property that their squares differ by $96$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 1897,
"solution": "To find the number of ordered pairs $(m,n)$ of positive integers such that $m \\ge n$ and $m^2 - n^2 = 96$, we start by factoring the expression for the difference of squares:\n\n\\[ m^2 - n^2 = (m+n)(m-n) = 96. \\]\n\nWe need to find all pairs of factors of $96$ th... |
deepscaler | [
{
"role": "user",
"content": "Find the value of $x$ for the following expressions.\n1. $4x^2 = 9$\n2. $(1 - 2x)^3 = 8$ 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": 1898,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(a\\), \\(b\\), \\(c\\), and \\(d\\) be distinct positive integers such that \\(a+b\\), \\(a+c\\), and \\(a+d\\) are all odd and are all squares. Let \\(L\\) be the least possible value of \\(a + b + c + d\\). What is the value of \\(10L\\)? Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "670"
} | {
"split": "train",
"index": 1899,
"solution": ""
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.