data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "A student named Zhang has a set of 6 questions to choose from, with 4 categorized as type A and 2 as type B. Zhang randomly selects 2 questions to solve. \n(1) What is the probability that both selected questions are type A? \n(2) What is the probability that the selected que... | math | {
"style": "rule",
"ground_truth": "\\frac{8}{15}"
} | {
"index": 3800,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student needs to provide his waist size in centimeters for a customized lab coat, based on the measurements in inches. If there are $10$ inches in a foot and $25$ centimeters in a foot, then what size should the student specify in centimeters if his waist size is $40$ inches?... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 3801,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student passes through three intersections with traffic lights, labeled \\\\(A\\\\), \\\\(B\\\\), and \\\\(C\\\\), on the way to school. It is known that the probabilities of encountering a red light at intersections \\\\(A\\\\), \\\\(B\\\\), and \\\\(C\\\\) are \\\\( \\dfrac... | math | {
"style": "rule",
"ground_truth": "\\dfrac {235}{3}"
} | {
"index": 3802,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student reads a book, reading 35 pages on the first day and then 5 more pages each subsequent day, until only 35 pages are left on the last day. The second time he reads it, he reads 45 pages on the first day and then 5 more pages each subsequent day, until only 40 pages are ... | math | {
"style": "rule",
"ground_truth": "385"
} | {
"index": 3803,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student recorded the exact percentage frequency distribution for a set of measurements, as shown below.\nHowever, the student neglected to indicate $N$, the total number of measurements. What is the smallest possible value of $N$?\n\\begin{tabular}{c c}\\text{measured value}&... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 3804,
"solution": "1. **Understanding the Problem:**\n The problem provides a frequency distribution in percentages for a set of measurements. We need to find the smallest possible total number of measurements, $N$, such that all the given percentages can be converted into integer counts of measurement... |
DeepScaleR | [
{
"role": "user",
"content": "A student research group at a school found that the attention index of students during class changes with the listening time. At the beginning of the lecture, students' interest surges; then, their interest remains in a relatively ideal state for a while, after which students' ... | math | {
"style": "rule",
"ground_truth": "\\dfrac {85}{3}"
} | {
"index": 3805,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student rolls two dice simultaneously, and the scores obtained are a and b respectively. The eccentricity e of the ellipse $\\frac{x^{2}}{a^{2}}+ \\frac{y^{2}}{b^{2}}=1$ (a > b > 0) is greater than $\\frac{\\sqrt{3}}{2}$. What is the probability of this happening?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"index": 3806,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student travels from his university to his hometown, a distance of 150 miles, in a sedan that averages 25 miles per gallon. For the return trip, he drives his friend's truck, which averages only 15 miles per gallon. Additionally, they make a detour of 50 miles at an average o... | math | {
"style": "rule",
"ground_truth": "16.67"
} | {
"index": 3807,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student typed out several circles on the computer as follows: ○●○○●○○○●○○○○●○○○○○●… If this pattern continues, forming a series of circles, then the number of ● in the first 120 circles is ______."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 3808,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student types the following pattern on a computer (where '〇' represents an empty circle and '●' represents a solid circle): 〇●〇〇●〇〇〇●〇〇〇〇●... If this pattern of circles continues, what is the number of solid circles among the first 2019 circles?"
}
] | math | {
"style": "rule",
"ground_truth": "62"
} | {
"index": 3809,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student used the \"five-point method\" to draw the graph of the function $f(x)=A\\sin(\\omega x+\\varphi)$ ($\\omega\\ \\gt 0$, $|\\varphi|＜\\frac{π}{2}$) within one period. The student listed and filled in some of the data in the table below:\n\n| $\\omega x+\\varphi$ | $0$ ... | math | {
"style": "rule",
"ground_truth": "\\frac{7\\pi}{24}"
} | {
"index": 3810,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student walks from intersection $A$ to intersection $B$ in a city layout as described: the paths allow him to move only east or south. Every morning, he walks from $A$ to $B$, but now he needs to pass through intersections $C$ and then $D$. The paths from $A$ to $C$ have 3 ea... | math | {
"style": "rule",
"ground_truth": "\\frac{15}{77}"
} | {
"index": 3811,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student's final score on a 150-point test is directly proportional to the time spent studying multiplied by a difficulty factor for the test. The student scored 90 points on a test with a difficulty factor of 1.5 after studying for 2 hours. What score would the student receiv... | math | {
"style": "rule",
"ground_truth": "300"
} | {
"index": 3812,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student's score on a 150-point test is directly proportional to the hours she studies. If she scores 90 points after studying for 2 hours, what would her score be if she studied for 5 hours?"
}
] | math | {
"style": "rule",
"ground_truth": "225"
} | {
"index": 3813,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student's written work has a two-grade evaluation system; i.e., the work will either pass if it is done well, or fail if it is done poorly. The works are first checked by a neural network that gives incorrect answers in 10% of cases, and then all works deemed failed are reche... | math | {
"style": "rule",
"ground_truth": "69"
} | {
"index": 3814,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student, Alex, is required to do a specified number of homework assignments to earn homework points using a different system: for the first four points, each point requires one homework assignment; for the next four points (points 5-8), each requires two homework assignments;... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 3815,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student, Ellie, was supposed to calculate $x-y-z$, but due to a misunderstanding, she computed $x-(y+z)$ and obtained 18. The actual answer should have been 6. What is the value of $x-y$?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 3816,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student, Leo, needs to earn 30 study points for a special credit. For the first 6 points, he needs to complete 1 project each. For the next 6 points, he needs 2 projects each; for the next 6 points, 3 projects each, and so on. Determine the minimum number of projects Leo need... | math | {
"style": "rule",
"ground_truth": "90"
} | {
"index": 3817,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student, Liam, wants to earn a total of 30 homework points. For earning the first four homework points, he has to do one homework assignment each; for the next four points, he has to do two homework assignments each; and so on, such that for every subsequent set of four point... | math | {
"style": "rule",
"ground_truth": "128"
} | {
"index": 3818,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student, Theo, needs to earn a total of 30 homework points. For the first six homework points, he has to do one assignment each; for the next six points, he needs to do two assignments each; and so on, such that for every subsequent set of six points, the number of assignment... | math | {
"style": "rule",
"ground_truth": "186"
} | {
"index": 3819,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A subscriber forgot the last digit of a phone number and therefore dials it randomly. What is the probability that they will have to dial the number no more than three times?"
}
] | math | {
"style": "rule",
"ground_truth": "0.3"
} | {
"index": 3820,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A subset $B$ of $\\{1, 2, \\dots, 2017\\}$ is said to have property $T$ if any three elements of $B$ are the sides of a nondegenerate triangle. Find the maximum number of elements that a set with property $T$ may contain."
}
] | math | {
"style": "rule",
"ground_truth": "1009"
} | {
"index": 3821,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A subset $M$ of $\\{1, 2, . . . , 2006\\}$ has the property that for any three elements $x, y, z$ of $M$ with $x < y < z$ , $x+ y$ does not divide $z$ . Determine the largest possible size of $M$ ."
}
] | math | {
"style": "rule",
"ground_truth": "1004"
} | {
"index": 3822,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A subset $S$ of the nonnegative integers is called supported if it contains 0, and $k+8, k+9 \\in S$ for all $k \\in S$. How many supported sets are there?"
}
] | math | {
"style": "rule",
"ground_truth": "1430"
} | {
"index": 3823,
"solution": "Note that every supported set $S$ contains $0,8,9,16,17,18,24-27,32-36,40-45$, 48-54, and all $n \\geq 55$. Now define $\\bar{S}:=\\mathbb{Z}^{+} \\backslash S$, which is a subset of $\\{1-7,10-15,19-23,28-31,37,38,39,46,47,55\\}$ satisfying the opposite property that $k \\in \\bar{S} ... |
DeepScaleR | [
{
"role": "user",
"content": "A subset $S$ of the set $\\{1,2, \\ldots, 10\\}$ is chosen randomly, with all possible subsets being equally likely. Compute the expected number of positive integers which divide the product of the elements of $S$. (By convention, the product of the elements of the empty set is... | math | {
"style": "rule",
"ground_truth": "\\frac{375}{8}"
} | {
"index": 3824,
"solution": "For primes $p=2,3,5,7$, let the random variable $X_{p}$ denote the number of factors of $p$ in the product of the elements of $S$, plus 1 . Then we wish to find $\\mathbb{E}\\left(X_{2} X_{3} X_{5} X_{7}\\right)$. If there were only prime powers between 1 and 10, then all $X_{p}$ would... |
DeepScaleR | [
{
"role": "user",
"content": "A subset \\( H \\) of the set of numbers \\(\\{1, 2, \\ldots, 100\\}\\) has the property that if an element is in \\( H \\), then ten times that element is not in \\( H \\). What is the maximum number of elements that \\( H \\) can have?"
}
] | math | {
"style": "rule",
"ground_truth": "91"
} | {
"index": 3825,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A subset \\( S \\) of the set of integers \\{ 0, 1, 2, ..., 99 \\} is said to have property \\( A \\) if it is impossible to fill a 2x2 crossword puzzle with the numbers in \\( S \\) such that each number appears only once. Determine the maximal number of elements in sets \\( S... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 3826,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A subset of a student group is called an [i]ideal company[/i] if\n1) in this subset, all girls are liked by all young men,\n2) no one can be added to this subset without violating condition $1$.\nIn a certain group, $9$ female students and $15$ students study. Warden of the gro... | math | {
"style": "rule",
"ground_truth": "512"
} | {
"index": 3827,
"solution": "\nTo solve this problem, we need to understand the concept of an \"ideal company\" as defined by the question. An ideal company is a subset of the student group where all female students in the subset are liked by all male students within the same subset, and no additional student can ... |
DeepScaleR | [
{
"role": "user",
"content": "A subset of the integers $1,2,\\cdots,100$ has the property that none of its members is 3 times another. What is the largest number of members such a subset can have?\n$\\text{(A) } 50\\quad \\text{(B) } 66\\quad \\text{(C) } 67\\quad \\text{(D) } 76\\quad \\text{(E) } 78$"
}... | math | {
"style": "rule",
"ground_truth": "76"
} | {
"index": 3828,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A suitcase lock has 3 dials with the digits $0, 1, 2,..., 9$ on each. How many different settings are possible if all three digits have to be different?"
}
] | math | {
"style": "rule",
"ground_truth": "720"
} | {
"index": 3829,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A summer camp organizes 5 high school students to visit five universities, including Peking University and Tsinghua University. Determine the number of different ways in which exactly 2 students choose Peking University."
}
] | math | {
"style": "rule",
"ground_truth": "640"
} | {
"index": 3830,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A super ball is dropped from 100 feet and rebounds half the distance it falls each time it bounces. How many feet will the ball have traveled when it hits the ground the fourth time?"
}
] | math | {
"style": "rule",
"ground_truth": "275"
} | {
"index": 3831,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A supermarket has $128$ crates of apples. Each crate contains at least $120$ apples and at most $144$ apples.\nWhat is the largest integer $n$ such that there must be at least $n$ crates containing the same number of apples?"
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"index": 3832,
"solution": "1. **Identify the range of possible apple counts per crate**: Each crate contains between $120$ and $144$ apples, inclusive. Therefore, the number of different possible apple counts per crate is calculated as:\n \\[\n 144 - 120 + 1 = 25\n \\]\n This means there are 25 different... |
DeepScaleR | [
{
"role": "user",
"content": "A supermarket has 6 checkout lanes, each with two checkout points numbered 1 and 2. Based on daily traffic, the supermarket plans to select 3 non-adjacent lanes on Monday, with at least one checkout point open in each lane. How many different arrangements are possible for the c... | math | {
"style": "rule",
"ground_truth": "108"
} | {
"index": 3833,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A supermarket purchases two types of goods, $A$ and $B$. Buying 4 items of type $A$ costs $10$ yuan less than buying 5 items of type $B$. Buying 20 items of type $A$ and 10 items of type $B$ costs a total of $160$ yuan. \n$(1)$ Find the cost price per item of goods $A$ and $B$... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 3834,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A survey conducted at a conference found that 70% of the 150 male attendees and 75% of the 850 female attendees support a proposal for new environmental legislation. What percentage of all attendees support the proposal?"
}
] | math | {
"style": "rule",
"ground_truth": "74.2\\%"
} | {
"index": 3835,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A survey of $120$ teachers determined the following:\n\n$70$ had high blood pressure\n\n$40$ had heart trouble\n\n$20$ had both high blood pressure and heart trouble\n\nWhat percent of the teachers surveyed had neither high blood pressure nor heart trouble?"
}
] | math | {
"style": "rule",
"ground_truth": "25\\%"
} | {
"index": 3836,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A survey of $150$ teachers determined the following:\n- $90$ had high blood pressure\n- $60$ had heart trouble\n- $50$ had diabetes\n- $30$ had both high blood pressure and heart trouble\n- $20$ had both high blood pressure and diabetes\n- $10$ had both heart trouble and diabet... | math | {
"style": "rule",
"ground_truth": "3.33\\%"
} | {
"index": 3837,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A survey of participants was conducted at the Olympiad. $50\\%$ of the participants liked the first round, $60\\%$ of the participants liked the second round, $70\\%$ of the participants liked the opening of the Olympiad. It is known that each participant liked either one... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 3838,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A sweater costs 160 yuan, it was first marked up by 10% and then marked down by 10%. Calculate the current price compared to the original."
}
] | math | {
"style": "rule",
"ground_truth": "0.99"
} | {
"index": 3839,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A swimming pool can be filled by any of three hoses A, B or C. Hoses A and B together take 4 hours to fill the pool. Hoses A and C together take 5 hours to fill the pool. Hoses B and C together take 6 hours to fill the pool. How many hours does it take hoses A, B and C working ... | math | {
"style": "rule",
"ground_truth": "3.24"
} | {
"index": 3840,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A swimming pool is in the shape of a circle with diameter 60 ft. The depth varies linearly along the east-west direction from 3 ft at the shallow end in the east to 15 ft at the diving end in the west but does not vary at all along the north-south direction. What is the volume ... | math | {
"style": "rule",
"ground_truth": "8100 \\pi"
} | {
"index": 3841,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A system of inequalities defines a region on a coordinate plane as follows:\n$$\n\\begin{cases}\nx+y \\leq 5 \\\\\n3x+2y \\geq 3 \\\\\nx \\geq 1 \\\\\ny \\geq 1\n\\end{cases}\n$$\nDetermine the number of units in the length of the longest side of the quadrilateral formed by the... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{2}"
} | {
"index": 3842,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A systematic sampling method is used to select 5 representatives from 752 students, after removing 2 students randomly. Calculate the probability that student A is selected."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{752}"
} | {
"index": 3843,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A table $110\\times 110$ is given, we define the distance between two cells $A$ and $B$ as the least quantity of moves to move a chess king from the cell $A$ to cell $B$ . We marked $n$ cells on the table $110\\times 110$ such that the distance between any two cell... | math | {
"style": "rule",
"ground_truth": "6050"
} | {
"index": 3844,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A table can seat 6 people. Two tables joined together can seat 10 people. Three tables joined together can seat 14 people. Following this pattern, if 10 tables are arranged in two rows with 5 tables in each row, how many people can sit?"
}
] | math | {
"style": "rule",
"ground_truth": "44"
} | {
"index": 3845,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A table consisting of 1861 rows and 1861 columns is filled with natural numbers from 1 to 1861 such that each row contains all numbers from 1 to 1861. Find the sum of the numbers on the diagonal that connects the top left and bottom right corners of the table if the filling of ... | math | {
"style": "rule",
"ground_truth": "1732591"
} | {
"index": 3846,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tangent and a secant drawn from the same point to a circle are mutually perpendicular. The length of the tangent is 12, and the internal segment of the secant is 10. Find the radius of the circle."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 3847,
"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."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{17}"
} | {
"index": 3848,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tangent line is drawn to the moving circle $C: x^2 + y^2 - 2ay + a^2 - 2 = 0$ passing through the fixed point $P(2, -1)$. If the point of tangency is $T$, then the minimum length of the line segment $PT$ is \\_\\_\\_\\_\\_\\_."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt {2}"
} | {
"index": 3849,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tank is to be filled with water. When the tank is one-sixth full, 130 gallons of water are added, making the tank three-fifths full. How many gallons does the tank contain when it is completely full?"
}
] | math | {
"style": "rule",
"ground_truth": "300"
} | {
"index": 3850,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tank with a mass of $m_{1}=2$ kg rests on a cart with a mass of $m_{2}=10$ kg, which is accelerated with an acceleration of $a=5 \\, \\text{m/s}^2$. The coefficient of friction between the tank and the cart is $\\mu=0.6$. Determine the frictional force acting on the tank from... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 3851,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A target consisting of five zones is hanging on the wall: a central circle (bullseye) and four colored rings. The width of each ring equals the radius of the bullseye. It is known that the number of points for hitting each zone is inversely proportional to the probability of hi... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"index": 3852,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A target consists of five zones: the center circle (bullseye) and four colored rings. The width of each ring is equal to the radius of the bullseye. It is known that the score for hitting each zone is inversely proportional to the probability of hitting that zone, and hitting t... | math | {
"style": "rule",
"ground_truth": "45"
} | {
"index": 3853,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A target is a triangle divided by three sets of parallel lines into 100 equal equilateral triangles with unit sides. A sniper shoots at the target. He aims at a triangle and hits either it or one of the adjacent triangles sharing a side. He can see the results of his shots and ... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 3854,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A taxi driver passes through six traffic checkpoints on the way from the restaurant to the train station. Assuming that the events of encountering a red light at each checkpoint are independent of each other and the probability is $\\frac{1}{3}$ at each checkpoint, calculate th... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{27}"
} | {
"index": 3855,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A taxi has a starting fare of 10 yuan. After exceeding 10 kilometers, for every additional kilometer, the fare increases by 1.50 yuan (if the increase is less than 1 kilometer, it is rounded up to 1 kilometer; if the increase is more than 1 kilometer but less than 2 kilometers,... | math | {
"style": "rule",
"ground_truth": "61"
} | {
"index": 3856,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A taxi ride costs $\\$1.50$ plus $\\$0.25$ per mile traveled. How much, in dollars, does a 5-mile taxi ride cost?"
}
] | math | {
"style": "rule",
"ground_truth": "\\$2.75"
} | {
"index": 3857,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher asks her class what the value of $\\left(5^2-4^2\\right)^3$ is. What is the value of the expression?"
}
] | math | {
"style": "rule",
"ground_truth": "729"
} | {
"index": 3858,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher drew a rectangle $ABCD$ on the board. A student named Petya divided this rectangle into two rectangles with a line parallel to side $AB$. It turned out that the areas of these parts are in the ratio 1:2, and their perimeters are in the ratio 3:5 (in the same order). A... | math | {
"style": "rule",
"ground_truth": "20/19"
} | {
"index": 3859,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher finds that when she offers candy to her class of 30 students, the mean number of pieces taken by each student is 5. If every student takes some candy, what is the greatest number of pieces one student could have taken?"
}
] | math | {
"style": "rule",
"ground_truth": "121"
} | {
"index": 3860,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher gave a test to a class in which $10\\%$ of the students are juniors and $90\\%$ are seniors. The average score on the test was $84.$ The juniors all received the same score, and the average score of the seniors was $83.$ What score did each of the juniors receive on t... | math | {
"style": "rule",
"ground_truth": "93"
} | {
"index": 3861,
"solution": "1. **Assume the total number of students**: Let's assume there are $10$ students in the class for simplicity, as $10\\%$ of any number of students being juniors will always be $10\\%$ of that number. This assumption makes calculations straightforward without loss of generality.\n\n2. *... |
DeepScaleR | [
{
"role": "user",
"content": "A teacher has a class with $24$ students in it. If she wants to split the students into equal groups of at most $10$ students each, what is the least number of groups that she needs?"
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 3862,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher has prepared three problems for the class to solve. In how many different ways can he present these problems to the students if there are 30 students in the class?"
}
] | math | {
"style": "rule",
"ground_truth": "24360"
} | {
"index": 3863,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher intends to give the children a problem of the following type. He will tell them that he has thought of a polynomial \\( P(x) \\) of degree 2017 with integer coefficients and a leading coefficient of 1. Then he will provide them with \\( k \\) integers \\( n_{1}, n_{2}... | math | {
"style": "rule",
"ground_truth": "2017"
} | {
"index": 3864,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher must divide 221 apples evenly among 403 students. What is the minimal number of pieces into which she must cut the apples? (A whole uncut apple counts as one piece.)"
}
] | math | {
"style": "rule",
"ground_truth": "611"
} | {
"index": 3865,
"solution": "Consider a bipartite graph, with 221 vertices representing the apples and 403 vertices representing the students; each student is connected to each apple that she gets a piece of. The number of pieces then equals the number of edges in the graph. Each student gets a total of $221 / 403... |
DeepScaleR | [
{
"role": "user",
"content": "A teacher offers candy to her class of 50 students, with the mean number of pieces taken by each student being 7. If every student takes at least one candy but no more than 20 candies, what is the greatest number of pieces one student could have taken?"
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 3866,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher received 10, 6, 8, 5, and 6 letters from Monday to Friday, respectively. The variance $s^2$ of this set of data is ______."
}
] | math | {
"style": "rule",
"ground_truth": "3.2"
} | {
"index": 3867,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher received a number of letters from Monday to Friday, which were 10, 6, 8, 5, 6, respectively. The variance $s^2$ of this set of data is \\_\\_\\_\\_\\_\\_."
}
] | math | {
"style": "rule",
"ground_truth": "3.2"
} | {
"index": 3868,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher received letters on Monday through Friday with counts of $10$, $6$, $8$, $5$, $6$ respectively. Calculate the variance (${s^{2}} =$) of this data set."
}
] | math | {
"style": "rule",
"ground_truth": "3.2"
} | {
"index": 3869,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher received letters on Monday to Friday with counts of $10$, $6$, $8$, $5$, $6$ respectively. Calculate the standard deviation of this data set."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac {4 \\sqrt {5}}{5}"
} | {
"index": 3870,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher tells the class,\n\n\"Think of a number, add 1 to it, and double the result. Give the answer to your partner. Partner, subtract 1 from the number you are given and double the result to get your answer.\"\n\nBen thinks of $6$, and gives his answer to Sue. What shoul... | math | {
"style": "rule",
"ground_truth": "26"
} | {
"index": 3871,
"solution": "1. **Ben's Calculation:**\n - Ben thinks of a number, which is $6$.\n - He adds $1$ to this number: $6 + 1 = 7$.\n - He then doubles the result: $7 \\times 2 = 14$.\n - Ben gives the number $14$ to Sue.\n\n2. **Sue's Calculation:**\n - Sue receives the number $14$.\n - She ... |
DeepScaleR | [
{
"role": "user",
"content": "A teacher wants to arrange 3 copies of Introduction to Geometry and 4 copies of Introduction to Number Theory on a bookshelf. In how many ways can he do that?"
}
] | math | {
"style": "rule",
"ground_truth": "35"
} | {
"index": 3872,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A teacher was leading a class of four perfectly logical students. The teacher chose a set $S$ of four integers and gave a different number in $S$ to each student. Then the teacher announced to the class that the numbers in $S$ were four consecutive two-digit positive integers, ... | math | {
"style": "rule",
"ground_truth": "258"
} | {
"index": 3873,
"solution": "We know right away that $42\\not\\in S$ and $84\\not\\in S$ as stated in Solution 1.\n To get a feel for the problem, let’s write out some possible values of $S$ based on the teacher’s remarks. The first multiple of 7 that is two-digit is 14. The closest multiple of six from 14 is 12, ... |
DeepScaleR | [
{
"role": "user",
"content": "A teacher wrote a sequence of consecutive odd numbers starting from 1 on the blackboard: $1, 3, 5, 7, 9, 11, \\cdots$ After writing, the teacher erased two numbers, dividing the sequence into three segments. If the sums of the first two segments are 961 and 1001 respectively, w... | math | {
"style": "rule",
"ground_truth": "154"
} | {
"index": 3874,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A team consisting of Petya, Vasya, and a single-seat scooter is participating in a race. The distance is divided into 42 equal-length segments, with a checkpoint at the beginning of each segment. Petya completes a segment in 9 minutes, Vasya in 11 minutes, and either of them ca... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 3875,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A team of fishermen planned to catch 1800 centners of fish within a certain timeframe. During one-third of this period, there was a storm, causing them to fall short of their daily target by 20 centners each day. However, on the remaining days, the team managed to catch 20 cent... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 3876,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A team of four students goes to LMT, and each student brings a lunch. However, on the bus, the students’ lunches get mixed up, and during lunch time, each student chooses a random lunch to eat (no two students may eat the same lunch). What is the probability that each student c... | math | {
"style": "rule",
"ground_truth": "1/24"
} | {
"index": 3877,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A team of loggers was scheduled to harvest $216 \\mathrm{~m}^{3}$ of wood over several days. For the first three days, the team met the daily target set by the plan. Then, they harvested an additional $8 \\mathrm{~m}^{3}$ above the daily target each day. As a result, they harve... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 3878,
"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?"
}
] | math | {
"style": "rule",
"ground_truth": "23"
} | {
"index": 3879,
"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{70}{100} = \\frac{7}{... |
DeepScaleR | [
{
"role": "user",
"content": "A teen age boy wrote his own age after his father's. From this new four place number, he subtracted the absolute value of the difference of their ages to get $4,289$ . The sum of their ages was"
}
] | math | {
"style": "rule",
"ground_truth": "59"
} | {
"index": 3880,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A telephone number has the form \\text{ABC-DEF-GHIJ}, where each letter represents\na different digit. The digits in each part of the number are in decreasing\norder; that is, $A > B > C$, $D > E > F$, and $G > H > I > J$. Furthermore,\n$D$, $E$, and $F$ are consecutive even di... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 3881,
"solution": "1. **Identify the constraints**: The telephone number is in the form $\\text{ABC-DEF-GHIJ}$ where each segment has digits in decreasing order. Additionally, $D$, $E$, and $F$ are consecutive even digits; $G$, $H$, $I$, and $J$ are consecutive odd digits; and $A + B + C = 9$.\n\n2. **An... |
DeepScaleR | [
{
"role": "user",
"content": "A telephone number has the form \\text{ABC-DEF-GHIJ}, where each letter represents a different digit. The digits in each part of the number are in decreasing order; that is, $A > B > C$, $D > E > F$, and $G > H > I > J$. Furthermore, $D$, $E$, and $F$ are consecutive even digit... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 3882,
"solution": "1. **Identify the constraints**: The telephone number is in the form $\\text{ABC-DEF-GHIJ}$, where each segment has digits in decreasing order. Additionally, $D$, $E$, and $F$ are consecutive even digits; $G$, $H$, $I$, and $J$ are consecutive odd digits; and $A + B + C = 9$.\n\n2. **L... |
DeepScaleR | [
{
"role": "user",
"content": "A telephone pole is supported by a steel cable which extends from the top of the pole to a point on the ground 3 meters from its base. When Leah walks 2.5 meters from the base of the pole toward the point where the cable is attached to the ground, her head just touches the cabl... | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 3883,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A telephone station serves 400 subscribers. For each subscriber, the probability of calling the station within an hour is 0.01. Find the probabilities of the following events: \"within an hour, 5 subscribers will call the station\"; \"within an hour, no more than 4 subscribers ... | math | {
"style": "rule",
"ground_truth": "0.7619"
} | {
"index": 3884,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A television station is broadcasting 5 advertisements in a row, which include 3 different commercial advertisements and 2 different National Games promotional advertisements. The requirements are that the last advertisement must be one of the National Games promotional advertis... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 3885,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A television station is set to broadcast 6 commercials in a sequence, which includes 3 different business commercials, 2 different World Expo promotional commercials, and 1 public service commercial. The last commercial cannot be a business commercial, and neither the World Exp... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 3886,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A television's price was discounted $40\\%$ and then slashed another $40\\%$ during a liquidation sale. By what percent has the original price been reduced?"
}
] | math | {
"style": "rule",
"ground_truth": "64\\%"
} | {
"index": 3887,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. At the start of a weekend, her win ratio is exactly $.500$. During the weekend, she plays four matches, winning three and losing one. At the end o... | math | {
"style": "rule",
"ground_truth": "164"
} | {
"index": 3888,
"solution": "Let $n$ be the number of matches won, so that $\\frac{n}{2n}=\\frac{1}{2}$, and $\\frac{n+3}{2n+4}>\\frac{503}{1000}$.\n Cross multiplying, $1000n+3000>1006n+2012$, so $n<\\frac{988}{6}=164 \\dfrac {4}{6}=164 \\dfrac{2}{3}$. Thus, the answer is $\\boxed{164}$.\n The problems on this pa... |
DeepScaleR | [
{
"role": "user",
"content": "A test has ten questions. Points are awarded as follows:\n\n- Each correct answer is worth 3 points.\n- Each unanswered question is worth 1 point.\n- Each incorrect answer is worth 0 points.\n\nA total score that is not possible is:"
}
] | math | {
"style": "rule",
"ground_truth": "29"
} | {
"index": 3889,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tetrahedron $ABCD$ satisfies the following conditions: the edges $AB,AC$ and $AD$ are pairwise orthogonal, $AB=3$ and $CD=\\sqrt2$ . Find the minimum possible value of $$ BC^6+BD^6-AC^6-AD^6. $$"
}
] | math | {
"style": "rule",
"ground_truth": "1998"
} | {
"index": 3890,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tetrahedron $PQRS$ has edges of lengths $8, 14, 19, 28, 37,$ and $42$ units. If the length of edge $PQ$ is $42$, determine the length of edge $RS$."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 3891,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tetrahedron \\( P-ABC \\) has edge lengths \\( PA = BC = \\sqrt{6} \\), \\( PB = AC = \\sqrt{8} \\), and \\( PC = AB = \\sqrt{10} \\). Find the radius of the circumsphere of this tetrahedron."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"index": 3892,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tetrahedron \\(ABCD\\) has edge lengths 7, 13, 18, 27, 36, 41, with \\(AB = 41\\). Determine the length of \\(CD\\)."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 3893,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tetrahedron \\(ABCD\\) has six edges with lengths \\(7, 13, 18, 27, 36, 41\\) units. If the length of \\(AB\\) is 41 units, then the length of \\(CD\\) is"
}
] | math | {
"style": "rule",
"ground_truth": "27"
} | {
"index": 3894,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tetrahedron has a triangular base with sides all equal to 2, and each of its three lateral faces are squares. A smaller tetrahedron is placed within the larger one so that its base is parallel to the base of the larger tetrahedron and its vertices touch the midpoints of the l... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{12}"
} | {
"index": 3895,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tetrahedron has all its faces triangles with sides $13,14,15$. What is its volume?"
}
] | math | {
"style": "rule",
"ground_truth": "42 \\sqrt{55}"
} | {
"index": 3896,
"solution": "Let $A B C$ be a triangle with $A B=13, B C=14, C A=15$. Let $A D, B E$ be altitudes. Then $B D=5, C D=9$. (If you don't already know this, it can be deduced from the Pythagorean Theorem: $C D^{2}-B D^{2}=\\left(C D^{2}+A D^{2}\\right)-\\left(B D^{2}+A D^{2}\\right)=A C^{2}-A B^{2}=56$... |
DeepScaleR | [
{
"role": "user",
"content": "A tetrahedron is formed using the vertices of a cube. How many such distinct tetrahedrons can be formed?"
}
] | math | {
"style": "rule",
"ground_truth": "58"
} | {
"index": 3897,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A tetrahedron of spheres is formed with thirteen layers and each sphere has a number written on it. The top sphere has a 1 written on it and each of the other spheres has written on it the number equal to the sum of the numbers on the spheres in the layer above with which it is... | math | {
"style": "rule",
"ground_truth": "772626"
} | {
"index": 3898,
"solution": "First, we fill in the numbers on the top four layers. The top layer consists of only one sphere, labelled 1. In the second layer, each sphere touches only one sphere in the layer above. This sphere is labelled 1, so each sphere in the second layer is labelled 1. In the third layer, eac... |
DeepScaleR | [
{
"role": "user",
"content": "A tetrahedron with each edge length equal to $\\sqrt{2}$ has all its vertices on the same sphere. Calculate the surface area of this sphere."
}
] | math | {
"style": "rule",
"ground_truth": "3\\pi"
} | {
"index": 3899,
"solution": ""
} |
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