data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
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"
} | {
"index": 1000,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain cafeteria serves ham and cheese sandwiches, ham and tomato sandwiches, and tomato and cheese sandwiches. It is common for one meal to include multiple types of sandwiches. On a certain day, it was found that 80 customers had meals which contained both ham and cheese; ... | math | {
"style": "rule",
"ground_truth": "230"
} | {
"index": 1001,
"solution": "230. Everyone who ate just one sandwich is included in exactly one of the first three counts, while everyone who ate more than one sandwich is included in all four counts. Thus, to count each customer exactly once, we must add the first three figures and subtract the fourth twice: $80+... |
DeepScaleR | [
{
"role": "user",
"content": "A certain calculator has only two keys [+1] and [x2]. When you press one of the keys, the calculator automatically displays the result. For instance, if the calculator originally displayed \"9\" and you pressed [+1], it would display \"10.\" If you then pressed [x2], it would d... | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 1002,
"solution": "To solve this problem, we will work backwards from 200 to 1, determining the optimal sequence of operations that corresponds to the fewest number of keystrokes on the calculator. The operations we use in reverse (working from 200 to 1) will be dividing by 2 (corresponding to the multip... |
DeepScaleR | [
{
"role": "user",
"content": "A certain car beauty company launched a promotional activity to attract customers: for first-time customers, the charge is $200 per visit, and they can register as members. Members will receive corresponding discounts for each subsequent visit, as shown in the table below:\n\n|... | math | {
"style": "rule",
"ground_truth": "\\frac{8}{15}"
} | {
"index": 1003,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain chemical reaction requires a catalyst to accelerate the reaction, but using too much of this catalyst affects the purity of the product. If the amount of this catalyst added is between 500g and 1500g, and the 0.618 method is used to arrange the experiment, then the am... | math | {
"style": "rule",
"ground_truth": "882"
} | {
"index": 1004,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\\pi$. What is the radius of the circle, in units?"
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 1005,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain clothing factory produces jackets and $T$-shirts, with each jacket priced at $100$ yuan and each $T$-shirt priced at $60$ yuan. During a promotional period, the factory offers two discount options to customers:<br/>① Buy one jacket and get one $T$-shirt for free;<br/>... | math | {
"style": "rule",
"ground_truth": "3480"
} | {
"index": 1006,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain clothing wholesale market sells a type of shirt, with a purchase price of $50$ yuan per shirt. It is stipulated that the selling price of each shirt is not lower than the purchase price. According to a market survey, the monthly sales volume $y$ (in units) and the sel... | math | {
"style": "rule",
"ground_truth": "19500"
} | {
"index": 1007,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain coin is weighted such that the chance of flipping heads is $\\frac{1}{3}$ and the chance of flipping tails is $\\frac{2}{3}$. Suppose that we win $\\$3$ if we flip a heads on a coin toss, but lose $\\$2$ if we flip tails. What is the expected value, in dollars, of o... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{3}"
} | {
"index": 1008,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain collection of numbered indexed cards includes one card with a 1 written on it, two cards with a 2, and so forth up to $n$ cards showing an $n,$ for some positive integer $n$. Determine $n,$ if the average value of a card in this collection is 2017."
}
] | math | {
"style": "rule",
"ground_truth": "3025"
} | {
"index": 1009,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain college student had the night of February 23 to work on a chemistry problem set and a math problem set (both due on February 24, 2006). If the student worked on his problem sets in the math library, the probability of him finishing his math problem set that night is 9... | math | {
"style": "rule",
"ground_truth": "95/159"
} | {
"index": 1010,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain commodity has a cost price of 200 yuan and a marked price of 400 yuan. What is the maximum discount that can be offered to ensure that the profit margin is not less than 40%?"
}
] | math | {
"style": "rule",
"ground_truth": "30\\%"
} | {
"index": 1011,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain company has two research and development teams, Team A and Team B. The probability of success for developing a new product by Team A is $\\frac{4}{5}$, and for Team B is $\\frac{3}{4}$. Team A is assigned to develop a new product $A$, and Team B is assigned to develop... | math | {
"style": "rule",
"ground_truth": "188"
} | {
"index": 1012,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain company implements an annual salary system, where an employee's annual salary consists of three components: basic salary, housing allowance, and medical expenses, as specified below:\n\n| Item | Salary in the First Year (in ten thousand yuan) | Calculation Me... | math | {
"style": "rule",
"ground_truth": "20\\%"
} | {
"index": 1013,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain company, in response to the national call for garbage classification, has launched a project with the support of the research department to innovate technologies. The project processes kitchen waste into reusable chemical products. It is known that the daily processin... | math | {
"style": "rule",
"ground_truth": "1800"
} | {
"index": 1014,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain department store sells a batch of shirts. The cost price of each shirt is $80. On average, 30 shirts can be sold per day, with a profit of $50 per shirt. In order to increase sales and profits, the store decides to take appropriate price reduction measures. After inve... | math | {
"style": "rule",
"ground_truth": "120"
} | {
"index": 1015,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain department store sells suits and ties, with each suit priced at $1000$ yuan and each tie priced at $200 yuan. During the \"National Day\" period, the store decided to launch a promotion offering two discount options to customers.<br/>Option 1: Buy one suit and get one... | math | {
"style": "rule",
"ground_truth": "21800"
} | {
"index": 1016,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain district's education department wants to send 5 staff members to 3 schools for earthquake safety education. Each school must receive at least 1 person and no more than 2 people. How many different arrangements are possible? (Answer with a number)"
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"index": 1017,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain electronic device contains three components, with probabilities of failure for each component being $0.1, 0.2, 0.3$, respectively. If the probabilities of the device failing when one, two, or three components fail are $0.25, 0.6, 0.9$, respectively, find the probabili... | math | {
"style": "rule",
"ground_truth": "0.1601"
} | {
"index": 1018,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain ellipse is tangent to both the $x$-axis and the $y$-axis, and its foci are at $(2, -3 + \\sqrt{5})$ and $(2, -3 - \\sqrt{5}).$ Find the length of the major axis."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"index": 1019,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain fruit store deals with two types of fruits, A and B. The situation of purchasing fruits twice is shown in the table below:\n\n| Purchase Batch | Quantity of Type A Fruit ($\\text{kg}$) | Quantity of Type B Fruit ($\\text{kg}$) | Total Cost ($\\text{元}$) |\n|----------... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 1020,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain function $f$ has the properties that $f(3x) = 3f(x)$ for all positive real values of $x$, and that $f(x) = 1 - |x - 2|$ for $1\\leq x \\leq 3$. Find the smallest $x$ for which $f(x) = f(2001)$."
}
] | math | {
"style": "rule",
"ground_truth": "429"
} | {
"index": 1021,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain function $f$ has the properties that $f(3x) = 3f(x)$ for all positive real values of $x$, and that $f(x) = 1-|x-2|$ for $1\\le x \\le 3$. Find the smallest $x$ for which $f(x) = f(2001)$."
}
] | math | {
"style": "rule",
"ground_truth": "429"
} | {
"index": 1022,
"solution": "Iterating the condition $f(3x) = 3f(x)$, we find that $f(x) = 3^kf\\left(\\frac{x}{3^k}\\right)$ for positive integers $k$. We know the definition of $f(x)$ from $1 \\le x \\le 3$, so we would like to express $f(2001) = 3^kf\\left(\\frac{2001}{3^k}\\right),\\ 1 \\le \\frac{2001}{3^k} \... |
DeepScaleR | [
{
"role": "user",
"content": "A certain high school encourages students to spontaneously organize various sports competitions. Two students, A and B, play table tennis matches in their spare time. The competition adopts a \"best of seven games\" format (i.e., the first player to win four games wins the matc... | math | {
"style": "rule",
"ground_truth": "\\frac{19}{9}"
} | {
"index": 1023,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain high school has 1000 students in the first year. Their choices of elective subjects are shown in the table below:\n\n| Subject | Physics | Chemistry | Biology | Politics | History | Geography |\n|---------|---------|-----------|---------|----------|---------|---------... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{10}"
} | {
"index": 1024,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain high school has three mathematics teachers. For the convenience of the students, they arrange for a math teacher to be on duty every day from Monday to Friday, and two teachers are scheduled to be on duty on Monday. If each teacher is on duty for two days per week, th... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 1025,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain high school is planning to hold a coming-of-age ceremony for senior students on the \"May Fourth\" Youth Day to motivate the seniors who are preparing for the college entrance examination. The Student Affairs Office has prepared five inspirational songs, a video speec... | math | {
"style": "rule",
"ground_truth": "20160"
} | {
"index": 1026,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain integer has $4$ digits when written in base $8$. The same integer has $d$ digits when written in base $2$. What is the sum of all possible values of $d$?"
}
] | math | {
"style": "rule",
"ground_truth": "33"
} | {
"index": 1027,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain intelligence station has four different kinds of passwords $A$, $B$, $C$, and $D$. Each week, one of these passwords is used, and each week a password is chosen uniformly at random from the three passwords that were not used the previous week. Given that password $A$ ... | math | {
"style": "rule",
"ground_truth": "61/243"
} | {
"index": 1028,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain intelligence station has four different passwords A, B, C, and D. Each week, one of the passwords is used, and the password for each week is equally likely to be randomly selected from the three passwords not used in the previous week. If password A is used in the fir... | math | {
"style": "rule",
"ground_truth": "1/3"
} | {
"index": 1029,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain interest group conducted a survey on the reading of classic literature by people of different age groups in a certain region. The relevant data is shown in the table below:\n\n| Age Interval | $[0,10)$ | $[10,15)$ | $[15,20)$ | $[20,25)$ | $[25,30)$ |\n|--------------... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 1030,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain item has a cost price of $4$ yuan and is sold at a price of $5$ yuan. The merchant is planning to offer a discount on the selling price, but the profit margin must not be less than $10\\%$. Find the maximum discount rate that can be offered."
}
] | math | {
"style": "rule",
"ground_truth": "12\\%"
} | {
"index": 1031,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain item has a cost price of $4$ yuan and is sold at a price of $5$ yuan. The merchant is preparing to offer a discount on the selling price, but the profit margin must not be less than $10\\%$. Find the maximum discount rate that can be offered."
}
] | math | {
"style": "rule",
"ground_truth": "12\\%"
} | {
"index": 1032,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain item is always sold with a 30% discount, and the profit margin is 47%. During the shopping festival, the item is sold at the original price, and there is a \"buy one get one free\" offer. Calculate the profit margin at this time. (Note: Profit margin = (selling price ... | math | {
"style": "rule",
"ground_truth": "5\\%"
} | {
"index": 1033,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain lottery has tickets labeled with the numbers $1,2,3, \\ldots, 1000$. The lottery is run as follows: First, a ticket is drawn at random. If the number on the ticket is odd, the drawing ends; if it is even, another ticket is randomly drawn (without replacement). If this... | math | {
"style": "rule",
"ground_truth": "1/501"
} | {
"index": 1034,
"solution": "Notice that the outcome is the same as if the lottery instead draws all the tickets, in random order, and awards a prize to the holder of the odd ticket drawn earliest and each even ticket drawn before it. Thus, the probability of your winning is the probability that, in a random order... |
DeepScaleR | [
{
"role": "user",
"content": "A certain machine has a display showing an integer $x$, and two buttons, $\\mathrm{A}$ and $\\mathrm{B}$. When button $\\mathrm{A}$ is pressed, the number $x$ on the display is replaced by $2x + 1$. When button $\\mathrm{B}$ is pressed, the number $x$ on the display is replaced... | math | {
"style": "rule",
"ground_truth": "95"
} | {
"index": 1035,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain middle school assigns numbers to each student, where the last digit indicates the gender of the student: 1 for male and 2 for female. If 028432 represents \"a female student who is number 43 in class 8 and enrolled in the year 2002,\" then the number for a male studen... | math | {
"style": "rule",
"ground_truth": "086231"
} | {
"index": 1036,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain model of hybrid car travels from point $A$ to point $B$ with a fuel cost of $76$ yuan, and with an electricity cost of $26 yuan. It is known that for every kilometer traveled, the fuel cost is $0.5$ yuan more than the electricity cost. \n$(1)$ Find the cost of travel... | math | {
"style": "rule",
"ground_truth": "74"
} | {
"index": 1037,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain number is written in the base-12 numeral system. For which divisor \\( m \\) is the following divisibility rule valid: if the sum of the digits of the number is divisible by \\( m \\), then the number itself is divisible by \\( m \\)?"
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 1038,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain number of books are distributed among children. If each child gets $m$ books, there are 14 books left. If each child gets 9 books, the last child only gets 6 books. How many children are there in total? And how many books are there?"
}
] | math | {
"style": "rule",
"ground_truth": "150"
} | {
"index": 1039,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain number with a sum of digits equal to 2021 was divided by 7 and resulted in a number composed exclusively of the digit 7. How many digits 7 can this number contain? If there are multiple answers, provide their sum."
}
] | math | {
"style": "rule",
"ground_truth": "503"
} | {
"index": 1040,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain operation is performed on a positive integer: if it is even, divide it by 2; if it is odd, add 1. This process continues until the number becomes 1. How many integers become 1 after exactly 10 operations?"
}
] | math | {
"style": "rule",
"ground_truth": "55"
} | {
"index": 1041,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain orange orchard has a total of 120 acres, consisting of both flat and hilly land. To estimate the average yield per acre, a stratified sampling method is used to survey a total of 10 acres. If the number of hilly acres sampled is 2 times plus 1 acre more than the flat ... | math | {
"style": "rule",
"ground_truth": "84"
} | {
"index": 1042,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain organism begins as three cells. Each cell splits and becomes two cells at the end of two days. At the end of another two days, every cell of the organism splits and becomes two cells. This process lasts for a total of 8 days, and no cells die during this time. How man... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"index": 1043,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain organism starts with 4 cells. Each cell splits into two cells at the end of three days. However, at the end of each 3-day period, 10% of the cells die immediately after splitting. This process continues for a total of 9 days. How many cells are there at the end of the... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"index": 1044,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain organization consists of five leaders and some number of regular members. Every year, the current leaders are kicked out of the organization. Next, each regular member must find two new people to join as regular members. Finally, five new people are elected from outsi... | math | {
"style": "rule",
"ground_truth": "2435"
} | {
"index": 1045,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain pharmaceutical company has developed a new drug to treat a certain disease, with a cure rate of $p$. The drug is now used to treat $10$ patients, and the number of patients cured is denoted as $X$. \n$(1)$ If $X=8$, two patients are randomly selected from these $10$ ... | math | {
"style": "rule",
"ground_truth": "\\frac{90}{11}"
} | {
"index": 1046,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain point has rectangular coordinates $(10,3)$ and polar coordinates $(r, \\theta).$ What are the rectangular coordinates of the point with polar coordinates $(r^2, 2 \\theta)$?"
}
] | math | {
"style": "rule",
"ground_truth": "(91,60)"
} | {
"index": 1047,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain product costs $6$ per unit, sells for $x$ per unit $(x > 6)$, and has an annual sales volume of $u$ ten thousand units. It is known that $\\frac{585}{8} - u$ is directly proportional to $(x - \\frac{21}{4})^2$, and when the selling price is $10$ dollars, the annual sa... | math | {
"style": "rule",
"ground_truth": "135"
} | {
"index": 1048,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain product has a cost price of $40$ yuan per unit. When the selling price is $60$ yuan per unit, 300 units can be sold per week. It is now necessary to reduce the price for clearance. According to market research, for every $1$ yuan reduction in price, an additional 20 u... | math | {
"style": "rule",
"ground_truth": "6125"
} | {
"index": 1049,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain product has a purchase price of 50 yuan per item and a selling price of 60 yuan per item, with a daily sales volume of 190 items. If the selling price of each item increases by 1 yuan, then 10 fewer items are sold each day. Let the selling price increase by $x$ yuan (... | math | {
"style": "rule",
"ground_truth": "2100"
} | {
"index": 1050,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain product in a shopping mall sells an average of 30 items per day, with a profit of 50 yuan per item. In order to reduce inventory quickly, the mall decides to take appropriate price reduction measures. After investigation, it was found that for each item, for every 1 y... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 1051,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain product in a shopping mall sells an average of 30 units per day, with a profit of 50 yuan per unit. To reduce inventory as quickly as possible, the mall decides to take appropriate price reduction measures. It has been found that for every 1 yuan reduction in price pe... | math | {
"style": "rule",
"ground_truth": "17.5"
} | {
"index": 1052,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain product in a shopping mall sells an average of 70 items per day, with a profit of $50 per item. In order to reduce inventory quickly, the mall decides to take appropriate price reduction measures. After investigation, it was found that for each item, for every $1 decr... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 1053,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain product was bought in the fall, and 825 rubles were paid for it. In the fall, the price per kilogram of this product was 1 ruble cheaper than in the spring. Therefore, for the same amount in the spring, 220 kg less was bought. How much does 1 kg of the product cost in... | math | {
"style": "rule",
"ground_truth": "550"
} | {
"index": 1054,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain quadratic polynomial is known to have the following properties: its leading coefficient is equal to one, it has integer roots, and its graph (parabola) intersects the line \\( y = 2017 \\) at two points with integer coordinates. Can the ordinate of the vertex of the p... | math | {
"style": "rule",
"ground_truth": "-1016064"
} | {
"index": 1055,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain real estate property is holding a lottery for homebuyers, with the following rules: For homeowners who purchase the property, they can randomly draw 2 balls from box $A$, which contains 2 red balls and 2 white balls, and 2 balls from box $B$, which contains 3 red ball... | math | {
"style": "rule",
"ground_truth": "3,675"
} | {
"index": 1056,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain rectangle had its dimensions expressed in whole numbers of decimeters. Then, it changed its dimensions three times. First, one of its dimensions was doubled and the other was adjusted so that the area remained the same. Then, one dimension was increased by $1 \\mathrm... | math | {
"style": "rule",
"ground_truth": "4:1"
} | {
"index": 1057,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain regular tetrahedron has three of its vertices at the points $(0,1,2),$ $(4,2,1),$ and $(3,1,5).$ Find the coordinates of the fourth vertex, given that they are also all integers."
}
] | math | {
"style": "rule",
"ground_truth": "(3,-2,2)"
} | {
"index": 1058,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain scenic area has two attractions that require tickets for visiting. The three ticket purchase options presented at the ticket office are as follows: \nOption 1: Visit attraction A only, $30$ yuan per person; \nOption 2: Visit attraction B only, $50$ yuan per person; ... | math | {
"style": "rule",
"ground_truth": "188.1"
} | {
"index": 1059,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain school arranges $5$ senior high school teachers to visit $3$ schools for exchange and learning. One school has $1$ teacher, one school has $2$ teachers, and one school has $2$ teachers. The total number of different arrangements is _______."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"index": 1060,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain school club has 10 members, and two of them are put on duty each day from Monday to Friday. Given that members A and B must be scheduled on the same day, and members C and D cannot be scheduled together, the total number of different possible schedules is (▲). Choices... | math | {
"style": "rule",
"ground_truth": "5400"
} | {
"index": 1061,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain school conducted a survey on the daily reading time of students during the summer vacation, as shown in the table below:\n\n| | Mean | Variance | Number of Students |\n|---------|------|----------|--------------------|\n| Grade 10 | $2.7$ | $1$ | $800$ |\n| Gr... | math | {
"style": "rule",
"ground_truth": "1.966"
} | {
"index": 1062,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain school conducted physical fitness tests on the freshmen to understand their physical health conditions. Now, $20$ students are randomly selected from both male and female students as samples. Their test data is organized in the table below. It is defined that data $\\... | math | {
"style": "rule",
"ground_truth": "\\frac{31}{250}"
} | {
"index": 1063,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain school has $7$ members in its student art department (4 males and 3 females). Two members are to be selected to participate in the school's art performance event. \n$(1)$ Find the probability that only one female member is selected. \n$(2)$ Given that a male member,... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"index": 1064,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain school has a total of 1,000 students, including 380 first-year students and 180 male second-year students. It is known that the probability of drawing a female second-year student from all the students is 0.19. If stratified sampling (by grade) is used to draw 100 stu... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 1065,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain school holds a men's table tennis team competition. The final match adopts a points system. The two teams in the final play three matches in sequence, with the first two matches being men's singles matches and the third match being a men's doubles match. Each particip... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 1066,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain school is actively preparing for the \"Sunshine Sports\" activity and has decided to purchase a batch of basketballs and soccer balls totaling $30$ items. At a sports equipment store, each basketball costs $80$ yuan, and each soccer ball costs $60$ yuan. During the pu... | math | {
"style": "rule",
"ground_truth": "2080"
} | {
"index": 1067,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain school organized a Chinese traditional culture activity week to promote traditional Chinese culture. During the activity period, a Chinese traditional culture knowledge competition was held, with classes participating in the competition. Each class selected 5 represen... | math | {
"style": "rule",
"ground_truth": "\\frac{537}{125}"
} | {
"index": 1068,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain school randomly selected several students to investigate the daily physical exercise time of students in the school. They obtained data on the daily physical exercise time (unit: minutes) and organized and described the data. Some information is as follows:\n- $a$. Di... | math | {
"style": "rule",
"ground_truth": "86"
} | {
"index": 1069,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain school sends two students, A and B, to form a \"youth team\" to participate in a shooting competition. In each round of the competition, A and B each shoot once. It is known that the probability of A hitting the target in each round is $\\frac{1}{2}$, and the probabil... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{24}"
} | {
"index": 1070,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain senior high school has a total of 3200 students, with 1000 students each in the second and third grades. A stratified sampling method is used to draw a sample of size 160. The number of first-grade students that should be drawn is ______ ."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 1071,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain set of integers is assigned to the letters of the alphabet such that $H=10$. The value of a word is the sum of its assigned letter values. Given that $THIS=50$, $HIT=35$ and $SIT=40$, find the value of $I$."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 1072,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain shopping mall purchased a batch of daily necessities. If they are sold at a price of $5$ yuan per item, they can sell $30,000$ items per month. If they are sold at a price of $6$ yuan per item, they can sell $20,000$ items per month. It is assumed that the monthly sal... | math | {
"style": "rule",
"ground_truth": "40000"
} | {
"index": 1073,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain shopping mall sells a batch of brand-name shirts, with an average daily sales of 20 pieces and a profit of $40 per piece. In order to expand sales and reduce inventory quickly, the mall decides to take appropriate price reduction measures. After investigation, it was ... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 1074,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain shopping mall sells two types of products, A and B. The profit margin for each unit of product A is $40\\%$, and for each unit of product B is $50\\%$. When the quantity of product A sold is $150\\%$ of the quantity of product B sold, the total profit margin for selli... | math | {
"style": "rule",
"ground_truth": "47.5\\%"
} | {
"index": 1075,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain shopping mall's sales volume (unit: ten thousand pieces) for five consecutive years is as shown in the table below:\n\n| $x$(year) | 1 | 2 | 3 | 4 | 5 |\n|-----------|---|---|---|---|---|\n| $y$(sales volume) | 5 | 5 | 6 | 7 | 7 |\n\n$(1)$ Find the linear regression e... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{5}"
} | {
"index": 1076,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain state issues license plates consisting of six digits (from 0 through 9). The state requires that any two plates differ in at least two places. (Thus the plates $\\boxed{027592}$ and $\\boxed{020592}$ cannot both be used.) Determine, with proof, the maximum number of d... | math | {
"style": "rule",
"ground_truth": "\\[ 10^5 \\]"
} | {
"index": 1077,
"solution": "Consider license plates of $n$ digits, for some fixed $n$ , issued with the same criteria.\nWe first note that by the pigeonhole principle, we may have at most $10^{n-1}$ distinct plates. Indeed, if we have more, then there must be two plates which agree on the first $n-1$ digits; the... |
DeepScaleR | [
{
"role": "user",
"content": "A certain stationery store stipulates that if one purchases 250 or more exercise books at a time (including 250 books), they can pay at the wholesale price; if one purchases fewer than 250 books, they must pay at the retail price. Li, a teacher, went to the store to buy exercis... | math | {
"style": "rule",
"ground_truth": "200"
} | {
"index": 1078,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain store in Hefei plans to sell a newly launched stationery item, with a purchase price of 20 yuan per item. During the trial marketing phase, it was found that when the selling price is 25 yuan per item, the daily sales volume is 150 items; for every 1 yuan increase in ... | math | {
"style": "rule",
"ground_truth": "960"
} | {
"index": 1079,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain store sells a batch of helmets for $80 each. It can sell 200 helmets per month. During the \"Creating a Civilized City\" period, the store plans to reduce the price of the helmets for sale. After investigation, it was found that for every $1 decrease in price, an addi... | math | {
"style": "rule",
"ground_truth": "65"
} | {
"index": 1080,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain store sells a batch of thermal shirts, with an average daily sales of 20 pieces and a profit of $40 per piece. In order to increase sales and profits, the store has taken appropriate price reduction measures. After investigation, it was found that within a certain ran... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 1081,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain store sells a product, and because the purchase price decreased by 6.4% compared to the original purchase price, the profit margin increased by 8 percentage points. What was the original profit margin for selling this product?"
}
] | math | {
"style": "rule",
"ground_truth": "17\\%"
} | {
"index": 1082,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain store sells a type of handbag, and it is known that the cost price of this handbag is $50$ yuan per unit. Market research shows that the daily sales quantity $y$ (unit: units) of this handbag is related to the selling price $x$ (unit: yuan) as follows: $y=-x+80$ $(50 ... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 1083,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain store sells a type of student backpack. It is known that the cost price of this backpack is $30$ yuan each. Market research shows that the daily sales quantity $y$ (in units) of this backpack is related to the selling price $x$ (in yuan) as follows: $y=-x+60$ ($30\\le... | math | {
"style": "rule",
"ground_truth": "225"
} | {
"index": 1084,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain teacher received $10$, $6$, $8$, $5$, $6$ letters from Monday to Friday, then the variance of this data set is $s^{2}=$____."
}
] | math | {
"style": "rule",
"ground_truth": "3.2"
} | {
"index": 1085,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain tour group checked the weather conditions on the day of the outing. A weather forecasting software predicted that the probability of rain during the time periods $12:00$ to $13:00$ and $13:00$ to $14:00$ on the day of the outing are $0.5$ and $0.4$ respectively. Then,... | math | {
"style": "rule",
"ground_truth": "0.7"
} | {
"index": 1086,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain township responded to the call of \"green waters and green mountains are mountains of gold and silver\" and tailored the town to be a \"ecological fruit characteristic town\" according to local conditions. After investigation, it was found that the yield $W$ (unit: kg... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 1087,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain type of alloy steel production company needs to ensure that the carbon content percentage of the alloy steel is within a specified range. Under the same test conditions, the inspector randomly samples $10$ times each day and measures the carbon content (unit: $\\%$). ... | math | {
"style": "rule",
"ground_truth": "0.026"
} | {
"index": 1088,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain type of beverage with a prize promotion has bottle caps printed with either \"reward one bottle\" or \"thank you for your purchase\". If a bottle is purchased and the cap is printed with \"reward one bottle\", it is considered a winning bottle, with a winning probabil... | math | {
"style": "rule",
"ground_truth": "\\frac{25}{27}"
} | {
"index": 1089,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain type of ray, when passing through a glass plate, attenuates to $\\text{a}\\%$ of its original intensity for every $1 \\mathrm{~mm}$ of thickness. It was found that stacking 10 pieces of $1 \\mathrm{~mm}$ thick glass plates results in the same ray intensity as passing ... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"index": 1090,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain type of rice must comply with the normal distribution of weight $(kg)$, denoted as $\\xi ～N(10,{σ}^{2})$, according to national regulations. Based on inspection results, $P(9.9≤\\xi≤10.1)=0.96$. A company purchases a bag of this packaged rice as a welfare gift for eac... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 1091,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain unit decides to invest $3200$ yuan to build a warehouse (in the shape of a rectangular prism) with a constant height. The back wall will be built reusing the old wall at no cost, the front will be made of iron grilles at a cost of $40$ yuan per meter in length, and th... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 1092,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain unit has 160 young employees. The number of middle-aged employees is twice the number of elderly employees. The total number of elderly, middle-aged, and young employees is 430. In order to understand the physical condition of the employees, a stratified sampling meth... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 1093,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain unit is planning to build a rectangular room that is backed against a wall with a ground surface area of 12 square meters. Due to geographical constraints, the side length x of the room cannot exceed 5 meters. The cost of constructing the front face of the room is 400... | math | {
"style": "rule",
"ground_truth": "13000"
} | {
"index": 1094,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain university needs $40L$ of helium gas to make balloon decorations for its centennial celebration. The chemistry club voluntarily took on this task. The club's equipment can produce a maximum of $8L$ of helium gas per day. According to the plan, the club must complete t... | math | {
"style": "rule",
"ground_truth": "4640"
} | {
"index": 1095,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A charity sells $140$ benefit tickets for a total of $2001$ dollars. Some tickets sell for full price (a whole dollar amount), and the rest sells for half price. How much money is raised by the full-price tickets?"
}
] | math | {
"style": "rule",
"ground_truth": "$782"
} | {
"index": 1096,
"solution": "\nLet $f$ be the number of full-price tickets and $h$ be the number of half-price tickets. Let $p$ be the price of a full-price ticket. We know that the total number of tickets sold is $140$, and the total revenue is $2001$. Therefore, we can set up the following equations:\n\n1. \\( f... |
DeepScaleR | [
{
"role": "user",
"content": "A charity sells $140$ benefit tickets for a total of $2001$. Some tickets sell for full price (a whole dollar amount), and the rest sells for half price. How much money is raised by the full-price tickets?"
}
] | math | {
"style": "rule",
"ground_truth": "$782"
} | {
"index": 1097,
"solution": "\nLet's denote the number of full-price tickets as $f$ and the number of half-price tickets as $h$. Let $p$ be the price of a full-price ticket. Then, the price of a half-price ticket is $\\frac{p}{2}$. The total number of tickets sold is $140$, and the total revenue is $2001$ dollars.... |
DeepScaleR | [
{
"role": "user",
"content": "A checker can move in one direction on a divided strip into cells, moving either to the adjacent cell or skipping one cell in one move. In how many ways can it move 10 cells? 11 cells?"
}
] | math | {
"style": "rule",
"ground_truth": "144"
} | {
"index": 1098,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A checkerboard of $13$ rows and $17$ columns has a number written in each square, beginning in the upper left corner, so that the first row is numbered $1,2,\\ldots,17$, the second row $18,19,\\ldots,34$, and so on down the board. If the board is renumbered so that the left col... | math | {
"style": "rule",
"ground_truth": "555"
} | {
"index": 1099,
"solution": "1. **Indexing and Numbering the Board:**\n - Let $i$ be the index for rows, where $i = 1, 2, 3, \\ldots, 13$.\n - Let $j$ be the index for columns, where $j = 1, 2, 3, \\ldots, 17$.\n - The numbering of the board in the first system (row-wise) for a cell in row $i$ and column $j$... |
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