data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "A mail carrier delivers mail to the nineteen houses on the east side of Elm Street. The carrier notices that no two adjacent houses ever get mail on the same day, but that there are never more than two houses in a row that get no mail on the same day. How many different pattern... | math | {
"style": "rule",
"ground_truth": "351"
} | {
"index": 2200,
"solution": "Let $a_n$ be the number of ways if the first house has mail, and let $b_n$ be the number of ways if the first house does not get mail.\n$a_n=a_{n-2}+a_{n-3}$ because if the first house gets mail, the next house that gets mail must either be the third or fourth house.\n$b_n=a_{n-1}+a_{n... |
DeepScaleR | [
{
"role": "user",
"content": "A majority of the $30$ students in Ms. Demeanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than $1$. The cost of a pencil in cents was greater than the number of pencils each student boug... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 2201,
"solution": "1. **Define Variables:**\n Let $s$ be the number of students that bought pencils, $c$ be the cost of each pencil in cents, and $n$ be the number of pencils each student bought. We need to find $c$.\n\n2. **Analyze Given Information:**\n - Since a majority of the 30 students bought ... |
DeepScaleR | [
{
"role": "user",
"content": "A malfunctioning digital clock shows the time $9: 57 \\mathrm{AM}$; however, the correct time is $10: 10 \\mathrm{AM}$. There are two buttons on the clock, one of which increases the time displayed by 9 minutes, and another which decreases the time by 20 minutes. What is the mi... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 2202,
"solution": "We need to increase the time by 13 minutes. If we click the 9 minute button $a$ times and the 20 minute button $b$ times, then we must have $9 a-20 b=13$. Note that if this equation is satisfied, then $b$ increases as $a$ increases, so it suffices to minimize $a$. This means that $a$ m... |
DeepScaleR | [
{
"role": "user",
"content": "A malfunctioning thermometer shows a temperature of $+1^{\\circ}$ in freezing water and $+105^{\\circ}$ in the steam of boiling water. Currently, this thermometer shows $+17^{\\circ}$; what is the true temperature?"
}
] | math | {
"style": "rule",
"ground_truth": "15.38"
} | {
"index": 2203,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A man and a dog are walking. The dog waits for the man to start walking along a path and then runs to the end of the path and back to the man a total of four times, always moving at a constant speed. The last time the dog runs back to the man, it covers the remaining distance o... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 2204,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A man and his faithful dog simultaneously started moving along the perimeter of a block from point \\( A \\) at time \\( t_{0} = 0 \\) minutes. The man moved at a constant speed clockwise, while the dog ran at a constant speed counterclockwise. It is known that the first time t... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 2205,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A man asks: \"How old are you, my son?\"\n\nTo this question, I answered:\n\n\"If my father were seven times as old as I was eight years ago, then one quarter of my father's current age would surely be fourteen years now. Please calculate from this how many years weigh upon my ... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 2206,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A man born in the first half of the nineteenth century was $x$ years old in the year $x^2$. He was born in:"
}
] | math | {
"style": "rule",
"ground_truth": "1806"
} | {
"index": 2207,
"solution": "1. **Formulate the equation**: Given that a man was $x$ years old in the year $x^2$, the year of birth can be expressed as $x^2 - x$.\n\n2. **Determine the range of $x$**: Since he was born in the first half of the 19th century, we have $x^2 - x < 1850$.\n\n3. **Estimate the possible v... |
DeepScaleR | [
{
"role": "user",
"content": "A man bought a number of ping-pong balls where a 16% sales tax is added. If he did not have to pay tax, he could have bought 3 more balls for the same amount of money. If \\( B \\) is the total number of balls that he bought, find \\( B \\)."
}
] | math | {
"style": "rule",
"ground_truth": "18.75"
} | {
"index": 2208,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A man buys a house for $10,000 and rents it. He puts $12\\frac{1}{2}\\%$ of each month's rent aside for repairs and upkeep; pays $325 a year taxes and realizes $5\\frac{1}{2}\\%$ on his investment. The monthly rent (in dollars) is:"
}
] | math | {
"style": "rule",
"ground_truth": "83.33"
} | {
"index": 2209,
"solution": "1. **Understanding the problem**: A man buys a house for $10,000 and aims to realize a $5\\frac{1}{2}\\%$ return on his investment. This means he wants to earn $5.5\\%$ of $10,000$ annually:\n \\[\n 0.055 \\times 10,000 = 550 \\text{ dollars per year}\n \\]\n\n2. **Accounting for... |
DeepScaleR | [
{
"role": "user",
"content": "A man buys a house for $15,000 and wants to achieve a $6\\%$ return on his investment while incurring a yearly tax of $450$, along with an additional $200$ yearly for owner's insurance. The percentage he sets aside from monthly rent for maintenance remains $12\\frac{1}{2}\\%$. ... | math | {
"style": "rule",
"ground_truth": "147.62"
} | {
"index": 2210,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A man buys a house for $20,000 and wants to earn a $6\\%$ annual return on his investment. He pays $650 a year in taxes and sets aside $15\\%$ of each month's rent for repairs and upkeep. Determine the required monthly rent (in dollars) to meet his financial goals.\nA) $165.25$... | math | {
"style": "rule",
"ground_truth": "181.38"
} | {
"index": 2211,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A man can commute either by train or by bus. If he goes to work on the train in the morning, he comes home on the bus in the afternoon; and if he comes home in the afternoon on the train, he took the bus in the morning. During a total of $x$ working days, the man took the bus t... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 2212,
"solution": "Let's analyze the problem by defining the variables and equations based on the given information:\n\n1. **Define Variables:**\n - Let $a$ be the number of days he took the morning train and afternoon bus (m.t., a.b.).\n - Let $b$ be the number of days he took the morning bus and af... |
DeepScaleR | [
{
"role": "user",
"content": "A man chooses two positive integers \\( m \\) and \\( n \\). He defines a positive integer \\( k \\) to be good if a triangle with side lengths \\( \\log m \\), \\( \\log n \\), and \\( \\log k \\) exists. He finds that there are exactly 100 good numbers. Find the maximum possi... | math | {
"style": "rule",
"ground_truth": "134"
} | {
"index": 2213,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A man has $10,000 to invest. He invests $4000 at 5% and $3500 at 4%. In order to have a yearly income of $500, he must invest the remainder at:"
}
] | math | {
"style": "rule",
"ground_truth": "6.4\\%"
} | {
"index": 2214,
"solution": "1. **Calculate the total amount invested at known rates:**\n The man invests $\\$4000$ at 5% and $\\$3500$ at 4%. We need to calculate the income from these investments.\n \\[\n \\text{Income from } \\$4000 = \\$4000 \\times \\frac{5}{100} = \\$200\n \\]\n \\[\n \\text{Inco... |
DeepScaleR | [
{
"role": "user",
"content": "A man has $2.73 in pennies, nickels, dimes, quarters and half dollars. If he has an equal number of coins of each kind, then the total number of coins he has is"
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 2215,
"solution": "Let $x$ represent the number of each type of coin the man has. Since he has pennies, nickels, dimes, quarters, and half dollars, and he has an equal number of each, we can set up the following equation to represent the total value of his coins in cents:\n\n- Pennies contribute $1x$ cen... |
DeepScaleR | [
{
"role": "user",
"content": "A man has part of $4500 invested at 4% and the rest at 6%. If his annual return on each investment is the same, the average rate of interest which he realizes of the $4500 is:"
}
] | math | {
"style": "rule",
"ground_truth": "4.8\\%"
} | {
"index": 2216,
"solution": "1. **Identify the amounts invested at different rates:**\n Let $x$ be the amount invested at $6\\%$. Then, the amount invested at $4\\%$ is $(4500 - x)$.\n\n2. **Set up the equation based on equal annual returns:**\n The annual return from the investment at $4\\%$ is $0.04(4500 - x... |
DeepScaleR | [
{
"role": "user",
"content": "A man is standing on a platform and sees his train move such that after $t$ seconds it is $2 t^{2}+d_{0}$ feet from his original position, where $d_{0}$ is some number. Call the smallest (constant) speed at which the man have to run so that he catches the train $v$. In terms of... | math | {
"style": "rule",
"ground_truth": "4^{n-1}"
} | {
"index": 2217,
"solution": "The train's distance from the man's original position is $t^{2}+d_{0}$, and the man's distance from his original position if he runs at speed $v$ is $v t$ at time $t$. We need to find where $t^{2}+d_{0}=v t$ has a solution. Note that this is a quadratic equation with discriminant $D=\\... |
DeepScaleR | [
{
"role": "user",
"content": "A man named Juan has three rectangular solids, each having volume 128. Two of the faces of one solid have areas 4 and 32. Two faces of another solid have areas 64 and 16. Finally, two faces of the last solid have areas 8 and 32. What is the minimum possible exposed surface area... | math | {
"style": "rule",
"ground_truth": "688"
} | {
"index": 2218,
"solution": "Suppose that $x, y, z$ are the sides of the following solids. Then Volume $=xyz=128$. For the first solid, without loss of generality (with respect to assigning lengths to $x, y, z$), $xy=4$ and $yz=32$. Then $xy^{2}z=128$. Then $y=1$. Solving the remaining equations yields $x=4$ and $... |
DeepScaleR | [
{
"role": "user",
"content": "A man on his way to dinner shortly after $6:00$ p.m. observes that the hands of his watch form an angle of $110^{\\circ}$. Returning before $7:00$ p.m. he notices that again the hands of his watch form an angle of $110^{\\circ}$. The number of minutes that he has been away is:"... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 2219,
"solution": "1. **Define the angles of the hands**: Let $n$ be the number of minutes after 6:00 PM. The angle of the hour hand from the top (12:00 position) can be calculated as follows:\n - In one hour, the hour hand moves $30^\\circ$ (since $360^\\circ / 12 = 30^\\circ$).\n - In $n$ minutes, ... |
DeepScaleR | [
{
"role": "user",
"content": "A man travels $m$ feet due north at $2$ minutes per mile. He returns due south to his starting point at $2$ miles per minute. The average rate in miles per hour for the entire trip is:"
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"index": 2220,
"solution": "To find the average rate in miles per hour for the entire trip, we need to calculate the total distance traveled and the total time taken, and then use the formula for average speed:\n\n\\[\n\\text{Average speed} = \\frac{\\text{Total distance}}{\\text{Total time}}\n\\]\n\n1. **Convert... |
DeepScaleR | [
{
"role": "user",
"content": "A man walked a certain distance at a constant rate. If he had gone $\\frac{1}{2}$ mile per hour faster, he would have walked the distance in four-fifths of the time; if he had gone $\\frac{1}{2}$ mile per hour slower, he would have been $2\\frac{1}{2}$ hours longer on the road.... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 2221,
"solution": "1. **Set up the equations based on the problem statement:**\n Let $x$ be the man's usual speed in miles per hour, and $t$ be the usual time in hours it takes him to walk the distance. The distance he walks can be represented as $d = xt$.\n\n2. **Equation for increased speed:**\n If... |
DeepScaleR | [
{
"role": "user",
"content": "A man went to a bank to cash a check. The cashier made a mistake and gave him the same number of cents instead of dollars and the same number of dollars instead of cents. The man did not count the money, put it in his pocket, and additionally dropped a 5-cent coin. When he got ... | math | {
"style": "rule",
"ground_truth": "31.63"
} | {
"index": 2222,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A man, standing on a lawn, is wearing a circular sombrero of radius 3 feet. The hat blocks the sunlight, causing the grass directly under it to die instantly. If the man walks in a circle of radius 5 feet, what area of dead grass will result?"
}
] | math | {
"style": "rule",
"ground_truth": "60\\pi"
} | {
"index": 2223,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A man, standing on a lawn, is wearing a circular sombrero of radius 3 feet. Unfortunately, the hat blocks the sunlight so effectively that the grass directly under it dies instantly. If the man walks in a circle of radius 5 feet, what area of dead grass will result?"
}
] | math | {
"style": "rule",
"ground_truth": "60\\pi"
} | {
"index": 2224,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A manager schedules a consultation session at a café with two assistant managers but forgets to set a specific time. All three aim to arrive randomly between 2:00 and 5:00 p.m. The manager, upon arriving, will leave if both assistant managers are not present. Each assistant man... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 2225,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A manager schedules an informal review at a café with two of his team leads. He forgets to communicate a specific time, resulting in all parties arriving randomly between 2:00 and 4:30 p.m. The manager will wait for both team leads, but only if at least one has arrived before h... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 2226,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A manufacturer built a machine which will address $500$ envelopes in $8$ minutes. He wishes to build another machine so that when both are operating together they will address $500$ envelopes in $2$ minutes. The equation used to find how many minutes $x$ it would require the se... | math | {
"style": "rule",
"ground_truth": "$\\frac{1}{8}+\\frac{1}{x}=\\frac{1}{2}$"
} | {
"index": 2227,
"solution": "1. **Understanding the problem**: The first machine addresses 500 envelopes in 8 minutes. We need to find the time $x$ it would take for a second machine to address 500 envelopes alone such that both machines working together can address 500 envelopes in 2 minutes.\n\n2. **Representing... |
DeepScaleR | [
{
"role": "user",
"content": "A manufacturer of airplane parts makes a certain engine that has a probability $p$ of failing on any given flight. There are two planes that can be made with this sort of engine, one that has 3 engines and one that has 5. A plane crashes if more than half its engines fail. For ... | math | {
"style": "rule",
"ground_truth": "0, \\frac{1}{2}, 1"
} | {
"index": 2228,
"solution": "They have the same probability of failing if $\\binom{5}{2} p^{3}(1-p)^{2}+\\binom{5}{1} p^{4}(1-p)+p^{5}=\\binom{3}{1} p^{2}(1-p)+p^{3}$, which is true iff $p^{2}\\left(6 p^{3}-15 p^{2}+12 p-3\\right)=0$. This is clearly true for $p=0$. We know it is true for $p=1$, since both probabi... |
DeepScaleR | [
{
"role": "user",
"content": "A map of the town that Annie, Barbara, and Charlie live in can be represented by the Cartesian plane. Annie is located at $(6,-20)$ and Barbara is located at $(1, 14)$. They agree to meet at the closest point that is equidistant from their current locations and walk upwards tog... | math | {
"style": "rule",
"ground_truth": "5"
} | {
"index": 2229,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A marathon is $26$ miles and $385$ yards. One mile equals $1760$ yards.\n\nLeila has run ten marathons in her life. If the total distance Leila covered in these marathons is $m$ miles and $y$ yards, where $0\\le y<1760$, what is the value of $y$?"
}
] | math | {
"style": "rule",
"ground_truth": "330"
} | {
"index": 2230,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A marathon is $26$ miles and $400$ yards. One mile equals $1760$ yards.\n\nMark has run fifteen marathons in his life. If the total distance Mark covered in these marathons is $m$ miles and $y$ yards, where $0 \\leq y < 1760$, what is the value of $y$?"
}
] | math | {
"style": "rule",
"ground_truth": "720"
} | {
"index": 2231,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A marathon of 42 km started at 11:30 AM and the winner finished at 1:45 PM on the same day. What was the average speed of the winner, in km/h?"
}
] | math | {
"style": "rule",
"ground_truth": "18.6"
} | {
"index": 2232,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A marble is placed on each $33$ unit square of a $10*10$ chessboard. After that, the number of marbles in the same row or column with that square is written on each of the remaining empty unit squares. What is the maximum sum of the numbers written on the board?"
}
] | math | {
"style": "rule",
"ground_truth": "438"
} | {
"index": 2233,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A marine biologist interested in monitoring a specific fish species population in a coastal area. On January 15, he captures and tags 80 fish, then releases them back into the water. On June 15, he captures another sample of 100 fish, finding that 6 of them are tagged. He assum... | math | {
"style": "rule",
"ground_truth": "533"
} | {
"index": 2234,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A market survey shows that the price $f(t)$ and sales volume $g(t)$ of a particular product in Oriental Department Store over the past month (calculated based on 30 days) approximately satisfy the functions $f(t)=100(1+ \\frac {1}{t})$ and $g(t)= \\begin{cases} 100+t & 1\\leqsl... | math | {
"style": "rule",
"ground_truth": "12100"
} | {
"index": 2235,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A market survey shows that the price $f(x)$ (in yuan) and the sales volume $g(x)$ (in units) of a certain product in the past $20$ days are both functions of time $x$ (in days), and the price satisfies $f(x)=20-\\frac{1}{2}|x-10|$, and the sales volume satisfies $g(x)=80-2x$, w... | math | {
"style": "rule",
"ground_truth": "600"
} | {
"index": 2236,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A market survey shows that the sales volume and price of a certain product in the past 50 days are functions of the sales time t(days), and the sales volume approximately satisfies f(t)=−2t+200(1≤t≤50,t∈N). The price for the first 30 days is g(x)=12t+30(1≤t≤30,t∈N), and for the... | math | {
"style": "rule",
"ground_truth": "54600"
} | {
"index": 2237,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mason has bricks with dimensions $2\\times5\\times8$ and other bricks with dimensions $2\\times3\\times7$ . She also has a box with dimensions $10\\times11\\times14$ . The bricks and the box are all rectangular parallelepipeds. The mason wants to pack bricks into the box ... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 2238,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A massive vertical plate is fixed to a car moving at a speed of $5 \\, \\text{m/s}$. A ball is flying towards it at a speed of $6 \\, \\text{m/s}$ with respect to the ground. Determine the speed of the ball with respect to the ground after a perfectly elastic normal collision."... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 2239,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math class has fewer than $40$ students. When the students try to sit in rows of $7$, $3$ students sit in the last row. When the students try to sit in rows of $5$, $1$ student is left in the last row. How many students are in this class?"
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"index": 2240,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math class has fewer than 50 students. When the students try to sit in rows of 8, 5 students are left in the last row. When the students try to sit in rows of 6, 3 students remain in the last row. How many students are in this class?"
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"index": 2241,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math competition consists of three problems, each of which receives an integer score from 0 to 7. For any two competitors, it is known that there is at most one problem in which they received the same score. Find the maximum number of competitors in this competition."
}
] | math | {
"style": "rule",
"ground_truth": "64"
} | {
"index": 2242,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math competition problem has probabilities of being solved independently by person \\( A \\), \\( B \\), and \\( C \\) as \\( \\frac{1}{a} \\), \\( \\frac{1}{b} \\), and \\( \\frac{1}{c} \\) respectively, where \\( a \\), \\( b \\), and \\( c \\) are positive integers less th... | math | {
"style": "rule",
"ground_truth": "4/15"
} | {
"index": 2243,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math competition problem: The probabilities that A, B, and C solve the problem independently are $\\frac{1}{a}$, $\\frac{1}{b}$, and $\\frac{1}{c}$ respectively, where $a$, $b$, and $c$ are all single-digit numbers. If A, B, and C attempt the problem independently and the pro... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{15}"
} | {
"index": 2244,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math conference is hosting a series of lectures by seven distinct lecturers. Dr. Smith's lecture depends on Dr. Jones’s lecture, and additionally, Dr. Brown's lecture depends on Dr. Green’s lecture. How many valid orders can these seven lecturers be scheduled, given these dep... | math | {
"style": "rule",
"ground_truth": "1260"
} | {
"index": 2245,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math conference is presenting a lecture series with six different lecturers. If Dr. Smith's lecture depends on Dr. Jones's lecture, so that Dr. Smith must be scheduled at some time after Dr. Jones, in how many orders can the six lecturers be scheduled?"
}
] | math | {
"style": "rule",
"ground_truth": "360"
} | {
"index": 2246,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math field day competition is held in a room with many tables, and there are 6 stools at each table. Each stool has 3 legs, and each table has 4 legs. If there is a total of 484 legs on all the tables and stools in the room, how many tables are in the room?"
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 2247,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math professor stands up in front of a room containing 100 very smart math students and says, 'Each of you has to write down an integer between 0 and 100, inclusive, to guess 'two-thirds of the average of all the responses.' Each student who guesses the highest integer that i... | math | {
"style": "rule",
"ground_truth": "0"
} | {
"index": 2248,
"solution": "Since the average cannot be greater than 100, no student will write down a number greater than $\\frac{2}{3} \\cdot 100$. But then the average cannot be greater than $\\frac{2}{3} \\cdot 100$, and, realizing this, each student will write down a number no greater than $\\left(\\frac{2}{... |
DeepScaleR | [
{
"role": "user",
"content": "A math teacher randomly selects 3 questions for analysis from a test paper consisting of 12 multiple-choice questions, 4 fill-in-the-blank questions, and 6 open-ended questions. The number of different ways to select questions such that at least one multiple-choice question and... | math | {
"style": "rule",
"ground_truth": "864"
} | {
"index": 2249,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math teacher requires Noelle to do one homework assignment for each of the first five homework points she wants to earn; for each of the next five homework points, she needs to do two homework assignments; and so on, so that to earn the $n^{\\text{th}}$ homework point, she ha... | math | {
"style": "rule",
"ground_truth": "75"
} | {
"index": 2250,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math teacher requires Noelle to do one homework assignment for each of the first four homework points she wants to earn; for each of the next four homework points, she needs to do two homework assignments; and so on, so that to earn the $n^{\\text{th}}$ homework point, she ha... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 2251,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math test consists of 12 multiple-choice questions, each worth 5 points. It is known that a student is confident in correctly answering 6 of these questions. For another three questions, the student can eliminate one incorrect option. For two questions, the student can elimin... | math | {
"style": "rule",
"ground_truth": "41.25"
} | {
"index": 2252,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A math test starts at 12:35 PM and lasts for $4 \\frac{5}{6}$ hours. At what time does the test end?"
}
] | math | {
"style": "rule",
"ground_truth": "17:25"
} | {
"index": 2253,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mathematical contest had $3$ problems, each of which was given a score between $0$ and $7$ ( $0$ and $7$ included). It is known that, for any two contestants, there exists at most one problem in which they have obtained the same score (for example, there are no two c... | math | {
"style": "rule",
"ground_truth": "64"
} | {
"index": 2254,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mathematical demonstration showed that there were distinct positive integers such that $97^4 + 84^4 + 27^4 + 3^4 = m^4$. Calculate the value of $m$."
}
] | math | {
"style": "rule",
"ground_truth": "108"
} | {
"index": 2255,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mathematical organization is producing a set of commemorative license plates. Each plate contains a sequence of five characters chosen from the four letters in AIME and the four digits in 2007. No character may appear in a sequence more times than it appears among the four le... | math | {
"style": "rule",
"ground_truth": "372"
} | {
"index": 2256,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mathematical organization is producing a set of commemorative license plates. Each plate contains a sequence of five characters chosen from the four letters in AIME and the four digits in 2007. No character may appear in a sequence more times than it appears among the four le... | math | {
"style": "rule",
"ground_truth": "372"
} | {
"index": 2257,
"solution": "There are 7 different characters that can be picked, with 0 being the only number that can be repeated twice.\nIf $0$ appears 0 or 1 times amongst the sequence, there are $\\frac{7!}{(7-5)!} = 2520$ sequences possible.\nIf $0$ appears twice in the sequence, there are ${5\\choose2} = 10... |
DeepScaleR | [
{
"role": "user",
"content": "A mathematician $M^{\\prime}$ is called a descendent of mathematician $M$ if there is a sequence of mathematicians $M=M_{1}, M_{2}, \\ldots, M_{k}=M^{\\prime}$ such that $M_{i}$ was $M_{i+1}$ 's doctoral advisor for all $i$. Estimate the number of descendents that the mathemati... | math | {
"style": "rule",
"ground_truth": "82310"
} | {
"index": 2258,
"solution": "First let's estimate how many \"generations\" of mathematicians there have been since 1300. If we suppose that a mathematician gets his PhD around age 30 and becomes a PhD advisor around age 60, then we'll get a generation length of approximately 30 years. However, not all mathematicia... |
DeepScaleR | [
{
"role": "user",
"content": "A mathematician is working on a geospatial software and comes across a representation of a plot's boundary described by the equation $x^2 + y^2 + 8x - 14y + 15 = 0$. To correctly render it on the map, he needs to determine the diameter of this plot."
}
] | math | {
"style": "rule",
"ground_truth": "10\\sqrt{2}"
} | {
"index": 2259,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A meal at a diner includes a burger weighing 150 grams, of which 40 grams are filler. What percent of the burger is not filler?"
}
] | math | {
"style": "rule",
"ground_truth": "73.33\\%"
} | {
"index": 2260,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A merchant acquires goods at a discount of $30\\%$ of the list price and intends to sell them with a $25\\%$ profit margin after a $25\\%$ discount on the marked price. Determine the required percentage of the original list price that the goods should be marked."
}
] | math | {
"style": "rule",
"ground_truth": "124\\%"
} | {
"index": 2261,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A merchant bought some goods at a discount of $20\\%$ of the list price. He wants to mark them at such a price that he can give a discount of $20\\%$ of the marked price and still make a profit of $20\\%$ of the selling price. The per cent of the list price at which he should m... | math | {
"style": "rule",
"ground_truth": "125"
} | {
"index": 2262,
"solution": "1. **Define the variables:**\n Let $L$ be the list price of the goods.\n Let $C$ be the cost price for the merchant after the discount.\n Let $M$ be the marked price set by the merchant.\n Let $S$ be the selling price after giving a discount on the marked price.\n\n2. **Calcula... |
DeepScaleR | [
{
"role": "user",
"content": "A merchant buys $n$ radios for $d$ dollars, where $d$ is a positive integer. The merchant sells two radios at half the cost price to a charity sale, and the remaining radios at a profit of 8 dollars each. If the total profit is 72 dollars, what is the smallest possible value of... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 2263,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A merchant buys goods at $25\\%$ off the list price. He desires to mark the goods so that he can give a discount of $20\\%$ on the marked price and still clear a profit of $25\\%$ on the selling price. What percent of the list price must he mark the goods?"
}
] | math | {
"style": "rule",
"ground_truth": "125\\%"
} | {
"index": 2264,
"solution": "1. **Setting the List Price**: Assume the list price of the goods is $L = 100$ units. This simplification does not affect the generality of the problem since we are asked for a percentage.\n\n2. **Calculating the Purchase Price**: The merchant buys the goods at a $25\\%$ discount. Ther... |
DeepScaleR | [
{
"role": "user",
"content": "A merchant had 10 barrels of sugar, which he arranged into a pyramid as shown in the illustration. Each barrel, except one, was numbered. The merchant accidentally arranged the barrels such that the sum of the numbers along each row equaled 16. Could you rearrange the barrels s... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 2265,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A merchant offers a large group of items at $30\\%$ off. Later, the merchant takes $20\\%$ off these sale prices and claims that the final price of these items is $50\\%$ off the original price. As a percentage of the original price, what is the difference between the true di... | math | {
"style": "rule",
"ground_truth": "6\\%"
} | {
"index": 2266,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A merchant placed on display some dresses, each with a marked price. He then posted a sign \"$1/3$ off on these dresses.\" The cost of the dresses was $3/4$ of the price at which he actually sold them. Then the ratio of the cost to the marked price was:"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 2267,
"solution": "1. **Define Variables:**\n Let $x$ be the marked price of the dresses.\n\n2. **Calculate the Selling Price:**\n The dresses are sold at $\\frac{1}{3}$ off the marked price. Therefore, the selling price is:\n \\[\n \\text{Selling Price} = x - \\frac{1}{3}x = \\frac{2}{3}x\n \\... |
DeepScaleR | [
{
"role": "user",
"content": "A merchant purchases a gadget for $30$ less $15\\%$. He aims to sell the gadget at a gain of $25\\%$ on his cost after allowing a $10\\%$ discount on his marked price. At what price, in dollars, should the gadget be marked?"
}
] | math | {
"style": "rule",
"ground_truth": "35.42"
} | {
"index": 2268,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A merchant's cumulative sales from January to May reached 38.6 million yuan. It is predicted that the sales in June will be 5 million yuan, and the sales in July will increase by x% compared to June. The sales in August will increase by x% compared to July. The total sales in S... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 2269,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A merchant's cumulative sales from January to May reached 38.6 million yuan. It is predicted that the sales in June will be 5 million yuan, the sales in July will increase by x% compared to June, and the sales in August will increase by x% compared to July. The total sales in S... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 2270,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A metal bar at a temperature of $20^{\\circ} \\mathrm{C}$ is placed in water at a temperature of $100^{\\circ} \\mathrm{C}$. After thermal equilibrium is established, the temperature becomes $80^{\\circ} \\mathrm{C}$. Then, without removing the first bar, another identical meta... | math | {
"style": "rule",
"ground_truth": "68"
} | {
"index": 2271,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A metal bar with a temperature of $20{ }^{\\circ} \\mathrm{C}$ is placed into water that is initially at $80{ }^{\\circ} \\mathrm{C}$. After thermal equilibrium is reached, the temperature is $60{ }^{\\circ} \\mathrm{C}$. Without removing the first bar from the water, another m... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"index": 2272,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A metal weight has a mass of 20 kg and is an alloy of four metals. The mass of the first metal in this alloy is one and a half times greater than that of the second, the mass of the second metal is in the ratio $3:4$ to the mass of the third, and the mass of the third metal is ... | math | {
"style": "rule",
"ground_truth": "4.91"
} | {
"index": 2273,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A metallic weight has a mass of 20 kg and is an alloy of four metals. The first metal in this alloy is one and a half times the amount of the second metal. The mass of the second metal relates to the mass of the third metal as $3:4$, and the mass of the third metal to the mass ... | math | {
"style": "rule",
"ground_truth": "5.89"
} | {
"index": 2274,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A metallic weight has a mass of 25 kg and is an alloy of four metals. The first metal in this alloy is one and a half times more than the second; the mass of the second metal is related to the mass of the third as \\(3: 4\\), and the mass of the third metal to the mass of the f... | math | {
"style": "rule",
"ground_truth": "7.36"
} | {
"index": 2275,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A metro network has at least 4 stations on each line, with no more than three transfer stations per line. No transfer station has more than two lines crossing. What is the maximum number of lines such a network can have if it is possible to travel from any station to any other ... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 2276,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A middle school cafeteria regularly purchases rice from a grain store at a price of 1500 yuan per ton. Each time rice is purchased, a transportation fee of 100 yuan is required. The cafeteria needs 1 ton of rice per day, and the storage cost for rice is 2 yuan per ton per day (... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 2277,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mineralogist is hosting a competition to guess the age of an ancient mineral sample. The age is provided by the digits 2, 2, 3, 3, 5, and 9, with the condition that the age must start with an odd number."
}
] | math | {
"style": "rule",
"ground_truth": "120"
} | {
"index": 2278,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mini soccer team has 12 members. We want to choose a starting lineup of 5 players, which includes one goalkeeper and four outfield players (order of outfield players does not matter). In how many ways can we choose this starting lineup?"
}
] | math | {
"style": "rule",
"ground_truth": "3960"
} | {
"index": 2279,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mischievous child mounted the hour hand on the minute hand's axle and the minute hand on the hour hand's axle of a correctly functioning clock. The question is, how many times within a day does this clock display the correct time?"
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 2280,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mix of blue paint and yellow paint is required such that the ratio of blue paint to yellow paint is 5 to 3. If Julia plans to create 45 cans of this mix and each can contains the same volume, determine how many cans of blue paint will Julia need."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"index": 2281,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mixture of $30$ liters of paint is $25\\%$ red tint, $30\\%$ yellow tint and $45\\%$ water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture?"
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 2282,
"solution": "1. **Calculate the amount of yellow tint in the original mixture:**\n The original mixture contains $30\\%$ yellow tint in $30$ liters. Therefore, the amount of yellow tint is:\n \\[\n 0.30 \\times 30 = 9 \\text{ liters}\n \\]\n\n2. **Add the additional yellow tint:**\n Five ... |
DeepScaleR | [
{
"role": "user",
"content": "A modified deck of cards contains 60 cards consisting of 15 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Prince, and Princess) and 4 suits ($\\spadesuit$, $\\heartsuit$, $\\diamondsuit$, $\\clubsuit$). Hence, each suit now has 15 cards. Four suits are still divide... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{20}"
} | {
"index": 2283,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A modified octahedron consists of two pyramids, each with a pentagonal base, glued together along their pentagonal bases, forming a polyhedron with twelve faces. An ant starts at the top vertex and walks randomly to one of the five adjacent vertices in the middle ring. From thi... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"index": 2284,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A modified sign pyramid with five levels, where a cell gets a \"+\" if the two cells below it have the same sign, and it gets a \"-\" if the two cells below it have different signs. If a \"-\" is to be at the top of the pyramid, calculate the number of possible ways to fill the... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 2285,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mole has chewed a hole in a carpet in the shape of a rectangle with sides of 10 cm and 4 cm. Find the smallest size of a square patch that can cover this hole (a patch covers the hole if all points of the rectangle lie inside the square or on its boundary)."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{58}"
} | {
"index": 2286,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A monic polynomial of degree $n$, with real coefficients, has its first two terms after $x^n$ as $a_{n-1}x^{n-1}$ and $a_{n-2}x^{n-2}$. It’s known that $a_{n-1} = 2a_{n-2}$. Determine the absolute value of the lower bound for the sum of the squares of the roots of this polynomi... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 2287,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A monkey in Zoo becomes lucky if he eats three different fruits. What is the largest number of monkeys one can make lucky, by having $20$ oranges, $30$ bananas, $40$ peaches and $50$ tangerines? Justify your answer."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 2288,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A monomial term $x_{i_{1}} x_{i_{2}} \\ldots x_{i_{k}}$ in the variables $x_{1}, x_{2}, \\ldots x_{8}$ is square-free if $i_{1}, i_{2}, \\ldots i_{k}$ are distinct. (A constant term such as 1 is considered square-free.) What is the sum of the coefficients of the squarefree term... | math | {
"style": "rule",
"ground_truth": "764"
} | {
"index": 2289,
"solution": "Let $a_{n}$ be the sum of the coefficients of the square-terms in the product $\\prod_{1 \\leq i<j \\leq n}(1+$ $x_{i} x_{j}$ ). Square-free terms in this product come in two types: either they include $x_{n}$, or they do not. The sum of the coefficients of the terms that include $x_{n... |
DeepScaleR | [
{
"role": "user",
"content": "A month with $31$ days has the same number of Mondays and Wednesdays. How many of the seven days of the week could be the first day of this month?"
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 2290,
"solution": "To solve this problem, we need to determine how many days of the week could be the first day of a month with 31 days such that the number of Mondays and Wednesdays in that month are equal.\n\n1. **Understanding the Weekday Distribution:**\n A month with 31 days spans exactly 4 weeks ... |
DeepScaleR | [
{
"role": "user",
"content": "A monthly cell phone plan costs $30 per month, plus $10 cents per text message, plus $15 cents for each minute used over 25 hours, and an additional $5 for every gigabyte of data used over 15GB. In February, Emily sent 150 text messages, talked for 26 hours, and used 16GB of da... | math | {
"style": "rule",
"ground_truth": "59.00"
} | {
"index": 2291,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A motel bills its customers by charging a flat fee for the first night and then adding on a fixed amount for every night thereafter. If it costs George $\\$155$ to stay in the motel for 3 nights and Noah $\\$290$ to stay in the motel for 6 nights, how much is the flat fee for t... | math | {
"style": "rule",
"ground_truth": "\\$65"
} | {
"index": 2292,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A moth starts at vertex $A$ of a certain cube and is trying to get to vertex $B$, which is opposite $A$, in five or fewer \"steps,\" where a step consists in traveling along an edge from one vertex to another. The moth will stop as soon as it reaches $B$. How many ways can the ... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"index": 2293,
"solution": "Let $X, Y, Z$ be the three directions in which the moth can initially go. We can symbolize the trajectory of the moth by a sequence of stuff from $X \\mathrm{~s}, Y \\mathrm{~s}$, and $Z \\mathrm{~s}$ in the obvious way: whenever the moth takes a step in a direction parallel or opposit... |
DeepScaleR | [
{
"role": "user",
"content": "A mother gives pocket money to her children sequentially: 1 ruble to Anya, 2 rubles to Borya, 3 rubles to Vitya, then 4 rubles to Anya, 5 rubles to Borya, and so on until Anya receives 202 rubles, and Borya receives 203 rubles. How many more rubles will Anya receive compared to... | math | {
"style": "rule",
"ground_truth": "68"
} | {
"index": 2294,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mother purchases 5 blue plates, 2 red plates, 2 green plates, and 1 orange plate. How many ways are there for her to arrange these plates for dinner around her circular table if she doesn't want the 2 green plates to be adjacent?"
}
] | math | {
"style": "rule",
"ground_truth": "588"
} | {
"index": 2295,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A motorcycle travels due west at $\\frac{5}{8}$ mile per minute on a long straight road. At the same time, a circular storm, whose radius is $60$ miles, moves southwest at $\\frac{1}{2}$ mile per minute. At time $t=0$, the center of the storm is $100$ miles due north of the mot... | math | {
"style": "rule",
"ground_truth": "160"
} | {
"index": 2296,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A motorcyclist left point A for point B, and at the same time, a pedestrian left point B for point A. When they met, the motorcyclist took the pedestrian on his motorcycle to point A and then immediately went back to point B. As a result, the pedestrian reached point A 4 times ... | math | {
"style": "rule",
"ground_truth": "2.75"
} | {
"index": 2297,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A motorist left point A for point D, covering a distance of 100 km. The road from A to D passes through points B and C. At point B, the GPS indicated that 30 minutes of travel time remained, and the motorist immediately reduced speed by 10 km/h. At point C, the GPS indicated th... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 2298,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A mouse has a wheel of cheese which is cut into $2018$ slices. The mouse also has a $2019$ -sided die, with faces labeled $0,1,2,\\ldots, 2018$ , and with each face equally likely to come up. Every second, the mouse rolls the dice. If the dice lands on $k$ , and the mouse ... | math | {
"style": "rule",
"ground_truth": "2019"
} | {
"index": 2299,
"solution": ""
} |
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