prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "What is the smallest palindromic number that, when squared, results in a four-digit number? Additionally, confirm if this number is a perfect square by calculating its square root. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33",
"style": "rule"
}
|
numina_math
|
{
"index": 1700,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A magician has a collection of 6 distinct wands and 8 distinct potions. He needs to select a set of 5 items, where the number of wands selected is at least twice the number of potions selected. How many different ways can he make this selection? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "126",
"style": "rule"
}
|
numina_math
|
{
"index": 1701,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden measures 120 feet in length and 80 feet in width. You want to install a fence around the garden, but the fencing material is sold in meters. If 1 meter equals approximately 3.28 feet, how many meters of fencing material do you need to purchase to enclose the entire garden? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "122",
"style": "rule"
}
|
numina_math
|
{
"index": 1702,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces a certain number of widgets each day. On Mondays, the number of widgets produced is always divisible by both 6 and 8. On Tuesdays, the number of widgets produced is always divisible by 10. What is the smallest number of widgets the factory must produce on Mondays if they produce more than 100 widgets, and the number of widgets produced on Mondays is also divisible by the number of widgets produced on Tuesdays? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 1703,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial $P(x) = 2x^2 + 3x - 5$, find the value of $P(2)$ and simplify the expression. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 1704,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the sum of the series:\n\\[ S = \\sum_{n=0}^{5} (-1)^n \\left(2^n + 3^{5-n} \\right). \\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "161",
"style": "rule"
}
|
numina_math
|
{
"index": 1705,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given two functions \\( f(x) = 2x + 3 \\) and \\( g(x) = \\frac{x - 1}{4} \\), find the value of \\( x \\) when \\( f(g(x)) = 5 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1706,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation involving a square root: $\\sqrt{x + 10} = 6$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "26",
"style": "rule"
}
|
numina_math
|
{
"index": 1707,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company is analyzing the electricity usage of its two office buildings. Building A consumes electricity at a rate of 15 kilowatt-hours (kWh) per day, while Building B consumes electricity at a rate of 25 kWh per day. The cost of electricity is $0.12 per kWh. If the company wants to calculate the total cost of electricity for both buildings over a period of 30 days, what will be the total cost? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "144",
"style": "rule"
}
|
numina_math
|
{
"index": 1708,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a factory produces 7,500 milliliters of juice per hour, and each bottle can hold 250 milliliters, how many bottles can the factory fill in 5 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 1709,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial \\( P(x) = 4x^3 + ax^2 + bx + 8 \\), find the values of \\(a\\) and \\(b\\) such that when \\(P(x)\\) is divided by \\(2x + 1\\), the quotient is \\(2x^2 + 3x + 4\\) and the remainder is 5. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 1710,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah runs a charity marathon at an average speed of 7 miles per hour. She starts running at 8:15 a.m. and finishes at 11:45 a.m. How many miles did Sarah run during the marathon? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1711,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A committee of 5 members is to be formed from a group of 12 people. In how many ways can this committee be formed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "792",
"style": "rule"
}
|
numina_math
|
{
"index": 1712,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a sequence of positive integers \\( b_1, b_2, b_3, \\ldots \\), each term is defined recursively as \\( b_{n+2} = 2b_{n+1} + b_n \\) for all \\( n \\ge 1 \\). Given that \\( b_5 = 52 \\) and \\( b_6 = 123 \\), find \\( b_7 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "298",
"style": "rule"
}
|
numina_math
|
{
"index": 1713,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A library needs to categorize 2000 books into 50 equal sections. If each section can hold 40 books, how many more sections will the library need to completely categorize all the books? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 1714,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A large art gallery has four rooms shaped as follows: a square, a rectangle, a triangle, and a hexagon. Each room is decorated with paintings. If 40% of the paintings are in the square room, 30% in the rectangle room, 20% in the triangle room, and the remaining paintings are in the hexagon room, how many paintings are there in the hexagon room if the gallery has a total of 250 paintings? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 1715,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the expression \\(\\left(\\frac{3}{4}\\right)^2 \\div \\left(\\frac{9}{16}\\right)\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 1716,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa is planning a trip to Europe and needs to convert her money from US dollars to Euros. She has $800, and the exchange rate is 1 USD = 0.85 Euros. She spends 100 Euros on her first day. How many Euros does she have left after the first day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "580",
"style": "rule"
}
|
numina_math
|
{
"index": 1717,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A circular garden has a radius of 14 meters. There is a straight path that touches the garden tangentially and runs for 20 meters. How far is the point where the path touches the garden from a point directly opposite to it on the circumference of the garden? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "28",
"style": "rule"
}
|
numina_math
|
{
"index": 1718,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is organizing a charity event. She plans to sell 150 tickets at $20 each. However, she decides to offer a 10% discount on the ticket price for early bird buyers, and 40% of the tickets are sold at this discounted price. If she sells all the tickets, what is the total revenue from the ticket sales? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2880",
"style": "rule"
}
|
numina_math
|
{
"index": 1719,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sara drives from City A to City B at an average speed of 60 miles per hour. On her return trip, she encounters traffic and can only drive at an average speed of 40 miles per hour, taking 1.5 hours longer than her trip from City A to City B. How far is City A from City B? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 1720,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( 2^{16} \\times 3^4 \\times 5^2 \\) is divided by \\( 2^4 \\times 3^2 \\times 5 \\), what is the sum of the exponents of the prime factors in the quotient? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 1721,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation \\( 3(2x - 5) + 4 = 19 \\) for \\( x \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1722,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenny is planning her study schedule for the week. She wants to spend 3 hours each day studying math, science, and English, divided equally among the three subjects. She also wants to spend 2 hours on sports activities every day. If she can only study and play sports between 4 PM and 10 PM each day, how many minutes of free time will she have left each day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 1723,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jack is preparing a budget for his upcoming trip. He plans to spend a total of $450 on transportation and accommodation. If he spends $30 more on accommodation than three times the amount he spends on transportation, how much will Jack spend on transportation? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "105",
"style": "rule"
}
|
numina_math
|
{
"index": 1724,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A population of bacteria grows according to the formula \\( P(t) = P_0 e^{kt} \\), where \\( P_0 \\) is the initial population, \\( k \\) is a constant growth rate, and \\( t \\) is the time in hours. After 2 hours, the population triples. After how many hours will the population be 27 times the initial population? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1725,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the rational function \\( f(x) = \\frac{x^2 - 9}{x^2 - 4x + 3} \\). Identify the domain of \\( f(x) \\) and find the distance between the points where the function is undefined. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 1726,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex and Ben are brothers. Alex is three times as old as Ben was five years ago. If Ben is currently 10 years old, how old is Alex? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 1727,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a park, there are two playgrounds, one rectangular and one triangular. The rectangular playground has a length of 30 feet and a width of 20 feet. The triangular playground has one right angle and its legs measure 15 feet and 20 feet. The park management plans to connect the two farthest corners of the playgrounds by a straight path. What is the length of this path in feet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "58.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1728,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the coefficient of \\( x^5 \\) in the expansion of \\( (3x + \\frac{1}{x^2})^7 \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 1729,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the smallest positive integer \\( n \\) such that the decimal representation of \\( \\frac{1}{n} \\) has a repeating period of 6 digits? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "111",
"style": "rule"
}
|
numina_math
|
{
"index": 1730,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Express the sum of the repeating decimals $0.\\overline{3}$, $0.\\overline{6}$, and $0.\\overline{9}$ as a common fraction in its simplest form. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 1731,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many distinct ordered pairs of positive integers $(x, y)$ satisfy the equation $3x + 5y = 100$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1732,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a fitness class, exercises are done in cycles. Jumping jacks are done every 5 minutes, push-ups are done every 8 minutes, and squats are done every 10 minutes. If the class starts with all three exercises being done at the same time, after how many minutes will all three exercises be done together again? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 1733,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Nikki's garden is arranged in such a way that the ratio of irises to roses is 2:5. She currently has 25 roses. She plans to add 20 more roses and enough irises to keep the same ratio. How many irises will Nikki have in total after this addition? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 1734,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces widgets in batches of 8. Each batch requires 3 hours of labor and 5 kilograms of raw material. If the factory has 45 hours of labor available and 80 kilograms of raw material, what is the maximum number of widgets the factory can produce? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 1735,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( \\frac{x^3 \\cdot x^5 \\cdot x^7 \\cdot x^9}{x^2 \\cdot x^4 \\cdot x^6 \\cdot x^8} = 64 \\), find the value of \\( x \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 1736,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma makes handcrafted candles that she sells at local markets. She buys wax in bulk at $10 per kilogram and wicks for $5 per pack. Each candle she makes requires 0.5 kg of wax and one wick. She sells each candle for $25. If Emma buys 10 kg of wax and 20 packs of wicks, and she sells all the candles she makes, what is her total revenue and profit? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 1737,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 3,000 items per hour. If the factory operates for 7 hours a day, how many items does it produce in a week (assuming the factory operates 5 days a week)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "105000",
"style": "rule"
}
|
numina_math
|
{
"index": 1738,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a small community, the population follows a pattern similar to the Fibonacci sequence. The population for the first two years is given as 1000 and 1500 respectively. For each subsequent year, the population is the sum of the populations of the previous two years. What will be the population in the 6th year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10500",
"style": "rule"
}
|
numina_math
|
{
"index": 1739,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa works as a freelance graphic designer. She completed 5 projects in January, each earning her $300. In February, she completed 4 projects, each earning her $450. However, she had to pay $200 in software subscription fees each month. How much more did Lisa earn in January compared to February after paying the software fees? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 1740,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\(x\\): \n\\[4^{x+1} = 2^{3x-2}.\\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 1741,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( n! \\) (n factorial) is equal to \\( 2 \\times 3 \\times 4 \\times 5 \\times 6 \\), what is the value of \\( n \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1742,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anne is 5 years older than Bob, and Bob is twice as old as Carol. If Carol is 10 years old, how old is Anne? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 1743,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A school is organizing a math competition, and each student will receive a unique participation number. The participation numbers are to be distributed such that each number is a multiple of 36 and within the range from 1 to 1000. How many unique participation numbers can the school distribute? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "27",
"style": "rule"
}
|
numina_math
|
{
"index": 1744,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex and Jamie decided to split the cost of a gift for their friend equally. The gift cost 120 yuan. Additionally, Alex found a discount coupon that reduced the total price by half. How much does each person need to pay after applying the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 1745,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a road trip and drives at a constant speed of 60 miles per hour. She plans to take a break after driving for 2 hours. Her friend, who is driving a separate car, drives the same route at a constant speed of 75 miles per hour but starts 30 minutes later than Sarah. How many minutes will Sarah's friend take to catch up with her? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 1746,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the endpoints of a line segment are \\( A(2, 3) \\) and \\( B(8, -5) \\), find the coordinates of the midpoint \\( M \\). Then, determine the value of \\( k \\) if the midpoint \\( M \\) is also a point on the line \\( y = 2x + k \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-11",
"style": "rule"
}
|
numina_math
|
{
"index": 1747,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical container has a radius of 4 cm and a height of 10 cm. If the container is filled with water, what is the volume of the water in the container? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "502.4",
"style": "rule"
}
|
numina_math
|
{
"index": 1748,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company has 200 more than three times the number of employees in its marketing department compared to its sales department. If the total number of employees in both departments is 800, how many employees are in each department? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "650",
"style": "rule"
}
|
numina_math
|
{
"index": 1749,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert \\( 45_{10} \\) to binary. Then, take this binary number and multiply it by \\( 3_{10} \\). Finally, convert the resulting binary number back to decimal. What is the final decimal result? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "119",
"style": "rule"
}
|
numina_math
|
{
"index": 1750,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where all items are 25% off. Sarah wants to buy a jacket that originally costs $120 and a pair of shoes that originally costs $80. She has a coupon that gives an additional 10% off the total sale price. How much will Sarah pay for the jacket and shoes after applying the discounts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "135",
"style": "rule"
}
|
numina_math
|
{
"index": 1751,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store sells color TVs at a discount of 10% off the marked price and still makes a profit of 20%. If the cost price of the color TV is 2400 yuan, what is the marked price? Express the marked price in yuan. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3200",
"style": "rule"
}
|
numina_math
|
{
"index": 1752,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a class, the ratio of the number of boys to girls is 4:5 over a period of 6 years. If there are 20 boys in the class, how many girls are there? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 1753,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A local bakery sells three types of bread: white, whole wheat, and rye. One day, the bakery sold a total of 120 loaves of bread. They sold twice as many white loaves as whole wheat loaves, and 10 more rye loaves than whole wheat loaves. How many loaves of each type of bread were sold that day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "54",
"style": "rule"
}
|
numina_math
|
{
"index": 1754,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the sum of all integers from 1 to 1000 that are divisible by either 3 or 5? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "234168",
"style": "rule"
}
|
numina_math
|
{
"index": 1755,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is training for a marathon and practices running on two different tracks. Track A is 3 miles long, and Track B is 5 miles long. One day, he runs 4 laps on Track A and 3 laps on Track B. If his running pace is consistently 8 minutes per mile, how long, in minutes, does John spend running that day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "216",
"style": "rule"
}
|
numina_math
|
{
"index": 1756,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In triangle $ABC$, $\\angle ABC$ is a right angle, $AB = 8$ units, and $BC = 6$ units. Point $D$ is the midpoint of $AC$, and point $E$ is the midpoint of $AB$. Determine the area of quadrilateral $BDEC$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 1757,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Bob bought 3 show dogs for $400.00 each to breed as a side business. The female had a litter of 8 puppies. If he sells each puppy for $500.00, what is his total profit? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2800",
"style": "rule"
}
|
numina_math
|
{
"index": 1758,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider two numbers, \\( x \\) and \\( y \\), such that \\( x + y = 50 \\) and \\( x \\) is greater than \\( y \\). If the difference between \\( x \\) and \\( y \\) is \\( 10 \\), what are the values of \\( x \\) and \\( y \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 1759,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider an integer \\( x \\). If the square of \\( x \\) is greater than 4 times the value of \\( x \\) and less than 5 times the value of \\( x \\), what are the possible values of \\( x \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1760,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A worker completes a project at a rate of 5% per hour. If the worker works for 6 hours each day, how many days will it take for the worker to complete a project that is equivalent to 3 weeks of work assuming a 40-hour work week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 1761,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "When a number \\( n \\) is divided by 17, the remainder is 5. Compute the sum of all possible three-digit values of \\( n \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "29097",
"style": "rule"
}
|
numina_math
|
{
"index": 1762,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Triangle \\(ABC\\) is defined by the points \\(A(0, 0)\\), \\(B(6, 0)\\), and \\(C(3, 3\\sqrt{3})\\). Find the measure of angle \\(ACB\\) in degrees. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 1763,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A fence is to be built along a straight path using posts placed 2 meters apart. If the first post is placed at the beginning of the path and the last post is placed at the end of the path, how many posts are needed to build a fence along a 50-meter long path? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "26",
"style": "rule"
}
|
numina_math
|
{
"index": 1764,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sophia is planning a party and wants to make sure there are enough chairs for everyone. She has 3 times as many guests as there are tables, and each table seats 4 guests. If she has a total of 48 guests, how many tables does she need? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 1765,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning her monthly budget. She has a total income of $4,500. Her fixed expenses include rent at $1,200, utilities at $300, and a car payment of $400. She also plans to allocate $600 for groceries and $500 for entertainment. After setting aside $400 for savings, how much money will Sarah have left for miscellaneous expenses? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1100",
"style": "rule"
}
|
numina_math
|
{
"index": 1766,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two adjacent sides of a rectangle together measure 30 meters, and the length is 5 meters longer than the width. What are the dimensions of the rectangle, and what is its perimeter? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 1767,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate \\(\\lceil 4.7 \\rceil + \\lceil 5.3 \\rceil - \\lceil 2.9 \\rceil\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 1768,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa drives from her home to her office every day. The distance between her home and her office is 30 miles. She drives at an average speed of 40 miles per hour. On her way, she stops at a coffee shop for 10 minutes. Calculate the total time it takes for Lisa to reach her office from home, including the stop at the coffee shop. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "55",
"style": "rule"
}
|
numina_math
|
{
"index": 1769,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The time it takes for two workers, Alice and Bob, to complete a job is inversely proportional to their individual efficiencies. Together, they can complete the job in 6 hours. If Alice alone can finish the job in 10 hours, how long will it take Bob to complete the job alone? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 1770,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Calculate the square root of 441 by using prime factorization. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "21",
"style": "rule"
}
|
numina_math
|
{
"index": 1771,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria wants to save money for a new laptop that costs $1200. She decides to save $150 each month. After some expenses, she realizes she can only save $100 per month starting from the fourth month. How many months in total will it take Maria to save enough money to buy the laptop? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 1772,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If 3/5 of a number is 24, what is the number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 1773,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A painter is mixing paint to achieve a specific color for a mural. He needs to mix red, blue, and yellow paint in the ratio 2:3:5. If he has already poured 4 liters of red paint, how much blue and yellow paint does he need to add to maintain the ratio? Additionally, if each liter of paint costs $15, what will be the total cost of the paint used? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 1774,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company manufactures two types of products, A and B. The fixed cost for production is $1000 per month. Each unit of product A costs $20 to produce and sells for $50, while each unit of product B costs $30 to produce and sells for $60. If the company wants to ensure a minimum profit of $2000 per month, how many units of product A and B combined should be sold, given that at least 10 units of each product must be sold? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 1775,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex is planning his study schedule for the week. He has 15 hours available to study and wants to divide this time equally among 5 subjects: Math, Science, English, History, and Art. How many hours will he spend on each subject? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 1776,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Calculate the value of \\( 45 - 23 + 17 - 8 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "31",
"style": "rule"
}
|
numina_math
|
{
"index": 1777,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The value of \\(y\\) varies inversely as \\(\\sqrt{x}\\). If \\(y = 8\\) when \\(x = 4\\), find \\(y\\) when \\(x = 16\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 1778,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A map has a scale of 1 inch = 20 miles. If the distance between two cities on the map is 7.5 inches, what is the actual distance between these two cities in miles? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 1779,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a parallelogram with an area of 18 square units. One of its sides is given by the quadratic function \\( f(x) = x^2 + 2x + 1 \\) and the height corresponding to this side is represented by the quadratic function \\( g(x) = x^2 - 4x + 5 \\). Determine the values of \\( x \\) for which the area of the parallelogram is 18 square units. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.539",
"style": "rule"
}
|
numina_math
|
{
"index": 1780,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A coin collection consists of nickels and dimes. The total value of the coins is $2.00, and there are 30 coins in total. How many nickels and how many dimes are in the collection? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 1781,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence of numbers: 2, 5, 8, 11, 14, ..., which is an arithmetic sequence with the first term \\( a = 2 \\) and common difference \\( d = 3 \\). If we add the digits of the 100th term of this sequence, what is the sum? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 1782,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Three whole numbers \\( A \\), \\( B \\), and \\( C \\) satisfy the conditions \\( A \\times B = 45 \\) and \\( B \\times C = 50 \\). What is the value of \\( A + B + C \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 1783,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation \\(3x - 4 = 2x + 5\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 1784,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Ed runs a pet store. He sells 2 dogs, 3 cats, and twice as many fish as the total number of dogs and cats combined. If each dog sells for $50, each cat for $30, and each fish for $10, how much money does Ed make in total from selling all these pets? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "290",
"style": "rule"
}
|
numina_math
|
{
"index": 1785,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a right triangle, the lengths of the legs are in the ratio 3:4, and the length of the hypotenuse is 20 units. Find the lengths of the legs of the triangle. Round your answers to the nearest whole number. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 1786,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate $\\lfloor \\sqrt{50} \\rfloor^2 + \\lceil \\sqrt{50} \\rceil^2$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "113",
"style": "rule"
}
|
numina_math
|
{
"index": 1787,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jessica is planning her study schedule for the week. She decides to study for 2 hours each day from Monday to Friday and 3 hours each day on the weekend. How many hours in total will Jessica spend studying in a week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 1788,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The line \\( y = -x + 3 \\) intersects the graph of \\( y = x^2 - 4x + 2 \\). The x-coordinates of the points of intersection can be written as \\( \\frac{p \\pm \\sqrt{q}}{r} \\), where \\( p, q, \\) and \\( r \\) are integers that do not share any factors other than one. Find the sum \\( p + q + r \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 1789,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the maximum or minimum value of the quadratic function \\( f(x) = -3x^2 + 12x - 5 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 1790,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( z = e^{2\\pi i / 7} \\) be a primitive 7th root of unity. Simplify the expression \n\\[ E = \\frac{1 + z + z^2 + z^3 + z^4 + z^5 + z^6}{1 - z}. \\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 1791,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Connie redeemed all her arcade tickets today. She spent half of them on a stuffed koala bear. She spent 10 tickets on a pair of earbuds. She spent another 15 tickets on glow bracelets. If she had 25 tickets left after all these purchases, how many tickets did Connie redeem today? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 1792,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has 153 apples and wants to distribute them evenly among 7 baskets. After filling each basket with the same number of apples, how many apples will be left over? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1793,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A movie theater offers two types of tickets: a \"premium\" ticket for $25, which includes unlimited snacks, and a \"regular\" ticket for $8, with each snack costing an additional $3. To make the \"premium\" ticket a better deal than the \"regular\" ticket, how many snacks must a person consume? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1794,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria invests $5000 in a savings account that earns a simple interest rate of 4% per annum. However, this interest is subject to a 15% tax. How much money will Maria have in her account after 3 years, after paying the taxes on the interest earned? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5510",
"style": "rule"
}
|
numina_math
|
{
"index": 1795,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is organizing a charity walkathon and needs to calculate the total distance walked by all participants. Each participant will walk a route that is 3 miles long. If there are 150 participants, and each participant walks the route twice, how many total miles will be walked by all participants? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "900",
"style": "rule"
}
|
numina_math
|
{
"index": 1796,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the smallest positive integer \\( n \\) such that \\( n \\) is both a perfect square and a perfect cube and greater than 1,000. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4096",
"style": "rule"
}
|
numina_math
|
{
"index": 1797,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A spherical water tank has a radius of 5 meters. The water tank is filled up to 60% of its capacity. If water costs $2.50 per cubic meter, how much would it cost to fill the tank to its current level? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "785.40",
"style": "rule"
}
|
numina_math
|
{
"index": 1798,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Martin has a mixed basket of fruits consisting of oranges and limes. After eating half of the fruits he had, he was left with twice as many oranges as limes. If he has 50 oranges now, how many fruits did he initially have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 1799,
"name": "numina_math",
"split": "train"
}
|
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