prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "Alex and Jordan are working together to paint a fence. If Alex can paint the entire fence in 6 hours and Jordan can paint the same fence in 4 hours, how long will it take them to paint the fence together? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.4",
"style": "rule"
}
|
numina_math
|
{
"index": 10400,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a number \\( x \\) that, when divided by 4, leaves a remainder of 3, when divided by 5, leaves a remainder of 2, and when divided by 6, leaves a remainder of 1. What is the smallest positive integer \\( x \\) that satisfies all these conditions? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 10401,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a positive integer \\( N \\) such that the sum of its digits is 10, and \\( N \\) has exactly 6 positive divisors. What is the value of \\( N \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "28",
"style": "rule"
}
|
numina_math
|
{
"index": 10402,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has three types of fruits: apples, oranges, and bananas. When he divides the apples into groups of 4, he has 3 remaining. When he divides the oranges into groups of 5, he has 2 remaining. When he divides the bananas into groups of 6, he has 5 remaining. If the total number of each type of fruit is less than 100, what is the sum of all possible quantities of apples, oranges, and bananas that he could have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3065",
"style": "rule"
}
|
numina_math
|
{
"index": 10403,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The first term of an arithmetic sequence is \\(2\\) and the common difference is \\(5\\). If the \\(n\\)-th term of the sequence is given by \\(a_n\\), find the value of \\(n\\) for which \\(a_n = 502\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "101",
"style": "rule"
}
|
numina_math
|
{
"index": 10404,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $a$ and $b$ be relatively prime positive integers such that $\\frac{a}{b} = \\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\cdots + \\frac{1}{50}$. Find $a + b$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4219",
"style": "rule"
}
|
numina_math
|
{
"index": 10405,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The equation $x^2 + y^2 + 4x - 8y + k = 0$ represents a circle. What is the value of $k$ if the radius of the circle is $5$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-5",
"style": "rule"
}
|
numina_math
|
{
"index": 10406,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "For some positive integer \\( n \\), the equation \\( 2^x = 3^y \\cdot 5^z \\) holds, where \\( x, y, z \\) are positive integers. Determine the number of solutions for \\( x \\) in the range \\( 1 \\leq x \\leq 100 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 10407,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires that the amount of sugar be 0.75 times the amount of flour. If you have 3 cups of sugar, how many cups of flour do you need? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 10408,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the sum of all the divisors of the number 84 and explain the steps involved. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "224",
"style": "rule"
}
|
numina_math
|
{
"index": 10409,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a contest, there are 5 unique prizes to be awarded to 5 participants. Additionally, there are 3 consolation prizes to be given out, but no participant can receive more than one prize. How many distinct ways are there to distribute all the prizes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "720",
"style": "rule"
}
|
numina_math
|
{
"index": 10410,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cake was cut into 12 equal slices. Sarah ate 1/3 of the cake, and Jake ate 1/4 of the cake. How many slices are left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 10411,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "My pay is the same every day I work. I worked every day in 1992, including weekends. In March, I earned $930. How much did I earn for the entire year of 1992? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10980",
"style": "rule"
}
|
numina_math
|
{
"index": 10412,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Dr. Chen deposits 8,000 yuan in a bank for a fixed term of 4 years with an annual interest rate of 3.20%. How much money will he receive in total, including the principal and interest, when the term is over? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9024",
"style": "rule"
}
|
numina_math
|
{
"index": 10413,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tommy has a collection of coins consisting of nickels, dimes, and quarters. The number of dimes is three more than twice the number of nickels. The number of quarters is five less than the number of dimes. If Tommy has a total of 50 coins, how many nickels, dimes, and quarters does he have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 10414,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer's rectangular field has a length of \\( (x + 4) \\) meters and a width of \\( (x - 2) \\) meters. The area of the field is 120 square meters. Find the value of \\( x \\). Then, calculate the new area of the field if both the length and width are increased by 20%. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "172.8",
"style": "rule"
}
|
numina_math
|
{
"index": 10415,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jane is planning her study schedule. She needs to study for 3 subjects: Math, Science, and History. She decides to spend 1.5 hours on Math, twice as much time on Science as on Math, and half as much time on History as on Science. How many hours in total will Jane spend studying? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 10416,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company increased its employees' salaries by 20% last year and plans to decrease them by 25% this year. If an employee's salary was $50,000 before the increase last year, what will their salary be after this year's decrease? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45000",
"style": "rule"
}
|
numina_math
|
{
"index": 10417,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A delivery truck travels a total of 15 kilometers daily. Every hour, the truck covers 2 kilometers more than it did in the previous hour. On the first hour, it travels 1 kilometer. How many meters does the truck travel in the first 5 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25000",
"style": "rule"
}
|
numina_math
|
{
"index": 10418,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, the number of boys is 1/4 more than the number of girls. Additionally, there are 6 fewer girls than boys. How many girls are there in the sixth grade? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 10419,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider all natural numbers \\( n \\) between 1000 and 2000 inclusive. For how many of these numbers is the sum of the digits a power of 3? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "43",
"style": "rule"
}
|
numina_math
|
{
"index": 10420,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A passenger train transports passengers between two stations located in two separate cities. On a particular day, the train carried 120 passengers from one station to the other one way, and on the return trip carried 80 passengers. If the train made four more round trips that day, taking the same number of people as the first trip in each trip, calculate the total number of passengers transported between both stations for the entire day. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1000",
"style": "rule"
}
|
numina_math
|
{
"index": 10421,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a train travels at 60 miles per hour and another train travels at 80 miles per hour, both starting from the same station but in opposite directions, after how many hours will the two trains be 350 miles apart? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.5",
"style": "rule"
}
|
numina_math
|
{
"index": 10422,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A library has 5 different books on mathematics and 4 different books on science. A student wants to select 3 books to borrow, ensuring that at least one book is on mathematics and at least one book is on science. How many different ways can the student select the books? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "70",
"style": "rule"
}
|
numina_math
|
{
"index": 10423,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length of 15 meters and a width of 10 meters. If the owner decides to plant flowers along the perimeter and leaves a space of 0.5 meters at each corner, what is the total length of the planted area around the garden? Express your answer to the nearest tenth of a meter. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48.0",
"style": "rule"
}
|
numina_math
|
{
"index": 10424,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory can produce 200 gadgets in 8 hours. If the factory's efficiency increases by 25%, how many gadgets can it produce in 10 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "313",
"style": "rule"
}
|
numina_math
|
{
"index": 10425,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Three painters, Alice, Bob, and Carol, work together to paint a house. Alice can paint the house in 12 hours by herself, Bob can paint the house in 10 hours by himself, and Carol can paint the house in 15 hours by herself. How long will it take them to paint the house if they work together? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 10426,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company manufactures two types of widgets: standard widgets and premium widgets. The cost to produce each standard widget is $5, and the cost to produce each premium widget is $10. The company needs to spend at least $2000 on production to meet a specific target. If the company produces 100 premium widgets, how many standard widgets must they produce to meet the production cost requirement? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "200",
"style": "rule"
}
|
numina_math
|
{
"index": 10427,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two trains, Train X and Train Y, depart from stations P and Q respectively and travel towards each other. Train X travels at a speed of 90 kilometers per hour, and Train Y travels at a speed of 70 kilometers per hour. After a certain period of time, when they meet, Train X has traveled 40 kilometers more than Train Y. What is the distance between stations P and Q? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "320",
"style": "rule"
}
|
numina_math
|
{
"index": 10428,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the polynomial \\( P(x) = 2x^3 - 5x^2 + 3x - 7 \\) at \\( x = -2 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-49",
"style": "rule"
}
|
numina_math
|
{
"index": 10429,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a parking lot, there are 100 parking spaces arranged in a grid with 10 rows and 10 columns. Due to maintenance work, the last row and the last column are unavailable for parking. How many parking spaces remain available? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "81",
"style": "rule"
}
|
numina_math
|
{
"index": 10430,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A play has two different male roles, two different female roles, and two different roles that can be either gender. Only a man can be assigned to a male role, and only a woman can be assigned to a female role. If five men and six women audition, in how many ways can the six roles be assigned? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25200",
"style": "rule"
}
|
numina_math
|
{
"index": 10431,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Henry is training for a marathon. He runs 5 miles each day for 5 days a week. On the weekend, he runs half as many miles as he does on a weekday. Over four weeks, what is the average number of miles Henry runs per week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 10432,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex is training for a marathon and runs a specific training route every day. The route consists of running 3/5 of a mile on a flat road and 1/4 of a mile up a hill. After reaching the top, he runs the same 1/4 mile back down the hill and then finishes by running another 3/5 of a mile back to his starting point. How many miles does Alex run in total for one training session? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.7",
"style": "rule"
}
|
numina_math
|
{
"index": 10433,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the value of \\( k \\) such that \\( (x-2) \\) is a factor of the polynomial \\( 3x^3 + kx^2 - 14x + 8 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-1",
"style": "rule"
}
|
numina_math
|
{
"index": 10434,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A certain bacteria culture doubles in size every 3 hours. If the initial population of the bacteria is 500, what will the population be after 12 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8000",
"style": "rule"
}
|
numina_math
|
{
"index": 10435,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anna is currently 24 years old, which is twice the age of her younger brother, Ben. In how many years will Anna be 1.5 times as old as Ben? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 10436,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John has a collection of quarters and dimes worth a total of $7.10. If the number of quarters is 4 more than twice the number of dimes, how many of each coin does he have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 10437,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah and Tom are collecting seashells. Sarah collects three times as many seashells as Tom. Together, they collect a total of 52 seashells. How many seashells did Tom collect? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 10438,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the equations \\( a^2 \\cdot a^3 = a^x \\) and \\( b^{x-2} = b^3 \\cdot b^{-1} \\), find the values of \\(a\\) and \\(x\\) that satisfy both equations. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 10439,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anna and Bella are traveling to a conference. Anna's car travels at a speed of 60 miles per hour, while Bella's car travels at a speed of 75 miles per hour. If Bella starts her journey 30 minutes after Anna, how long will it take for Bella to catch up to Anna? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 10440,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( x = 0.75 \\) and \\( y = 120 \\), calculate the value of \\( y \\times (x \\times 100\\%) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 10441,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A line segment is divided into parts whose lengths form a Fibonacci sequence. The total length of the line segment is 233 units. Determine the length of the 7th part of the line segment. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 10442,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A barrel of maple syrup weighs 20 kilograms. After pouring out half of the syrup, the barrel and the remaining syrup weigh a total of 12 kilograms. If the selling price of the syrup is $10 per kilogram, how much can the remaining syrup be sold for? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 10443,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mrs. Thompson is baking cookies for a bake sale. She plans to give away 1/4 of her cookies to her neighbors and sell the remaining 3/4 at the bake sale. If she wants to keep 5 cookies for herself and still have 60 cookies to sell, how many cookies does she need to bake in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "87",
"style": "rule"
}
|
numina_math
|
{
"index": 10444,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jennifer is training for a marathon and wants to determine her average speed during her training sessions. On Monday, she ran for 1 hour and 15 minutes covering a distance of 10 kilometers. On Wednesday, she ran for 45 minutes covering 6 kilometers. On Friday, she ran for 1 hour covering 8 kilometers. What was her average speed in kilometers per hour for these three training sessions? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 10445,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The sum of the roots of the quadratic equation \\( ax^2 + bx + c = 0 \\) is equal to 5, and the product of the roots is 6. If \\( a = 1 \\), determine the values of \\( b \\) and \\( c \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 10446,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a certain language, words are created from the letters A, B, C, and D. How many 4-letter words can be formed where each word must contain at least one A, and the letters can be repeated? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "175",
"style": "rule"
}
|
numina_math
|
{
"index": 10447,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samuel is preparing for a long-distance bike race. He needs to load his bike with enough water to stay hydrated throughout the race. His bike has two water bottles, each holding 750 milliliters of water. He also carries a hydration pack that holds 2.5 liters of water. If Samuel drinks 500 milliliters of water every hour, how many hours can he bike before he runs out of water? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 10448,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from town A to town B at an average speed of 60 miles per hour. On the return trip, it travels at an average speed of 40 miles per hour. If the total travel time for the round trip is 5 hours, what is the distance between town A and town B? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 10449,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A warehouse has 5 crates. Each crate contains 150 apples. If 3 crates are sold, how many apples are left in the warehouse? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 10450,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has 5 fields, each planted with 30 rows of corn. If each row produces 12 bushels of corn, how many bushels of corn does the farmer harvest in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1800",
"style": "rule"
}
|
numina_math
|
{
"index": 10451,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Paul is organizing a gift basket for a charity auction. He has 5 different types of chocolates, 4 different types of fruit, and 3 different types of wine. He wants to include 2 types of chocolates, 1 type of fruit, and 1 type of wine in the basket. If the cost of each type of chocolate is $3, each type of fruit is $2, and each type of wine is $10, what is the total cost of the gift basket? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 10452,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store offers a discount on a laptop that originally costs $1200. The discount rate is 15%. After applying the discount, the store charges an additional 8% sales tax on the discounted price. What is the final price of the laptop after applying the discount and including the sales tax? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1101.60",
"style": "rule"
}
|
numina_math
|
{
"index": 10453,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa has a bag of mixed nuts that weighs 500 grams. She eats 30% of the nuts in the bag. Later, she adds another 150 grams of nuts to the bag. What is the final weight of the nuts in the bag? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "500",
"style": "rule"
}
|
numina_math
|
{
"index": 10454,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 10,000 widgets a week. Each widget weighs 500 grams. If the factory needs to ship the widgets in boxes that can hold up to 20 kilograms each, how many boxes are needed to ship all the widgets produced in a week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "250",
"style": "rule"
}
|
numina_math
|
{
"index": 10455,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, there are 24 students. The ratio of boys to girls is 3:5. If 1/3 of the boys and 1/4 of the girls participate in the school choir, how many students from the classroom participate in the choir? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 10456,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily bought a laptop for $850 and a printer for $150. If the sales tax rate is 8%, how much does she pay in total, including tax? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1080",
"style": "rule"
}
|
numina_math
|
{
"index": 10457,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels a certain distance using 10 gallons of fuel. If the car's fuel efficiency in miles per gallon is an integer, and the total distance traveled is a sum of five consecutive integers, what is the total distance traveled if the average fuel efficiency is 20 miles per gallon? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "200",
"style": "rule"
}
|
numina_math
|
{
"index": 10458,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The cost of three notebooks and two erasers is \\$4.75, and the cost of two notebooks and five erasers is \\$6.25. What is the cost of one notebook and one eraser? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.86",
"style": "rule"
}
|
numina_math
|
{
"index": 10459,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: \\(\\frac{2x}{3} + \\frac{3x}{4} - \\frac{x}{6}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{5x}{4}",
"style": "rule"
}
|
numina_math
|
{
"index": 10460,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A number \\( N \\) is such that when divided by 7, it leaves a remainder of 3. When the same number \\( N \\) is divided by 5, it leaves a remainder of 2. What is the smallest positive integer value of \\( N \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17",
"style": "rule"
}
|
numina_math
|
{
"index": 10461,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the product of the greatest common divisor (GCD) and the least common multiple (LCM) of two positive integers \\(a\\) and \\(b\\) is 200, how many different values can the GCD of \\(a\\) and \\(b\\) take? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 10462,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( z_1, z_2, z_3, \\ldots, z_{12} \\) be the 12 zeroes of the polynomial \\( z^{12} - 2^{36} = 0 \\). For each \\( j \\), let \\( w_j \\) be one of \\( z_j \\) or \\( i z_j \\). Find the maximum possible value of the real part of\n\\[\n\\sum_{j = 1}^{12} w_j.\n\\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 10463,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, 40% of the students participate in the science club. There are 500 students in total. If 60% of the science club members also participate in the math club, how many students are members of both clubs? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 10464,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( f(x) = 3x + 2 \\) and \\( g(x) = x - 4 \\), find \\( f(g(6)) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 10465,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Li Wei invested 15,000 yuan in a bank for a period of 4 years with an annual interest rate of 4%. If the interest income is subject to a 10% tax, how much money will Li Wei have, including the principal and after-tax interest, at the end of the 4 years? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17160",
"style": "rule"
}
|
numina_math
|
{
"index": 10466,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\): \\( 2^{2x+1} = 32 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 10467,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a community garden, there are 120 square meters of land available for planting. The garden is divided equally into sections for vegetables, flowers, and herbs. If the vegetables section is further divided into 3 equal parts for tomatoes, carrots, and beans, how many square meters are allocated to each type of plant? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13.33",
"style": "rule"
}
|
numina_math
|
{
"index": 10468,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a park, 60% of the area is covered in trees, and the remaining 40% is open space. If the total area of the park is 5000 square meters, how much area is covered in trees and how much is open space? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2000",
"style": "rule"
}
|
numina_math
|
{
"index": 10469,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria tutors students in algebra for $25 per hour. She tutors for 10 hours each week. How much money will she earn in 4 weeks? Additionally, if she spends $50 each week on transportation, how much will she have left after 4 weeks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "800",
"style": "rule"
}
|
numina_math
|
{
"index": 10470,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "David wants to buy packs of pencils for his classroom. He finds that when he buys packs of 5 pencils, he has 3 pencils left over. When he buys packs of 7 pencils, he has 4 pencils left over. When he buys packs of 11 pencils, he has 6 pencils left over. What is the smallest number of pencils David could have bought? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "193",
"style": "rule"
}
|
numina_math
|
{
"index": 10471,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A local theater sells tickets for a play. The adult tickets cost $12 each, and the child tickets cost $8 each. The total revenue from selling 200 tickets is $2000. If the number of adult tickets sold is twice the number of child tickets sold, how many adult and child tickets were sold? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 10472,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car rental company offers two types of rental packages. Package A charges a flat rate of $50 per day plus $0.20 per mile driven. Package B charges a flat rate of $70 per day plus $0.10 per mile driven. If a customer plans to rent a car for 3 days and drive a total of 150 miles, which package offers the better rate, and by how much? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 10473,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the smallest positive integer \\( n \\) such that the polynomial \\( P(x) = x^n - 1 \\) has a root that is a radical expression of the form \\( \\sqrt[m]{k} \\), where \\( k \\) is a positive integer and \\( m \\) is an integer greater than 1. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 10474,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A project in Xinfeng Village requires budgeting for road repairs. The total cost to repair the road is $12,000. If 30% of the budget has been spent on materials, and the labor costs are twice the remaining budget, how much has been spent on labor? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16800",
"style": "rule"
}
|
numina_math
|
{
"index": 10475,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom drives his car at a speed of 60 kilometers per hour. How many meters per minute is he traveling? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1000",
"style": "rule"
}
|
numina_math
|
{
"index": 10476,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the equations \\(2x + y = 10\\) and \\(x^2 + xy + y^2 = 50\\), find the value of \\(x + y\\) if \\(x\\) and \\(y\\) are integers. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 10477,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah borrowed $1,200 from a bank at an annual interest rate of 6%. She agreed to repay the loan in 24 equal monthly installments. What will be her monthly payment? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "56",
"style": "rule"
}
|
numina_math
|
{
"index": 10478,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Hilton had a box of 26 marbles that he was playing with. He found 6 marbles while he was playing, but afterward realized that he had lost 10 marbles. Lori felt bad and gave Hilton twice as many marbles as he lost. How many marbles did Hilton have in the end? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "42",
"style": "rule"
}
|
numina_math
|
{
"index": 10479,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The number $N = 72n^2$ has 72 positive integer divisors, including 1 and $N$. How many positive integer divisors does the number $144n^3$ have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "132",
"style": "rule"
}
|
numina_math
|
{
"index": 10480,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x) \\) be a third-degree polynomial with real coefficients satisfying \\(|f(1)| = |f(2)| = |f(3)| = |f(5)| = |f(6)| = |f(7)| = 12\\). Find \\(|f(0)|\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 10481,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is offering a discount on a television. The original price of the television is $800. The store is offering a 15% discount on the television. After the discount is applied, the store also adds a sales tax of 8%. What is the final price of the television after the discount and the sales tax? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "734.4",
"style": "rule"
}
|
numina_math
|
{
"index": 10482,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery makes cupcakes and cookies. 60% of the bakery's products are cupcakes and the rest are cookies. If the bakery produces 500 items in total, how many cupcakes and cookies does the bakery make? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "200",
"style": "rule"
}
|
numina_math
|
{
"index": 10483,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 5000 widgets per day. Each widget weighs 0.75 kilograms. How many metric tons of widgets does the factory produce in a week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "26.25",
"style": "rule"
}
|
numina_math
|
{
"index": 10484,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is a freelance graphic designer who charges $50 per hour. She works 6 hours a day, 5 days a week. How much does she earn in a week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1500",
"style": "rule"
}
|
numina_math
|
{
"index": 10485,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the parabola \\( y = x^2 \\) and the lines \\( y = 2x + 3 \\) and \\( y = -x + 1 \\). Find the area of the triangle formed by the intersection points of these curves. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 10486,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the largest three-digit number \\( ABC \\) where \\( A \\), \\( B \\), and \\( C \\) are digits, such that the number is divisible by 3 and the sum of its digits is equal to 15? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "960",
"style": "rule"
}
|
numina_math
|
{
"index": 10487,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given a triangle \\( \\Delta ABC \\) with vertices \\( A(1, 2) \\), \\( B(3, 4) \\), and \\( C(-1, 5) \\), find the area of the triangle using matrix determinants and trigonometric simplifications. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 10488,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa has $150 to spend on books. Each book costs $12. She also wants to save some money for lunch, which costs $15. How many books can she buy, and how much money will she have left after buying the books and saving for lunch? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 10489,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Annie is 3 years older than her friend Betty. In 5 years, the sum of their ages will be 41 years. How old are Annie and Betty now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 10490,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden is 10 meters long and 5 meters wide. To cover the garden with a protective mulch, it costs $15 per square meter. Using mental math strategies and multiplication, calculate the total cost to cover the entire garden with mulch. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "750",
"style": "rule"
}
|
numina_math
|
{
"index": 10491,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If two-thirds of the days in a month are weekdays, how many weekdays are there in February during a non-leap year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "19",
"style": "rule"
}
|
numina_math
|
{
"index": 10492,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangle has a length that is 3 units more than twice its width. If the perimeter of the rectangle is 54 units, what is the width of the rectangle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 10493,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is preparing a fruit punch for a party. She uses 3 times as much apple juice as orange juice. She also adds twice as much grape juice as orange juice. If the total volume of fruit punch she makes is 15 liters, how many liters of each type of juice did she use? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 10494,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If $\\frac{7}{12}$ is expressed in decimal form, what is the 50th digit to the right of the decimal point? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 10495,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial function \\( f(x) = x^4 + 2x^3 - 7x^2 - 8x + 6 \\), find the remainder when \\( f(x) \\) is divided by \\( x-2 \\). Then, determine if \\( x-2 \\) is a factor of \\( f(x) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-6",
"style": "rule"
}
|
numina_math
|
{
"index": 10496,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a group of 90 people, 50 people like tea, 40 people like coffee, and 20 people like both tea and coffee. How many people like neither tea nor coffee? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 10497,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is offering a discount on a popular rectangular rug. The original price is $120 and the discount is 15%. After purchasing the rug, the customer wants to place a border around it using a special trim that costs $2 per meter. If the rug measures 3 meters by 4 meters, how much will the customer spend in total, including the discounted price of the rug and the cost of the trim? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "130",
"style": "rule"
}
|
numina_math
|
{
"index": 10498,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The first term of an arithmetic sequence is 7, and the common difference is 5. What is the 15th term of the sequence? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "77",
"style": "rule"
}
|
numina_math
|
{
"index": 10499,
"name": "numina_math",
"split": "train"
}
|
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