prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "A factory produced a total of 1,344 units of a product over a period of 7 days. What is the average number of units produced per day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "192",
"style": "rule"
}
|
numina_math
|
{
"index": 2900,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a normal distribution, one of the values is 55, and its z-score is 2. If the mean of the distribution is 45, what is the standard deviation of the distribution? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2901,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John and Sarah decide to go on a road trip. John drives for the first 2 hours at a speed of 60 miles per hour. Sarah then drives for the next 3 hours at a speed of 50 miles per hour. If they take a 45-minute break for lunch, how far do they travel in total, and how much time do they spend on the trip including the break? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "345",
"style": "rule"
}
|
numina_math
|
{
"index": 2902,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Divide $0.\\overline{6}$ by $0.\\overline{3}$ and express the result as a common fraction in 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": 2903,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bag contains 3 types of nuts: almonds, cashews, and walnuts. The total weight of the nuts is 500 grams. The weight of the cashews is twice the weight of the walnuts, and the weight of the almonds is 50 grams more than the weight of the walnuts. What is the weight of the walnuts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "112.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2904,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the matrix \\(\\mathbf{A} = \\begin{pmatrix} 4 & 1 \\\\ 2 & 3 \\end{pmatrix},\\) find the determinant of \\(\\mathbf{A}^2 - 5\\mathbf{A} + 6\\mathbf{I}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2905,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels 120.5 miles using 5.5 gallons of fuel. If it continues to travel at the same rate, how many gallons of fuel will it need to travel 200 miles? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9.09",
"style": "rule"
}
|
numina_math
|
{
"index": 2906,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mark invested $1200 in a savings account that offers an annual interest rate of 5%. If he leaves the money in the account for 3 years and the interest is compounded annually, how much money will Mark have in the account at the end of the 3 years? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1390.55",
"style": "rule"
}
|
numina_math
|
{
"index": 2907,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice is planning to cut a 120-meter-long ribbon into smaller pieces, each 2.5 meters long. After cutting the ribbon, she plans to sell each piece for $5.50. If her monthly expense for purchasing ribbons is $200 and she sells all the pieces every month, calculate her monthly savings. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "64",
"style": "rule"
}
|
numina_math
|
{
"index": 2908,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length that is a prime number and a width that is another prime number. If the area of the garden is 221 and one dimension is 13, what is the other dimension? Calculate the perimeter of the garden and determine what percentage of the perimeter is contributed by the length. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "21.67",
"style": "rule"
}
|
numina_math
|
{
"index": 2909,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length that is 3 times its width. If the width of the garden is 5 meters, what is the area of the garden in square meters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 2910,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "There were 200 students in a school event. Out of these, one-fifth participated in a painting competition. Of those who participated in the painting competition, 18 students also participated in a singing competition. How many students participated only in the painting competition? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22",
"style": "rule"
}
|
numina_math
|
{
"index": 2911,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is organizing a charity event and needs to distribute 240 gift bags evenly among 8 tables. Each table will have an equal number of gift bags. How many gift bags will each table receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2912,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A large water tank can hold 5000 liters of water. Two smaller tanks have capacities that are one-third and one-fifth of the large tank's capacity, respectively. If the large tank is full and the water is evenly distributed into the two smaller tanks, how many liters of water will be left in the large tank? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2333.33",
"style": "rule"
}
|
numina_math
|
{
"index": 2913,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells cookies in packages of 5. Each package costs $6. A customer wants to buy enough packages to have a total of 40 cookies. How much will the customer need to pay in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 2914,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a store, there are three types of cheese: white, swiss, and blue cheese. Each cheese is packaged, and there are 200 grams of cheese in each package. The package prices are $5 for white cheese, $6 for swiss cheese, and $8 for blue cheese. Miley needed to get some for her party, and she decided to buy 5 packs of swiss cheese, 600 grams of blue cheese, and one-third less white cheese than swiss cheese. How much did she need to pay for all the cheese? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "69",
"style": "rule"
}
|
numina_math
|
{
"index": 2915,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore received a shipment of 800 books and plans to sell them over a period of 20 days. Each book is priced at $15. However, due to a special promotion, the bookstore decided to offer a 10% discount on each book for the first 10 days. If the bookstore sold the same number of books each day during the promotion and the remaining days, how much total revenue did the bookstore earn from the sales over the 20 days? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22800",
"style": "rule"
}
|
numina_math
|
{
"index": 2916,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Divide 144 by 12 and find the quotient. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2917,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jane wants to save up for a new computer that costs $1,200. She also needs to pay off a credit card bill of $800. Jane saves $150 each month. How many months will it take for Jane to save enough to buy the computer and pay off her credit card bill? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 2918,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A magician has a set of 120 magical stones. He wants to distribute them equally among his apprentices. He thinks of different ways to divide them and realizes that the number of stones each apprentice receives must be a multiple of both 3 and 5. How many possible ways can the magician distribute the stones? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2919,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maya wants to make a fruit salad for her family. She needs to add 1/3 cup of blueberries, 1/4 cup of strawberries, and 1/6 cup of raspberries to the salad. How many cups of fruit does she need in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{3}{4}",
"style": "rule"
}
|
numina_math
|
{
"index": 2920,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer needs to transport apples and oranges to the market. Each crate of apples weighs 8 kilograms, and each carton of oranges weighs 5 kilograms. If the farmer has 15 crates of apples and 20 cartons of oranges, how much total weight of apples and oranges does the farmer need to transport? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "220",
"style": "rule"
}
|
numina_math
|
{
"index": 2921,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many distinct ways can you partition the integer 7 into a sum of three positive integers, considering that different orderings of the same partition count as distinct? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2922,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells cupcakes in boxes of 12. Each box costs $15. If a customer buys 8 boxes, what is the total cost? Additionally, if a 10% discount is applied on the total cost, how much does the customer pay after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "108",
"style": "rule"
}
|
numina_math
|
{
"index": 2923,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "James is saving money to buy a new bicycle that costs $300. He decides to save $20 each week. After 10 weeks, his parents decide to contribute an additional amount equal to half of what he has already saved. How much money will James have in total after his parents' contribution? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 2924,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The school cafeteria sells sandwiches for $5 each and drinks for $2 each. During lunch, they sold 120 sandwiches and 80 drinks. The cost to prepare each sandwich is $3 and each drink is $1. Calculate the total profit made by the cafeteria during lunch. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "320",
"style": "rule"
}
|
numina_math
|
{
"index": 2925,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A box contains 5 red balls, 7 blue balls, and 8 green balls. If one ball is picked at random, what is the probability that the ball is either red or blue? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 2926,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A solution is made by mixing a $20\\%$ salt solution with a $50\\%$ salt solution to get $200$ milliliters of a $35\\%$ salt solution. If the cost of the $20\\%$ solution is $2$ dollars per milliliter and the cost of the $50\\%$ solution is $3$ dollars per milliliter, what is the total cost of the final mixture? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "500",
"style": "rule"
}
|
numina_math
|
{
"index": 2927,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where all items are marked down by 20%. If the original price of a jacket is $80 and the sales tax is 7%, what is the total price of the jacket after the discount and including sales tax? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "68.48",
"style": "rule"
}
|
numina_math
|
{
"index": 2928,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist rides around a rectangular park that has a length of 200 meters and a width of 150 meters. If the cyclist rides at a constant speed of 10 meters per second, how long will it take the cyclist to complete 3 laps around the park? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2929,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is organizing a bake sale. She buys 5 boxes of cupcakes, each containing 12 cupcakes, for $3 per box. She plans to sell each cupcake for $0.50. How much profit will she make if she sells all the cupcakes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 2930,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A laboratory has a certain chemical that decays over time. The amount of chemical remaining after \\( t \\) hours is inversely proportional to the square of the time elapsed. Initially, there are 100 grams of the chemical. After 2 hours, 25 grams remain. How much of the chemical will remain after 5 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2931,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is driving to visit his friend who lives 120 miles away. He drives at a constant speed of 40 miles per hour. After reaching his friend's house, they decide to go for a road trip together and drive twice the distance that John originally drove, at the same speed. How much time in total does John spend driving? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2932,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels at a constant speed of 15 miles per hour. If he needs to travel a distance of 90 miles, how many hours will it take him to complete his journey? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2933,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the polynomial function \\( P(x) = (x^2 + 2x + 1)(x^3 - x + 2)(x - 3) \\). Find the degree of the polynomial \\( P(x) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2934,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A garden has 9 rows of plants. Each row has 16 plants. If each plant grows to be 4 feet tall, what is the total height of all the plants combined in the garden? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "576",
"style": "rule"
}
|
numina_math
|
{
"index": 2935,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe for a cake requires 2 cups of sugar for every 5 cups of flour. If you want to make a larger batch using 35 cups of flour, how many cups of sugar will you need? After making the larger batch, if you discover that you only have 30 cups of sugar, what percentage of the required sugar do you have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "214.29",
"style": "rule"
}
|
numina_math
|
{
"index": 2936,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine the integer value of \\(x\\) between 0 and 15 inclusive that satisfies the congruence \\(5x \\equiv 3 \\pmod{16}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 2937,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 150 widgets in 5 hours. If the production rate is increased by 20%, how many widgets will the factory produce in 8 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "288",
"style": "rule"
}
|
numina_math
|
{
"index": 2938,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah buys a laptop that is listed at $800. The sales tax rate in her state is 7%. After applying the sales tax, what is the total amount Sarah has to pay for the laptop? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "856",
"style": "rule"
}
|
numina_math
|
{
"index": 2939,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A stationery store owner calculated the mean and median price of all types of pen to be $5 and $3, respectively. He plans to have a 20% off sale on all pens. What are the new mean and median prices of the pens in that store after applying the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.4",
"style": "rule"
}
|
numina_math
|
{
"index": 2940,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jen bought a bag of cookies and ate three-quarters of the bag that day. The next day, she ate half of the remaining cookies. She has 8 cookies left on the third day. How many cookies were in the bag to start? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "64",
"style": "rule"
}
|
numina_math
|
{
"index": 2941,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Megan is shopping for school supplies. She buys 3 notebooks at $5 each, 2 packs of pens at $7 each, and 4 folders at $3 each. The store is offering a 10% discount on the total purchase. How much does Megan spend after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36.9",
"style": "rule"
}
|
numina_math
|
{
"index": 2942,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jack and Jill live 300 miles apart and decide to meet halfway. Jack drives from his house to the meeting point at a speed of 60 miles per hour, while Jill drives from her house to the meeting point at a speed of 50 miles per hour. If they both start driving at the same time, how long will it take for them to meet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.727",
"style": "rule"
}
|
numina_math
|
{
"index": 2943,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 80 gadgets every hour. If the factory runs for 5 days a week, operating 8 hours each day, and 10% of the gadgets are defective and discarded, how many non-defective gadgets are produced in a week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2880",
"style": "rule"
}
|
numina_math
|
{
"index": 2944,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A meeting is scheduled to last 2 hours longer than twice the time it takes to travel to the venue. If the total time (traveling to the venue and the duration of the meeting) is 8 hours, how long does it take to travel to the venue? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2945,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Brenda bakes 20 cakes a day for 9 days and then sells half of the cakes. How many cakes are left with Brenda? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2946,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A new streaming service offers two subscription plans. Plan A charges a fixed amount of \\$10 per month. Plan B charges \\$0.50 per hour of streaming. If a user streams 40 hours in a month, for what number of hours would the cost of Plan B equal the cost of Plan A? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 2947,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has 120 apples. He decides to sell them at a local market. He sells the first batch of apples to a customer, keeping 10% of the apples for himself. He then sells half of the remaining apples to another customer. After these sales, he gives 15 apples to a friend. How many apples does the farmer have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "39",
"style": "rule"
}
|
numina_math
|
{
"index": 2948,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In the diagram below, lines \\( m \\) and \\( n \\) are parallel. If angle \\( \\angle ABC \\) is \\( 120^\\circ \\) and \\( \\angle BCD \\) is formed by extending line \\( BC \\) such that \\( BC \\) is a transversal between \\( m \\) and \\( n \\), find the measure of angle \\( \\angle BCD \\).\n\n```\nm ---------------------\n \\ /\n \\ 120° /\n \\ /\n \\ /\n \\ /\n \\ /\n \\ /\n \\ /\n n\n``` Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2949,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Bob enters cycling competitions every single week and hopes to win the 100-dollar grand prize each time. For the first 2 weeks, he managed first place and got 100 dollars each week. He is saving up for a puppy that costs 1000 dollars. What is the minimum number of additional weeks Bob must win first place? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2950,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah decided to start a small business selling handmade candles. Each candle costs $4.75 to produce, and she plans to make 120 candles. If she sells each candle for $10, how much profit will she make if all candles are sold? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "630",
"style": "rule"
}
|
numina_math
|
{
"index": 2951,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice is planning a trip to Europe and needs to convert her US dollars to Euros. She has $500 and the conversion rate is 1 USD = 0.85 EUR. She wants to allocate 40% of her Euros for accommodation and the rest for other expenses. How many Euros will Alice have for other expenses? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "255",
"style": "rule"
}
|
numina_math
|
{
"index": 2952,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where all items are 20% off. If a customer buys an item originally priced at $150 and another item originally priced at $80, what is the total amount the customer saves due to the sale? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "46",
"style": "rule"
}
|
numina_math
|
{
"index": 2953,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A truck is transporting bags of sand. Each bag weighs 50 kg. The truck can carry a maximum weight of 2,000 kg. If the truck has already loaded 1,200 kg of sand, how many more bags can the truck carry without exceeding its maximum weight limit? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 2954,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma is planning a road trip and needs to cover a total distance of 1200 miles. She drove 350 miles on the first day and 420 miles on the second day. If she plans to drive the remaining distance on the third day, how many miles does she need to drive on the third day to complete her trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "430",
"style": "rule"
}
|
numina_math
|
{
"index": 2955,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels at a speed of 15 miles per hour. If the cyclist increases their speed by 20% for the last hour of a 5-hour journey, what will be the total distance covered? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "78",
"style": "rule"
}
|
numina_math
|
{
"index": 2956,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( z = \\sqrt{3} + i \\). Compute \\( |z^3| \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2957,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces toys at a rate of 120 toys per hour. If the factory operates at 75% capacity for 8 hours a day, how many toys does it produce in a week (7 days)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5040",
"style": "rule"
}
|
numina_math
|
{
"index": 2958,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery offers 5 types of bread, 3 types of cookies, and 4 types of cakes. If you want to buy one item from each category (bread, cookies, and cakes), how many different combinations of these items can you choose? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 2959,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenny has 40 candies. She decides to give 8 candies to each of her 4 friends and keep the rest for herself. How many candies does Jenny have left after sharing with her friends? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2960,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Aria is planning a birthday party and wants to prepare goodie bags for her guests. She has 18 chocolates, 24 candies, and some toys. She wants to make sure each goodie bag has the same number of items and that each type of item is equally distributed among the bags. If she can make 6 goodie bags, how many toys does she have if each goodie bag has exactly 10 items in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 2961,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the expression: \\( 16^{\\frac{3}{4}} + 27^{\\frac{2}{3}} \\) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17",
"style": "rule"
}
|
numina_math
|
{
"index": 2962,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, the ratio of the number of boys to the number of girls is 3:5. If there are 240 students in total, how many boys and girls are there in the school? Additionally, if the average age of the boys is 14 years old and the average age of the girls is 12 years old, what is the average age of all the students in the school? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12.75",
"style": "rule"
}
|
numina_math
|
{
"index": 2963,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the sum of all positive integer solutions to the equation \\( x^4 - 13x^2 + 36 = 0 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2964,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store sells a dining table set at a listed price of $1500. The store is currently offering a 20% discount on all dining table sets. Additionally, during a promotional event, customers receive an extra 15% discount on the already discounted price if they sign up for the store's loyalty program. After these discounts, the store still makes a profit of 10% over the cost price. What is the original cost price of the dining table set? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "928.18",
"style": "rule"
}
|
numina_math
|
{
"index": 2965,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a math competition, the number of teams is reduced by half each round. If there are 32 teams at the start, how many teams are left after 3 rounds? Additionally, if each team consists of 5 members, how many team members are left after 3 rounds? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 2966,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a certain habitat, the population of a species of bacteria doubles every hour. Initially, there are \\( P_0 \\) bacteria. Write an expression for the population after \\( t \\) hours. Then, simplify the expression for the population after 5 hours, given that \\( P_0 = 10 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "320",
"style": "rule"
}
|
numina_math
|
{
"index": 2967,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Nancy buys a jacket priced at $120, but she has a 25% discount coupon. She also has a $20 gift card that she uses towards the purchase. After applying the discount and the gift card, how much does she pay for the jacket? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "70",
"style": "rule"
}
|
numina_math
|
{
"index": 2968,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a garden, there are 45 rose bushes and 35 tulip plants. The gardener decides to plant sunflowers, and the number of sunflowers planted is three times the total number of rose bushes and tulip plants. How many sunflowers were planted? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "240",
"style": "rule"
}
|
numina_math
|
{
"index": 2969,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify and solve for \\( x \\) in the equation \\(\\frac{\\log_2 x + \\log_4 x}{\\log_2 x - \\log_2 4} = 2\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "256",
"style": "rule"
}
|
numina_math
|
{
"index": 2970,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A garden had 15 flowers. During a storm, 6 flowers were destroyed. After the storm, the gardener planted 4 new flowers each day for 3 days. How many flowers are in the garden now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "21",
"style": "rule"
}
|
numina_math
|
{
"index": 2971,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Renaldo drove 15 kilometers. Ernesto drove 7 kilometers more than one-third of Renaldo's distance. How many kilometers did the two men drive in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "27",
"style": "rule"
}
|
numina_math
|
{
"index": 2972,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A radioactive substance decays such that the amount remaining after \\( n \\) years is given by \\( A_n = A_0 \\left( \\frac{1}{2} \\right)^n \\), where \\( A_0 \\) is the initial amount. If \\( A_0 = 100 \\) grams, find the total amount of the substance remaining after 3 years. \n\nAdditionally, express the remaining amount after 3 years in terms of a summation of quantities using the binomial theorem. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2973,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory needs to allocate resources to produce metal rods. The production of each rod requires a cylindrical piece of metal with a volume of 100 cubic centimeters. The factory has a total of 5000 cubic centimeters of metal available. If the production efficiency is such that for every 10 units of volume used, 1 unit is wasted, how many rods can the factory produce? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 2974,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the sum of the digits in the product of $35$ and $27$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 2975,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a circle with center \\(O\\) and radius \\(r\\), a right triangle \\(ABC\\) is inscribed such that \\(AB\\) is the diameter of the circle. The lengths of the legs \\(AC\\) and \\(BC\\) are 9 and 12, respectively. If \\(D\\) is the midpoint of the hypotenuse \\(AB\\), find the radius \\(r\\) of the circle. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2976,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where all items are marked down by 25%. If the original price of a jacket is $80 and the original price of a pair of shoes is $60, what is the total price of both items after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "105",
"style": "rule"
}
|
numina_math
|
{
"index": 2977,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A charity event managed to raise 80% of its target amount from donations. If the amount raised so far is $12,000, what is the target amount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15000",
"style": "rule"
}
|
numina_math
|
{
"index": 2978,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a sequence, each term is 3 more than the previous term, starting from the first term which is 2. What is the 15th term in the sequence? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "44",
"style": "rule"
}
|
numina_math
|
{
"index": 2979,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In how many ways can you distribute 10 identical apples to 3 children such that each child gets at least one apple? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 2980,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex is organizing a charity run and needs to distribute 475 T-shirts among the participants. Each participant receives 3 T-shirts. After distributing the T-shirts, how many T-shirts will Alex have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2981,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where all items are 15% off. If a customer buys a jacket originally priced at $80 and a pair of shoes originally priced at $50, how much will the customer save in total from the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "19.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2982,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "There are 30 chickens and rabbits in a pen, and the total number of legs is 80. How many rabbits are in the pen? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2983,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer needs to divide his 72 meters long fence equally into sections for planting trees. He decides each section should be 6 meters long. How many sections will he have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2984,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A club has 50 members. Some members only play chess, some only play checkers, and some play both chess and checkers. If 30 members play chess, 25 play checkers, and 10 members play both games, how many members play only chess or only checkers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35",
"style": "rule"
}
|
numina_math
|
{
"index": 2985,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: $\\log _{2}(2^6 \\cdot 4^3 \\cdot 8^2)$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 2986,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 1200 widgets in a week. 3/5 of the widgets are checked for quality control, and 1/4 of those checked are found to be defective. How many defective widgets are there in a week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 2987,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two workers, Alex and Bailey, are painting a fence together. Alex can paint the entire fence in 6 hours, while Bailey can paint it in 4 hours. If they work together, how long will it take them to paint the fence? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.4",
"style": "rule"
}
|
numina_math
|
{
"index": 2988,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "At a charity bake sale, there were 12 adults and 18 children. Each adult bought 3 cupcakes, and each child bought 2 cupcakes. If each cupcake costs $2, how much total revenue was generated from the sale of the cupcakes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "144",
"style": "rule"
}
|
numina_math
|
{
"index": 2989,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, the ratio of boys to girls is 3:5. If there are 240 students in total, how many boys are there in the school? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2990,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Karen had $120 in her savings account. She spent 25% of her savings on a new pair of shoes and 15% on a book. How much money does Karen have left in her savings account after these purchases? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
numina_math
|
{
"index": 2991,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale on electronics. First, they apply a 20% discount to a laptop originally priced at $1,000. Then, they apply an additional 10% discount on the reduced price. What is the final price of the laptop after both discounts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "720",
"style": "rule"
}
|
numina_math
|
{
"index": 2992,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a regular pentagon \\(ABCDE\\), each exterior angle measures \\(x\\) degrees. Calculate the degree measure of the supplement of the exterior angle of \\( \\triangle ABC \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "108",
"style": "rule"
}
|
numina_math
|
{
"index": 2993,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is baking cookies for a bake sale. She needs to convert a recipe that calls for 3 cups of flour into tablespoons. Knowing that there are 16 tablespoons in a cup, how many tablespoons of flour does Sarah need? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 2994,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If $C\\ \\clubsuit\\ D$ is defined as $C\\ \\clubsuit\\ D = 4C - D + 7$, what is the value of $C$ for which $C\\ \\clubsuit\\ 5 = 23$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5.25",
"style": "rule"
}
|
numina_math
|
{
"index": 2995,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\[f(x) = \\sqrt{x-2}\\]. What is the smallest real number $x$ in the domain of $f(f(x))$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2996,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah went shopping and bought three items. The first item cost $24.95, the second item cost $15.75, and the third item cost $9.50. She received a 10% discount on the total cost. What was the total amount she paid after the discount? Round your final answer to the nearest cent. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45.18",
"style": "rule"
}
|
numina_math
|
{
"index": 2997,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels 300 miles using 15 gallons of gasoline. What is the unit rate of miles per gallon? If the car needs to travel a total of 1200 miles, how many gallons of gasoline will it need? Also, if each gallon of gasoline costs $3, how much will it cost to travel 1200 miles? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 2998,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, the ratio of the number of boys to girls is 3:4. If there are 70 more girls than boys, how many students are there in total in the school? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "490",
"style": "rule"
}
|
numina_math
|
{
"index": 2999,
"name": "numina_math",
"split": "train"
}
|
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