prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "A factory produces 1200 gadgets per day. If the gadgets are to be packed into boxes such that each box contains an equal number of gadgets, and the number of gadgets in each box must be a divisor of 1200, how many different possible ways can the gadgets be packed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 700,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence of integers from 1 to \\( n \\). Find a simplified expression for the arithmetic mean of the sequence if the sum of the sequence is \\( S \\). Then, calculate the arithmetic mean for \\( n = 100 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50.5",
"style": "rule"
}
|
numina_math
|
{
"index": 701,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the number \\( N = 2^{12} \\times 3^9 \\times 5^6 \\), find the smallest positive integer \\( k \\) such that \\( \\sqrt[3]{kN} \\) is an integer. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "125",
"style": "rule"
}
|
numina_math
|
{
"index": 702,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the mixed number \\( 2 \\frac{3}{4} \\) to a decimal. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.75",
"style": "rule"
}
|
numina_math
|
{
"index": 703,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical water tank has a diameter of 10 feet and a height of 12 feet. A conical funnel is used to fill the tank, and the funnel has a diameter of 5 feet and a height of 6 feet. How many times must the funnel be filled to completely fill the tank? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 704,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a speed of \\( 20 \\) meters per second. How many kilometers does it travel in \\( 2 \\) hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "144",
"style": "rule"
}
|
numina_math
|
{
"index": 705,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria sells handmade crafts. She initially bought supplies for $120. She sold her crafts for a total of $180. If she wants to calculate her profit percentage, what would it be? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 706,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that \\( n! \\) is the factorial of \\( n \\), find the greatest common divisor (GCD) of the sum of the digits of \\( 100! \\) and \\( 200! \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 707,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a constant speed of 60 miles per hour. How long will it take to travel 240 miles if the speed is increased by 20% halfway through the journey?\n\n### Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.67",
"style": "rule"
}
|
numina_math
|
{
"index": 708,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 2/3 cup of sugar for every 1/2 cup of butter. If a baker uses 3 cups of butter, how many cups of sugar should the baker use? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 709,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the largest prime factor of 187? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17",
"style": "rule"
}
|
numina_math
|
{
"index": 710,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Eva is organizing a picnic and needs to buy sandwiches and drinks for her friends. Each sandwich costs $5.50, and each drink costs $2.25. If she buys 8 sandwiches and 16 drinks, how much does Eva spend in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80.00",
"style": "rule"
}
|
numina_math
|
{
"index": 711,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a fruit basket, there are 40 fruits in total, consisting of apples and oranges. If there are three times as many apples as oranges, how many oranges are there in the basket? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 712,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a factory produces 300 widgets every hour and operates for 8 hours a day, how many widgets does the factory produce in a week, assuming it works 5 days a week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12000",
"style": "rule"
}
|
numina_math
|
{
"index": 713,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and all but 4 are blue. How many marbles are in the jar? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 714,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is planning a road trip and estimates that he will need to drive for 5 hours each day. However, for every additional hour he drives beyond 5 hours, he will reduce his driving time the next day by 1 hour. On the first day, he drives for 7 hours. Over a 3-day period, what is the average number of hours he drives per day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5.67",
"style": "rule"
}
|
numina_math
|
{
"index": 715,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company wants to design a new rectangular garden. The length of the garden is twice the width. They want to put a fence around the garden, and they have 60 meters of fencing available. What will be the dimensions of the garden? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 716,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a survey about favorite ice cream flavors, 30% of the respondents chose chocolate, 40% chose vanilla, and the remaining 45 people chose strawberry. If the total number of respondents is twice the number of those who chose vanilla, find the total number of respondents and the number of respondents who chose each flavor. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 717,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has 3 fields. The first field is planted with corn and has 150 rows. The second field has twice as many rows of wheat as the first field has rows of corn. The third field has 3/4 times as many rows of barley as the second field has rows of wheat. How many total rows of crops does the farmer have across all three fields? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "675",
"style": "rule"
}
|
numina_math
|
{
"index": 718,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical water tank has a radius of 5 meters and a height of 10 meters. A smaller cylindrical container has a radius of 1 meter and a height of 2 meters. If you want to fill the larger tank with water using the smaller container, how many times will you need to fill and pour the smaller container to completely fill the larger tank? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "125",
"style": "rule"
}
|
numina_math
|
{
"index": 719,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Liam bought a new bicycle originally priced at $450. The store was offering a 15% discount on all bicycles. After the discount, he also had to pay a 7% sales tax on the discounted price. How much did Liam pay in total for the bicycle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "409.28",
"style": "rule"
}
|
numina_math
|
{
"index": 720,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anita wants to buy a new bicycle that costs $180. She has already saved $70 and her parents have agreed to contribute $50 towards the purchase. How much more money does Anita need to buy the bicycle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 721,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length of 15 meters and a width of 10 meters. If a fence is to be placed around the perimeter of the garden, how many meters of fencing material are needed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 722,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A textile factory produces 500 meters of fabric in 2 hours. The factory needs to fulfill an order of 7500 meters. If the factory operates 8 hours a day, how many days will it take to complete the order? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 723,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria is making a recipe that requires 4 cups of flour. She realizes her measuring cup is missing and only has a tablespoon, which holds 0.0625 cups. How many tablespoons of flour does she need to use to get the 4 cups required by the recipe? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "64",
"style": "rule"
}
|
numina_math
|
{
"index": 724,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A polynomial \\( P(x) \\) is given by \\( P(x) = (x^2 + 5x + 6)(x^2 - 2x + 1) \\). Find the coefficient of the \\( x^3 \\) term in the expanded form of \\( P(x) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 725,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 3/4 cup of sugar for every 1/2 cup of flour. If you have 2 cups of flour, how many cups of sugar will you need? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 726,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A garden center sells rose bushes and tulip bulbs. Each rose bush costs $15, and each tulip bulb costs $2. Jane wants to buy 8 rose bushes and 20 tulip bulbs. If there is a discount of 10% on the total purchase, how much does Jane have to pay after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "144",
"style": "rule"
}
|
numina_math
|
{
"index": 727,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe calls for a ratio of 2:3 of sugar to flour. If you have 8 cups of sugar, how many cups of flour do you need to maintain the same ratio? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 728,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells 3/4 of a cake for $9. If the bakery sold 12 cakes in total, but only 2/3 of these cakes were sold as whole cakes and the rest were sold as 3/4 cakes, how much total revenue did the bakery make from selling the cakes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "132",
"style": "rule"
}
|
numina_math
|
{
"index": 729,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A gardener has 8 distinct plants that need to be placed in a single row along a garden bed. However, the gardener realizes that 3 specific plants (let's call them A, B, and C) cannot be placed next to each other in any order. How many possible arrangements of the 8 plants are there? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36000",
"style": "rule"
}
|
numina_math
|
{
"index": 730,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is training for a marathon. Each week she increases her running distance by 2 kilometers compared to the previous week. If she starts with running 5 kilometers in the first week, how many total kilometers will she have run by the end of the 8th week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "96",
"style": "rule"
}
|
numina_math
|
{
"index": 731,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Calculate: \\(2.3 \\times 3.1 + 4.6 \\times 2.5\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18.63",
"style": "rule"
}
|
numina_math
|
{
"index": 732,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the function \\( h(x) = 3^{x+1} \\) and \\( k(x) = \\log_3(x) \\), evaluate \\( h(k(27)) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "81",
"style": "rule"
}
|
numina_math
|
{
"index": 733,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store has a clearance sale on a jacket originally priced at $100. The store first applies a 20% discount and then an additional 10% discount on the new price. How much does the jacket cost after both discounts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
numina_math
|
{
"index": 734,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice and Bob are training for a race. Alice runs at a constant speed of 8 km/h, while Bob runs at a constant speed of 6 km/h. They both start running from the same point but in opposite directions along a straight path. If they run for 1.5 hours, how far apart will they be at the end of their run? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "21",
"style": "rule"
}
|
numina_math
|
{
"index": 735,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The sum of five integers is 2023. If exactly three of the integers are odd, what is the remainder when the sum of the two even integers is divided by 4? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 736,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer needs to buy bags of feed for his livestock. Each bag of feed can support 5 animals for a week. The farmer has a total of 30 animals. He wants to ensure he has enough feed for at least 4 weeks, but he can only buy up to 35 bags of feed due to budget constraints. What is the minimum number of bags of feed he needs to buy to support all his animals for 4 weeks, and does he stay within his budget constraints? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 737,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the function \\( f(x) = \\frac{1}{1 - x} \\). Find the Taylor series expansion of \\( f(x) \\) up to and including the term \\( x^3 \\). Then, for the polynomial \\( P(x) = x^3 + ax^2 + bx + c \\), use Vieta's formulas to determine the coefficients \\( a, b, \\) and \\( c \\) if the roots of \\( P(x) \\) are the first three positive integers. Finally, compute the value of \\( \\sum_{i=1}^3 f(\\alpha_i) \\), where \\( \\alpha_i \\) are the roots of \\( P(x) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-1.8333",
"style": "rule"
}
|
numina_math
|
{
"index": 738,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine the number of ways to arrange the letters in the word \"MISSISSIPPI\" so that no two \"S\"s are adjacent. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33390",
"style": "rule"
}
|
numina_math
|
{
"index": 739,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah walked a total distance of 5 miles from her house to the park. Along the way, she stopped at a coffee shop that was 2.5 miles from her house. After reaching the park, she decided to walk back home but stopped at a bookstore that was 1.75 miles from the park. How many miles are between the coffee shop and the bookstore? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.25",
"style": "rule"
}
|
numina_math
|
{
"index": 740,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a set of complex numbers \\( \\omega \\) such that \\( \\omega^6 = 1 \\) and \\( \\omega \\neq 1 \\). If three complex numbers \\( z_1, z_2, z_3 \\) are chosen independently and uniformly at random from the set \\( \\{ \\omega, \\omega^2, \\omega^3, \\omega^4, \\omega^5 \\} \\), what is the probability that the product \\( z_1 z_2 z_3 = 1 \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{4}{25}",
"style": "rule"
}
|
numina_math
|
{
"index": 741,
"name": "numina_math",
"split": "train"
}
|
[
{
"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": 742,
"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": "5.75",
"style": "rule"
}
|
numina_math
|
{
"index": 743,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has 2/3 of a chocolate bar, and John has 5/6 of the same chocolate bar. What percentage of the chocolate bar does Sarah have compared to John? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 744,
"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": 745,
"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": "9.13",
"style": "rule"
}
|
numina_math
|
{
"index": 746,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A three-digit number consists of three consecutive digits in increasing order. If the number is divided by 37, it leaves a remainder of 10. What is the number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "567",
"style": "rule"
}
|
numina_math
|
{
"index": 747,
"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": "1389.15",
"style": "rule"
}
|
numina_math
|
{
"index": 748,
"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": 749,
"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": "43.33",
"style": "rule"
}
|
numina_math
|
{
"index": 750,
"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": 751,
"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": 752,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from City A to City B, a distance of 300 kilometers, at a constant speed. On the return journey, it travels at a speed that is 20 kilometers per hour faster and takes 1 hour less than the initial journey. What were the speeds of the car on the initial journey and the return journey? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "88.1",
"style": "rule"
}
|
numina_math
|
{
"index": 753,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A clock chimes every hour on the hour. How many times does it chime from 12:00 PM to 12:00 AM? Use divisibility and modular arithmetic to determine the total number of chimes. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 754,
"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": 755,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two workers, Alex and Bob, are working together to paint a triangular wall. Alex can paint the wall by himself in 6 hours, while Bob can paint the wall by himself in 9 hours. They decide to split the wall into two triangular sections using an angle bisector from one of the vertices of the triangular wall. If the angle bisector divides the opposite side in the ratio of 2:3, how long will it take for Alex and Bob to paint their respective sections together? Express your answer as a fraction in lowest terms. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{108}{65}",
"style": "rule"
}
|
numina_math
|
{
"index": 756,
"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": 757,
"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": 758,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the minimum value of the expression \\(2x^2 + 2y^2 - 8x - 12y + 20\\) subject to the constraints given by the system of linear equations:\n\\[2x + y = 5\\]\n\\[x + y = 4\\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-5",
"style": "rule"
}
|
numina_math
|
{
"index": 759,
"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": 760,
"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": 761,
"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": 762,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a coordinate plane, four points \\(A\\), \\(B\\), \\(C\\), and \\(D\\) are located such that \\(A = (0, 0)\\), \\(B = (6, 0)\\), \\(C = (6, 8)\\), and \\(D = (0, 8)\\). A fifth point \\(P\\) is randomly placed inside the rectangle formed by \\(A\\), \\(B\\), \\(C\\), and \\(D\\). What is the minimum distance \\(d\\) such that there always exists at least one pair of these five points that are within distance \\(d\\) of each other? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 763,
"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": "\\frac{3}{5}",
"style": "rule"
}
|
numina_math
|
{
"index": 764,
"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": 765,
"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": 766,
"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": 767,
"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": 768,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the number of positive integers \\( n \\leq 1000 \\) that can be expressed in the form\n\\[ \\lfloor x \\rfloor \\cdot \\lfloor 2x \\rfloor = n \\]\nfor some real number \\( x \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "44",
"style": "rule"
}
|
numina_math
|
{
"index": 769,
"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": 770,
"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": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 771,
"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": 772,
"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": 773,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train leaves City A traveling towards City B at a constant speed of 60 kilometers per hour. Two hours later, another train leaves City A traveling towards City B at a speed of 90 kilometers per hour. If the distance between City A and City B is 450 kilometers, how long will it take for the second train to catch up to the first train? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 774,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider an ellipse with equation \\(\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1\\) and a hyperbola with equation \\(\\frac{x^2}{c^2} - \\frac{y^2}{d^2} = 1\\). If the derivative of the equation of the ellipse at a point where it intersects the hyperbola is equal to the derivative of the equation of the hyperbola at that same point, and if the ellipse has semi-major axis \\(a = 3\\) and semi-minor axis \\(b = 2\\), find the value of \\(d\\) when \\(c = 3\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 775,
"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": "81.82",
"style": "rule"
}
|
numina_math
|
{
"index": 776,
"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": 777,
"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": 778,
"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": 779,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(a, b, c\\) be positive real numbers such that \\(a + b + c = 12\\) and \\(ab + bc + ca = 30\\). Find the minimum value of \\(abc\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "64",
"style": "rule"
}
|
numina_math
|
{
"index": 780,
"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": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 781,
"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": 782,
"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": 783,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from point \\(A\\) to point \\(B\\) at a speed of 60 km/h, and then from point \\(B\\) to point \\(C\\) at a speed of 80 km/h. The distance from \\(A\\) to \\(B\\) is 120 km, and the distance from \\(B\\) to \\(C\\) is 160 km. If the car returns from \\(C\\) to \\(A\\) along the same route, what is the average speed of the car for the entire trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "70",
"style": "rule"
}
|
numina_math
|
{
"index": 784,
"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": 785,
"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": 786,
"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": 787,
"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": 788,
"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": "927.27",
"style": "rule"
}
|
numina_math
|
{
"index": 789,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery bakes a total of 200 cookies and packs them in boxes. Each box must contain the same number of cookies. After packing, there are 7 cookies left over. What is the maximum number of cookies that could be in each box? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "193",
"style": "rule"
}
|
numina_math
|
{
"index": 790,
"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": 791,
"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": 792,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the harmonic series given by \n\\[ H_n = 1 + \\frac{1}{2} + \\frac{1}{3} + \\dotsb + \\frac{1}{n}. \\]\nDetermine the smallest integer \\( n \\) such that the partial sum \\( H_n \\) exceeds 10. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12301",
"style": "rule"
}
|
numina_math
|
{
"index": 793,
"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": 794,
"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": 795,
"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": 796,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom is baking cookies for a school fundraiser. Each batch requires 2 cups of flour. Tom has a total of 15 cups of flour. He wants to donate a third of the cookies he bakes to the school library. How many batches of cookies can he bake, and how many batches will he have left for the fundraiser after donating to the library? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 797,
"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": 798,
"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": 799,
"name": "numina_math",
"split": "train"
}
|
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