prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "In a fruit packing warehouse, there are three types of fruit boxes. Box A contains 12 oranges and costs $3 each. Box B contains 20 apples and costs $5 each. Box C contains 15 bananas and costs $4 each. If a customer orders 10 boxes of A, 8 boxes of B, and 5 boxes of C, what is the total cost, and what is the average cost per fruit? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.25",
"style": "rule"
}
|
numina_math
|
{
"index": 2300,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is planning to buy a new laptop that costs $1200. He currently has $400 saved and plans to save an additional $100 per month. He also needs to keep at least $200 in his savings account at all times. In how many months will John have enough money to buy the laptop without going below his required minimum savings? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2301,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a factory, machines A, B, and C produce gadgets in the ratio 2:3:4. If machine B produces 60 gadgets, how many gadgets are produced by machines A and C combined? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2302,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A book originally costs $48. It is now reduced by \\( \\frac{1}{8} \\) of the original price. How much is the reduction in dollars? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2303,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a club, there are 60 members. One-third of the members are part of the chess team, and another quarter of the members are part of the debate team. The rest are part of the music team. How many members are part of the music team? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 2304,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Patricia and Geoffrey are planning to buy new fishing gear. Patricia earns $12 per hour and worked for 8 hours on Monday, while Geoffrey earns $15 per hour and worked for 6 hours on Monday. How much money did they earn together on Monday? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "186",
"style": "rule"
}
|
numina_math
|
{
"index": 2305,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many distinct palindromic sequences of length 6 can be formed using the digits 1, 2, and 3? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "27",
"style": "rule"
}
|
numina_math
|
{
"index": 2306,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily has $50. She spends $15 on a book and $7 on a snack. How much money does she have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "28",
"style": "rule"
}
|
numina_math
|
{
"index": 2307,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe calls for 3/4 cup of sugar. If you want to make a batch that is 2/3 the size of the original recipe, how much sugar do you need? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2308,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from Town A to Town B in a straight line at a constant speed of 60 km/h. It then returns from Town B to Town A at a different constant speed of 90 km/h. The total time taken 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": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 2309,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Bowen has 80 grams of a 30% sugar solution. After some amount of water evaporates, the percent concentration of the solution is 40%. What is the mass of the water that evaporated? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 2310,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a promotional discount where customers get 25% off on any item. If the original price of a jacket is $120, and a customer also has a $10 coupon that can be applied after the discount, what is the final price the customer pays for the jacket? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 2311,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jamal has 7 nickels. He decides to buy a toy that costs 35 cents. After buying the toy, how many nickels does Jamal have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2312,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a charity bake sale. She buys ingredients costing $150 in total. She plans to make 300 cupcakes and sell them in packs of 6 for $12 per pack. If she sells all the cupcakes, calculate her total revenue and determine her profit. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "450",
"style": "rule"
}
|
numina_math
|
{
"index": 2313,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells cookies at $2 each. They had 120 cookies and sold 2/3 of them by the end of the day. If the cost of making one cookie is $0.50, what is the profit the bakery made from the sold cookies? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2314,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find all real solutions to the polynomial equation \\(x^3 + 3x^2 + 3x + 1 = 0\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-1",
"style": "rule"
}
|
numina_math
|
{
"index": 2315,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x) = x^2 + 2x + 1 \\) and \\( g(x) = 3x + 4 \\). What is the value of \\( f(g(2)) + g(f(2)) \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "152",
"style": "rule"
}
|
numina_math
|
{
"index": 2316,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A chemist needs to prepare 500 mL of a 20% alcohol solution by mixing a 10% alcohol solution with a 30% alcohol solution. How many milliliters of each solution should the chemist use? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "250",
"style": "rule"
}
|
numina_math
|
{
"index": 2317,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a parallelogram, the lengths of the adjacent sides are 10 cm and 15 cm. If the longer side is increased by 20% and the shorter side is decreased by 10%, what will be the new perimeter of the parallelogram? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "54",
"style": "rule"
}
|
numina_math
|
{
"index": 2318,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is on a weight loss journey and decides to follow a new diet plan. At the start of the month, she weighs 150 pounds. She loses 3 pounds every week and there are 4 weeks in a month. How much does Sarah weigh at the end of the month? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "138",
"style": "rule"
}
|
numina_math
|
{
"index": 2319,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that $x$ is a multiple of $420$, what is the greatest common divisor of $f(x) = (5x + 3)(8x + 2)$ and $x$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2320,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the decimal representation of the fraction $\\frac{7}{20}$? Simplify the fraction first if necessary and then convert it to its decimal form. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.35",
"style": "rule"
}
|
numina_math
|
{
"index": 2321,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there are 144 students in the 7th grade. One-fourth of the students are in the school band, and the rest are split equally among 4 different sports teams. How many students are in each sports team? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "27",
"style": "rule"
}
|
numina_math
|
{
"index": 2322,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "**\nA bakery sells cakes in boxes. Each box contains 8 cakes. If a customer buys 5 boxes and each cake costs $2.75, how much will the customer spend in total?\n\n** Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "110",
"style": "rule"
}
|
numina_math
|
{
"index": 2323,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily's annual salary after a 15% tax deduction is $42,500. What was her gross salary before the tax deduction? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50,000",
"style": "rule"
}
|
numina_math
|
{
"index": 2324,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the price of an item increases by 25% and then by an additional 10%, what is the total percentage increase in the price of the item? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "37.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2325,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah earns $50,000 annually. She is required to allocate 30% of her income for federal taxes, 8% for state taxes, and $2,500 for her retirement fund. How much money does Sarah have left after these deductions? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "28500",
"style": "rule"
}
|
numina_math
|
{
"index": 2326,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A solution contains 20% salt and 80% water by weight. If you have 200 grams of this solution and you evaporate 50 grams of water, what will be the new percentage concentration of salt in the remaining solution? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "26.67",
"style": "rule"
}
|
numina_math
|
{
"index": 2327,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore sells notebooks for $2 each and pens for $1.50 each. The store owner wants to analyze the cost of a promotion where customers can buy 3 notebooks and 5 pens for a discounted total price of $12.50. If the store sold 40 such promotional bundles, how much profit did the store make if the cost to the store for each notebook is $1 and each pen is $0.75? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "230",
"style": "rule"
}
|
numina_math
|
{
"index": 2328,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mr. Johnson deposits \\$12,000 into a savings account that pays an annual simple interest rate of 5%. How much interest will Mr. Johnson earn after 4 years, and what will be the total amount in his account at the end of this period? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14,400",
"style": "rule"
}
|
numina_math
|
{
"index": 2329,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A chef is preparing a large batch of fruit punch for a party. The recipe calls for a combination of fruit juice and soda water. The total volume of the punch must be 15 liters, and the ratio of fruit juice to soda water must be 2:3. How many liters of fruit juice and soda water does the chef need? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2330,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the greatest positive integer that must divide the sum of the first ten terms of any arithmetic sequence whose terms are positive integers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2331,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where all items are 25% off. If the original price of an item is $80, and the sales tax is 8%, what is the final price of the item after applying the discount and adding the tax? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "64.8",
"style": "rule"
}
|
numina_math
|
{
"index": 2332,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a 20% off sale on all items. Sarah wants to buy a jacket that originally costs $150. After the discount is applied, she also has to pay a 5% sales tax on the discounted price. How much will Sarah pay in total for the jacket? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "126",
"style": "rule"
}
|
numina_math
|
{
"index": 2333,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the greatest common divisor of 12345 and 9876? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2469",
"style": "rule"
}
|
numina_math
|
{
"index": 2334,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A small coffee shop has two types of workers: baristas and cashiers. Baristas are paid $15 per hour, while cashiers are paid $12 per hour. If a barista works for 6 hours and a cashier works for 8 hours, what is the total amount paid to both workers? Additionally, if the shop sold 50 cups of coffee at $4 each during their shifts, what is the shop's profit after paying the workers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 2335,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah, who is 30 years old, decides to take a road trip. She drives to a city 120 miles away at an average speed of 60 miles per hour. After spending a few hours in the city, she drives back home at an average speed of 40 miles per hour. What is her average speed for the entire trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 2336,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria is planning to build a rectangular garden in her backyard. The length of the garden is 12 meters, and the width is 8 meters. She wants to put a fence around the garden and also plant flowers along the perimeter, spaced 2 meters apart. How many flowers will she need, and how much fence will she need to buy in total meters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2337,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Percius has a collection of marbles. 40% of them are clear, and 20% are black. The rest are of other colors. If Percius has 50 marbles in total, how many marbles of other colors are there? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 2338,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a right triangle \\( \\triangle ABC \\) with \\( \\angle C \\) as the right angle, the length of \\( \\overline{BC} \\) is 8 units, and the length of \\( \\overline{AC} \\) is 6 units. If \\( \\tan \\theta = \\frac{1}{\\sqrt[3]{2}} \\), where \\( \\theta \\) is an acute angle in the triangle, find the length of \\( \\overline{AB} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2339,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sam, Jill, and Tom are working on a school project. Sam contributes 8 pages, and Tom contributes 15 pages. If the total project has 30 pages, how many pages did Jill contribute? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2340,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine the vertex of the parabola and the maximum product of two integers whose sum is given by the equation \\( y = x^2 - 6x + 9 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2341,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Amy is planning a community event and needs to buy chairs and tables. Each chair costs $25 and each table costs $150. She needs to buy a total of 40 items (chairs and tables combined) and has a budget of $2500. How many chairs and tables should she buy to stay within her budget? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2342,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( f(x) = |2x - 5| \\), evaluate \\( f(-2) \\) and \\( f(3) \\). Then, find the average of these two values. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2343,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A gardener is planting a rectangular garden. The garden's length is 12 meters and its width is 8 meters. The gardener wants to place a fence around the entire garden. If fencing costs $15 per meter, how much will the entire fencing cost? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 2344,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a factory, there are three machines, A, B, and C, working together to produce widgets. Machine A can produce 30 widgets per hour, machine B can produce 40 widgets per hour, and machine C can produce 50 widgets per hour. If the factory needs to produce a total of 600 widgets, how many hours will it take for all three machines working together to complete the job? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2345,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Round the sum of 45.678 and 34.321 to the nearest tenth. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 2346,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a math competition, there are three participants: Alice, Bob, and Charlie. Alice scored twice as many points as Bob. Charlie scored 20 points less than Alice. If the total score of all three participants is 380 points, how many points did each participant score? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "140",
"style": "rule"
}
|
numina_math
|
{
"index": 2347,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A grocery store sells a 2.5-pound bag of apples for $7.50. If a customer buys a 5-pound bag of apples and uses a $2 coupon, how much did the customer pay per pound of apples? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.60",
"style": "rule"
}
|
numina_math
|
{
"index": 2348,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jane is a freelance graphic designer. She can design 4 logos in 3 hours. How many logos can she design in 24 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32",
"style": "rule"
}
|
numina_math
|
{
"index": 2349,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where all items are 25% off. If Akira buys a jacket and a pair of shoes, and the original price of the jacket is $80 while the original price of the shoes is $60, how much will Akira pay in total 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": 2350,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 500 gadgets per day. Due to increased demand, the factory decides to increase production by 20%. If the increase in production is achieved equally over a period of 5 days, how many more gadgets does the factory produce each day at the end of this period? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 2351,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a camping trip and needs to buy some supplies. She found that each tent she needs costs $45. If she buys 4 tents and also decides to buy 3 sleeping bags for $30 each, how much will she spend in total on these supplies? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "270",
"style": "rule"
}
|
numina_math
|
{
"index": 2352,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A two-digit number has a decimal part that extends to four decimal places. The number is represented as 34.5678. First, round the decimal part to the nearest thousandth, and then round the resulting number to the nearest whole number. What is the final result? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35",
"style": "rule"
}
|
numina_math
|
{
"index": 2353,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there are 8 classes. Each class has a different number of students: 25, 32, 27, 30, 29, 34, 28, and 31. How many classes have an odd number of students? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2354,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 2/3 cup of sugar for every 1/4 cup of butter. If you have 3 cups of sugar and 1 cup of butter, how many complete batches of the recipe can you make? Express your answer as a common fraction. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2355,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the set \\( A = \\{1, 2, 3, 4, 5, 6, 7, 8, 9\\} \\). Let \\( f \\) and \\( g \\) be functions from \\( A \\) to \\( A \\) such that \\( f(x) = x + 1 \\) mod 9 and \\( g(x) = x + 2 \\) mod 9. Calculate the number of elements in the set \\( \\{x \\in A : (f \\circ g)(x) = (g \\circ f)(x)\\} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2356,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(r\\), \\(s\\), and \\(t\\) be the roots of the polynomial \\(x^3 - 6x^2 + 11x - 6 = 0\\). If \\(r\\), \\(s\\), and \\(t\\) satisfy the equation \\(r^2 + s^2 + t^2 = 14\\), find the value of \\(r^2 + s^2\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2357,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company is budgeting for a new project and needs to allocate funds for equipment and labor. The total budget for the project is $50,000. The cost of equipment is three times the cost of labor. Additionally, they need to allocate $5,000 for unforeseen expenses. How much is allocated for labor? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11,250",
"style": "rule"
}
|
numina_math
|
{
"index": 2358,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 250 gadgets per day. Each gadget requires 3 components to be assembled. Over a period of 10 days, how many components are used in total by the factory? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7500",
"style": "rule"
}
|
numina_math
|
{
"index": 2359,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A number has four digits and the sum of its digits is 24. If the digits form an arithmetic sequence with a common difference of 2, what is the number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3579",
"style": "rule"
}
|
numina_math
|
{
"index": 2360,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a nature reserve, there are initially 1500 deer. The reserve authorities decide to relocate some of the deer to control the population. On the first relocation, they move 1/3 of the deer to another park. In the second relocation, they move half of the remaining deer to a wildlife sanctuary. How many deer are left in the nature reserve after both relocations? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "500",
"style": "rule"
}
|
numina_math
|
{
"index": 2361,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( h(x) = 4x + 1 \\) and \\( k(x) = x^2 - 2x \\). What is the value of \\( h(k(3)) \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 2362,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "An amusement park has a collection of scale models, with a ratio of \\(1:45\\), of buildings and other sights from around the country. If the height of the Empire State Building is \\(1250\\) feet, what is the height in feet of its replica to the nearest whole number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "28",
"style": "rule"
}
|
numina_math
|
{
"index": 2363,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma runs a small juice shop where she sells freshly squeezed orange juice. She buys oranges at $0.10 each, and each orange yields 0.25 liters of juice. If she sells the juice for $2.00 per liter, how much profit does she make in a week if she buys 500 oranges each day and sells all the juice produced? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1400",
"style": "rule"
}
|
numina_math
|
{
"index": 2364,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has a rectangular plot of land, and the length of the plot is 4 times its width. He decides to build a fence around the plot and plant a tree at each corner. The total length of the fence is 200 meters. What are the dimensions of the plot? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 2365,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence where each term is half of the previous term, starting with 32. Write down the first five terms of this sequence and calculate the sum of these five terms. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "62",
"style": "rule"
}
|
numina_math
|
{
"index": 2366,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the piecewise function \\( f(x) \\) defined as follows:\n\\[ \nf(x) = \n\\begin{cases} \nx^2 - 4x + 3 & \\text{if } x \\leq 2 \\\\\n2x^2 - 8x + 6 & \\text{if } x > 2\n\\end{cases}\n\\]\nFind the value of \\( f(x) \\) at \\( x = 1 \\) and \\( x = 3 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2367,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A school cafeteria serves fruit in cycles. Apples are delivered every 5 days, bananas every 7 days, and oranges every 9 days. Today, the cafeteria received all three types of fruit. How many days will pass before the cafeteria receives all three types of fruit on the same day again? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "315",
"style": "rule"
}
|
numina_math
|
{
"index": 2368,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Approximate the value of $\\log_{10}{5000}$ and determine the two consecutive integers between which it lies. Then, find the sum of these integers. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2369,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Liam is biking a 60-kilometer trail. He has already completed 3/5 of the distance. How many kilometers does Liam still need to bike to finish the trail? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 2370,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is buying 3 packs of pencils. Each pack contains 12 pencils, and she gets a 10% discount on the total price. If each pack costs $5, how much will she pay in total after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2371,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha runs a small bakery and receives 8 cake orders every day. She is able to bake and deliver 5 cakes each day. How many cake orders will she have remaining to fulfill after 7 days? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "21",
"style": "rule"
}
|
numina_math
|
{
"index": 2372,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If you reverse the digits of a decimal number \\(0.47\\) and then round the result to the nearest tenth, what is the resulting number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2373,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A laboratory technician has a 100 mL solution that is 15% alcohol. He adds some pure alcohol to the solution to increase the concentration to 25%. How much pure alcohol did he add? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13.33",
"style": "rule"
}
|
numina_math
|
{
"index": 2374,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom is planning a road trip and wants to ensure he has enough gas. His car's fuel efficiency is 25 miles per gallon, and the gas tank holds 12 gallons when full. Gas costs $3.50 per gallon. Tom plans to drive a total of 600 miles. How much will he need to budget for gas for the entire trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "84",
"style": "rule"
}
|
numina_math
|
{
"index": 2375,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A water tank is being filled at a constant rate of 15 liters per minute and simultaneously being drained at a constant rate of 5 liters per minute. If the tank initially contains 100 liters of water, how many minutes will it take for the tank to reach 250 liters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 2376,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex has to attend a series of meetings spread over several days. Each meeting lasts 45 minutes. If Alex has 12 meetings to attend, how many total hours will Alex spend in these meetings? Additionally, if there are 3 different possible time slots each day and Alex can attend only one meeting per time slot, how many days will it take for Alex to complete all the meetings? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2377,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the expression \\((3^{1024} + 4^{1024})^2 - (3^{1024} - 4^{1024})^2\\). Simplify this expression and express it in the form \\(k \\cdot 10^{1024}\\) for some positive integer \\(k\\). What is the value of \\(k\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1024",
"style": "rule"
}
|
numina_math
|
{
"index": 2378,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "An international flight travels from New York to Paris, covering a distance of 5,850 kilometers. The flight consumes 12 liters of fuel per kilometer. If the fuel cost is $1.20 per liter, calculate the total fuel cost for the flight. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "84240",
"style": "rule"
}
|
numina_math
|
{
"index": 2379,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a class, 60% of the students are boys. Out of the boys, 1/3 play soccer and the rest play basketball. If there are 120 students in total, how many boys play basketball? Provide your answer as a percentage of the total number of students. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2380,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store sells a batch of smartphones at a discount of 15% off the marked price and still makes a profit of 25%. If the cost price of each smartphone is $320, what is the marked price of each smartphone? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "470.59",
"style": "rule"
}
|
numina_math
|
{
"index": 2381,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company has decided to distribute a bonus of $12,000 among its 15 employees. Each employee will receive a percentage of the total bonus based on their performance rating. If an employee receives 8% of the total bonus, how much money does that employee receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "960",
"style": "rule"
}
|
numina_math
|
{
"index": 2382,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A triangular garden has sides of lengths 7 meters, 10 meters, and 12 meters. If a person wants to plant a flower at each vertex and along each side at 1-meter intervals, how many flowers will they plant in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "29",
"style": "rule"
}
|
numina_math
|
{
"index": 2383,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha works as a freelance graphic designer and charges $20 per hour. She decides to take a day off from work to attend a workshop that costs $80. If she typically works 6 hours a day, what is her total opportunity cost for attending the workshop? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "200",
"style": "rule"
}
|
numina_math
|
{
"index": 2384,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels a distance of 180 miles using 15 gallons of gasoline. At this rate, how many gallons of gasoline are needed for the car to travel 300 miles? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 2385,
"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 bake a cake using 15 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": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2386,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces rectangular metal bars that measure 12 cm by 8 cm by 5 cm. Each bar weighs 7.5 kg. The factory plans to melt down 20 of these bars and mold the metal into new rectangular bars measuring 24 cm by 16 cm by 10 cm. If each new bar weighs 30 kg, how many new bars can be produced from the melted metal? Ensure that your calculations take into account unit consistency and summing up the total weight. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2387,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "James is shopping for a new laptop. Store A offers a 20% discount on a $900 laptop but includes a $50 shipping fee. Store B offers a 25% discount on the same laptop with free shipping. Which store should James buy from to spend the least amount of money, and how much will he save compared to the other store? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "95",
"style": "rule"
}
|
numina_math
|
{
"index": 2388,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a collection of 120 marbles. She decides to give 25% of her marbles to her friend. After giving away the marbles, she decides to divide the remaining marbles equally among her 3 siblings. How many marbles does each sibling get? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2389,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is planning to buy a new phone. She wants to save at least $500 in 5 months. If she has already saved $100 and plans to save an equal amount each month for the next 5 months, how much does she need to save each month to meet her goal? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 2390,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mary is planning to purchase a new laptop for $1,200. She has a coupon that gives her a 10% discount on the laptop. Additionally, the store is running a promotion that offers an extra 5% discount on the already discounted price. How much will Mary save in total, and what will be the final price she pays for the laptop? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1026",
"style": "rule"
}
|
numina_math
|
{
"index": 2391,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the rational equation and simplify: \\(\\frac{3}{x-2} + \\frac{5}{x+4} = \\frac{7}{x-2}\\) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "26",
"style": "rule"
}
|
numina_math
|
{
"index": 2392,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily and Sarah are planning a trip together. Emily has $120 saved up, while Sarah has $80 saved up. They decide to save a total of $500 together for their trip. If Emily saves $15 per week and Sarah saves $25 per week, how many weeks will it take for them to reach their goal of $500 together? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2393,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A charity organization collected a total of $2,400 to distribute equally among four different community projects. If one of the projects decides to donate 20% of its share back to the charity, how much money will be left for that project after the donation? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "480",
"style": "rule"
}
|
numina_math
|
{
"index": 2394,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A pet store has 3 types of pets: dogs, cats, and rabbits. The total weight of all the dogs is 120 kg, the total weight of all the cats is 90 kg, and the total weight of all the rabbits is 45 kg. If there are 5 dogs, 9 cats, and 15 rabbits, what is the average weight of each type of pet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2395,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A swimming pool is in the shape of a rectangular prism and measures 25 meters in length, 10 meters in width, and 2 meters in depth. If it takes 1 minute to fill 1 cubic meter of water into the pool, how many hours will it take to fill the pool completely? Additionally, if each cubic meter of water costs $0.50, how much will it cost to fill the pool? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "250",
"style": "rule"
}
|
numina_math
|
{
"index": 2396,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train travels a distance of 300 kilometers at a constant speed. If the train increases its speed by 20 kilometers per hour, it would take 1 hour less to travel the same distance. What is the train's original speed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "68.1",
"style": "rule"
}
|
numina_math
|
{
"index": 2397,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the parabola \\( y = 2x^2 - 4x + 3 \\) and the line \\( y = mx + c \\). Find the value of \\( c \\) such that the line passes through the vertex of the parabola and intersects it at exactly one other point. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2398,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory plans to produce 500 gadgets in 20 days. However, due to an increase in efficiency, they end up producing 3 additional gadgets per day compared to their original plan. How many days did it actually take for the factory to complete the production? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 2399,
"name": "numina_math",
"split": "train"
}
|
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