prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "In the diagram below, a regular hexagon is inscribed in a circle. One of the triangles formed by connecting the center of the circle to two adjacent vertices of the hexagon is highlighted. What is the measure of each angle of this highlighted triangle?\n\n[asy]\nsize(100);\nimport graph;\ndraw(Circle((0,0),2));\npair A = dir(0), B = dir(60), C = dir(120), D = dir(180), E = dir(240), F = dir(300);\ndraw(A--B--(0,0)--A--cycle);\ndraw((0,0)--C); draw((0,0)--D); draw((0,0)--E); draw((0,0)--F);\nlabel(\"A\", A, dir(A));\nlabel(\"B\", B, dir(B));\nlabel(\"C\", C, dir(C));\nlabel(\"D\", D, dir(D));\nlabel(\"E\", E, dir(E));\nlabel(\"F\", F, dir(F));\nlabel(\"O\", (0,0), S);\n\\end{asy] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 3000,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jordan works part-time and earns $15 per hour. He worked for 3 hours on Monday, 4 hours on Tuesday, and 5 hours on Wednesday. If Jordan then spent $30 on a new video game, how much money does he have left from his earnings? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 3001,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends is planning a road trip from Chicago to Miami. They intend to drive at a constant speed of 70 miles per hour. They plan to take a 45-minute break every 4 hours of driving. Upon reaching Miami, they will spend an additional 1 hour locating their accommodation. If the total distance from Chicago to Miami is 1,380 miles, how many hours will the trip, including breaks and finding accommodation, take? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "23.71",
"style": "rule"
}
|
numina_math
|
{
"index": 3002,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A boat travels 60 miles downstream in 2 hours and the same distance upstream in 3 hours. Find the speed of the boat in still water and the speed of the current. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 3003,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels from Town A to Town B at a speed of 12 miles per hour. He takes a break for 30 minutes at Town B and then returns to Town A at a speed of 8 miles per hour. The total time for the entire trip, including the break, is 5 hours. How far is Town A from Town B? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "21.6",
"style": "rule"
}
|
numina_math
|
{
"index": 3004,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a factory produces 1,200 gadgets in a 5-hour shift, how many gadgets does it produce in a 30-hour workweek? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7200",
"style": "rule"
}
|
numina_math
|
{
"index": 3005,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John drives from his home to the office at a speed of 45 miles per hour. The office is 30 miles away from his home. After working, he drives another 20 miles to visit a friend. How many miles does John travel in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 3006,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In how many ways can 7 people be arranged in a circle such that two specific people, Alice and Bob, are not seated next to each other? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "480",
"style": "rule"
}
|
numina_math
|
{
"index": 3007,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces three types of widgets: Type A, Type B, and Type C. The factory produces 50 units of Type A widgets, 30 units of Type B widgets, and 20 units of Type C widgets. The cost per unit of Type A, Type B, and Type C widgets are $5, $7, and $10 respectively. What is the average cost per unit of all the widgets produced by the factory? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6.6",
"style": "rule"
}
|
numina_math
|
{
"index": 3008,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah and her brother decided to cycle to a nearby park which is 9 miles away from their home. They cycled at a constant speed and it took them 45 minutes to reach the park. If their friend's house is 6 miles away from their home and they cycle at the same constant speed, how long will it take them to reach their friend's house? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 3009,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company decides to offer a special discount on its new product. The price of the product is defined by the function $P(x) = 100 \\times (0.9)^x$, where $x$ represents the number of months since the product was launched. If the company also offers a flat discount of $20$ after 6 months, what will be the cost of the product after 6 months? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33.14",
"style": "rule"
}
|
numina_math
|
{
"index": 3010,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha invested $10,000 in a savings account that pays a simple interest rate of 5% per year. After how many years will her investment grow to $12,500? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 3011,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tara's parents gave her $90 for her birthday. Not wanting to spend it, Tara put the money in a new bank account that gains 10% interest annually. If she doesn't withdraw the money at all, how much will she have after two years? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "108.9",
"style": "rule"
}
|
numina_math
|
{
"index": 3012,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If you have $13.50 and you want to split it equally among 4 friends, how much money will each friend get? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.38",
"style": "rule"
}
|
numina_math
|
{
"index": 3013,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A team of painters is hired to paint a large building. They have been working for 5 days and have painted 3,000 square meters at a constant rate. If they want to finish painting the remaining 12,000 square meters in the next 10 days, what must be their new daily painting rate in square meters per day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1,200",
"style": "rule"
}
|
numina_math
|
{
"index": 3014,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels a distance of 240 kilometers at an average speed. On the way back, the car's speed increased by 20 kilometers per hour, and it took 1 hour less to travel the same distance. What was the car's average speed on the way to the destination? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 3015,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In two similar triangles, the ratio of the lengths of their corresponding sides is \\( \\frac{3}{5} \\). If the area of the smaller triangle is \\( 27 \\) square units, find the area of the larger triangle. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 3016,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the remainder when \\( 81^{12} \\div 27^5 \\) is divided by 9. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 3017,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two friends, Alice and Bob, are comparing the costs of their favorite subscription services. Alice subscribes to a music streaming service that costs $10 per month, while Bob subscribes to a video streaming service that costs $15 per month. They both plan to keep their subscriptions for a year. How much more will Bob spend on his subscription service than Alice over the year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 3018,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(a\\), \\(b\\), and \\(c\\) be the roots of the polynomial \\(x^3 - 6x^2 + 11x - 6 = 0\\). Find the value of \\(a^3 + b^3 + c^3\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 3019,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length of 15 meters and a width of 10 meters. The school decided to add a 1-meter wide path around the outside of the garden. Calculate the total area of the garden including the path. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "204",
"style": "rule"
}
|
numina_math
|
{
"index": 3020,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A community park is planning to plant flowers and trees in a new garden. They plan to plant 50 flower beds, each containing 120 flowers, and 20 trees, each bearing an average of 300 fruits. How many total flowers and fruits will the garden have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12000",
"style": "rule"
}
|
numina_math
|
{
"index": 3021,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the series \\(\\sum_{n=1}^{\\infty} \\frac{2}{n(n+1)}\\), find its sum using partial fraction decomposition and convergence of series. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 3022,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A professional poultry farmer has a number of geese that is 2/3 of the number of ducks and 3/4 of the number of chickens. The farmer has 54 ducks. How many chickens does the farmer have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 3023,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The interior angles of a regular polygon are each equal to \\( (2x + 30)^\\circ \\). If the polygon has 12 sides, find the value of \\( x \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 3024,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels 60 miles on 3 gallons of gasoline. How many kilometers can the car travel on 15 liters of gasoline? (Note: 1 mile = 1.60934 kilometers, 1 gallon = 3.78541 liters) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "128",
"style": "rule"
}
|
numina_math
|
{
"index": 3025,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jessica went shopping and bought four items: a dress for $50, a pair of shoes for $30, a bag for $20, and a hat for $10. The store was having a sale where a 20% discount was applied to the total purchase if it exceeded $50. How much did Jessica spend after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "88",
"style": "rule"
}
|
numina_math
|
{
"index": 3026,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the sum of the infinite series: \\[\\sum_{n=1}^\\infty \\frac{1}{(n+1) H_n H_{n+1}},\\] where \\(H_n\\) is the \\(n\\)-th harmonic number defined as \\(H_n = 1 + \\frac{1}{2} + \\frac{1}{3} + \\cdots + \\frac{1}{n}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 3027,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A classroom has 48 students, and they need to be divided into groups where each group has 5 students. After forming as many full groups as possible, how many students will be left without a group? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 3028,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels at a speed of 15 km/h and a car travels at a speed of 60 km/h. If both start from the same point and travel in the same direction, after how many hours will the car be 90 kilometers ahead of the cyclist? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 3029,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore sells notebooks at 12 dollars each. They are having a sale where the price of each notebook is reduced by 1/4 of its original price. If a customer buys 8 notebooks at the sale price, how much do they pay in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
numina_math
|
{
"index": 3030,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Nina has a collection of 60 marbles. She wants to divide them equally among 4 friends, but she also wants to keep 1/5 of the total marbles for herself. After giving the marbles to her friends and keeping some for herself, how many marbles does each friend get, and how many does Nina keep? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 3031,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah borrowed $500 from a friend. She agreed to repay the loan in 5 equal monthly installments. After making the first payment, she realized she needed to borrow an additional $200. She now plans to repay the total amount (initial loan plus additional loan) in the remaining 4 months. How much will each of her monthly payments be? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "175",
"style": "rule"
}
|
numina_math
|
{
"index": 3032,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the sum of two numbers is 30, and one of the numbers is 12, what is the other number? Additionally, if you divide the other number by 3, what is the result? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 3033,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A florist is arranging bouquets for a wedding. Each bouquet requires 5 roses, 3 lilies, and 2 orchids. If the florist needs to prepare 10 bouquets, and each rose costs $2, each lily costs $3, and each orchid costs $4, what is the total cost of the flowers for all the bouquets? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "270",
"style": "rule"
}
|
numina_math
|
{
"index": 3034,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily went shopping and bought three items: a shirt for $23.45, a pair of pants for $42.89, and a hat for $15.99. She had a gift card worth $30.00. How much did she have to pay out of pocket after using the gift card? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "52.33",
"style": "rule"
}
|
numina_math
|
{
"index": 3035,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the rational function \\( h(x) = \\frac{3}{1 + x^2} \\), find the range of this function. Express the range as an interval in the form \\((a, b]\\). What is \\( a + b \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 3036,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer is planning to plant trees in his orchard. He wants to plant trees in rows, with each row having the same number of trees. If he plants 3 rows, he will have a total of 24 trees. How many trees will he have if he plants 5 rows, assuming the number of trees per row remains constant? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 3037,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the greatest three-digit number that leaves a remainder of 1 when divided by 9 and a remainder of 3 when divided by 5? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "973",
"style": "rule"
}
|
numina_math
|
{
"index": 3038,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If 1 Euro equals 1.2 US Dollars, how many US Dollars will you get if you exchange 150 Euros? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 3039,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train travels from City A to City B at a speed of 60 miles per hour. On its return trip, due to maintenance work, it travels at a speed of 40 miles per hour. If the total travel time for the round trip is 5 hours, what is the distance between City A and City B? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 3040,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company manufactures 500 units of a product. Quality control finds that 10% of the units are defective. Of the non-defective units, 20% are designated for a special promotion. How many units are left to be sold as regular stock? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "360",
"style": "rule"
}
|
numina_math
|
{
"index": 3041,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from city A to city B, a distance of 300 miles, in 5 hours. If the car continues at the same rate of speed, how long will it take to travel an additional 180 miles? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 3042,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maya is traveling to Europe and wants to exchange her US dollars to Euros. The exchange rate is $1 = €0.85. Maya has $500, but the currency exchange office charges a 2% fee on the amount exchanged. How many Euros will Maya receive after the fee is applied? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "416.5",
"style": "rule"
}
|
numina_math
|
{
"index": 3043,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the polynomial \\( P(x) = x^3 - 4x^2 + x + 6 \\) for \\( x = 2 \\cdot 10^3 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7984002006",
"style": "rule"
}
|
numina_math
|
{
"index": 3044,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A circular garden has a radius of 10 meters. A smaller circular flower bed is placed inside the garden such that the area of the flower bed is 25% of the area of the garden. What is the radius of the flower bed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 3045,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jessica is planning her monthly budget. She starts with a savings of $500. She decides to allocate $120 for groceries, $85 for transportation, and $65 for entertainment. Additionally, she receives a $200 bonus from her work this month. After all these expenses and the bonus, how much money will Jessica have left in her savings at the end of the month? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "430",
"style": "rule"
}
|
numina_math
|
{
"index": 3046,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A square with side length \\( s \\) is inscribed in a circle. A right triangle is then inscribed in the same circle such that one of its legs is equal to the side length of the square. What is the ratio of the area of the square to the area of the right triangle? Express your answer as a common fraction. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 3047,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A survey showed that 60% of the employees in a company are satisfied with their job. If 3/5 of the satisfied employees are from the marketing department and there are 180 satisfied employees from the marketing department, how many employees are in the company? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "500",
"style": "rule"
}
|
numina_math
|
{
"index": 3048,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify: $\\frac{8}{\\sqrt[4]{16}}$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 3049,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In how many ways can you arrange the digits $0$, $1$, $3$, $7$, $9$ to form a five-digit number that is even? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 3050,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify and find the degree of the polynomial: \\(2x^2(3x^4 - x^2 + 1) - x(4x^5 - 2x^3 + x)\\) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2x^6+x^2",
"style": "rule"
}
|
numina_math
|
{
"index": 3051,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Point \\( M(5, -2) \\) is the midpoint of \\( \\overline{AB} \\). If point \\( A \\) has coordinates \\( (2, 4) \\), what are the coordinates of point \\( B \\), and what is the sum of the coordinates of point \\( B \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 3052,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A class is completing an art project. Each of the 30 students is assigned to a separate group and will need to take markers from the 22 boxes of markers. The first group has 10 students who will have 2 markers each and the second group has 15 students who will have 4 markers each. The last group takes the remaining markers and divides them equally. If each box of markers contains 5 markers, how many markers does each of the students in the last group receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 3053,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "During a sale, a store offers a 20% discount on all items. If a customer buys a jacket that originally costs $75 and a pair of shoes that originally costs $50, how much does the customer save in total due to the discount? What is the final amount the customer pays after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 3054,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The rain starts at 8:00 AM and pours until it stops at 4:00 PM on the first day. On the second day, the rain lasts 3 more hours than it did on the first day. On the third day, the rain lasts twice as long as it did on the second day. Calculate the total amount of time it was raining over the three days. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "41",
"style": "rule"
}
|
numina_math
|
{
"index": 3055,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the algebraic expression \\( 3x^2 - 2xy + y^2 \\), substitute \\( x = 4 \\) and \\( y = 5 \\). What is the value of the expression? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33",
"style": "rule"
}
|
numina_math
|
{
"index": 3056,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria is planning to buy souvenirs for her friends during her trip to Europe. She wants to buy 3 keychains for 5 euros each, 2 T-shirts for 15 euros each, and 4 postcards for 2 euros each. If the exchange rate is 1 euro = 1.2 dollars, how much will Maria spend in dollars? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "63.6",
"style": "rule"
}
|
numina_math
|
{
"index": 3057,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A jacket originally costs $80. During a sale, the price of the jacket is reduced by 25%. After the sale, the store further reduces the sale price by 20%. What is the final price of the jacket? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 3058,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Triangle $DEF$ has vertices $D(1, 3)$, $E(4, 8)$, and $F(7, 2)$. Determine the area of $\\triangle DEF$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16.5",
"style": "rule"
}
|
numina_math
|
{
"index": 3059,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company manufactures widgets and sells them for $30 each. The cost to produce each widget is $20. The company also has fixed costs of $500 per month. How many widgets must the company sell in a month to break even? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 3060,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore initially priced a popular novel at $18. Due to a pricing error, they mistakenly added an extra $6 to the price. If a customer bought 5 copies of the novel at the erroneous price, how much should the bookstore refund the customer after correcting the error? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 3061,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a circle centered at \\( O \\), \\( AB \\) is a diameter, and \\( C \\) is a point on the circle such that \\( \\angle ACB = 90^\\circ \\). \\( D \\) is the midpoint of \\( AC \\), and \\( E \\) is the midpoint of \\( BC \\). If the angle bisector of \\( \\angle AOB \\) intersects \\( DE \\) at point \\( F \\), what is the measure of \\( \\angle AOF \\), in degrees? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 3062,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length that is 4 meters longer than its width. If the perimeter of the garden is 32 meters, what are the dimensions of the garden (length and width)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 3063,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah wants to buy a new laptop that costs $1200. The store is offering a 15% discount on all electronics. If Sarah also has a coupon that gives an additional 5% off the discounted price, how much will she pay for the laptop? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "969",
"style": "rule"
}
|
numina_math
|
{
"index": 3064,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Four friends, Alex, Ben, Charlie, and Dave, decide to share the cost of a weekend trip. They agreed that the total cost, which includes $100 for fuel, $200 for accommodation, and $300 for food, should be split equally among them. However, Alex and Ben can only pay a maximum of $100 each. If Charlie and Dave agree to cover the remaining cost equally, how much will each of them (Charlie and Dave) need to pay?\n\n### Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "200",
"style": "rule"
}
|
numina_math
|
{
"index": 3065,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a park, there are three types of trees: 250 oak trees, 320 pine trees, and 410 maple trees. A group of volunteers wants to plant 50 more trees of each type in the park. After planting the new trees, they decide to evenly distribute the total number of trees into 5 different sections of the park. How many trees will each section have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "226",
"style": "rule"
}
|
numina_math
|
{
"index": 3066,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length of 80 meters and a width of 50 meters. The garden is divided into smaller rectangular plots such that the ratio of the length to the width of each plot is 4:1. If each plot covers an area of 100 square meters, how many plots can be made from the entire garden? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 3067,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression \\( \\log_2 (8 \\cdot 16) - \\log_2 (4 \\cdot 2^3) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 3068,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Pat's stick is 30 inches long. He covers 7 inches of the stick in dirt. The portion that is not covered in dirt is half as long as Sarah’s stick. Jane’s stick is two feet shorter than Sarah’s stick. How many inches long is Jane’s stick? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22",
"style": "rule"
}
|
numina_math
|
{
"index": 3069,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f: \\mathbb{R} \\to \\mathbb{R} \\) be a function such that \\( f(x + y) = f(x) + f(y) \\) for all real numbers \\( x \\) and \\( y \\), and \\( f(1) = 2 \\). Find \\( f(2023) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4046",
"style": "rule"
}
|
numina_math
|
{
"index": 3070,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John can paint a fence in 8 hours, while his friend Mark can paint the same fence in 12 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": "4.8",
"style": "rule"
}
|
numina_math
|
{
"index": 3071,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A theater offers a special discount on tickets. The regular ticket price is $20. A group of students can receive a discount such that the total price for the group is no more than $15 per ticket if the group consists of at least 10 students. If a group contains fewer students, the price per ticket is reduced by $1 for each additional student beyond 5. What is the minimum number of students required in the group to ensure the ticket price is $15 or less per ticket? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 3072,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John cycles to his friend's house which is 15 km away. On the way to his friend's house, he cycles at an average speed of 12 km/hr, and on the way back, he cycles at an average speed of 10 km/hr. How much time does John spend cycling in total, and what is his average speed for the entire trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10.91",
"style": "rule"
}
|
numina_math
|
{
"index": 3073,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Paul and Lisa are collecting marbles. Paul has twice as many marbles as Lisa. Together, they have 90 marbles. How many marbles does each of them have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 3074,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels 150 miles in 3 hours and another 200 miles in 4 hours. Calculate the average speed of the car over the entire journey. Then, subtract the average speed from 60 mph. What is the result? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 3075,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical water tank is filled to 0.75 of its capacity. The tank has a total capacity of 800 liters. If 20% of the water is used for irrigation, how many liters of water are left in the tank? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "480",
"style": "rule"
}
|
numina_math
|
{
"index": 3076,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Ella is planning to buy new pens. Each pen costs $2. She has a budget of $24 and wants to buy as many pens as possible without exceeding her budget. How many pens can Ella buy, and how much money will she have left after buying the pens? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 3077,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily has a collection of ribbons in three different colors: red, blue, and green. She has $\\frac{1}{3}$ as many red ribbons as blue ribbons and twice as many green ribbons as blue ribbons. If she has 24 blue ribbons, how many ribbons does she have in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 3078,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider two employees, Alex and Jordan. Alex earns $25 per hour and receives a bonus of $50 at the end of every week. Jordan earns $28 per hour but does not receive any bonus. If both employees work 35 hours per week, what is the weekly savings (if any) by hiring the cheaper employee? Compare the total weekly earnings of both employees to determine who is more cost-effective. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "55",
"style": "rule"
}
|
numina_math
|
{
"index": 3079,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa drives from City A to City B, which are 120 miles apart, at an average speed of 60 miles per hour. On her way back from City B to City A, she encounters roadwork and has to drive at an average speed of 40 miles per hour. If she spends 30 minutes at City B before driving back, what is the total time Lisa spent on this round trip? What is her average speed for the entire round trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "43.64",
"style": "rule"
}
|
numina_math
|
{
"index": 3080,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A watch is being sold in New York for $500. There is a 25% discount on the watch. New York is in the Eastern Time Zone (ET). If the same watch is being sold in Los Angeles, which is in the Pacific Time Zone (PT) and is 3 hours behind New York, at the same discounted price, but an additional 10% discount is applied for local customers, what is the final price of the watch in Los Angeles and how much cheaper is it compared to the discounted price in New York? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "37.5",
"style": "rule"
}
|
numina_math
|
{
"index": 3081,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A smartphone costs 400 euros, and the price of a tablet is 75% of the price of the smartphone. How much does it cost to buy both the smartphone and the tablet together? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "700",
"style": "rule"
}
|
numina_math
|
{
"index": 3082,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a car dealership with 600 cars, 60% of the cars are hybrids, and 40% of the hybrids contain only one headlight. How many of the hybrids have full headlights? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "216",
"style": "rule"
}
|
numina_math
|
{
"index": 3083,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a perimeter of 200 meters. One side of the garden is 60 meters long. The garden also includes a 5-meter wide path along one of the shorter sides. How long is the remaining side of the garden, excluding the path? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 3084,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John has a bag of 36 apples. He decides to give 1/4 of the apples to his friend and then gives 1/3 of the remaining apples to his neighbor. How many apples does John have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 3085,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels at a constant speed and covers a distance of 45 kilometers in 3 hours. How far would the cyclist travel in 7 hours at the same speed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "105",
"style": "rule"
}
|
numina_math
|
{
"index": 3086,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels from Town A to Town B, which is 150 miles apart. He rides at a constant speed of 15 miles per hour. Midway through the journey, he stops for a 45-minute break. How long does it take for the cyclist to reach Town B, including the break? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10.75",
"style": "rule"
}
|
numina_math
|
{
"index": 3087,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the set of numbers \\{2, 5, 8, 11, 14, 17\\}, determine the average of the odd numbers in the set. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 3088,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A triangular garden has a base of 10 meters and a height of 8 meters. The garden is being divided into smaller sections by drawing lines parallel to the base. Each new section has an area that is half of the previous section. If the process of dividing continues until the smallest section has an area of 1 square meter, how many sections will there be in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 3089,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the functions \\( f(x) = \\log_2(x) \\) and \\( g(x) = \\sqrt{x} \\), find \\( (f \\circ g)(16) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 3090,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is organizing a charity run. She has 240 participants and wants to group them into teams with 7 members each. After forming as many teams as possible, how many participants will be left without a team? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 3091,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train leaves Station A traveling to Station B at 60 miles per hour. Two hours later, another train leaves Station A traveling to Station B on a parallel track at 90 miles per hour. How long after the second train departs will it catch up to the first train? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.8",
"style": "rule"
}
|
numina_math
|
{
"index": 3092,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train travels at a constant speed of 60 miles per hour. It takes 3 hours to travel from City A to City B. If another train travels the same route but at a speed of 80 miles per hour, how long will it take the second train to complete the journey? Provide your answer in minutes. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "135",
"style": "rule"
}
|
numina_math
|
{
"index": 3093,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa has a total of $500$ dollars in her savings account. During a month, she makes three withdrawals of $50$ dollars each and two deposits of $100$ dollars each. How much money does she have in her savings account at the end of the month? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "550",
"style": "rule"
}
|
numina_math
|
{
"index": 3094,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Define the custom binary operation \\( a \\circ b = a^2 + b \\). Evaluate the expression \\( (2 \\circ 3) \\circ 4 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "53",
"style": "rule"
}
|
numina_math
|
{
"index": 3095,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular playground is drawn on a scale drawing with a length of 15 cm and a width of 10 cm. The scale of the drawing is 1 cm : 2 m. Calculate the actual area of the playground in square meters. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 3096,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A tourist has $150 and wants to exchange it for euros. If the exchange rate is 1 euro = $1.25, how many euros will the tourist receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 3097,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex is planning a birthday party and needs to manage his expenses. He buys 3 packs of balloons, each costing $5, 2 birthday cakes costing $15 each, and 10 party hats costing $1 each. He also buys 4 pizzas, each costing $12. How much money does Alex spend in total on the party supplies? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "103",
"style": "rule"
}
|
numina_math
|
{
"index": 3098,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A number \\( N \\) is constructed by repeating the digit sequence \\( 123456 \\) a total of \\( k \\) times, i.e., \\( N = 123456123456 \\ldots 123456 \\) (repeated \\( k \\) times). Determine the smallest positive integer \\( k \\) such that the sum of the digits of \\( N \\) is divisible by 11. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 3099,
"name": "numina_math",
"split": "train"
}
|
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