prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "How many different 5-letter words can be formed using the letters A, B, C, D, and E if no letter is repeated and the word must start with a vowel? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 2100,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is planning a road trip and has allocated his budget for gas and food. He decides to spend 70% of his budget on gas and the remaining on food. He estimates that he will need $210 for gas. If gas costs $3 per gallon and his car travels 30 miles per gallon, how far can John travel on his road trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2100",
"style": "rule"
}
|
numina_math
|
{
"index": 2101,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression \\(\\frac{\\sqrt{72}}{2\\sqrt{2}}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2102,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends goes on a week-long vacation. During the first four days, they spend an average of $150 per day. On the fifth day, they spend $200. How much should they spend on average for the remaining two days if they want their total average daily spending for the week to be $160? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "160",
"style": "rule"
}
|
numina_math
|
{
"index": 2103,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many 5-letter \"words\" can be made using the letters A, B, and C if repetition of letters is allowed? Express the total count of such \"words\" using the Counting Principle. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "243",
"style": "rule"
}
|
numina_math
|
{
"index": 2104,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a collection of U.S. coins consisting of 3 nickels, 4 dimes, and 2 quarters. If she multiplies the total value of these coins by 5, what is the resulting amount in cents? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "525",
"style": "rule"
}
|
numina_math
|
{
"index": 2105,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A triangular garden has a base of 10 meters and a height of 6 meters. The owner decides to expand the garden by adding a trapezoidal section on one side, where the new section has a height of 6 meters, the same as the original triangle, and the top and bottom lengths of the trapezoid are 5 meters and 10 meters, respectively. What is the percentage increase in the area of the garden after the expansion? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 2106,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a sequence of integers from 1 to 50. What is the sum of all the multiples of 5 in this sequence? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "275",
"style": "rule"
}
|
numina_math
|
{
"index": 2107,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A marathon race covers a distance of 42 kilometers. If a runner maintains a constant speed of 10 kilometers per hour, how much time does it take for the runner to complete the marathon? After the marathon, the runner drinks water at a rate of 0.5 liters every 15 minutes for the next hour. How many liters of water does the runner drink in total during this time? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2108,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Riley is baking cookies for a charity event. She uses a recipe that requires 2.5 cups of flour for every dozen cookies. If she has a total of 10 cups of flour, how many dozen cookies can she bake? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2109,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A local animal shelter is preparing for an adoption event. They have three times as many cats as dogs, and twice as many rabbits as cats. If there are 12 dogs at the shelter, how many animals are there in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2110,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore is having a sale where all items are 20% off. If a customer buys a book that originally costs $45, how much will the customer pay after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 2111,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In the Fibonacci sequence, let \\( F_n \\) denote the \\( n \\)-th Fibonacci number. If \\( F_1 = 1 \\) and \\( F_2 = 1 \\), find the remainder when \\( F_{50} \\) is divided by 7. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2112,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a car rental service charges a fixed rate of $30 per day plus $0.25 per mile driven, and a customer drives the car for 3 days and covers a total distance of 240 miles, what is the total cost for the customer? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 2113,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A theater has seats arranged in an arithmetic sequence where the first row has 15 seats, the second row has 18 seats, the third row has 21 seats, and so on. If the theater has 20 rows in total, how many seats are there in the theater? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "870",
"style": "rule"
}
|
numina_math
|
{
"index": 2114,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah needs to bake 5 batches of cookies for a bake sale. Each batch requires 250 grams of chocolate chips. Chocolate chips are sold in bags of 500 grams each, with each bag costing $4.50. How much will it cost Sarah to buy enough chocolate chips for all 5 batches of cookies? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2115,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Three friends, Alice, Bob, and Charlie, collectively have $200. The amount Alice has is 4 times what Bob has, and Bob has $20 more than Charlie. How much money does Charlie have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16.67",
"style": "rule"
}
|
numina_math
|
{
"index": 2116,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the number \\(2520\\), find the number of positive divisors of \\(2520\\) that are also prime numbers. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2117,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a certain city, the number of bicycles to the number of cars is in the ratio 7:3. If there are 210 bicycles, how many cars are there in the city? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2118,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Round $\\frac{7}{15}$ to the nearest hundredth. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.47",
"style": "rule"
}
|
numina_math
|
{
"index": 2119,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $\\mathbf{a}$ and $\\mathbf{b}$ be vectors such that $\\|\\mathbf{a}\\| = 3$, $\\|\\mathbf{b}\\| = 4$, and $\\mathbf{a} \\cdot \\mathbf{b} = 0$. Find the magnitude of the vector $\\mathbf{a} \\times \\mathbf{b}$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2120,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the function \\( f(x) = 3x + 4 \\), find the inverse function \\( f^{-1}(x) \\) and then determine \\( f^{-1}(10) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2121,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( P(x) = 6x^2 + 15x \\) and \\( Q(x) = 3x \\), simplify the expression \\(\\frac{P(x)}{Q(x)}\\) for \\( x = 5 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 2122,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Paul is saving money to buy a new bike that costs $600. He starts by saving $50 in the first month. Each subsequent month, he saves $20 more than the previous month. How many months will it take Paul to save enough money to buy the bike? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2123,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the following expression and evaluate it at \\( x = 2 \\): \n\\[ (2x^4 - 3x^3 + 5x^2 - x + 7) - (x^4 + 2x^3 - 4x^2 + 6x - 3) \\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2124,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider two functions, \\( f(x) = 2x + 3 \\) and \\( g(x) = x - 5 \\). Find the value of \\( f(g(10)) + g(f(10)) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "31",
"style": "rule"
}
|
numina_math
|
{
"index": 2125,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex spends 2 hours and 15 minutes on his homework every day from Monday to Friday and 1 hour and 30 minutes on his homework on Saturday and Sunday. How many minutes does Alex spend on his homework in a week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "855",
"style": "rule"
}
|
numina_math
|
{
"index": 2126,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there is a need to schedule six exams across six different subjects (Math, English, Physics, Chemistry, Biology, History). Each exam must be scheduled on one of six different days, with no more than one exam per day. The constraint is that the exams for Math and Physics cannot be on consecutive days. How many different ways can the exams be scheduled under this constraint? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "480",
"style": "rule"
}
|
numina_math
|
{
"index": 2127,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Compute $3 \\times (8 - 2) + 12 \\div (6 - 4)$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 2128,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires a mix of apples and oranges in the ratio of 3:2. If you need to use a total of 40 pieces of fruit, how many apples and how many oranges should you use? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 2129,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore is having a sale where all books are discounted by 25%. Emily wants to buy 3 novels and 2 non-fiction books. Each novel originally costs $20, and each non-fiction book originally costs $30. How much will Emily spend after the discount is applied? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2130,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A charity organization has $10,000 to distribute among 5 local schools. The organization decides to distribute 40% of the funds equally among the schools and keep the remaining amount for future projects. After the distribution, they realize one school received an additional $200 by mistake, and they need to adjust the distribution by taking back the extra amount. How much does each school receive after the adjustment, and how much is left for future projects? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "760",
"style": "rule"
}
|
numina_math
|
{
"index": 2131,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends decided to share the cost of a vacation rental. The rental costs $2,400 for a week. If there are 8 friends, how much does each friend need to contribute to cover the total cost? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 2132,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In coordinate geometry, consider a polynomial \\( P(x) = x^2 + 11x + 30 \\). Find the remainder when \\( P(5) \\) is divided by the prime number \\( 7 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2133,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bike race is planned over a stretch of 120 kilometers. Racer A cycles at a speed of 24 kilometers per hour, while Racer B cycles at a speed of 30 kilometers per hour. If Racer A starts the race 30 minutes before Racer B, how long after Racer B starts will he catch up with Racer A? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2134,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\(\\alpha\\) and \\(\\beta\\) are two angles such that \\(\\alpha + \\beta = 45^\\circ\\), express \\(\\tan(\\alpha - \\beta)\\) in terms of \\(\\tan \\alpha\\) and \\(\\tan \\beta\\) using angle addition and subtraction formulas. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{\\tan\\alpha-\\tan\\beta}{1+\\tan\\alpha\\tan\\beta}",
"style": "rule"
}
|
numina_math
|
{
"index": 2135,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A person decides to follow a weight loss program where they lose 10% of their weight in the first week, then 10% of the remaining weight in the second week, and so on. If the person starts at 100 kg, what will their weight be after 4 weeks? Express your answer to the nearest tenth of a kilogram. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "65.6",
"style": "rule"
}
|
numina_math
|
{
"index": 2136,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A clothing store had a clearance sale where they decided to reduce the price of all items by 25%. If a jacket originally cost $80, what is the sale price of the jacket after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 2137,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A large water container holds 500 liters of water. You need to transfer all this water into smaller containers that each hold 750 milliliters. How many smaller containers will you need to transfer all the water? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "667",
"style": "rule"
}
|
numina_math
|
{
"index": 2138,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces widgets at a constant rate of 150 widgets per day. If the factory operates 5 days a week, how many widgets will the factory produce in 4 weeks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3000",
"style": "rule"
}
|
numina_math
|
{
"index": 2139,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels at a constant speed of 15 miles per hour. If he cycles for 3 hours and then increases his speed to 20 miles per hour for the next 2 hours, how far does he travel in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "85",
"style": "rule"
}
|
numina_math
|
{
"index": 2140,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the sum of the arithmetic series: \\( \\sum_{n=1}^{50} \\frac{n}{100} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12.75",
"style": "rule"
}
|
numina_math
|
{
"index": 2141,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given a triangle \\( \\triangle ABC \\) with integer side lengths, one side measures 3 units and another side measures 4 units. Using the triangle inequality theorem, determine the smallest possible perimeter for \\( \\triangle ABC \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2142,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x) = 2x + 1 \\) and \\( g(x) = x^2 - 4 \\). If \\( h(x) = f(g(x)) \\), for how many values of \\( x \\) does \\( h(h(x)) = 17 \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2143,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school of 200 students, 120 students are enrolled in the Science Club, and 90 students are enrolled in the Math Club. If 50 students are enrolled in both clubs, how many students are not enrolled in either the Science Club or the Math Club? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2144,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular tank has a length of 20 meters, a width of 10 meters, and a height of 5 meters. How many liters of water can this tank hold if 1 cubic meter is equal to 1000 liters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1000000",
"style": "rule"
}
|
numina_math
|
{
"index": 2145,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The length of a rectangle is 3 times its width. If the perimeter of the rectangle is 64 units, find the dimensions of the rectangle. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 2146,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenna has twice as many marbles as Kevin. If Kevin has 15 marbles, and Lisa has 5 more marbles than Jenna, how many marbles does Lisa have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35",
"style": "rule"
}
|
numina_math
|
{
"index": 2147,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x) = \\left\\lfloor \\frac{3x+7}{2} \\right\\rfloor \\) and \\( g(x) = \\left\\lceil \\frac{5x-3}{4} \\right\\rceil \\). Determine \\( f(5) + g(5) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17",
"style": "rule"
}
|
numina_math
|
{
"index": 2148,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer harvested three types of crops from his fields: corn, wheat, and soybeans. He harvested 200 bushels of corn, 150 bushels of wheat, and 250 bushels of soybeans. If he sells the corn for $3.50 per bushel, the wheat for $4.00 per bushel, and the soybeans for $5.00 per bushel, how much total revenue does the farmer generate from selling all his crops? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2550",
"style": "rule"
}
|
numina_math
|
{
"index": 2149,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two painters, Alice and Bob, can paint a house together in 6 hours. Working alone, Alice can paint the house in 10 hours. How long will it take Bob to paint the house by himself? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 2150,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The greatest common divisor of two integers is \\(d\\) and their least common multiple is \\(l\\). If \\(d \\times l = 240\\), how many different values could \\(d\\) be? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 2151,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 120 gadgets per hour. If the factory operates 8 hours a day, how many gadgets are produced in a week? Assume the factory operates 5 days a week. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4800",
"style": "rule"
}
|
numina_math
|
{
"index": 2152,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the logarithm of 125 to the base 5 is represented as \\( \\log_5 125 \\), use the change of base formula to convert this logarithm to a natural logarithm (base \\( e \\)) and solve for its value. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2153,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is offering a promotional discount where the final price is a third of the original price. If the discounted price of a jacket is 45 dollars, what was the original price of the jacket? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "135",
"style": "rule"
}
|
numina_math
|
{
"index": 2154,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "At a pool party, there are 6 pizzas cut into 8 slices each. If the guests eat 35 slices, how many slices are left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 2155,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the product of the numbers \\(1101_2\\) and \\(24_5\\) to base 10, and then find the sum of the digits of the resulting base 10 number. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 2156,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "David purchased a jacket during a clearance sale where the store offered a 25% discount on all items. The original price of the jacket was $200. After purchasing the jacket, David realized he had a coupon that gave an additional 10% off the discounted price. How much did David pay for the jacket after applying both discounts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "135",
"style": "rule"
}
|
numina_math
|
{
"index": 2157,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In an equilateral triangle \\(ABC\\), the altitudes from vertices \\(A\\), \\(B\\), and \\(C\\) meet the opposite sides at points \\(D\\), \\(E\\), and \\(F\\) respectively. Suppose the altitude from \\(A\\) to \\(BC\\) is extended to a point \\(P\\) such that \\(AP = 3 \\times AD\\). Similarly, the altitude from \\(B\\) to \\(AC\\) is extended to a point \\(Q\\) such that \\(BQ = 3 \\times BE\\). Finally, the altitude from \\(C\\) to \\(AB\\) is extended to a point \\(R\\) such that \\(CR = 3 \\times CF\\). Find the ratio of the areas of triangle \\(PQR\\) to triangle \\(ABC\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2158,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company decided to distribute a bonus of $25,000 among its employees based on their departments' performance. There are two departments: Department A and Department B. Department A will receive twice as much as Department B. How much will each department receive, and what percentage of the total bonus does each department get? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "66.67",
"style": "rule"
}
|
numina_math
|
{
"index": 2159,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory has two machines, Machine A and Machine B, working together to produce widgets. Machine A can produce 15 widgets per hour, while Machine B can produce 10 widgets per hour. If the factory needs to produce 500 widgets in total, how many hours will it take for both machines working together to complete the job? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 2160,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma is organizing a charity run and needs to prepare medals for the participants. She expects 75% of the 240 registered participants to complete the run. If she needs to order each medal individually and each medal costs $3, how much will Emma spend on the medals? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "540",
"style": "rule"
}
|
numina_math
|
{
"index": 2161,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A, B, and C start from the same place at the same time and chase a cyclist in front of them along the same road. The three cars catch up with him in 6, 10, and 12 minutes respectively. Given that car A's speed is 24 kilometers per hour, car B's speed is 20 kilometers per hour, find car C's speed. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2162,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenna is baking cookies and needs 3/4 of a cup of sugar for each batch. If she plans to bake 8 batches, how many cups of sugar will she need in total? Round your answer to the nearest whole number. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2163,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two companies, X and Y, are selling premium bottled juice. Company X sells each bottle for $5, and Company Y sells each bottle for $4.50. Company X was able to sell 400 bottles, while Company Y sold 450 bottles. How much more revenue did Company Y generate compared to Company X? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 2164,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires a ratio of 2 parts sugar to 3 parts flour. If a baker has 12 cups of sugar, how many cups of flour does the recipe need? Additionally, if the baker decides to divide the resulting mixture into 5 equal portions, how many cups of the mixture will each portion contain? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2165,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two trains leave two different stations at the same time heading towards each other. Train A travels at 60 km/h and Train B travels at 80 km/h. If the two stations are 350 km apart, how long will it take for the two trains to meet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2166,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah runs on a treadmill at a constant pace. She covers 2 miles in 15 minutes. If she maintains the same pace, how many miles will she run in 1 hour and 45 minutes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 2167,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train travels from station X to station Y at a speed of 80 kilometers per hour. After traveling for 3 hours, it is still 120 kilometers away from station Y. What is the distance between stations X and Y? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "360",
"style": "rule"
}
|
numina_math
|
{
"index": 2168,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom is planning to host a grand dinner and needs to buy dinner plates for all attendees. Each dinner plate costs $15. Tom expects 45 guests, and he already has $500 set aside for this purchase. How much additional money does Tom need to buy a dinner plate for each guest? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "175",
"style": "rule"
}
|
numina_math
|
{
"index": 2169,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sophia is shopping for a new wardrobe. She finds a jacket that originally costs $120 and a pair of shoes that originally costs $80. The store is offering a discount of 25% on the jacket and 15% on the shoes. How much does Sophia pay in total after the discounts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "158",
"style": "rule"
}
|
numina_math
|
{
"index": 2170,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice has 120 apples. She has 4 times as many apples as Bob. What fraction of Alice's apples does Bob have, and how many more apples does Alice have than Bob? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2171,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: \\(\\log_2(32) - \\log_2(8) + \\log_2(4)\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2172,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a road trip where she will drive a total of 300 miles. Her car's fuel efficiency is 25 miles per gallon, and the cost of gasoline is $3.20 per gallon. If she expects to complete the trip in 5 hours, what percentage of her total trip cost will be spent on gasoline? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 2173,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x, y) = 2x^2 + 3xy - y^2 \\). Find \\( f(3, 2) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32",
"style": "rule"
}
|
numina_math
|
{
"index": 2174,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company produces two types of widgets: Type A and Type B. The production of Type A widgets requires 3 hours of labor and 2 hours of machine time per unit. The production of Type B widgets requires 2 hours of labor and 4 hours of machine time per unit. The company has a maximum of 120 hours of labor and 160 hours of machine time available per week. If the company wants to produce at least 10 Type A widgets per week, what is the maximum number of Type B widgets it can produce while meeting all constraints? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2175,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine whether the function \\( f(x) = x^5 - 3x^3 + 2x \\) is even, odd, or neither. Then, evaluate \\( f(-2) \\) and simplify the expression. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-12",
"style": "rule"
}
|
numina_math
|
{
"index": 2176,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If $3(x + 4) = 6x - 9$, what is the value of $x$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2177,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a certain arithmetic sequence, the sum of the first four terms is 40. If the first term is 5 and the common difference is d, find the value of d. Then, determine the sum of the first 10 terms of this sequence. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "200",
"style": "rule"
}
|
numina_math
|
{
"index": 2178,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, there are 15 boys and a certain number of girls. If the total number of students in the classroom is 37, how many girls are there? Additionally, if 5 more girls join the class, what will be the new total number of students? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "42",
"style": "rule"
}
|
numina_math
|
{
"index": 2179,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A machine produces widgets at a constant rate. If the machine produces 120 widgets in 4 hours, how many widgets can it produce in 7 hours? Also, if each widget takes up 3 square inches of space, how much total space in square inches will these widgets occupy? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "630",
"style": "rule"
}
|
numina_math
|
{
"index": 2180,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A printing press can print 100 pages per hour. Another press can print 150 pages per hour. If both presses start printing at the same time and together they print a total of 2500 pages, how many hours does each press operate? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2181,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a small community, there are three friends: Alice, Bob, and Charlie. They decided to share a collection of toys equally among themselves. Initially, Alice had 10 toys, Bob had 20 toys, and Charlie had 15 toys. After redistributing some toys, each friend ended up with the same number of toys. How many toys did they each end up with, and how many toys did Alice give away or receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2182,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The average score of five students in a math test is 76. If four of the students scored 78, 74, 80, and 72 respectively, what score did the fifth student get? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "76",
"style": "rule"
}
|
numina_math
|
{
"index": 2183,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bamboo plant grows by 1/2 of its current height each week. If the plant is initially 4 meters tall, what will be its height after 3 weeks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2184,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Expand the expression \\((3x + 2)^5\\) and find the coefficient of the \\(x^3\\) term. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1080",
"style": "rule"
}
|
numina_math
|
{
"index": 2185,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery has 250 cookies that need to be packed into boxes. Each box can hold 12 cookies. After packing as many full boxes as possible, how many cookies will be left unpacked? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2186,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily has a ribbon that is 12 meters long. She decides to cut the ribbon into pieces that are each 3/4 of a meter long. How many pieces of ribbon can Emily cut from the original ribbon? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 2187,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A quality control manager is inspecting a batch of 1500 light bulbs. Out of these, 3% are found to be defective. If she decides to replace all the defective bulbs with new ones, how many new light bulbs will she need to order? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 2188,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In an equilateral triangle \\( \\triangle ABC \\), each side has a length of 12 units. The altitude is drawn from each vertex to the opposite side, intersecting at the centroid \\( G \\). If the altitudes are extended past the vertices \\( A \\), \\( B \\), and \\( C \\) to points \\( A' \\), \\( B' \\), and \\( C' \\), such that \\( AA' = 2BC \\), \\( BB' = 2AC \\), and \\( CC' = 2AB \\), what is the total length of \\( AA' + BB' + CC' \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
numina_math
|
{
"index": 2189,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mason is organizing a math competition where students solve problems in different categories. There are four categories: Algebra, Geometry, Calculus, and Number Theory. Each student has 15 minutes to solve problems in each category. If Mason wants to ensure that each student has enough time to complete all categories and he expects 20 students to participate, how many hours of competition time does he need to schedule in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 2190,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells three types of pastries: muffins, donuts, and croissants. The cost of a muffin is $2, a donut is $1.50, and a croissant is $3. In a week, the bakery sells 200 muffins, 300 donuts, and 150 croissants. If the bakery decides to increase the price of each pastry by 10%, what will be the total revenue generated from the sales of these pastries in a week after the price increase? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1430",
"style": "rule"
}
|
numina_math
|
{
"index": 2191,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A ladder is leaning against a wall such that it forms a right triangle with the ground. The base of the ladder is 9 feet away from the wall, and the ladder reaches a height of 12 feet on the wall. What is the length of the ladder? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 2192,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A parking lot has 120 spaces. Each vehicle takes up 1 space, but a caravan takes up 3 spaces. If there are 12 caravans already parked, how many spaces remain for other vehicles? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "84",
"style": "rule"
}
|
numina_math
|
{
"index": 2193,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The measure of one of two complementary angles is given by the expression $4x + 10$, and the measure of the other angle is $2x - 10$. Find the values of $x$ and the measures of both angles. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 2194,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Amy is 3 times older than her brother Tim, and their total combined age is 36 years. How old is Tim? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2195,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A school is organizing a charity event where they sell bundles of baked goods. Each bundle contains a different number of items in an arithmetic sequence. The first bundle contains 3 items, the second contains 5 items, and so on. The school wants to sell a total of 10 bundles. Each item in the bundles sells for $2. How much total revenue will the school generate from selling all 10 bundles? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "240",
"style": "rule"
}
|
numina_math
|
{
"index": 2196,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a different numeral system, the base-5 system, a certain number is represented as 243. What is the equivalent value of this number in the base-10 system? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "73",
"style": "rule"
}
|
numina_math
|
{
"index": 2197,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is planning his monthly budget. His monthly income is $3000, and he allocates $1200 for rent, $400 for groceries, $300 for utilities, and $200 for entertainment. He also wants to save the remainder of his income. Write down the algebraic expression for his monthly savings and calculate the amount he will save each month. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "900",
"style": "rule"
}
|
numina_math
|
{
"index": 2198,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "An unusual bicycle has 24 spokes on the front wheel and 50% more spokes on the back wheel. How many spokes does the bicycle have in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 2199,
"name": "numina_math",
"split": "train"
}
|
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