prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "A town's population in the year 2020 is 15,000 people. The population grows by 4% each year. If 1/3 of the population moves to a neighboring town in 2023, how many people are left in the town? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11249",
"style": "rule"
}
|
numina_math
|
{
"index": 1800,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( a, b, c \\) be positive real numbers such that \\( abc = 1 \\). Find the minimum value of\n\\[ S = a^3 + b^3 + c^3 + \\frac{3}{a} + \\frac{3}{b} + \\frac{3}{c}. \\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 1801,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a circle of radius 10 units, a chord \\( AB \\) is such that the perpendicular distance from the center \\( O \\) of the circle to the chord \\( AB \\) is 6 units. A point \\( P \\) on the major arc \\( AB \\) forms an isosceles triangle \\( APB \\) with the chord \\( AB \\). Determine the length of \\( AB \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 1802,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a geometric sequence where the first term \\(a_1 = 3\\) and the common ratio \\(r = 2\\). Compute the sum of the first 10 terms of the sequence using the properties of geometric sequences and the change of base formula. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3069",
"style": "rule"
}
|
numina_math
|
{
"index": 1803,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the expression: \\((-7) + 5 \\times (-3) + 12 \\div (-4)\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-25",
"style": "rule"
}
|
numina_math
|
{
"index": 1804,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a class of 20 students, the average score in a math exam was 75. When the teacher reviewed the scores, she found that one student's score was recorded incorrectly as 65 instead of 85. What is the correct average score of the class after this error is fixed? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "76",
"style": "rule"
}
|
numina_math
|
{
"index": 1805,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that \\( f(x) = x^2 - 4x + 3 \\) and \\( g(x) = x + 2 \\), find the simplified form of the composition \\( f(g(x)) \\). Then, evaluate \\( f(g(1)) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 1806,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the piecewise function \\( f(x) \\) defined as follows:\n\\[ f(x) = \\begin{cases} \n2x + 3 & \\text{if } x < 0 \\\\\nx^2 - 1 & \\text{if } 0 \\leq x \\leq 2 \\\\\n3x - 4 & \\text{if } x > 2 \n\\end{cases} \\]\nEvaluate \\( f(-1) \\), \\( f(1) \\), and \\( f(3) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "f(-1)=1f(1)=0f(3)=5",
"style": "rule"
}
|
numina_math
|
{
"index": 1807,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length that is 5 meters more than twice its width. The area of the garden is 150 square meters. Find the dimensions of the garden using discriminant analysis to solve the quadratic equation formed. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{width} = 7.5 \\text{ meters}, \\text{length} = 20 \\text{ meters}",
"style": "rule"
}
|
numina_math
|
{
"index": 1808,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train travels a certain route every day. On the first day, it travels 100 miles. Each subsequent day, the train travels 10 miles more than the previous day. How many total miles will the train have traveled after 7 days? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "910",
"style": "rule"
}
|
numina_math
|
{
"index": 1809,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two trains start from two different stations, 300 miles apart, and travel towards each other. Train A travels at a speed of 50 miles per hour and Train B travels at a speed of 70 miles per hour. If Train B starts 2 hours after Train A, how long after Train A starts do the trains meet? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 1810,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation for \\(x\\):\n\\[\n\\frac{4x + 5}{x^2 - 4} = \\frac{A}{x - 2} + \\frac{B}{x + 2}.\n\\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{4x+5}{x^2-4}=\\frac{13/4}{x-2}+\\frac{3/4}{x+2}",
"style": "rule"
}
|
numina_math
|
{
"index": 1811,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a certain community, 20% of the households have subscribed to the local newspaper. If there are 480 households in the community and 75% of the newspaper subscribers have also subscribed to the weekend edition, how many households have subscribed only to the weekend edition? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
numina_math
|
{
"index": 1812,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( \\sqrt{x} = y \\) and \\( y^3 = 8 \\), what is \\( x \\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 1813,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The temperature in New York is currently 20°C. A weather station predicts that the temperature will decrease by half of the current temperature and then increase by 7°C by the evening. What will be the temperature in New York in the evening? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17°c",
"style": "rule"
}
|
numina_math
|
{
"index": 1814,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa has a 4-liter jug of lemonade. She pours it into cups, each holding 150 milliliters. However, she accidentally spills 300 milliliters of lemonade. If she gives away 15 cups of lemonade to her friends, how much lemonade does she have left? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.45",
"style": "rule"
}
|
numina_math
|
{
"index": 1815,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a closet, there are 4 different jackets, 3 different scarves, and 5 different hats. If you want to pick one jacket, one scarf, and one hat to wear, how many different combinations of outfits can you create? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 1816,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a particular school, there are 100 students enrolled in various extracurricular activities. 60 students are enrolled in the chess club, 45 students are enrolled in the music club, and 30 students are enrolled in both clubs. How many students are enrolled in neither the chess club nor the music club? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 1817,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces square tiles with side lengths increasing in whole numbers. The side length of the first tile is 1 cm, the second tile is 2 cm, and so on. The factory needs to determine how many tiles with a side length of 1 cm are needed to match the area of one tile with a side length of 7 cm. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "49",
"style": "rule"
}
|
numina_math
|
{
"index": 1818,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A model of a famous statue is built to a scale ratio of 1:25. If the actual statue is 1500 cm tall, what is the height of the model in centimeters to the nearest whole number? Additionally, if the model costs $45 and you need to buy 10 such models, what is the total cost in dollars? Express your answer to the nearest whole number. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "450",
"style": "rule"
}
|
numina_math
|
{
"index": 1819,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "George is planning a dinner party for three other couples, his wife, and himself. He plans to seat the four couples around a circular table for 8, and wants each husband to be seated opposite his wife. How many seating arrangements can he make, if rotations and reflections of each seating arrangement are not considered different? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 1820,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the functions \\( f(x) = 3x + 2 \\) and \\( g(x) = \\frac{x - 2}{3} \\), prove that these functions are inverses by finding the compositions \\( f(g(x)) \\) and \\( g(f(x)) \\) and showing that both equal \\( x \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "f(x) \\text{ and } g(x) \\text{ are inverses.}",
"style": "rule"
}
|
numina_math
|
{
"index": 1821,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the greatest integer less than 100 for which the greatest common divisor (GCD) of that integer and 18 is 3? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "93",
"style": "rule"
}
|
numina_math
|
{
"index": 1822,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The volume of a sphere is given by the formula \\( V = \\frac{4}{3} \\pi r^3 \\). A sphere has a volume of \\( 36\\pi \\) cubic units. If the volume of the sphere is increased by 50%, what will be the new radius of the sphere? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.44",
"style": "rule"
}
|
numina_math
|
{
"index": 1823,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a sequence of numbers written in base-5, starting from \\(0\\) to \\(24\\) (inclusive). Convert these base-5 numbers to base-10 and find the sum of all these numbers. Express your answer in factorial form. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 1824,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the integer solutions for the quadratic equation \\(2x^2 - 3x - 2 = 0\\). Express your answer in interval notation. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\{2\\}",
"style": "rule"
}
|
numina_math
|
{
"index": 1825,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In $\\triangle ABC$, $\\angle A$ is twice $\\angle B$, and $\\angle C$ is 20 degrees more than $\\angle B$. Calculate the measure of each angle in $\\triangle ABC$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\anglea=80\\\\angleb=40\\\\anglec=60",
"style": "rule"
}
|
numina_math
|
{
"index": 1826,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends plans to meet for a picnic at 15:30. They start preparing at 11:00. It takes Sarah 45 minutes to prepare the sandwiches, Jake 30 minutes to pack the drinks, Emily 1 hour to make a dessert, and Tom 1 hour and 15 minutes to gather all the picnic supplies. What time do they finish preparing, and how much time do they have left before they need to leave for the picnic? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 1827,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A sequence of letters is formed using the letters A, B, and C such that no two adjacent letters are the same. If the sequence is of length 10, how many such sequences can be formed? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1536",
"style": "rule"
}
|
numina_math
|
{
"index": 1828,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the largest 3-digit positive integer whose digits are all prime numbers and which is divisible by 3? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "777",
"style": "rule"
}
|
numina_math
|
{
"index": 1829,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A square garden has a total area of 144 square meters. If the garden is divided into smaller square plots such that the side length of each smaller square plot is 3 meters, how many smaller square plots can be created from the entire garden? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 1830,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John has a total of $100 in his savings account. He wants to invest in a project that will cost him $x dollars. If he spends $x dollars, he will have $\\frac{1}{3}$ of his remaining money left. How much will John invest in the project? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "66.67",
"style": "rule"
}
|
numina_math
|
{
"index": 1831,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Carlos is a delivery driver who travels 50 miles per hour. On Monday, he drives 120 miles. On Tuesday, he drives 180 miles. On Wednesday, he drives 150 miles. On Thursday, he drives 200 miles. On Friday, he drives 90 miles. What is the total number of hours that Carlos spends driving from Monday to Friday? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14.8",
"style": "rule"
}
|
numina_math
|
{
"index": 1832,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is preparing for her exams and records the number of hours she studies each day over a week. She studies 4 hours on Monday, 5 hours on Tuesday, 3 hours on Wednesday, 6 hours on Thursday, 2 hours on Friday, 7 hours on Saturday, and 3 hours on Sunday. What is the average number of hours she studies per day? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.29",
"style": "rule"
}
|
numina_math
|
{
"index": 1833,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is shopping for new clothes and finds a dress priced at $45.99 and a pair of shoes priced at $60.50. She has a coupon for 20% off the dress and another coupon for $10 off the shoes. After applying both discounts, how much does she spend in total on the dress and shoes? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "87.29",
"style": "rule"
}
|
numina_math
|
{
"index": 1834,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sam, Chris, and Alex are sharing a sum of money in a ratio of 2:3:5 respectively. If the total amount of money they have is $1000, how much money does each person receive? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "500",
"style": "rule"
}
|
numina_math
|
{
"index": 1835,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the quadratic equation \\( x^2 + 5x + 6 = 0 \\), factor the quadratic expression and solve for \\( x \\). Then, verify your solutions by using the quadratic formula. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-2",
"style": "rule"
}
|
numina_math
|
{
"index": 1836,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The Johnson Company has 600 laptops in inventory. They employ 15 salespeople, and each salesperson sells 8 laptops per week. How many weeks will it take for them to sell all the laptops? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1837,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(x\\) be a positive real number such that \\(x = \\lfloor \\frac{7x}{3} \\rfloor - \\frac{5}{3}\\). Find the value of \\(x\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{4}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 1838,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "James and Robert can complete a project together in 5 hours. If James works alone, he can complete the project in 8 hours. How long will it take for Robert to complete the project if he works alone? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{40}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 1839,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the remainder when the sum of the first 20 even numbers is divided by 9? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1840,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x) \\) and \\( g(x) \\) be two functions defined as \\( f(x) = 2x - 3 \\) and \\( g(x) = x^2 + x + 1 \\). Find all the fixed points of the composition \\( h(x) = (f \\circ g)(x) \\), where \\( h(x) = f(g(x)) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "x=\\frac{1}{2}x=-1",
"style": "rule"
}
|
numina_math
|
{
"index": 1841,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two friends, Alice and Bob, decide to meet at a park. Alice visits the park every 6 days, and Bob visits every 8 days. If they both meet at the park today, in how many days will they meet again at the park? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 1842,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice is 15 years older than Bob. In 10 years, Alice will be twice as old as Bob. How old is Bob now? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1843,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore sells 4 different genres of books (Fiction, Non-Fiction, Mystery, Science Fiction) and 3 different types of bookmarks (Magnetic, Ribbon, Elastic). If a customer decides to buy one book and one bookmark, how many different combinations of book and bookmark can the customer choose? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 1844,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the minimum value of the expression \\(x^2 + xy + y^2\\) for all real numbers \\(x\\) and \\(y\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 1845,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A square garden has an area of 144 square meters. If the side length of the square garden is increased by 2 meters, what will be the new area of the garden? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "196",
"style": "rule"
}
|
numina_math
|
{
"index": 1846,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the greatest common divisor of \\( 540 \\) and \\( 252 \\) using their prime factorizations. Then, compute the multiplicative inverse of \\( 540 \\) modulo \\( 252 \\) using the Extended Euclidean Algorithm. Express your answer as an integer from \\( 0 \\) to \\( 251 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "67",
"style": "rule"
}
|
numina_math
|
{
"index": 1847,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, the ratio of boys to girls is 3:4. If there are 120 boys, how many girls are there? Also, if 30 more boys and 50 more girls join the school, what will be the new ratio of boys to girls? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5:7",
"style": "rule"
}
|
numina_math
|
{
"index": 1848,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, 60 students are selected to participate in a science and art competition. Among these students, 18 win prizes in the science competition, and 22 win prizes in the art competition. If 5 students win prizes in both competitions, how many students did not win prizes in either competition? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 1849,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A business offers a piecewise payment plan for its employees based on the number of hours worked. For the first 20 hours, employees are paid $15 per hour. For any hours worked beyond 20 hours, they are paid $25 per hour. If an employee worked a total of 35 hours in a week, how much did they earn? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "675",
"style": "rule"
}
|
numina_math
|
{
"index": 1850,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\(x = \\frac{3}{4}\\) and \\(y = \\frac{2}{5}\\), solve the equation \\(5x + 4y = z\\). What is the value of \\(z\\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{107}{20}",
"style": "rule"
}
|
numina_math
|
{
"index": 1851,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah and Tom are working together to paint a fence. Sarah can paint the entire fence by herself in 5 hours, while Tom can paint it in 8 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": "3.08",
"style": "rule"
}
|
numina_math
|
{
"index": 1852,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two spherical water tanks have their radii in the ratio of 2:3. If the volume of the smaller tank is 32 cubic meters, what is the volume of the larger tank? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "108",
"style": "rule"
}
|
numina_math
|
{
"index": 1853,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the maximum product of two positive integers whose sum is 50. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "625",
"style": "rule"
}
|
numina_math
|
{
"index": 1854,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces light bulbs, and each light bulb has a 0.8 probability of being functional. If 10 light bulbs are produced, what is the probability that exactly 8 of them are functional? Express your answer as a decimal rounded to the nearest thousandth. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.302",
"style": "rule"
}
|
numina_math
|
{
"index": 1855,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Calculate: $5.6 \\times 3.2 + 5.6 \\times 4.8 - 5.6$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "39.2",
"style": "rule"
}
|
numina_math
|
{
"index": 1856,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The average of five distinct positive integers is 10. If the sum of the smallest two integers is less than the average and the sum of the largest two integers is greater than 25, what are the five integers? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12121520",
"style": "rule"
}
|
numina_math
|
{
"index": 1857,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that \\(\\tan(3x) = \\frac{3 \\tan(x) - \\tan^3(x)}{1 - 3 \\tan^2(x)}\\), find the smallest positive angle \\(x\\) in degrees such that \\(\\tan(3x) = \\sqrt{3}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 1858,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Robie filled some plastic boxes with hockey cards. There were 8 cards in each box but 7 cards were not placed in a box. He gave away 3 boxes to his friends and he has 4 boxes with him. How many cards did Robie have in the beginning? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "63",
"style": "rule"
}
|
numina_math
|
{
"index": 1859,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\(\\log_2 (x + 4) = 3\\), find \\( \\log_4 x \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 1860,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine whether the series \\(\\sum_{n=1}^{\\infty} \\frac{1}{2n^2 + 3n + 1}\\) converges or diverges. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{theseriesconverges.}",
"style": "rule"
}
|
numina_math
|
{
"index": 1861,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A new species of plant is discovered in a remote island. Initially, there is only 1 plant. Every month, the number of plants doubles. How many plants will there be after 6 months? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "64",
"style": "rule"
}
|
numina_math
|
{
"index": 1862,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence of numbers where each term is the product of its position in the sequence and the smallest prime factor of that position. The first few terms of the sequence are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100. Determine the 50th term in this sequence. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 1863,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company has three types of employees: junior, mid-level, and senior. The ratio of junior to mid-level employees is 3:2, and the ratio of mid-level to senior employees is 4:1. If there are 60 senior employees, how many employees are there in total in the company? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "660",
"style": "rule"
}
|
numina_math
|
{
"index": 1864,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a fundraising event, each participant donates a fixed amount of money. If 8 participants donate a total of $240, and additional participants join, bringing the total number of participants to 15, how much money will be raised in total? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "450",
"style": "rule"
}
|
numina_math
|
{
"index": 1865,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial \\( f(x) = x^3 + ax^2 + bx + c \\) has integer roots, and the average of its roots is 3. Find the value of \\(a + b + c\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-1",
"style": "rule"
}
|
numina_math
|
{
"index": 1866,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Nina received a scholarship worth $5000 more than half of Kelly's amount. Kelly received a scholarship worth twice the amount Wendy received. How much money did they receive in scholarships together if Wendy received a scholarship worth $15000? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "65000",
"style": "rule"
}
|
numina_math
|
{
"index": 1867,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a 3x3 magic square, the sum of each row, column, and diagonal is the same. If the middle cell of the magic square contains the variable \\( x \\), and the sum of the numbers in the magic square is 45, find the value of \\( x \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1868,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is planning her birthday party and she has a budget of $300. She wants to buy decorations, a cake, and party favors. The decorations will cost $75, the cake will cost $100, and the party favors will cost 20% of her total budget. How much money will Emily have left after purchasing all the items? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "65",
"style": "rule"
}
|
numina_math
|
{
"index": 1869,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom decided to donate books to a local library. He donated 80 books in total, consisting of fiction and non-fiction books. The number of fiction books he donated is five times the number of non-fiction books. How many fiction and non-fiction books did Tom donate? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 1870,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train travels from City A to City B at an average speed of 60 miles per hour, taking 2 hours to complete the journey. On the return trip, the train travels at a different constant speed and takes 3 hours to reach City A from City B. What is the average speed of the train on the return trip, and what is the total distance traveled by the train for the round trip? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "240",
"style": "rule"
}
|
numina_math
|
{
"index": 1871,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the piecewise function \\[f(x) =\n\\begin{cases}\n3x + 1 &\\text{if } x \\leq 4, \\\\\nbx - 5 &\\text{if } x > 4.\n\\end{cases}\n\\] Find the value of \\( b \\) such that the function \\( f(x) \\) is continuous at \\( x = 4 \\). Then, compute the sum of \\( b \\) and the value of the function at \\( x = 4 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1872,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length that is 2 meters more than three times its width. If the area of the garden is 90 square meters, what are the dimensions of the garden? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5.15 \\text{ meters by } 17.45 \\text{ meters}",
"style": "rule"
}
|
numina_math
|
{
"index": 1873,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The ratio of the ages of Alex and Ben is 3:4. If the sum of their ages is 56 years, what is the age of Ben? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32",
"style": "rule"
}
|
numina_math
|
{
"index": 1874,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah works two part-time jobs. In her first job, she earns $15 per hour, and in her second job, she earns $20 per hour. Last week, she worked a total of 25 hours combined across both jobs and earned a total of $450. How many hours did she work at each job? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 1875,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Expand and simplify the polynomial expression: \\((2x - 3)(x^2 + x - 4)\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2x^3-x^2-11x+12",
"style": "rule"
}
|
numina_math
|
{
"index": 1876,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lucas earns a base salary of $40,000 per year. He received a 5% raise this year. His colleague, Maria, earns the same base salary but received an 8% raise. How much more money will Maria make compared to Lucas after their raises? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1200",
"style": "rule"
}
|
numina_math
|
{
"index": 1877,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the smallest positive integer $n$ such that $n$ is an even number, it has at least one prime factor greater than 7, and the least common multiple (LCM) of $n$ and 12 is 60? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 1878,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is making a fruit punch for a party. She needs to mix three different fruit juices in the ratio of 2:3:5. If she has 2 liters of the first juice, how many liters of the second and third juices does she need to use? Additionally, if she adds 4 liters of water to the mixture, what will be the total volume of the fruit punch? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 1879,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A student deposits $1000 into a savings account for 4 years with an annual interest rate of 2.5%. How much interest will the student earn, and what will be the total amount in the account at the end of the 4 years? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1100",
"style": "rule"
}
|
numina_math
|
{
"index": 1880,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jack has a jar of coins containing only nickels, dimes, and quarters. The total value of the coins in the jar is \\$6.50. If Jack has twice as many dimes as nickels and three times as many quarters as dimes, how many nickels, dimes, and quarters does Jack have? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{theproblemneedsadjustmentforvalidintegersolution}",
"style": "rule"
}
|
numina_math
|
{
"index": 1881,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, the ratio of boys to girls is 3:4. If the total number of students is 280, what percentage of the students are boys? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "42.86",
"style": "rule"
}
|
numina_math
|
{
"index": 1882,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the greatest common divisor of 1444 and 1936? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 1883,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a car can travel 60 miles in 1 hour and a bicycle can travel the same distance in 4 hours, how long will it take for them to travel 60 miles together, assuming they can combine their speeds? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 1884,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a bakery, 3/5 of the cakes are chocolate, and the rest are vanilla. Half of the vanilla cakes have sprinkles. If there are 40 cakes in total, how many vanilla cakes have sprinkles? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 1885,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two similar triangles, \\(\\triangle ABC\\) and \\(\\triangle DEF\\), have side lengths in the ratio 2:3. If the perimeter of \\(\\triangle ABC\\) is $24$ cm and the cost per centimeter of the perimeter of \\(\\triangle DEF\\) is $0.50$, what is the total cost of \\(\\triangle DEF\\)'s perimeter? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18.00",
"style": "rule"
}
|
numina_math
|
{
"index": 1886,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has $60. She gives 25% of her money to her friend. Her friend then spends $10 on lunch and has $5 left. How much money did Sarah's friend have initially before spending on lunch? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 1887,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A fruit punch is made by mixing 5 ounces of orange juice, 10 ounces of pineapple juice, and 15 ounces of apple juice. What is the percentage of pineapple juice in the fruit punch? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33.33",
"style": "rule"
}
|
numina_math
|
{
"index": 1888,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the following algebraic fraction and state the simplified form:\n\\[ \\frac{x^2 - 9}{x^2 - 4x + 4} \\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{(x+3)(x-3)}{(x-2)^2}",
"style": "rule"
}
|
numina_math
|
{
"index": 1889,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x) = 2x + 3 \\) and \\( g(x) = \\sqrt{x - 1} \\). Given that \\( h(x) \\) is defined recursively by \\( h_{n+1}(x) = f(g(h_n(x))) \\) with \\( h_1(x) = x \\), find \\( h_3(4) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "h_3(4)=2\\sqrt{2\\sqrt{3}+2}+3",
"style": "rule"
}
|
numina_math
|
{
"index": 1890,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom fills a 250-pound sandbag 80% full. However, the filling material he is using is 40% heavier than sand. How much does the bag weigh? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "280\\\\text{pounds}",
"style": "rule"
}
|
numina_math
|
{
"index": 1891,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a group of 30 people, 18 people like jazz music, 15 people like classical music, and 7 people like both jazz and classical music. If a person is selected at random from this group, what is the probability that the person likes either jazz or classical music but not both? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{19}{30}",
"style": "rule"
}
|
numina_math
|
{
"index": 1892,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: \\(\\sqrt[3]{8a^6b^3} \\cdot \\sqrt{16a^4b^2}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8a^4b^2",
"style": "rule"
}
|
numina_math
|
{
"index": 1893,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from City A to City B, a distance of 200 kilometers, at an average speed of \\( v \\) km/h. On the return trip, the car travels at an average speed that is 20% slower. If the total travel time for the round trip is 5 hours, find the average speed \\( v \\) of the car on the trip from City A to City B. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 1894,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If Sarah can paint a fence in 8 hours and John can paint the same fence in 12 hours, how long will it take for them to paint the fence together, working at the same rate? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.8",
"style": "rule"
}
|
numina_math
|
{
"index": 1895,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah and Mike are planning a trip together. Sarah plans to drive to the destination and Mike plans to take a train. The total travel time for both of them combined is 10 hours. If Sarah's driving time is two hours more than twice Mike's train travel time, how long does each of them spend traveling? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{sarah spends } 7\\frac{1}{3} \\text{ hours driving and mike spends } 2\\frac{2}{3} \\text{ hours on the train.}",
"style": "rule"
}
|
numina_math
|
{
"index": 1896,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer sells apples at a rate of $1.25 per pound. If he sells 200 pounds of apples, how much revenue does he generate in cents? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25000",
"style": "rule"
}
|
numina_math
|
{
"index": 1897,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery bakes 240 cupcakes and distributes them evenly among 8 stores. If each store receives an equal number of cupcakes, how many cupcakes does each store get? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 1898,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert 150 minutes into hours and simplify your answer.\n\n### Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2\\frac{1}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 1899,
"name": "numina_math",
"split": "train"
}
|
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