prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "A delivery company charges $0.75 per mile for delivering packages. A driver delivers a package to a location 50 miles away and then returns to the starting point. The driver also spends $20 on fuel for the round trip. What is the total revenue generated from this delivery, and what is the net profit after deducting the fuel cost? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "55",
"style": "rule"
}
|
numina_math
|
{
"index": 2200,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A vendor constructs a storage unit by joining a rectangular prism and a cube. The rectangular prism has dimensions of 8 cm in length, 5 cm in width, and 10 cm in height. The cube has a side length of 4 cm. If the vendor buys the materials for constructing the storage unit at $0.50 per cubic centimeter and sells the unit for a total price of $300, what is his profit? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "68",
"style": "rule"
}
|
numina_math
|
{
"index": 2201,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many distinct four-digit numbers are divisible by 3 and have 78 as their last two digits? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "34",
"style": "rule"
}
|
numina_math
|
{
"index": 2202,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the system of equations:\n\\[ \n2x + 3y + z = 7 \n\\]\n\\[ \n4x - y + 2z = 3 \n\\]\n\\[ \n-x + 2y - z = 4 \n\\]\nfind the value of \\( x^2 + y^2 + z^2 \\).\n\n### Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1389}{49}",
"style": "rule"
}
|
numina_math
|
{
"index": 2203,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store buys gadgets at a wholesale price and sells them for $50 each. If the store wants to make a 25% profit on each gadget sold, what should be the wholesale price of each gadget? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2204,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many prime numbers are there between 50 and 200? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "31",
"style": "rule"
}
|
numina_math
|
{
"index": 2205,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\(A\\), \\(B\\), and \\(C\\) are non-zero distinct digits in base \\(6\\) such that \\(\\overline{ABC}_6 + \\overline{BCA}_6 + \\overline{CAB}_6 = \\overline{AAA0}_6\\), find \\(B+C\\) in base \\(6\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2206,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $a,$ $b,$ and $c$ be the roots of the cubic polynomial $x^3 + 2x^2 - x - 2 = 0.$ Find\n\\[a^2(b+c) + b^2(c+a) + c^2(a+b).\\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-4",
"style": "rule"
}
|
numina_math
|
{
"index": 2207,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the values of \\(x\\) for which the quadratic expression \\(x^2 + 4x + 8\\) is less than or equal to 0. Express the solutions in interval notation. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{norealsolutions}",
"style": "rule"
}
|
numina_math
|
{
"index": 2208,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex works as a freelance graphic designer. He charges $30 per hour. One week, he worked 3/5 of his time on a project for Client A and the remaining time on a project for Client B. If he worked a total of 40 hours that week, how much did he earn from each client? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "480",
"style": "rule"
}
|
numina_math
|
{
"index": 2209,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the sum of all positive integers \\( n \\) less than 100, such that both \\( n \\) and \\( n+1 \\) have exactly 4 positive divisors each. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2210,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A box contains 12 red, 8 blue, and 10 green marbles. If you randomly pick one marble at a time without replacement, what is the probability that the first marble you pick is red and the second marble is blue? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{16}{145}",
"style": "rule"
}
|
numina_math
|
{
"index": 2211,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In how many ways can 7 distinct beads be arranged on a bracelet if two arrangements are considered identical when one can be rotated or reflected to produce the other? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "360",
"style": "rule"
}
|
numina_math
|
{
"index": 2212,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the reciprocal of the product of the prime factors of 60. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{60}",
"style": "rule"
}
|
numina_math
|
{
"index": 2213,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given \\(y = \\arcsin \\left( \\frac{3}{5} \\right) + \\arccos \\left( \\frac{4}{5} \\right)\\), determine the value of \\(y\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{\\pi}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2214,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a grid of points in the $xy$-plane where $1 \\le x \\le 5$ and $1 \\le y \\le 5$, how many triangles with positive area can be formed using any three of these points as vertices? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2140",
"style": "rule"
}
|
numina_math
|
{
"index": 2215,
"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 50 widgets per hour, and Machine B can produce 30 widgets per hour. If both machines work together for 4 hours, how many total widgets will they produce? Additionally, if Machine A worked alone for 2 more hours after that, how many total widgets would be produced by both machines combined? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "420",
"style": "rule"
}
|
numina_math
|
{
"index": 2216,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sophia has a collection of nickels and dimes that totals 80 coins. The total value of these coins is $6.50. How many nickels and how many dimes does Sophia have? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 2217,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the improper fraction $\\frac{(2x^2 + 3x + 1) + (x^2 - 4x + 4)}{x^2 - 1}$, simplify it and then evaluate for $x = 2$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2218,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels 30 miles in 45 minutes. If the cyclist continues at the same speed, how many miles will they travel in 2 hours? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 2219,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the decimal expansion of \\(\\frac{1}{p}\\), where \\(p\\) is a prime number. If the decimal expansion is periodic with period length 6, what is the sum of all possible values of \\(p\\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "70",
"style": "rule"
}
|
numina_math
|
{
"index": 2220,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A project was initially scheduled to be completed in 12 days. Due to improved methods, the team managed to complete it in 9 days. By what percentage did the work efficiency increase? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 2221,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory operates 24 hours a day, producing 50 units of a product per hour. If the factory runs at full capacity for 30 days, how many units of the product are produced in total? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36000",
"style": "rule"
}
|
numina_math
|
{
"index": 2222,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for the integer \\( x \\) between \\( 0 \\) and \\( 15 \\) that satisfies the congruence \\( 5x \\equiv 3 \\pmod{16} \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2223,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John has a certain number of candies. If he gives 5 candies to his friend, he will have twice as many candies as his friend. If his friend initially has 10 candies, how many candies does John have now? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35",
"style": "rule"
}
|
numina_math
|
{
"index": 2224,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find all the roots of the polynomial \\[P(x) = x^4 - 4x^2 + 4.\\] Express your answer in terms of real and complex numbers. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\sqrt{2}-\\sqrt{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2225,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore sold 15 novels in the morning. In the afternoon, they sold twice as many novels as in the morning, and in the evening, they sold 5 fewer novels than in the afternoon. If each novel costs $10, what was the total revenue generated from selling the novels throughout the day? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "700",
"style": "rule"
}
|
numina_math
|
{
"index": 2226,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the infinite geometric series:\n\\[\\frac{1}{x} + \\frac{1}{x^2} + \\frac{1}{x^3} + \\cdots = 3,\\]\nwhere \\(x \\neq 1\\), find the value of \\(x\\) and then compute:\n\\[\\frac{1}{x} - \\frac{1}{x+1}.\\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{9}{28}",
"style": "rule"
}
|
numina_math
|
{
"index": 2227,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation \\(\\sqrt{2x + 5} - 3 = 0\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2228,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the product \\[\\frac{3}{2}\\cdot\\frac{5}{3}\\cdot\\frac{7}{5} \\cdots \\frac{2n+1}{2n} \\cdots \\frac{401}{400}.\\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{401}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2229,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 3 cups of flour for every 2 cups of sugar. If a baker wants to use 6 cups of sugar, how many cups of flour will be needed to maintain the same proportion? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2230,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is planning a birthday party. He wants to buy 3 packs of balloons, 2 packs of candles, and 4 party hats. Each pack of balloons costs $5, each pack of candles costs $3, and each party hat costs $2. If John has a budget of $30, how much money will he have left after buying all the items? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2231,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A square is inscribed such that one of its sides lies along the x-axis and the opposite vertices touch the parabola $y = x^2 - 6x + 8$. Find the side length of the square. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "s",
"style": "rule"
}
|
numina_math
|
{
"index": 2232,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate \\( \\left\\lfloor | -7.3 | \\right\\rfloor \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2233,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from City A to City B at an average speed of 60 kilometers per hour and returns from City B to City A at an average speed of 40 kilometers 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": 2234,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice is hosting a party and wants to distribute candies to her guests. She has a total of 84 candies. She decides to give each guest a number of candies equal to the number of divisors of their seat number. For example, if a guest sits at seat number 4, they would receive 3 candies because 4 has three divisors (1, 2, and 4). How many guests can she distribute candies to if she wants to ensure that every guest receives at least one candy? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 2235,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The average (mean) of four test scores is 85. Three of the test scores are 78, 92, and 87. What is the fourth test score? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "83",
"style": "rule"
}
|
numina_math
|
{
"index": 2236,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a sequence, each term is represented by the pattern \\(2, 5, 8, 11, 14, \\ldots\\). What is the sum of the first 20 terms in this sequence? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "610",
"style": "rule"
}
|
numina_math
|
{
"index": 2237,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cube is inscribed in a sphere such that all eight vertices of the cube touch the sphere. If the edge length of the cube is 4 units, how many distinct triangles can be formed by choosing three of the cube's vertices that are not collinear, and what is the surface area of the sphere? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "56 \\text{ triangles, } 48\\pi \\text{ square units}",
"style": "rule"
}
|
numina_math
|
{
"index": 2238,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenna decides to save money each week for a vacation. She starts by saving $20 in the first week and plans to increase her savings by $10 each subsequent week. How much money will she have saved in total after 8 weeks? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "440",
"style": "rule"
}
|
numina_math
|
{
"index": 2239,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Michael is calculating how much he needs to pay for his monthly gym membership. The base fee for the membership is $50 per month. However, if he uses the gym more than 15 times in a month, he gets charged an additional $3 per visit for every visit above 15. If Michael used the gym 20 times this month, how much does he need to pay for his gym membership? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "65",
"style": "rule"
}
|
numina_math
|
{
"index": 2240,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the average score of five students in a math test is 85 and the scores of four of the students are 78, 82, 88, and 91, what is the score of the fifth student? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "86",
"style": "rule"
}
|
numina_math
|
{
"index": 2241,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Triangle \\( \\Delta ABC \\) has vertices at \\( A(1, 2) \\), \\( B(4, 6) \\), and \\( C(7, 2) \\). The triangle is reflected over the line \\( y = x \\) to form triangle \\( \\Delta A'B'C' \\). What is the area of triangle \\( \\Delta A'B'C' \\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2242,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length that is 3 times its width. If the perimeter of the garden is 96 meters, what are the length and width of the garden? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 2243,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The length of a rectangle is 3/5 of its width. If the perimeter of the rectangle is 64 meters, what are the length and the width of the rectangle? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2244,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the rational expression \\(\\frac{3x^2 - 2x + 5}{x^2 - 4}\\), evaluate it for \\(x = 2\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{undefined}",
"style": "rule"
}
|
numina_math
|
{
"index": 2245,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is baking cookies for a charity event. She has 3/4 cup of sugar and 2/3 cup of chocolate chips left. She needs to use 1/2 cup of sugar and 1/4 cup of chocolate chips for each batch of cookies. After making as many batches as she can with the available ingredients, how much sugar and chocolate chips will she have left? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{5}{12}",
"style": "rule"
}
|
numina_math
|
{
"index": 2246,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Divide the numbers \\(4\\), \\(9\\), \\(10\\), \\(14\\), \\(15\\), and \\(21\\) into 2 groups with 3 numbers in each group such that the product of the numbers in each group is the same. How can we divide the numbers? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{group1:}41521\\text{and}\\text{group2:}91014",
"style": "rule"
}
|
numina_math
|
{
"index": 2247,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the following expression: \\(\\frac{\\left(\\frac{1}{2}\\right)^3 \\cdot \\left(\\frac{2}{3}\\right)^2}{\\left(\\frac{1}{4}\\right)^2}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{8}{9}",
"style": "rule"
}
|
numina_math
|
{
"index": 2248,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa can paint a fence in 8 hours, while Mike can paint the same fence in 6 hours. After Lisa has painted for 2 hours alone, how long will it take Mike to finish the rest of the fence if he works alone? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2249,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a company of 150 employees, 90 employees are involved in marketing, 70 are involved in sales, and 40 employees are involved in both marketing and sales. How many employees are involved in neither marketing nor sales? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2250,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cube has an edge length of 10 cm. Suppose this cube is scaled up by a factor of 3. What is the volume of the larger cube in cubic meters? Also, calculate the perimeter of a triangle with sides equal to the edge lengths of the larger cube and verify if it satisfies the Triangle Inequality Theorem. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2251,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The least common multiple (LCM) of two positive integers is 2520, and their greatest common divisor (GCD) is 10. If one of the integers is 140, what is the other integer? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 2252,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the decimal number 245 to its representation in base 5. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1440_5",
"style": "rule"
}
|
numina_math
|
{
"index": 2253,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice has three jars of candies. The first jar contains twice as many candies as the second jar, and the third jar contains 5 more candies than the first jar. If Alice combines all the candies from the three jars and equally distributes them into four bags, each bag will contain 15 candies. How many candies are in each jar? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{firstjar:22candiessecondjar:11candiesthirdjar:27candies}",
"style": "rule"
}
|
numina_math
|
{
"index": 2254,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A sample of gas at a constant temperature is divided into 4 equal parts. The pressure of each part is inversely proportional to its volume. Initially, the gas is in a container with a volume of 8 liters and pressure of 4 kPa. If each part is placed in a separate container with volumes following an arithmetic sequence starting with 2 liters and increasing by 1 liter, what is the total pressure of all four containers? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "41.07\\\\text{kpa}",
"style": "rule"
}
|
numina_math
|
{
"index": 2255,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the expression: \n$$\\left(403 \\frac{3}{5} + 183 \\frac{5}{11} + 155 \\frac{3}{13} + 118 \\frac{12}{17}\\right) \\div \\left(\\frac{1009}{15} + \\frac{1009}{33} + \\frac{1009}{39} + \\frac{1009}{51}\\right).$$ Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "61",
"style": "rule"
}
|
numina_math
|
{
"index": 2256,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A teacher has 36 markers and wants to distribute them equally among her 12 students. Each student will then use half of their markers for a project. How many markers does each student use for the project? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2257,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 2/3 cup of sugar for every batch of cookies. If Sarah wants to make 5 batches of cookies, and she has 4 cups of sugar, will she have enough? If not, how much more sugar does she need? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{yesshehasenough.}",
"style": "rule"
}
|
numina_math
|
{
"index": 2258,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence defined by \\( a_n = \\log(n) \\) for \\( n = 1, 2, 3, \\ldots \\). Find the sum of the first 10 terms of this sequence, i.e., find \\( \\sum_{n=1}^{10} a_n \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "s\\approx6.5599066",
"style": "rule"
}
|
numina_math
|
{
"index": 2259,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the equation of the line in point-slope form, \\( y - 3 = 2(x - 1) \\), find the y-intercept of this line. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2260,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the sum of the series:\n\\[ S = \\sum_{n=1}^\\infty \\frac{n(n+1)}{2^n}. \\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2261,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels at a constant speed of 12 miles per hour. After cycling for 2.5 hours, he takes a break for 30 minutes. He then continues cycling at a reduced speed of 9 miles per hour for another 2 hours. What is the total distance the cyclist traveled, and what percentage of the total cycling time was spent traveling at the reduced speed? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "44.44",
"style": "rule"
}
|
numina_math
|
{
"index": 2262,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A parabola is given by the equation \\( y = 2x^2 - 4x + k \\). A line intersects this parabola and is given by the equation \\( y = mx + b \\). Determine the value of \\( m \\) such that the line is tangent to the parabola. Assume \\( b = 3 \\) and \\( k = 1 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2263,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A collection of dimes and quarters is worth $15.25. There are 103 coins in all. How many of each type of coin are there? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "d=70q=33",
"style": "rule"
}
|
numina_math
|
{
"index": 2264,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the piecewise function:\n\\[ f(x) = \\left\\{\n\\begin{array}{cl}\n2x + 3 & \\text{if } x < 1, \\\\\nx^2 - 4x + 5 & \\text{if } 1 \\le x < 3, \\\\\nx + 2 & \\text{if } x \\ge 3.\n\\end{array}\n\\right. \\]\nEvaluate $f(-2) + f(2) + f(4)$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2265,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $\\mathbf{u}$ and $\\mathbf{v}$ be unit vectors such that the projection of $\\mathbf{u}$ onto $\\mathbf{v}$ is equal to $\\frac{1}{2} \\mathbf{v}$. If $\\mathbf{w}$ is another vector orthogonal to $\\mathbf{v}$, and $\\mathbf{u} \\cdot \\mathbf{w} = 2$, find the magnitude of $\\mathbf{u}$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\|\\mathbf{u}\\|=1",
"style": "rule"
}
|
numina_math
|
{
"index": 2266,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine the domain of the function \\( g(x) = \\frac{1}{\\sqrt{x^2 - 6x + 8}} \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(-\\infty2)\\cup(4\\infty)",
"style": "rule"
}
|
numina_math
|
{
"index": 2267,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the ellipse given by the equation \\(\\frac{x^2}{16} + \\frac{y^2}{9} = 1\\). Find the point on the ellipse that is closest to the point \\((4, 3)\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(43)",
"style": "rule"
}
|
numina_math
|
{
"index": 2268,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let the function \\( f \\) be defined for all real numbers such that:\n\\[ f(2x + 1) = 3f(x) + 2. \\]\nIf \\( f(1) = 5 \\), find the value of \\( f(3). \\) Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17",
"style": "rule"
}
|
numina_math
|
{
"index": 2269,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria has twice as many apples as Peter. If Peter gives away 3 apples to his friend, he will have one-third as many apples as Maria. How many apples does Maria have? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 2270,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A tank can be filled with water using two pipes. Pipe A can fill the tank in 6 hours, and Pipe B can fill the tank in 9 hours. If both pipes are turned on simultaneously, how long will it take to fill 2/3 of the tank? Express your answer in simplest fractional form. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{12}{5}",
"style": "rule"
}
|
numina_math
|
{
"index": 2271,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A flower shop noticed that its sales of tulips follow a growth pattern. In the first month, the shop sold 120 tulips. Each subsequent month, the shop sells twice as many tulips as the previous month. If this pattern continues, how many tulips will the shop have sold in total by the end of the fourth month? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1800",
"style": "rule"
}
|
numina_math
|
{
"index": 2272,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma has a ribbon that is 12 feet long. She cuts off a piece that is three-fifths of the total length to use for a craft project. She then cuts half of the remaining ribbon to use for another project. How many feet of ribbon does Emma have left? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.4",
"style": "rule"
}
|
numina_math
|
{
"index": 2273,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company is planning a community event and has a budget of $12,000. They need to allocate funds for three main categories: food, entertainment, and logistics. The cost for food is in the ratio of 3:5 compared to the cost for entertainment. The cost for logistics is double the cost for food. If the total cost for entertainment is $5,000, how much money is left from the budget after all expenses are paid? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{thecompanyhasoverspentby2000.}",
"style": "rule"
}
|
numina_math
|
{
"index": 2274,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Factor the polynomial expression \\( x^4 - 16 \\) completely and then evaluate it for \\( x = 2 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2275,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A box contains apples and oranges. The total weight of the box is 50 kg. The weight of the apples is 60% of the total weight of the box. If each apple weighs 200 grams, how many apples are in the box? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 2276,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, there are 35 students. The teacher wants to divide them into groups such that each group has exactly 4 students. How many groups can be formed, and 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": 2277,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily used to receive 15 emails a day on her old email address. After switching to a new email address, she now receives 45 emails a day. Assuming the number of emails from her friends remains the same, how many emails per week is Emily receiving that are not from her friends? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "210",
"style": "rule"
}
|
numina_math
|
{
"index": 2278,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells a dozen cookies for $18. If a customer wants to buy 30 cookies, how much will the customer need to pay? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 2279,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lucas runs a fruit market. He received a shipment of 1500 kg of oranges on Monday. On Tuesday, he sold 400 kg of oranges. On Wednesday, he had to discard 100 kg of spoiled oranges. On Thursday, Lucas received another shipment, twice the size of the first one. How many kilograms of oranges did Lucas have ready for sale on Friday? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4000",
"style": "rule"
}
|
numina_math
|
{
"index": 2280,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial \\( P(x) = \\frac{x^3 - 3x^2 + 2x}{x - 1} \\), simplify it and then find the inverse of the simplified polynomial function. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "p^{-1}(x)=1+\\sqrt{1+x}",
"style": "rule"
}
|
numina_math
|
{
"index": 2281,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A small sapling grows at a rate of 3 inches per month. After 4 months, the growth rate doubles. After 6 months from the start, the growth rate halves. How tall will the sapling be after 10 months? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 2282,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a reading competition, Emily read 1/3 of the total number of books read by all participants. If there were a total of 45 books read, how many books did the other participants read? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2283,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the $3 \\times 3$ matrix $\\mathbf{M}$ such that for any $3 \\times 1$ vector $\\mathbf{v} = \\begin{pmatrix} x \\\\ y \\\\ z \\end{pmatrix},$ $\\mathbf{M} \\mathbf{v}$ results in swapping the first and second entries of $\\mathbf{v}$ and negating the third entry. In other words,\n\\[\\mathbf{M} \\begin{pmatrix} x \\\\ y \\\\ z \\end{pmatrix} = \\begin{pmatrix} y \\\\ x \\\\ -z \\end{pmatrix}.\\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\mathbf{m}=\\begin{pmatrix}0&1&0\\1&0&0\\0&0&-1\\end{pmatrix}",
"style": "rule"
}
|
numina_math
|
{
"index": 2284,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has 5 packs of markers. Each pack contains 12 markers. If she gives 18 markers to her friend, how many markers does she have left? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "42",
"style": "rule"
}
|
numina_math
|
{
"index": 2285,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces three different types of widgets: Type A, Type B, and Type C. Each Type A widget takes 5 minutes to produce, each Type B widget takes 8 minutes to produce, and each Type C widget takes 12 minutes to produce. If the factory produces 40 Type A widgets, 30 Type B widgets, and 25 Type C widgets in one day, how many total minutes does the factory spend producing widgets in that day? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "740",
"style": "rule"
}
|
numina_math
|
{
"index": 2286,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the sum of the squares of the first $n$ natural numbers if the sum is equal to 3655. What is the value of $n$? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "21",
"style": "rule"
}
|
numina_math
|
{
"index": 2287,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(\\mathbf{v} = \\begin{pmatrix} 1 \\\\ 2 \\end{pmatrix}\\), \\(\\mathbf{w} = \\begin{pmatrix} -3 \\\\ 4 \\end{pmatrix}\\), and \\(\\mathbf{A} = \\begin{pmatrix} 2 & 0 \\\\ 0 & -1 \\end{pmatrix}\\). Compute \\(\\mathbf{A} (\\mathbf{v} + 3 \\mathbf{w})\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\begin{pmatrix}-16\\-14\\end{pmatrix}",
"style": "rule"
}
|
numina_math
|
{
"index": 2288,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the coefficient of \\( x \\) when \\( \\frac{1}{2} \\left( 8x^2 - 4x + 12 \\right) - \\frac{3}{4} \\left( 4x^2 + 8x - 16 \\right) \\) is simplified. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-8",
"style": "rule"
}
|
numina_math
|
{
"index": 2289,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a road trip from City A to City B, which is 480 kilometers away. She drives at a constant speed of 80 kilometers per hour. After driving for 3 hours, she takes a break for 45 minutes. How much more time will she need to reach City B after her break? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.75",
"style": "rule"
}
|
numina_math
|
{
"index": 2290,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is currently three times as old as his son, Dave. In five years, John will be twice as old as Dave. How old are John and Dave now? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2291,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A family drives for 3 hours at an average speed of 65 miles per hour. They then take a 1-hour break and drive for another 2 hours at an average speed of 55 miles per hour. What is the total distance they traveled, and what was their average speed for the entire trip? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "61\\\\text{milesperhour}",
"style": "rule"
}
|
numina_math
|
{
"index": 2292,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "To decorate the school garden, the school planted 45 rose bushes and 30 tulip bulbs. The number of sunflower plants planted is twice the total number of rose bushes and tulip bulbs. How many sunflower plants were planted? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 2293,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha has a collection of 24 marbles. She gives 1/4 of her marbles to her friend Alice and then gives 1/3 of the remaining marbles to her friend Bob. How many marbles does Samantha have left after giving marbles to Alice and Bob? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2294,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cube has six faces, and you want to color exactly three faces red and the other three faces blue. How many distinct ways can you color the cube, considering two colorings to be identical if one can be rotated to match the other? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2295,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Ella and her three friends decided to pool their money to buy a gift for their teacher. They collected a total of $120. If each friend, including Ella, contributed an equal amount, how much did each person contribute? One friend then needed to borrow $15 from the total collected amount. How much money was left after the loan? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "105",
"style": "rule"
}
|
numina_math
|
{
"index": 2296,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John and Maria are 60 miles apart and start moving towards each other at the same time. John is riding a bike at a speed of 12 miles per hour, and Maria is walking at a speed of 3 miles per hour. How long will it take for them to meet? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2297,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a factory, there are 4 types of machines that produce widgets. Each type of machine produces a different number of widgets per hour. Machine A produces 15 widgets per hour, Machine B produces 25 widgets per hour, Machine C produces 35 widgets per hour, and Machine D produces 45 widgets per hour. If the factory operates 8 hours a day, how many widgets are produced in a single day by all four machines combined? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "960",
"style": "rule"
}
|
numina_math
|
{
"index": 2298,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the infinite geometric series \\( S = a + ar + ar^2 + ar^3 + \\cdots \\) where the first term \\( a \\) and the common ratio \\( r \\) are such that the line \\( y = x + 2a \\) intersects the parabola \\( y = x^2 + bx \\) at exactly one point. Find the sum of the series \\( S \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-\\frac{(b-1)^2}{4}",
"style": "rule"
}
|
numina_math
|
{
"index": 2299,
"name": "numina_math",
"split": "train"
}
|
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