prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "The area of a rectangular garden is given by the polynomial expression \\(3x^2 + 9x\\) square meters. If the width of the garden is represented by \\(3x\\) meters, what is the length of the garden in meters, and what is the total area if \\(x = 2\\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2000,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company is hosting a seminar. So far, 30 attendees from company A have been registered; company B has twice the number of attendees as company A; company C has 10 more attendees than company A; company D has 5 fewer attendees than company C. If a total of 185 attendees have registered, how many attendees who registered are not from either company A, B, C, or D? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 2001,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A piece of fabric is 3/4 of a yard long. A tailor cuts off 1/3 of this piece to use in a project. Then, he cuts off another 1/2 of the remaining piece for another project. How much fabric does the tailor have left? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{4}",
"style": "rule"
}
|
numina_math
|
{
"index": 2002,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels 60 miles in the same time that a bike travels 20 miles. If the speed of the bike is 10 miles per hour slower than the car, what is the speed of the car? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 2003,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the value of $x$ that satisfies the equation where the slope of the line $2x - y = 5$ equals the slope of the line passing through the points $(x, 1)$ and $(2, 5)$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2004,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah decides to start saving money for a new bicycle that costs $300. In the first 5 weeks, she saves $20 each week. After that, she saves $15 each week for the next 6 weeks. How much more money does Sarah need to save to buy the bicycle? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "110",
"style": "rule"
}
|
numina_math
|
{
"index": 2005,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the greatest common divisor of \\( \\sqrt{50} \\) and \\( \\sqrt{72} \\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\sqrt{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2006,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A water tank is being filled by two pipes. Pipe A fills the tank at a rate of 10 liters per minute, and Pipe B fills the tank at a rate of 15 liters per minute. If both pipes are turned on simultaneously, how many minutes will it take to fill a 300-liter tank? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2007,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sophia has saved up $120. She wants to buy some books that are on sale for $15 each. After buying as many books as she can, how much money will Sophia have left? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2008,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the least common multiple (LCM) of two positive integers is 180, and their greatest common divisor (GCD) is 6, what are the two integers? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(6180)(1860)(3036)",
"style": "rule"
}
|
numina_math
|
{
"index": 2009,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In an isosceles triangle \\( \\triangle ABC \\), where \\( AB = AC \\) and \\( BC = 10 \\), the measure of \\( \\angle BAC \\) is \\( 120^\\circ \\). Determine the lengths of sides \\( AB \\) and \\( AC \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{10\\sqrt{3}}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 2010,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A jar contains 5 red marbles, 3 blue marbles, and 2 green marbles. Each marble is equally likely to be drawn. If you draw one marble at random, what is the expected value of the number of red marbles drawn in three draws with replacement? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{3}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2011,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( f(x) = 3x + 5 \\) and \\( g(x) \\) is the inverse of \\( f(x) \\), find \\( g(14) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2012,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 3 tablespoons of sugar, and each tablespoon is equivalent to 15 grams. If you want to make 10 batches of this recipe, how many kilograms of sugar will you need? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.45",
"style": "rule"
}
|
numina_math
|
{
"index": 2013,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In the coordinate plane, an equilateral triangle \\(ABC\\) is inscribed in a circle centered at the origin with radius \\(10\\) units. If the coordinates of vertex \\(A\\) are \\((10,0)\\), find the area of triangle \\(ABC\\). Express the area in simplest radical form, and if it can be written as \\(\\frac{a\\sqrt{b}}{c}\\), where \\(a\\), \\(b\\), and \\(c\\) are relatively prime integers, determine \\(a+b+c\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "79",
"style": "rule"
}
|
numina_math
|
{
"index": 2014,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a coordinate plane, line \\( L_1 \\) passes through the points (2, 3) and (6, 11). Line \\( L_2 \\) is parallel to \\( L_1 \\) and passes through the point (4, 5). What is the equation of line \\( L_2 \\)?\n\n### Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2x-3",
"style": "rule"
}
|
numina_math
|
{
"index": 2015,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the sequence \\( S_n \\) is defined as \\( S_n = \\frac{1}{n} + \\frac{1}{n+1} + \\frac{1}{n+2} + \\ldots + \\frac{1}{2n} \\), find \\( S_{10} \\) and express it as a simplified fraction. What percentage of the sequence \\( S_{10} \\) is \\( \\frac{1}{15} \\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8.45",
"style": "rule"
}
|
numina_math
|
{
"index": 2016,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A chemical laboratory needs to prepare a 250 mL solution that is 20% alcohol. They have a 50% alcohol solution and a 10% alcohol solution available. How many milliliters of each solution should they mix to obtain the desired concentration? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "x = 62.5 \\text{ ml}, y = 187.5 \\text{ ml}",
"style": "rule"
}
|
numina_math
|
{
"index": 2017,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa has a large book collection that she wants to distribute equally among her 7 friends. She has 1,234 books in total. After distributing as many books as possible equally, how many books will each friend receive, and how many books will be left undistributed? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2018,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many distinct 4-digit numbers can be formed using the digits 2, 3, 5, and 7, such that each number is a prime number? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2019,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A grocery store sells apples for $1.50 each. Sarah buys 10 apples, but she has a coupon for $5 off her total purchase. How much does Sarah pay after using the coupon? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10.00",
"style": "rule"
}
|
numina_math
|
{
"index": 2020,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the system of nonlinear equations\n\\[\n\\begin{cases}\nx^2 + y = 10 \\\\\nx + y^2 = 13\n\\end{cases}\n\\]\nfind the values of \\(x\\) and \\(y\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "x\\approx2.13y\\approx5.46",
"style": "rule"
}
|
numina_math
|
{
"index": 2021,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma runs a food truck and sells smoothies. Each smoothie costs $3.75 to make, and she sells each for $5.50. If she sells 120 smoothies in one day, how much profit does she make? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "210",
"style": "rule"
}
|
numina_math
|
{
"index": 2022,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah drives to her friend's house, which is 45 miles away. On her way there, she drives at a speed of 30 miles per hour. On her way back, she drives at a speed of 45 miles per hour. How much total time does Sarah spend driving to her friend's house and back? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2023,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the function \\( f(x) = (2x + 3)(x - 5) \\), simplify the expression for \\( f(x) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "f(x)=2x^2-7x-15",
"style": "rule"
}
|
numina_math
|
{
"index": 2024,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If Jennifer spends 2 hours studying for her math exam and takes a 10-minute break every 30 minutes, how much actual study time does she get? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 2025,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company produces custom T-shirts. The cost of producing 50 T-shirts is directly proportional to the number of T-shirts produced and is $\\$100$. If the company receives an order for 125 T-shirts, how much will it cost to produce them? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "250",
"style": "rule"
}
|
numina_math
|
{
"index": 2026,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a repeating decimal \\(0.\\overline{6}\\) is converted to a fraction, and then multiplied by 3, what is the resulting value? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2027,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find all rational values of \\( c \\) such that the quadratic equation \\( 2x^2 + cx + 5 = 0 \\) has rational roots. Express your answer as a set of values. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\{-11-7711\\}",
"style": "rule"
}
|
numina_math
|
{
"index": 2028,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A zoo currently has 8 different types of animals, and each animal type takes around 6 minutes to see. The zoo plans to import 4 new species. How much time will it take to see all animal types after the new species arrive? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
numina_math
|
{
"index": 2029,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sam has 3 friends: John, Mike, and Alex. He decides to distribute 120 candies among them in such a way that John gets 1/4 of the candies, Mike gets 1/3 of the candies, and Alex gets the rest. How many candies does each friend get? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 2030,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine the area of the triangle formed by the lines \\( y = \\frac{1}{x} \\), \\( y = -\\frac{1}{x} \\), and \\( y = \\frac{1}{2} \\) in the coordinate plane. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2031,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A team of construction workers is tasked with building two different types of structures: sheds and gazebos. Each shed requires 5 hours of work, and each gazebo requires 8 hours of work. The team consists of 10 workers who work 8 hours a day. In one day, they managed to build 4 sheds and 2 gazebos. How many hours would it take for the same team to build 10 sheds and 5 gazebos if they continue to work at the same rate? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2032,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the $x$-intercepts of the quadratic function $f(x) = x^2 - 4x + 5$ and determine if the function has a range that includes $y = -1$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "x\\text{-intercepts:}2\\pmi",
"style": "rule"
}
|
numina_math
|
{
"index": 2033,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company had 200 employees last year. This year, the company increased its workforce by 15%. After this increase, 20% of the new total number of employees left the company. How many employees does the company have now? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "184",
"style": "rule"
}
|
numina_math
|
{
"index": 2034,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Joe lives on the 3rd floor. He needs to spend 12 minutes to move from the 4th floor to the 5th floor. Assuming the time taken to move between any two consecutive floors is the same, how many minutes does Joe need to climb from the 1st floor to the 3rd floor? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 2035,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given two points on a line, \\( (2, 3) \\) and \\( (5, 11) \\), find the equation of the line in slope-intercept form. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{8}{3}x-\\frac{7}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 2036,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the convergence of the series \\(\\sum_{n=1}^\\infty \\frac{1}{(n+1)(n+2)}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2037,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a two-digit number, the digit in the ones place is 4. The digit in the tens place is 2 more than the digit in the ones place. What is the number? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "64",
"style": "rule"
}
|
numina_math
|
{
"index": 2038,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a collection of 50 marbles and wants to distribute them equally among her friends. After distributing, she finds that there are 5 marbles left over. If she gave each friend the same number of marbles, how many friends does Sarah have? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "135915",
"style": "rule"
}
|
numina_math
|
{
"index": 2039,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "At a school event, there are children and adults. Together, they make up a total of 100 people. If the number of adults is twice the number of children, how many children and adults are there? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{thereare25childrenand75adults.}",
"style": "rule"
}
|
numina_math
|
{
"index": 2040,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has 15 more marbles than Tom. If Tom has 28 marbles, how many marbles do they have together? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "71",
"style": "rule"
}
|
numina_math
|
{
"index": 2041,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The area of a triangle is 54 square meters, and the base of the triangle is 9 meters longer than its height. What are the base and height of the triangle? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{base=18metersheight=9meters}",
"style": "rule"
}
|
numina_math
|
{
"index": 2042,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "I have a collection of coins consisting of quarters, dimes, and nickels. The total value of these coins is a perfect square as well as a perfect cube. What is the minimum number of coins needed for this collection? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32",
"style": "rule"
}
|
numina_math
|
{
"index": 2043,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school library, there are 40 students. 22 students read mystery books, 19 students read fantasy books, and 8 students read both mystery and fantasy books. If a student is selected at random, what is the probability that the student reads either mystery or fantasy books? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{33}{40}",
"style": "rule"
}
|
numina_math
|
{
"index": 2044,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation \\( x^{-2} - 5x^{-1} + 6 = 0 \\) using factoring techniques. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{2}\\frac{1}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 2045,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jordan earns $15 per hour working at a bookstore. If he worked for 12 hours this week, how much did he earn in total? Additionally, convert his earnings to euros if the exchange rate is $1 = €0.85. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "153",
"style": "rule"
}
|
numina_math
|
{
"index": 2046,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the quadratic function \\( f(x, y) = 3x^2 + 2y^2 - 6x + 8y + 7 \\). Convert this quadratic function to its vertex form and determine the minimum value of \\( f(x, y) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-4",
"style": "rule"
}
|
numina_math
|
{
"index": 2047,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A new fitness program offers a monthly subscription fee of $25 per member. If the program currently has 450 members, how much total revenue does the program generate in a month? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11250",
"style": "rule"
}
|
numina_math
|
{
"index": 2048,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( \\omega \\) be a primitive 6th root of unity, i.e., \\( \\omega = e^{2\\pi i / 6} \\). Consider the equation \\( \\cos(6\\theta) + \\cos(4\\theta) + \\cos(2\\theta) = k \\) where \\( k \\) is an integer. Find all possible integer values of \\( k \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "k\\in\\{-3-113\\}",
"style": "rule"
}
|
numina_math
|
{
"index": 2049,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jessica is organizing a 5-hour charity event. She wants to allocate her time as follows: 1.5 hours for welcoming guests, 2 hours for activities, and the rest of the time for closing remarks and cleanup. How many minutes will Jessica spend on closing remarks and cleanup? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2050,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John was tasked with adding the numbers 735 and 481. He added them as 735 + 418 by mistake. What was his error, and what is the correct sum? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1216",
"style": "rule"
}
|
numina_math
|
{
"index": 2051,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that \\( f(x) \\) is an even function and \\( g(x) \\) is an odd function, we know the following:\n\\[ f(x) + g(x) = 12 \\]\n\\[ f(2) = 5 \\]\nFind the value of \\( g(2) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2052,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily has a collection of 150 marbles. She decided to give 40 marbles to her friend Sarah and another 25 marbles to her friend Jack. How many marbles does Emily have left? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "85",
"style": "rule"
}
|
numina_math
|
{
"index": 2053,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels north for 150 miles at a speed of 50 miles per hour, then travels east for 120 miles at a speed of 40 miles per hour. What is the total time taken for the journey, and what is the overall average speed in miles per hour? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 2054,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The combined age of two friends, Alice and Bob, is 45 years. Alice is 5 years older than twice Bob's age. How old are Alice and Bob? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{bobis12yearsoldandaliceis33yearsold.}",
"style": "rule"
}
|
numina_math
|
{
"index": 2055,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store sells two types of fruit baskets. The first type costs $120 and the second type is offered at a 25% discount. If you buy both types of fruit baskets, how much total money will you save compared to buying them at their original prices? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2056,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa spends $3.50 each day on coffee. If she decides to stop buying coffee and saves the money instead, how much will she save in a year? Assume there are 365 days in a year. Additionally, how much more would she save in a year compared to her friend, who spends $100 annually on coffee? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1177.50",
"style": "rule"
}
|
numina_math
|
{
"index": 2057,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the sum \\(\\left\\lfloor \\sum_{n=1}^{5} 2^n \\right\\rfloor\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "62",
"style": "rule"
}
|
numina_math
|
{
"index": 2058,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the following system of nonlinear equations:\n\\[ x^2 + y^2 = 25 \\]\n\\[ y = x + 1 \\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(34)",
"style": "rule"
}
|
numina_math
|
{
"index": 2059,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the rational equation: \\(\\frac{2x}{x^2 - 4} + \\frac{3}{x + 2} = \\frac{5}{x - 2}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{nosolution}",
"style": "rule"
}
|
numina_math
|
{
"index": 2060,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe calls for 2/3 cup of sugar for every 1/4 cup of butter. If you have 3 cups of sugar, how many cups of butter do you need to use to maintain the same ratio? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.125",
"style": "rule"
}
|
numina_math
|
{
"index": 2061,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Suppose \\( f(x) = 2x + 3 \\) and \\( g(x) = \\frac{x - 3}{2} \\). If the graphs of \\( y = f(g(x)) \\) and \\( y = g(f(x)) \\) are drawn, at how many points do they intersect? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{infinitelymany}",
"style": "rule"
}
|
numina_math
|
{
"index": 2062,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider points \\(A (2, 3)\\), \\(B (5, 7)\\), and \\(C (1, -2)\\) on a Cartesian plane. Calculate the distance from the origin to each of these points and determine which point is the farthest from the origin. Express the distance of the farthest point from the origin as a simplified fraction. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\sqrt{74}",
"style": "rule"
}
|
numina_math
|
{
"index": 2063,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a set of positive integers from \\(1\\) to \\(200\\). How many of these integers have a sum of divisors that is a prime number? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "27",
"style": "rule"
}
|
numina_math
|
{
"index": 2064,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is organizing a charity event and needs to buy 500 T-shirts. Each T-shirt costs $8, but she gets a 15% discount for buying in bulk. Additionally, she needs to customize the T-shirts, which costs an extra $2 per T-shirt. If she has a budget of $3500, how much money will she have left after buying and customizing the T-shirts? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "900",
"style": "rule"
}
|
numina_math
|
{
"index": 2065,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Five consecutive integers have an arithmetic mean of 10. What are the five integers? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "89101112",
"style": "rule"
}
|
numina_math
|
{
"index": 2066,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A solution containing 18% alcohol is mixed with a solution containing 12% alcohol. How many liters of each solution must be used to make 50 liters of a solution that is 15% alcohol? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "x = 25 \\text{ liters}, y = 25 \\text{ liters}",
"style": "rule"
}
|
numina_math
|
{
"index": 2067,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the equation \\( x^2 + y^2 - 8x + 10y + 4 = 0 \\), determine the center and the radius of the circle. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\sqrt{33}",
"style": "rule"
}
|
numina_math
|
{
"index": 2068,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Combine and simplify the following rational expressions: \n\\[\n\\frac{3x}{x^2 - 4} + \\frac{2}{x + 2}\n\\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{5x-4}{(x-2)(x+2)}",
"style": "rule"
}
|
numina_math
|
{
"index": 2069,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store has a sale where all items are first discounted by 15% and then an additional 10% off the already discounted price. If a jacket originally costs $200, how much will it cost after both discounts are applied? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "153",
"style": "rule"
}
|
numina_math
|
{
"index": 2070,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah loves to read books and she reads 15 pages every day. Each book she reads has an average of 300 pages. A new book costs $20. How much does Sarah spend on books in a year if she reads consistently every day? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "380",
"style": "rule"
}
|
numina_math
|
{
"index": 2071,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore is having a sale on notebooks and pens. Notebooks are priced at $7 each, and pens are priced at $3 each. Emma buys 3 notebooks and 5 pens, while Liam buys 2 notebooks and 7 pens. How much do Emma and Liam spend in total? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "71",
"style": "rule"
}
|
numina_math
|
{
"index": 2072,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In triangle \\(ABC\\), \\(\\angle BAC = 40^\\circ\\) and \\(\\angle ABC = 70^\\circ\\). The altitude from \\(A\\) to \\(BC\\) is \\(AD\\), and \\(O\\) is the center of the circle circumscribed about triangle \\(ABC\\). Let \\(E\\) be the point on the circle such that \\(AE\\) is a diameter. Determine the measure of \\(\\angle ADE\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2073,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice and Bob each arrive at a party at a random time between 1:00 and 2:00 p.m. If Alice arrives after Bob, what is the probability that Bob arrived before 1:30 p.m.? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{4}",
"style": "rule"
}
|
numina_math
|
{
"index": 2074,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A gardener planted 15 rose bushes and 20 tulip bulbs. After a week, 4 rose bushes and 6 tulip bulbs did not survive. If the gardener plants 7 more rose bushes and 5 more tulip bulbs, how many more tulip bulbs than rose bushes are there now? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2075,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Polly walks her dog every day. She walks at a pace of 3 miles per hour. On weekdays (Monday to Friday), she walks her dog for 30 minutes each day. On weekends (Saturday and Sunday), she increases the duration to 1 hour each day. How many miles does Polly walk her dog in a week? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2076,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex has 3/4 as many apples as oranges. He also has 2/3 as many oranges as bananas. If the total number of apples, oranges, and bananas is 81, how many of each fruit does Alex have? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "a=18o=25b=38",
"style": "rule"
}
|
numina_math
|
{
"index": 2077,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A regular hexagon is inscribed in a circle with a radius of 10 units. Calculate the area of one of the equilateral triangles formed by connecting the center of the circle to two adjacent vertices of the hexagon. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25\\sqrt{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 2078,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah spends 2 hours and 15 minutes on her homework every Monday, Wednesday, and Friday. On Tuesday and Thursday, she spends 1 hour and 30 minutes. On weekends, she spends a total of 3 hours on her homework. How much time in total does Sarah spend on her homework in a week, in hours and minutes? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12 \\text{ hours and } 45 \\text{ minutes}",
"style": "rule"
}
|
numina_math
|
{
"index": 2079,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The arithmetic mean of three numbers \\( x, y, z \\) is given to be 5. If \\( x + y = 8 \\), find the value of \\( z \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2080,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a magic show, the magician has a set of 5 different cards numbered \\{1, 2, 3, 4, 5\\}. He asks a volunteer to pick two cards randomly. The magician then multiplies the numbers on the selected cards and subtracts the smaller number from the product. What is the probability that the result is an even number? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{7}{10}",
"style": "rule"
}
|
numina_math
|
{
"index": 2081,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice and Bob are running a relay race on a triangular track. The sides of the triangle measure 3 km, 4 km, and 5 km. Alice runs the first side at a speed of 6 km/h, Bob runs the second side at a speed of 8 km/h, and Alice runs the third side at a speed of 10 km/h. Calculate the total time taken for Alice and Bob to complete the relay race. Express the answer in minutes. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2082,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the sum of the positive whole number divisors of 180? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "546",
"style": "rule"
}
|
numina_math
|
{
"index": 2083,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has 3 times as many marbles as Tom. Together, they have 48 marbles. How many marbles does each person have? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 2084,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( n \\) if \\( \\sqrt{4^n} = 8 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2085,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find all real values of \\( x \\) such that the rational expression \\(\\frac{x^2 - 5x + 6}{x^2 - x - 6} \\ge 0\\). Express your answer in interval notation. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(-\\infty-2)\\cup[23)\\cup(3\\infty)",
"style": "rule"
}
|
numina_math
|
{
"index": 2086,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A certain recipe requires 3 kilograms of apples for every 5 kilograms of total fruit used. If you have a total of 20 kilograms of fruit, how many kilograms of apples do you need? Additionally, if you use 2 kilograms of apples, how many kilograms of other fruits will you need to maintain the proportional relationship? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.33",
"style": "rule"
}
|
numina_math
|
{
"index": 2087,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\(\\frac{1}{x-1} + \\frac{1}{x+2} = \\frac{3}{4}\\), find the value of \\(x\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2088,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the numbers \\(\\frac{5}{16}\\), \\(\\frac{3}{8}\\), and \\(\\frac{7}{20}\\). Order these numbers from smallest to largest. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{5}{16}<\\frac{7}{20}<\\frac{3}{8}",
"style": "rule"
}
|
numina_math
|
{
"index": 2089,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A laboratory technician is preparing a saline solution. She needs to prepare 50 liters of a 20% saline solution by mixing a 10% saline solution and a 30% saline solution. How many liters of each solution does she need to use? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 2090,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a group of 200 participants at a conference, 120 attended a workshop on data science, 90 attended a workshop on machine learning, and 50 attended both workshops. Using the inclusion-exclusion principle, how many participants did not attend either workshop? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2091,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given a triangle with vertices at \\( (0, 0) \\), \\( (a, 0) \\), and \\( (b, c) \\), where \\( a \\) and \\( b \\) are positive integers and \\( c \\) is a positive integer. The perimeter of the triangle is 15 units. How many different sets of coordinates \\((a, b, c)\\) satisfy these conditions? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2092,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the following sequence of numbers: \\(1, 3, 5, \\cdots, 99\\), find the median of the sequence. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 2093,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels from town A to town B at an average speed of 15 miles per hour. On the return trip, the cyclist travels at an average speed of 10 miles per hour. If the total time taken for the entire trip is 5 hours, what is the distance between town A and town B? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2094,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex has a budget of $1500 to buy new furniture for his home. He wants to buy a sofa that costs $700, a dining table that costs $500, and a bed that is originally priced at $600 but has a 20% discount. How much money will Alex have left after making these purchases? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-180",
"style": "rule"
}
|
numina_math
|
{
"index": 2095,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning to build a small garden. She has a garden bed that is 5 feet long and 3 feet wide. She wants to place a border around the garden using bricks. Each brick is 9 inches long. How many bricks will she need to create the border around the entire garden? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22",
"style": "rule"
}
|
numina_math
|
{
"index": 2096,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the following expression:\n\\[ (2 + 3i)^{10} + (2 - 3i)^{10}. \\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2\\cdot13^5\\cos(10\\theta)",
"style": "rule"
}
|
numina_math
|
{
"index": 2097,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical container with a radius of 3 cm and a height of 10 cm is filled with water. A solid cube with a side length of 4 cm is then fully submerged into the container. Determine the fraction of the container's total volume that is occupied by the cube. Simplify your answer. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{32}{45\\pi}",
"style": "rule"
}
|
numina_math
|
{
"index": 2098,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In right triangle $JKL$, angle $J$ measures $60^\\circ$ and angle $K$ measures $30^\\circ$. When drawn, the angle bisectors of angles $J$ and $K$ intersect at a point $M$. What is the measure of obtuse angle $JMK$? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "135",
"style": "rule"
}
|
numina_math
|
{
"index": 2099,
"name": "numina_math",
"split": "train"
}
|
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