prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "A rectangular garden has a length that is 20% longer than its width. If the width of the garden is represented by \\( w \\) and the area of the garden is 600 square meters, find the width of the garden. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10\\sqrt{5}",
"style": "rule"
}
|
numina_math
|
{
"index": 2100,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma jogs around a park at a steady rate. She covers 2/5 of the park's circumference in 8 minutes. If she jogs at the same rate for 30 minutes, what percentage of the park's circumference will she have covered? Additionally, how many full laps of the park will she have completed in 30 minutes? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2101,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the expression \\(\\left(\\frac{x}{2}\\right)^4 - 3\\left(\\frac{x}{2}\\right)^2 + 1\\) simplifies to 0, find the value of \\(x\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\pm2\\sqrt{\\frac{3+\\sqrt{5}}{2}}\\pm2\\sqrt{\\frac{3-\\sqrt{5}}{2}}",
"style": "rule"
}
|
numina_math
|
{
"index": 2102,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is a salesperson who earns a commission of 15% on her sales. On Monday, she sold products worth $300, and on Tuesday, she sold products worth $450. How much commission did Sarah earn in total over these two days? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "112.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2103,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the expression $\\left\\lceil \\sqrt{64^{\\frac{3}{2}}} \\right\\rceil$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "23",
"style": "rule"
}
|
numina_math
|
{
"index": 2104,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends is planning to sit around a circular table for a game night. If there are 8 friends and reflections of the seating arrangement are considered equivalent, how many distinct ways can they arrange themselves around the table? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2520",
"style": "rule"
}
|
numina_math
|
{
"index": 2105,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anna baked a cake and decided to divide it into portions. She served 1/4 of the cake to her friends and then served another 1/4 of the cake to her family. What fraction of the cake has Anna served in total? 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": 2106,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "An engineering company needs to purchase 3500 meters of steel cable for a construction project. During inspection, 120 meters are found to be defective and cannot be used. The usable cable is then cut into 25-meter sections, each section costing $150. How much will the total cost be for the usable steel cable? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20250",
"style": "rule"
}
|
numina_math
|
{
"index": 2107,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company hires employees on a contract basis, depending on the availability of work. In a particular month, they hired 200 more employees on the first week than on the second week, and 150 fewer employees on the second week than on the third week. If the number of employees hired on the fourth week was twice the number hired in the third week, and the number of employees on the fourth week was 400, what's the average number of employees hired per week? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "225",
"style": "rule"
}
|
numina_math
|
{
"index": 2108,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria runs a small bakery and uses flour to make two types of cookies: sugar cookies and chocolate chip cookies. Each batch of sugar cookies requires 2 cups of flour, and each batch of chocolate chip cookies requires 3 cups of flour. If Maria makes 5 batches of sugar cookies and 7 batches of chocolate chip cookies, how many cups of flour does she use in total? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "31",
"style": "rule"
}
|
numina_math
|
{
"index": 2109,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two lines intersect at a point P in the coordinate plane. Line A has the equation \\(2x - 3y = 6\\), and Line B has the equation \\(4x + y = 9\\). What are the coordinates of point P? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(\\frac{33}{14}\\frac{1}{25})",
"style": "rule"
}
|
numina_math
|
{
"index": 2110,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given a sequence of terms defined by \\( a_n = n^2 + 3n + 2 \\) where \\( n \\ge 1 \\), find the greatest common divisor (GCD) of \\( a_{10} \\) and \\( a_{15} \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2111,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is organizing a charity event and plans to give everyone a gift bag. She starts by preparing 25 gift bags. In the following weeks, she doubles the number of gift bags each week for 3 weeks. Then, she decides to give 20% of the total gift bags to a local orphanage. How many gift bags does Sarah have left to give out at the charity event? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "160",
"style": "rule"
}
|
numina_math
|
{
"index": 2112,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A square garden has a side length of 12 meters. It is divided into smaller square plots, each with a side length that is a perfect square number of meters. If the total number of smaller square plots is 9, what is the side length of each smaller square plot? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2113,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company manufactures gadgets and incurs a cost given by the algebraic expression $3x + \\frac{5}{2}y$ dollars, where $x$ represents the number of basic gadgets produced and $y$ represents the number of advanced gadgets produced. The company decides to produce 100 basic gadgets and 40 advanced gadgets. If the company also needs to account for an additional fixed cost of $200 dollars, what is the total cost? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 2114,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A baker is preparing packages of cookies. He needs to bake 240 cookies in total. Each package contains 12 cookies. After baking 180 cookies, he realizes he needs to bake more. How many more packages can he complete with the remaining cookies he needs to bake? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2115,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah needs to paint a mural on a wall. She can paint 5 square feet per hour. The mural is to be painted in 2 days, working 3 hours each day. How many more hours will Sarah need if the mural's area is increased by 40 square feet? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2116,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Combine and simplify the following expression: \\(\\frac{2x+8}{x^2+6x+8} + \\frac{x-4}{x^2-4}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{3x^2+12x-32}{(x+2)(x+4)(x-2)}",
"style": "rule"
}
|
numina_math
|
{
"index": 2117,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden measures 15 feet in length and 10 feet in width. If you want to install a fence around the entire garden and the fencing costs $3 per foot, how much will it cost to install the fence? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 2118,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily buys a weekly pass for the gym for 70 yuan. She goes to the gym 5 days a week. What is the cost per day for Emily to go to the gym? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 2119,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a budget of $100 for her weekend shopping. She buys a dress for $45, a pair of shoes for $30, and a hat for $12. She realizes she still needs to buy a scarf. How much money does she have left to spend on the scarf? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 2120,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is planning a road trip and needs to rent a car. The car rental company charges a daily rental fee and an additional fee per mile driven. Emily rented the car for 3 days and drove 150 miles, and the total cost was $210. If the daily rental fee is $50, how much is the additional fee per mile? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.40",
"style": "rule"
}
|
numina_math
|
{
"index": 2121,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the function \\( f(x) = 3x + 2 \\), find the inverse function \\( f^{-1}(x) \\). Then, if \\( g(x) = 2x - 5 \\), determine \\( g(f^{-1}(11)) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "g(f^{-1}(11))=1",
"style": "rule"
}
|
numina_math
|
{
"index": 2122,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Compare the fractions \\(\\frac{64}{81}\\) and \\(\\frac{512}{729}\\) using an inequality sign. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": ">",
"style": "rule"
}
|
numina_math
|
{
"index": 2123,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: \\(\\frac{n^3 - 3n^2 - 4n + 12}{n^2 - 4} \\div \\frac{n^2 - n - 6}{n - 2}\\) Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{n-2}{n+2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2124,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the center, lengths of the major and minor axes, and the area of the ellipse given by \\( 4x^2 + 16x + y^2 - 6y = 11 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18\\pi",
"style": "rule"
}
|
numina_math
|
{
"index": 2125,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company produces widgets. The cost to produce \\( x \\) widgets is given by the function \\( C(x) = 5x + 200 \\). The company charges $10 per widget. If the company produces and sells 50 widgets, what is the profit? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 2126,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a physics experiment, two forces are acting on an object. The first force is represented by the vector \\( \\mathbf{F_1} = 3\\mathbf{i} + 4\\mathbf{j} \\) and the second force is represented by the vector \\( \\mathbf{F_2} = 7\\mathbf{i} + 2\\mathbf{j} \\). Find the magnitude of the resultant force acting on the object. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2\\sqrt{34}",
"style": "rule"
}
|
numina_math
|
{
"index": 2127,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is organizing her bookshelf and has two types of books: novels and textbooks. She has 5 novels, each costing $12, and 8 textbooks, each costing $25. If she wants to find the total cost of all her books, how much would that be? Additionally, if she sells all her novels for a total of $60 and all her textbooks for a total of $180, by how much would her selling price exceed the total cost? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-20",
"style": "rule"
}
|
numina_math
|
{
"index": 2128,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The sum of a negative integer \\(N\\) and twice its square is 10. Find the value of \\(N\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{novalidnegativeintegersolution}",
"style": "rule"
}
|
numina_math
|
{
"index": 2129,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify and solve for \\( x \\): \\(\\frac{2\\sqrt{3} - \\sqrt{x}}{\\sqrt{2}} = 1\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14-4\\sqrt{6}",
"style": "rule"
}
|
numina_math
|
{
"index": 2130,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where everything is 25% off. If a customer buys a jacket that originally costs $80, a pair of shoes that originally costs $60, and a hat that originally costs $20, how much will the customer spend after the discount? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2131,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation \\(\\sqrt{3x - 2} = 4 - \\sqrt{x}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17+2\\sqrt{13}",
"style": "rule"
}
|
numina_math
|
{
"index": 2132,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria went to a bookstore and bought a novel for $18, a notebook for $6, and three identical pens. If she spent a total of $36, how much did one pen cost? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2133,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has 24 marbles. She decides to give 1/3 of her marbles to her friend, Emily. After giving the marbles to Emily, Sarah's brother gives her 18 more marbles. How many marbles does Sarah have in the end? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "34",
"style": "rule"
}
|
numina_math
|
{
"index": 2134,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels to a town 60 miles away at an average speed of 15 miles per hour. On the return trip, due to fatigue, the cyclist's average speed drops to 10 miles per hour. How much total time does the cyclist spend traveling to and from the town? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2135,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the roots of the polynomial equation \\(2x^4 - 3x^3 - 5x^2 + 6x - 1 = 0\\) and determine which root is the largest. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.75",
"style": "rule"
}
|
numina_math
|
{
"index": 2136,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a regular decagon (10-sided polygon) inscribed in a circle. A point $P$ is chosen at random inside the circle. What is the probability that $P$ lies inside one of the triangles formed by drawing all the diagonals from one vertex of the decagon? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{8}",
"style": "rule"
}
|
numina_math
|
{
"index": 2137,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, 3/5 of the students are boys, and the rest are girls. If there are 16 more boys than girls, how many students are there in the classroom? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 2138,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert \\( 1011_2 \\) to its base ten equivalent, and then evaluate \\( (3^2)^2 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "81",
"style": "rule"
}
|
numina_math
|
{
"index": 2139,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the complex numbers \\(z_1 = 2 + 2i\\) and \\(z_2 = 1 - i\\). If these numbers are chosen independently at random from the set \\(\\{z_1, z_2\\}\\), what is the probability that the modulus of their product is an integer? Express your answer as a common fraction. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2140,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A contractor needs to paint a house, and he knows that he can complete the job in 5 days if he works 8 hours per day. He hires an assistant to help him, and together they can finish the job in 3 days working 7 hours per day. How many days would it take the assistant to paint the house alone if he works 8 hours per day? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5.53",
"style": "rule"
}
|
numina_math
|
{
"index": 2141,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the remainder when the decimal representation of $\\frac{19}{7}$ is divided by 9? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2142,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company has two machines, Machine A and Machine B, that produce widgets. Machine A produces 60% of the widgets, and Machine B produces 40% of the widgets. Each widget produced by Machine A has a 5% defect rate, while each widget produced by Machine B has a 10% defect rate. If a randomly selected widget is found to be defective, what is the probability that it was produced by Machine B? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.5714",
"style": "rule"
}
|
numina_math
|
{
"index": 2143,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is planning his monthly budget. He spends $720 on rent and plans to save the product of 15% of his monthly income, which is $3,000. How much does John save in total for the month? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1170",
"style": "rule"
}
|
numina_math
|
{
"index": 2144,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Heisenberg owns a pharmacy. He earned a total of $80 from 100 mg amoxicillin and $60 from 500 mg amoxicillin every week. If each capsule of 100 mg amoxicillin costs $5 and each capsule of 500 mg amoxicillin costs $2, how many capsules of each type of amoxicillin does he sell every week? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2145,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the matrix \\(\\mathbf{A} = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}\\), if \\(\\mathbf{A} \\mathbf{A}^T = \\mathbf{I}\\) where \\(\\mathbf{A}^T\\) is the transpose of \\(\\mathbf{A}\\) and \\(\\mathbf{I}\\) is the \\(2 \\times 2\\) identity matrix, find the values of \\(a, b, c,\\) and \\(d\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(abcd)=(1001)",
"style": "rule"
}
|
numina_math
|
{
"index": 2146,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A delivery company charges a base fee of $50 per shipment and an additional $0.75 per mile traveled. The company has a variable cost of $0.20 per mile for fuel and maintenance. If a shipment needs to travel 120 miles, what will be the total revenue generated from the shipment, and what is the net profit? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "116",
"style": "rule"
}
|
numina_math
|
{
"index": 2147,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If Sarah buys 12 apples for $3 and wants to buy 30 apples, how much will it cost her? Assume the price per apple remains constant. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7.50",
"style": "rule"
}
|
numina_math
|
{
"index": 2148,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Calculate the following expression: \\( 1234567 + 2345678 - 3 \\times (456789 + 567890) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "506208",
"style": "rule"
}
|
numina_math
|
{
"index": 2149,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the fraction $\\frac{11}{37}$ into its decimal representation and determine if it is a repeating decimal. If it is, find the repeating sequence. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "297",
"style": "rule"
}
|
numina_math
|
{
"index": 2150,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a garden, Maria planted 10 rows of flowers with 12 flowers in each row. Unfortunately, 3 rows of flowers died. If Maria decides to replant 3 times the number of flowers that died, how many flowers will she replant? How many flowers will be in the garden after replanting? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "192",
"style": "rule"
}
|
numina_math
|
{
"index": 2151,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe calls for \\( \\frac{3}{4} \\) cup of sugar and \\( \\frac{2}{3} \\) cup of flour. If you want to make half of the recipe, how many cups of sugar and flour will you need in total? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{17}{24}",
"style": "rule"
}
|
numina_math
|
{
"index": 2152,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A school library has 256 books that need to be equally distributed among 5 shelves. Each shelf can only hold a maximum of 50 books. How many books will be left over after filling each shelf to its maximum capacity? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2153,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a quadratic polynomial \\( p(x) \\) that is monic and has real coefficients. This polynomial is tangent to the parabola \\( y = x^2 - 4x + 3 \\) at exactly one point. Find the polynomial \\( p(x) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "x^2-4x+3",
"style": "rule"
}
|
numina_math
|
{
"index": 2154,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the intersection points of the curves given by the equations \\( y = 2x + 3 \\) and \\( y = -x^2 + 4x - 5 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2155,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression $(6x + 4)^2 - (6x - 4)^2$ and find its value when $x = 3$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "288",
"style": "rule"
}
|
numina_math
|
{
"index": 2156,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Triangle \\( PQR \\) has vertices at \\( P(3, 4) \\), \\( Q(6, 8) \\), and \\( R(9, 2) \\). Reflect the triangle over the \\( y \\)-axis to form triangle \\( P'Q'R' \\). What are the coordinates of points \\( P' \\), \\( Q' \\), and \\( R' \\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "p'(-34)q'(-68)r'(-92)",
"style": "rule"
}
|
numina_math
|
{
"index": 2157,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jamie is planning a road trip and needs to calculate the travel time. If she drives at a constant speed of 60 miles per hour, how long will it take her to travel to a destination that is 420 kilometers away? (Note: 1 mile ≈ 1.609 kilometers) Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.35",
"style": "rule"
}
|
numina_math
|
{
"index": 2158,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A transformation of the function \\( f(x) = x^2 \\) involves a vertical stretch by a factor of 2, followed by a horizontal shift to the left by 3 units, and finally a reflection across the x-axis. Write the equation of the transformed function and determine the coordinates of the vertices of an equilateral triangle formed with the x-intercepts of the transformed function. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(-30)(00)(-1.53\\sqrt{3})",
"style": "rule"
}
|
numina_math
|
{
"index": 2159,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two trains are traveling towards each other from different cities. Train A departs from City X at 9:00 AM traveling at a constant speed of 60 km/h, and Train B departs from City Y at 10:00 AM traveling at a constant speed of 80 km/h. The distance between City X and City Y is 400 km. At what time will the two trains meet? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12:26",
"style": "rule"
}
|
numina_math
|
{
"index": 2160,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A function \\( g \\) from the real numbers to the real numbers is defined as follows:\n\\[g(x) = \\left\\{\n\\begin{array}{cl}\n2x + 1 & \\text{if } x \\leq 2, \\\\\n3x - 4 & \\text{if } x > 2.\n\\end{array}\n\\right.\\]\nGiven another function \\( h(x) = x^2 - 3x + 2 \\), find \\( g(h(3)) + g(h(1)) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2161,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Calculate the sum of $0.\\overline{45}$ and $0.\\overline{36}$. Express your answer as a fraction in its simplest form. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{9}{11}",
"style": "rule"
}
|
numina_math
|
{
"index": 2162,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the series \\( S = \\sum_{n=1}^{10} \\frac{1}{n(n+1)} \\). Find the value of \\( S \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{10}{11}",
"style": "rule"
}
|
numina_math
|
{
"index": 2163,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In triangle \\(ABC\\), the lengths of the sides are \\(AB = 7\\), \\(BC = 10\\), and \\(CA = 5\\). Point \\(D\\) is the midpoint of \\(BC\\). Use the Law of Cosines and the Midpoint formula to find the coordinates of point \\(D\\) if the coordinates of \\(B\\) and \\(C\\) are \\((3, 4)\\) and \\((7, 8)\\) respectively. Then determine the distance \\(AD\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\sqrt{61}",
"style": "rule"
}
|
numina_math
|
{
"index": 2164,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Natalie is planning a fundraiser and wants to sell homemade cookies. She calculates that the ingredients for one batch of cookies cost $5. If she plans to sell each batch for $12, and she makes 15 batches, what will be her total profit? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "105",
"style": "rule"
}
|
numina_math
|
{
"index": 2165,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma goes to a coffee shop and buys a latte for $4.50. She pays with a $10 bill. How much change does she receive? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5.50",
"style": "rule"
}
|
numina_math
|
{
"index": 2166,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice is training for a marathon and wants to calculate her average running distance over a week. She runs 4 days a week, with distances of 5 miles, 7 miles, 3 miles, and 6 miles on each of those days. On the fifth day, she plans to run such that her average distance per day over the week will be exactly 6 miles. How many miles does she need to run on the fifth day? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2167,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer plants a field with crops. On the first day, he plants 2/5 of the field. On the second day, he plants 1/3 of the remaining field. After these two days, there is still 2.4 hectares of field left unplanted. What is the total area of the field? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2168,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is saving up to buy a new cylindrical water tank for her garden. She found a tank that has a radius of 1.5 meters and a height of 3 meters. The price of the tank is $300 per cubic meter of volume. Sarah plans to save 10% of her $60,000 annual salary each year to buy the tank. How many years will it take for Sarah to save enough money to buy the tank? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2169,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex is organizing a study schedule for his final exams. He has 5 subjects to study, and he plans to spend an equal amount of time on each subject. He has a total of 20 hours available for studying over the next four days. How many hours should Alex spend on each subject per day? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2170,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the functions \\( h(x) = 2x + 1 \\) and \\( k(x) = x^2 - 3 \\), find the value of \\( k(h(k(2))) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2171,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a number leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, and a remainder of 4 when divided by 7, what is the smallest positive integer that satisfies these conditions? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "53",
"style": "rule"
}
|
numina_math
|
{
"index": 2172,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom and Jerry are saving money to buy a new computer. Together, they have saved $150, but Jerry has saved $30 more than Tom. How much has each person saved? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2173,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation \\( (3x + 5) \\mod 7 = 2 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2174,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\(x\\): \\(3x - 5 = 2(x + 4)\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 2175,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(\\mathbf{A} = \\begin{pmatrix} 2 & 1 \\\\ 1 & 2 \\end{pmatrix}\\). Find all eigenvalues and eigenvectors of \\(\\mathbf{A}\\). Then, verify that the eigenvalues and eigenvectors satisfy the property \\(\\mathbf{A} \\mathbf{v} = \\lambda \\mathbf{v}\\) and explain the periodicity of \\(\\mathbf{A} \\mathbf{v}\\) when the cosine function is applied to the eigenvalue. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2\\pi",
"style": "rule"
}
|
numina_math
|
{
"index": 2176,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A trapezoid has a top base of 10 meters, a bottom base of 18 meters, and a height of 5 meters. What is the area of the trapezoid in square meters? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "70",
"style": "rule"
}
|
numina_math
|
{
"index": 2177,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A model train has a scale of 1.2 inches to 2.9 feet. If the model train is 5 inches tall, how tall is the real train in feet? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12.08",
"style": "rule"
}
|
numina_math
|
{
"index": 2178,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah drives from City A to City B, which is 150 kilometers apart. She drives the first 90 kilometers at an average speed of 60 kilometers per hour and the remaining 60 kilometers at an average speed of 40 kilometers per hour. If Sarah takes a 30-minute break halfway through her journey, what is her average speed for the entire trip, including the break time? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "42.86",
"style": "rule"
}
|
numina_math
|
{
"index": 2179,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory schedules the production of widgets over a 30-day period. Each day, the factory produces either 100 widgets or 150 widgets. Over the entire period, the factory produces a total of 3750 widgets. If the factory produces 150 widgets on 10 of the days, how many days does the factory produce 100 widgets? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2180,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a budget for her monthly expenses. She spends 30% of her salary on rent, 20% on food, and the remaining $1,200 on other expenses. If her monthly salary is represented by \\( S \\), determine her total monthly salary and the amounts spent on rent and food. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "480",
"style": "rule"
}
|
numina_math
|
{
"index": 2181,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the line equation \\(y = 2x + c\\), determine the value of \\(c\\) for which the line intersects the polynomial \\(y = x^3 - 4x + 2\\) at exactly one point. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "c=2-4\\sqrt{2}\\text{or}c=2+4\\sqrt{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2182,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A ball manufacturer creates rubber balls with a diameter of 6 cm. If the volume of a sphere is given by the formula \\( V = \\frac{4}{3} \\pi r^3 \\), what is the volume of one rubber ball? Assume \\( \\pi \\approx 3.14 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "113.04",
"style": "rule"
}
|
numina_math
|
{
"index": 2183,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the quadratic function \\( f(x) = 2x^2 + 4x + c \\), find the value of \\( c \\) such that the vertex of the function is at the point \\((h, k)\\) where \\( h = -1 \\) and \\( k = 3 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2184,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If $y = 3x^2 - 5x + 2$ and $z = 2x^2 + 4x - 3$, find the expression for $y - z$ in its simplest form. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "x^2-9x+5",
"style": "rule"
}
|
numina_math
|
{
"index": 2185,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the domain of the function: \\( f(x) = \\log \\left( \\frac{x+2}{x^2 - 4x + 3} \\right) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(-21)\\cup(3\\infty)",
"style": "rule"
}
|
numina_math
|
{
"index": 2186,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The school cafeteria serves 5 different kinds of fruit and 3 different kinds of sandwiches each day. If each student gets to choose one fruit and one sandwich, how many different combinations of fruit and sandwiches are possible? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 2187,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the following system of equations using both the elimination method and substitution method:\n\\[2x + 3y = 7\\]\n\\[4x - y = 5\\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{9}{7}",
"style": "rule"
}
|
numina_math
|
{
"index": 2188,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sam is planning a hiking trip. He hikes 5 miles north from his starting point, then 8 miles east, and finally 3 miles south. If he maintains an average speed of 4 miles per hour, how long will the entire hike take in hours and minutes? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2189,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The sum of two numbers is 21. One number is 3 more than twice the other number. What are the two numbers? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2190,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A construction team was initially planned to complete 0.56 kilometers of a road per day. However, they managed to complete 0.14 kilometers more than planned each day. After working for 7 days, there is still 3.5 kilometers of the road left to be constructed. What is the total length of the road they were constructing? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8.4",
"style": "rule"
}
|
numina_math
|
{
"index": 2191,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the range of the quadratic function \\( f(x) = -2x^2 + 4x + 1 \\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(-\\infty3]",
"style": "rule"
}
|
numina_math
|
{
"index": 2192,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the parametric equations \n\\[\nx = t^2 - 4t + 3\n\\]\nand \n\\[\ny = t^3 - 6t^2 + 11t - 6,\n\\]\nfind the points where the curve intersects itself. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(00)",
"style": "rule"
}
|
numina_math
|
{
"index": 2193,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two angles are supplementary, and the measure of one angle is 5 degrees more than three times the measure of the other angle. Find the measures of both angles. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{first angle: } 43.75 \\text{ degrees, second angle: } 136.25 \\text{ degrees}",
"style": "rule"
}
|
numina_math
|
{
"index": 2194,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A certain TV show aired for 10 seasons. The first 5 seasons had 20 episodes each, and the last 5 seasons had 25 episodes each. How many total episodes were there in the entire series? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "225",
"style": "rule"
}
|
numina_math
|
{
"index": 2195,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, the teacher wants to give out pieces of paper to students for a project. She has a total of 30 pieces of paper. She gives out $\\frac{1}{5}$ of the total pieces to the first group of students, and then $\\frac{1}{4}$ of the remaining pieces to the second group of students. Finally, she gives $\\frac{1}{3}$ of the leftover pieces to the third group. How many pieces of paper does she have left after distributing to all three groups? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2196,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a garden where she grows tomatoes and cucumbers. She has twice as many tomatoes as cucumbers. If she has a total of 48 plants, how many tomato plants and how many cucumber plants does she have? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32",
"style": "rule"
}
|
numina_math
|
{
"index": 2197,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lily is organizing a charity event and needs to prepare gift baskets. She decides to include 5 items in each basket. Initially, she has 7 baskets ready, but the number of baskets doubles when she receives more donations. Each basket contains 3 toys and 2 books. How many toys and books does Lily need in total? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "42 \\text{ toys and } 28 \\text{ books}",
"style": "rule"
}
|
numina_math
|
{
"index": 2198,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A set of blocks consists of 5 red blocks, 3 blue blocks, and 2 green blocks. Each block is a cube with a side length of 2 inches. If we arrange these blocks in a straight line, how many different arrangements are possible if blocks of the same color must be adjacent to each other? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8640",
"style": "rule"
}
|
numina_math
|
{
"index": 2199,
"name": "numina_math",
"split": "train"
}
|
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