prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "In a garden, there are 120 rose bushes. The number of tulip plants is (3/5) of the number of rose bushes, and it is also (1/4) of the number of daffodil plants. How many daffodil plants are there? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "288",
"style": "rule"
}
|
numina_math
|
{
"index": 600,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 2/3 of a cup of sugar. If the sugar is measured using a 1/4 cup, how many times will the 1/4 cup need to be filled to get the required amount of sugar? Use the ceiling function if necessary. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 601,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "There is a very large room that has 6 tables, 2 sofas and 3 chairs that have 4 legs each. There are also 4 tables with 3 legs each, 2 tables with 1 leg each, and 2 rocking chairs with 2 legs each. How many legs are there in the room? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "62",
"style": "rule"
}
|
numina_math
|
{
"index": 602,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is 12 years old, and her sister Emily is 24 years old. In how many years will Emily be 1.5 times Samantha's age at that time? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 603,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a book club, there are 5 different mystery novels, 4 different fantasy novels, and 3 different science fiction novels. The club wants to arrange these books on a shelf such that all books of the same genre are grouped together. In how many different ways can the books be arranged on the shelf? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "103680",
"style": "rule"
}
|
numina_math
|
{
"index": 604,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length of 15 meters and a width of 10 meters. If a fence is to be built around the entire garden, how many meters of fencing material are needed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 605,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many perfect square divisors of \\( 3600 \\) are divisible by 4 but not by 25? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 606,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa is training for a marathon and runs at a rate of 6 miles per hour. On Monday, she runs for 1.5 hours in the morning and 2/3 of that time in the evening. On Tuesday, she runs for 1.25 hours in the morning and twice that time in the evening. How many miles does Lisa run in total over the two days? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "37.5",
"style": "rule"
}
|
numina_math
|
{
"index": 607,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Percius has a collection of 100 marbles. 40% of them are clear, 20% are black, and the remainder are of other colors. A friend of his asks if he can take five marbles at random. On average, how many marbles of other colors will his friend end up getting? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 608,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many positive divisors do 8400 and 7560 have in common? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32",
"style": "rule"
}
|
numina_math
|
{
"index": 609,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sandra is comparing the cost of two gym memberships. The first gym charges $50 per month, while the second gym charges $45 per month with a one-time joining fee of $60. What is the total cost of each gym membership for a year, and which gym is cheaper over the course of one year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 610,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that \\( 7^{2023} \\) is an extremely large number, find the remainder when \\( 7^{2023} \\) is divided by 13. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 611,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the quadratic equation \\(x^2 + bx + c = 0\\). Suppose it has two rational roots. Determine the maximum value of \\(b\\) such that both roots are rational numbers and \\(c\\) is a positive integer. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 612,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the greatest common divisor of 1444 and 1936? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 613,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is buying apples and oranges. She buys apples that cost $3 per pound and oranges that cost $4 per pound. She buys 10 pounds of apples and 5 pounds of oranges. If she gets a 10% discount on the total cost, how much does she pay for the fruits? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 614,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial equation \\[(x^4 - 4x^3 + 6x^2 - 4x + 1)(x^4 + x^3 + x^2 + x + 1) = 5x^4,\\]\nfind all real number solutions. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 615,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given two positive integers \\(a\\) and \\(b\\), their least common multiple (LCM) is 180 and their greatest common divisor (GCD) is 6. If one of the integers is 30, what is the other integer? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 616,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells 1/3 of its cakes in the morning and 1/4 of the remaining cakes in the afternoon. If the bakery sells 50 cakes throughout the day, how many cakes did the bakery originally have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 617,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John and Mary are planning a road trip. John drives at an average speed of 60 miles per hour, while Mary drives at an average speed of 50 miles per hour. If they drive a total distance of 330 miles and John drives twice as many hours as Mary, how many hours does each of them drive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.88",
"style": "rule"
}
|
numina_math
|
{
"index": 618,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A school is organizing a field trip and needs to rent buses to transport 180 students. Each bus can hold 45 students, and the cost to rent each bus is $150. If the total budget for the bus rental is $600, will the school be within the budget, and how much money will be left or needed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 619,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the fraction \\(\\frac{7}{12}\\), convert it to its decimal form. Identify the repeating sequence, and then determine the digit in the 50th place to the right of the decimal point. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 620,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Karen started her new job on January 15, 2019. She completed her training period on April 10, 2019. How many days did her training period last? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "86",
"style": "rule"
}
|
numina_math
|
{
"index": 621,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A laptop originally costs $1,200. During a holiday sale, the store offers a 25% discount on the laptop. What is the sale price of the laptop and how much do you save by purchasing it during the sale? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 622,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the largest whole number that can be formed using each of the digits 7, 4, and 9 exactly once? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "974",
"style": "rule"
}
|
numina_math
|
{
"index": 623,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Catherine has an equal number of notebooks and erasers. She has 84 notebooks. If she gives 3 notebooks and 2 erasers to each of her 12 friends and keeps the rest for herself, how many notebooks and erasers does she have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 624,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces two types of widgets, A and B. The production ratio of widgets A to widgets B is 7:4. If the factory produces 560 widgets A in a day, how many widgets B does it produce in the same day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "320",
"style": "rule"
}
|
numina_math
|
{
"index": 625,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John deposits $1000 in a savings account that earns simple interest at an annual rate of 5%. After 3 years, he withdraws the interest earned and needs to pay a tax of 20% on this interest. How much tax does John have to pay? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 626,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Cristian has 50 more black cookies in his cookie jar than white cookies. He eats half of the black cookies and 3/4 of the white cookies. If he initially had 80 white cookies, how many cookies are remaining within the cookie jar altogether? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "85",
"style": "rule"
}
|
numina_math
|
{
"index": 627,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "There are 50 beads. Player A and Player B take turns taking beads from the pile, and Player A goes first. Each player can take between 1 and 4 beads per turn. The person who takes the last bead loses. If Player A wants to win, how many beads should they take on the first turn? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 628,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the smallest positive integer \\( n \\) such that \\( 2^n \\equiv 3 \\pmod{7} \\) and \\( 2^n \\equiv 5 \\pmod{11} \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 629,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A small town has a population of 5,000 people. The population increases by 5% each year. Additionally, every year, 200 people move into the town, and 50 people leave the town. What will be the population of the town after 3 years? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6261",
"style": "rule"
}
|
numina_math
|
{
"index": 630,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(\\mathbf{u}\\), \\(\\mathbf{v}\\), and \\(\\mathbf{w}\\) be unit vectors such that \\(\\mathbf{u} + \\mathbf{v} + \\mathbf{w} = \\mathbf{0}\\). If \\(\\mathbf{A}\\) is a matrix given by\n\\[\n\\mathbf{A} = \\begin{pmatrix}\n\\mathbf{u} \\cdot \\mathbf{v} & \\mathbf{u} \\cdot (\\mathbf{v} \\times \\mathbf{w}) \\\\\n\\mathbf{v} \\cdot (\\mathbf{w} \\times \\mathbf{u}) & \\mathbf{w} \\cdot (\\mathbf{u} \\times \\mathbf{v})\n\\end{pmatrix},\n\\]\nfind the determinant of the matrix \\(\\mathbf{A}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 631,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The price of a laptop increased by 20% over the past year. If the current price of the laptop is $900, what was the price of the laptop one year ago? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "750",
"style": "rule"
}
|
numina_math
|
{
"index": 632,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is planning his monthly budget. He earns $2500 per month. His expenses include $900 for rent, $300 for groceries, $200 for transportation, and $100 for utilities. John wants to save twice the amount he spends on transportation each month. How much money will John have left after covering all his expenses and setting aside his savings? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 633,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangle has a length of 50 inches and a width of 30 inches. If you need to find the perimeter of the rectangle in feet, what would it be? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13.33",
"style": "rule"
}
|
numina_math
|
{
"index": 634,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is keeping track of her expenses for the week. On Monday, she spent $12.35 on groceries, $8.49 on transportation, and $15.78 on dining out. On Tuesday, she spent $20.67 on groceries and $5.55 on transportation. She wants to round each of these amounts to the nearest whole number and then find the total expenses for both days combined. What is the total rounded expense for Monday and Tuesday? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "63",
"style": "rule"
}
|
numina_math
|
{
"index": 635,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A box contains 6 red balls, 8 blue balls, and 10 green balls. If Amy randomly picks balls from the box without looking, what is the minimum number of balls she must take out to be certain that she has at least one ball of each color? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 636,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a 20% off sale on all items. Before the sale, the mean price of all items was $50, and the median price was $40. After the sale, what are the new mean and median prices of all items? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32",
"style": "rule"
}
|
numina_math
|
{
"index": 637,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A team of researchers is planning their trips to a remote island for data collection. On their first trip, they stayed for 3 weeks. For their second trip, they stayed twice as long as the first trip. On their third trip, they stayed one and a half times longer than their second trip. How many days in total did the researchers spend on the island? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "126",
"style": "rule"
}
|
numina_math
|
{
"index": 638,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a 3x3 magic square, the sum of the numbers in each row, column, and diagonal is the same. The top left cell of the square is filled with the number 8, and the center cell is filled with the number 5. If the bottom right cell is twice the number in the top right cell, find the number in the bottom right cell. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 639,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning to renovate her kitchen. The initial cost estimate for the renovation is $5,000. However, due to an increase in material costs, the final cost is 15% higher than the initial estimate. How much more does Sarah have to pay due to the increase, and what is the total final cost of the renovation? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5750",
"style": "rule"
}
|
numina_math
|
{
"index": 640,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A polyhedron has 12 vertices, 30 edges, and 20 faces. Verify that this polyhedron satisfies Euler's Formula and calculate the number of faces that are pentagons if the polyhedron has 10 triangular faces and the rest are pentagons. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 641,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A landscaper is planting trees in a rectangular garden that measures 15 meters by 20 meters. Each tree requires a 2-meter radius of space around it, and the landscaper wants to plant the maximum number of trees possible without any overlap. How many trees can the landscaper plant? Express your answer to the nearest whole number. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 642,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence defined by \\( a_n = 3n + 2 \\). Evaluate the function for \\( n = 1, 2, 3, 4, \\) and \\( 5 \\). Then, identify the pattern and predict the value of \\( a_{10} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32",
"style": "rule"
}
|
numina_math
|
{
"index": 643,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a recipe that calls for 3/4 cup of sugar. She wants to make 5 batches of the recipe. How many cups of sugar does she need in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3\\frac{3}{4}",
"style": "rule"
}
|
numina_math
|
{
"index": 644,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A triangle has integer side lengths. If one side is $5$ units and another side is $12$ units, what is the minimum possible perimeter of the triangle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 645,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify \\(\\frac{\\frac{2}{1+i}}{1-\\frac{1}{1-i}}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 646,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A new recipe for a fruit punch requires 3/4 of a liter of orange juice and 2/5 of a liter of apple juice. The recipe can serve 10 people. If you want to make enough punch to serve 25 people, how many liters of each juice do you need? Also, convert the total amount of juice required into milliliters. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2875",
"style": "rule"
}
|
numina_math
|
{
"index": 647,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the smallest 3-digit number such that the sum of its digits is a prime number and the number itself is divisible by 3? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "102",
"style": "rule"
}
|
numina_math
|
{
"index": 648,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah wants to buy a new laptop that costs $1200. She has already saved $750. If she saves $45 per week, how many more weeks will it take for her to save enough money to buy the laptop? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 649,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a fruit market, the price of apples is 25% more than the price of bananas, and the price of oranges is 20% less than the price of apples. If the combined cost of buying 2 kilograms of bananas, 3 kilograms of apples, and 5 kilograms of oranges is \\$54, what is the price per kilogram of each type of fruit? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5.02",
"style": "rule"
}
|
numina_math
|
{
"index": 650,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the remainder when \\( p(x) = 2x^4 - 3x^3 + 5x^2 - 7x + 9 \\) is divided by \\( x - 2 \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "23",
"style": "rule"
}
|
numina_math
|
{
"index": 651,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A triangle has three different integer side lengths and a perimeter of 30 units. What is the maximum length of any one side? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 652,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore is having a sale where all books are discounted. A customer buys a book originally priced at $50, which is now being sold at 20% off. The customer also buys a magazine originally priced at $30, which is being sold at 10% off. What is the total amount the customer pays for both items after the discounts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "67",
"style": "rule"
}
|
numina_math
|
{
"index": 653,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Rebecca is organizing a bake sale. She bakes cookies and cupcakes. Each cookie costs \\$0.50 to make, while each cupcake costs \\$1.00 to make. She plans to bake 60 items in total, spending exactly \\$45 on ingredients. How many cookies and how many cupcakes does Rebecca bake? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 654,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the double summation\n\\[ \\sum_{m=1}^{\\infty} \\sum_{n=1}^{\\infty} \\frac{(-1)^{m+n}}{m^2 + n^2}. \\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 655,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist and a runner are training on a 10-mile loop. The cyclist travels at a speed of 15 miles per hour, while the runner travels at a speed of 6 miles per hour. If both start at the same point and time but travel in opposite directions, how long will it take before they meet each other on the loop? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "28.57",
"style": "rule"
}
|
numina_math
|
{
"index": 656,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a survey of 500 people about their favorite ice cream flavor, 60% of the respondents chose chocolate, and the remaining respondents were divided between vanilla and strawberry. If 20% of the remaining respondents chose vanilla, how many people chose strawberry? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "160",
"style": "rule"
}
|
numina_math
|
{
"index": 657,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa is planning a road trip and wants to ensure she manages her driving time efficiently. She can drive at a constant speed of 60 miles per hour. If she needs to cover a distance of 360 miles and plans to take a 15-minute break every 2 hours of driving, how many hours will the entire trip take, including breaks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6.75",
"style": "rule"
}
|
numina_math
|
{
"index": 658,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given a set of four-digit numbers, if you remove all four-digit numbers that have at least one digit as 2 or 3, how many four-digit numbers remain? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5416",
"style": "rule"
}
|
numina_math
|
{
"index": 659,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Michael wants to buy a new phone. He saved $40 in January, $60 in February, and $35 in March. Michael's uncle promised to give him $50 if he saved more than $100 by the end of March. Michael then spent $120 on accessories. How much money does Michael have left after buying the accessories? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "65",
"style": "rule"
}
|
numina_math
|
{
"index": 660,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is training for a marathon and needs to run a certain number of miles each week. She runs 4 miles a day for 5 days and then runs 10 kilometers on the sixth day. How many total miles does Sarah run in a week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "26.21371",
"style": "rule"
}
|
numina_math
|
{
"index": 661,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length that is 3 times its width. The area of the garden is expressed by the function \\( A(x) = k(x-2)^2 \\), where \\( x \\) is the width of the garden in meters, and \\( k \\) is a constant. If the area of the garden is 27 square meters when the width is 5 meters, find the value of \\( k \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 662,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A storage company sells boxes and cylindrical containers. A customer needs a cube-shaped box with an edge length of 3 feet but can only find a cylindrical container with a height of 3 feet and a diameter of 3 feet. If the customer buys the cylindrical container, what volume of space will remain unused compared to the cube-shaped box? Provide the answer in cubic feet. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5.795",
"style": "rule"
}
|
numina_math
|
{
"index": 663,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom and Jerry are participating in a charity race. Tom runs at a constant speed of 6 miles per hour, while Jerry runs at a constant speed of 4 miles per hour. They start at the same time from the same point and run in the same direction. After how many hours will Tom be 2 miles ahead of Jerry? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 664,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there are 300 students. The ratio of boys to girls is 3:2. 40% of the boys play football, and 30% of the girls play basketball. How many students do not play either football or basketball? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "192",
"style": "rule"
}
|
numina_math
|
{
"index": 665,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A population of rabbits in a certain region follows an arithmetic sequence where the population in year \\( n \\) is given by \\( P_n = an + b \\). Over a span of four years, the population data recorded was as follows:\n\n- Year 1: 50 rabbits\n- Year 2: 70 rabbits\n- Year 3: 90 rabbits\n- Year 4: 110 rabbits\n\nDetermine the values of \\( a \\) and \\( b \\). Additionally, predict the population in year 10. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "230",
"style": "rule"
}
|
numina_math
|
{
"index": 666,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenny and Mark are preparing a mixture of fruit juice. Jenny uses 3 times as many oranges as apples, while Mark uses twice as many apples as Jenny. If Mark uses 8 apples, calculate the number of oranges Jenny uses. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 667,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah can paint 2/5 of a wall in 3 hours. If she continues painting at the same rate, how long will it take her to paint the entire wall? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7.5",
"style": "rule"
}
|
numina_math
|
{
"index": 668,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 1234.5678 units of a product in one day. Due to some defects, 0.5678 units are discarded. What is the total number of units produced, rounded to the nearest whole number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1234",
"style": "rule"
}
|
numina_math
|
{
"index": 669,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Selina is selling some of her old clothes to a second-hand store. They will buy her pants for $5 each, her shorts for $3 each, and her shirts for $4 each. She sells 4 pairs of pants, 6 pairs of shorts, and some shirts. After she gets her money, she sees 3 shirts that she likes which cost $12 each and buys them. She leaves the store with $20. How many shirts did she sell to the store? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 670,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A sequence of numbers starts with 5 and follows the rule that each subsequent number is 3 more than the previous one. What is the sum of the first 15 numbers in this sequence? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "390",
"style": "rule"
}
|
numina_math
|
{
"index": 671,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria takes 1.5 hours to bake a cake. She realizes that if she doubles her baking time, she can make twice as many cakes. How many minutes will Maria spend baking if she decides to make twice as many cakes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 672,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the vertical asymptote of the rational function \\( f(x) = \\frac{x^2 + 5x + 6}{x^2 - 4} \\). Then, determine the value of \\( k \\) such that the quadratic equation \\( x^2 + kx + 16 = 0 \\) has a root at the vertical asymptote. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-10",
"style": "rule"
}
|
numina_math
|
{
"index": 673,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The sum of three numbers \\(a, b\\) and \\(c\\) is 60. If we decrease \\(a\\) by 7, we get the value \\(N\\). If we increase \\(b\\) by 7, we get the value \\(N\\). If we multiply \\(c\\) by 7, we also get the value \\(N\\). What is the value of \\(N\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "28",
"style": "rule"
}
|
numina_math
|
{
"index": 674,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A school conducted a survey to understand the parents' satisfaction with their children's online class experience. The survey results showed that 20% of the parents rated the experience as Excellent, 50% rated it as Very Satisfactory, 25% of the remaining parents rated it as Satisfactory, and the rest rated it as Needs Improvement. If 200 parents participated in the survey, how many parents rated the experience as Needs Improvement? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 675,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A gas cylinder contains 50 liters of gas at a pressure of 2 atmospheres. If the pressure is increased to 5 atmospheres, and 30 liters of gas are added to the cylinder, what is the final volume of gas in liters? Assume the temperature remains constant. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 676,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bag contains 8 numbered cards, each with a distinct prime number written on it. The prime numbers are: 2, 3, 5, 7, 11, 13, 17, and 19. A card is drawn at random from the bag, and the number on the card is multiplied by the next prime number after it. What is the probability that the product is a power of 2? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 677,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store sells apples at $1.50 per pound. If a customer buys 5 pounds of apples and then returns 2 pounds, how much does the customer pay in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.50",
"style": "rule"
}
|
numina_math
|
{
"index": 678,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the following expression: $\\frac{3}{8} + \\frac{5}{8} + \\frac{7}{8} + \\frac{9}{8}$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 679,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a small soccer tournament, there are 12 teams. Each team plays every other team exactly once. How many total matches are played in the tournament? Additionally, if each match results in either a win or a loss (no draws), how many matches would result in one team having a win and the other a loss? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "66",
"style": "rule"
}
|
numina_math
|
{
"index": 680,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a*b = 3a + 2b, what is the value of (2*3)*4? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "44",
"style": "rule"
}
|
numina_math
|
{
"index": 681,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A two-digit number has the property that the product of its digits plus the sum of its digits equals the number itself. What is the units digit of this number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 682,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sam and Alex are participating in a charity run. Sam has already run 1/3 of the total distance, which is 9 miles. Alex has run 1/4 of the remaining distance after Sam's part. How many miles does Alex still need to run to complete the race? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13.5",
"style": "rule"
}
|
numina_math
|
{
"index": 683,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Express $\\frac{5}{12}$ as a decimal, and then identify the repeating decimal sequence. Round the repeating decimal to the nearest thousandth. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.417",
"style": "rule"
}
|
numina_math
|
{
"index": 684,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The orchard of Grange Poser farm has 25 cherry trees, each producing 120 kg of cherries, and 35 pear trees, each yielding 80 kg of pears. What is the total mass of fruit harvested from this orchard? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5800",
"style": "rule"
}
|
numina_math
|
{
"index": 685,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company wants to optimize the production of two products, A and B, to maximize profit. The profit function is given by \\( P(x, y) = 5x + 8y - \\frac{3x^2}{2} - 2y^2 \\), where \\( x \\) is the number of units of product A, and \\( y \\) is the number of units of product B. The company has constraints on production such that \\( x + y \\leq 10 \\) and \\( x, y \\geq 0 \\). Determine the optimal number of units of products A and B that the company should produce to maximize profit. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.71",
"style": "rule"
}
|
numina_math
|
{
"index": 686,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A population of bacteria doubles every 3 hours. Initially, there are 200 bacteria. How many bacteria will there be after 18 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12800",
"style": "rule"
}
|
numina_math
|
{
"index": 687,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels to a park at a speed of 10 miles per hour and returns at a speed of 15 miles per hour. If the total travel time is 5 hours, how far is the park from the cyclist’s starting point? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 688,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company is analyzing its sales trends over the past few months. They found that in January, the sales totaled $2,000, and in February, the sales increased by $150 per month. If the sales in March can be represented by the linear equation $y = 150x + 2000$, where $x$ is the number of months after January, what will be the total sales in March? Additionally, if the sales in April are expected to increase by $200 from March's sales, what will be the total sales in April? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2500",
"style": "rule"
}
|
numina_math
|
{
"index": 689,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two similar triangles, \\(\\triangle ABC\\) and \\(\\triangle DEF\\), have areas of 25 square units and 100 square units respectively. If the length of side \\(AB\\) in \\(\\triangle ABC\\) is 5 units, find the length of the corresponding side \\(DE\\) in \\(\\triangle DEF\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.5",
"style": "rule"
}
|
numina_math
|
{
"index": 690,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom and Jerry are working together to paint a fence. Tom can paint the entire fence in 5 hours, while Jerry can paint the same fence in 7 hours. If they start painting together, but Jerry has to leave after 2 hours, how long in total will it take to paint the entire fence? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.57",
"style": "rule"
}
|
numina_math
|
{
"index": 691,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa wants to buy a new dress that costs $120. The store is having a promotion where if you buy one item, you get the second item at half price. Lisa decides to buy a pair of shoes as well, which costs twice as much as the dress before any discounts. How much will Lisa pay in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "240",
"style": "rule"
}
|
numina_math
|
{
"index": 692,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends decided to share the cost of a meal at a restaurant. The total cost of the meal was $180. Alice paid twice as much as Bob, and Charlie paid half as much as Bob. If the remaining amount was split equally among David and Emma, how much did each of them pay? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 693,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A map has a scale of 1 inch representing 10 miles. If the distance between two towns on the map is 3 inches and another town is located 4 inches from the second town on the map, what is the total actual distance between the first and the third town? If a new road is planned to connect the first and the third town directly and it will be 5 miles shorter than the calculated total distance, what will be the length of the new road? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "65",
"style": "rule"
}
|
numina_math
|
{
"index": 694,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, 50 students are enrolled in either a music class, an art class, or both. 30 students are enrolled in the music class, and 25 students are enrolled in the art class. How many students are enrolled in both classes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 695,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "During a clearance sale, Dana decided to buy a $900 laptop that was being offered at a 25% discount, and 3 external hard drives each priced at $60. How much did Dana pay in total for the laptop and the hard drives? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "855",
"style": "rule"
}
|
numina_math
|
{
"index": 696,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A right triangle has legs of lengths \\( 4 \\) units and \\( 3 \\) units. What is the length of the hypotenuse? Simplify your answer involving radicals. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 697,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a certain convex polygon, each interior angle is represented by the expression \\(3x + 20\\) degrees, where \\(x\\) is a variable. The polygon has \\(n\\) sides. If the sum of all interior angles is 1980 degrees, how many sides does the polygon have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 698,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of 10 students is to be divided into two teams of 5 each for a friendly competition. How many ways are there to form these two teams? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "126",
"style": "rule"
}
|
numina_math
|
{
"index": 699,
"name": "numina_math",
"split": "train"
}
|
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