prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "Given a transformation matrix $\\mathbf{T}$ that rotates a vector by 45 degrees and then reflects it over the vector $\\begin{pmatrix} 1 \\\\ 1 \\end{pmatrix},$ find the determinant of $\\mathbf{T}$. Assume the rotation matrix is applied first, followed by the reflection matrix. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-1",
"style": "rule"
}
|
numina_math
|
{
"index": 1500,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a theater, there are 15 rows of seats. Each row has 20 seats. However, during a particular event, 3 rows were left empty. Calculate the total number of seats that were occupied during the event. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "240",
"style": "rule"
}
|
numina_math
|
{
"index": 1501,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from City A to City B at a constant speed and covers the distance of 150 miles in 3 hours. On the return trip, the car travels at a speed that is 10 miles per hour slower. How long does it take for the car to travel from City B back to City A? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.75",
"style": "rule"
}
|
numina_math
|
{
"index": 1502,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice and Bob are working together to complete a task. Alice can complete the task in 4 hours, while Bob can complete the task in 6 hours. If they work together, how long will it take them to complete the task? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.4",
"style": "rule"
}
|
numina_math
|
{
"index": 1503,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenny has a recipe that calls for 500 milliliters of milk. However, her measuring cup only shows ounces. If 1 milliliter is approximately 0.0338 ounces, how many ounces of milk does Jenny need to use? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16.9",
"style": "rule"
}
|
numina_math
|
{
"index": 1504,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Nicole has 4 fish tanks. The first two tanks need 8 gallons of water each, and the other two need 2 fewer gallons of water each than the first two tanks. If Nicole needs to change the water of the aquariums every week, how many gallons of water will she need in four weeks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "112",
"style": "rule"
}
|
numina_math
|
{
"index": 1505,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a road trip and wants to calculate her fuel consumption. Her car travels 25 miles per gallon of fuel. She plans to drive 300 miles to her destination and 300 miles back. If fuel costs $3.50 per gallon, how much will she spend on fuel for the entire trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "84",
"style": "rule"
}
|
numina_math
|
{
"index": 1506,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha's birthday is on January 15th. This year, her birthday falls on a Tuesday. In how many years will her birthday fall on a Friday, considering that non-leap years have 365 days and leap years have 366 days? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 1507,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Compare the total product of multiplying 12 by 8 with the sum of 150 and the result of subtracting 45 from 125. What is the difference between these two values? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "134",
"style": "rule"
}
|
numina_math
|
{
"index": 1508,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cone has a base diameter of 8 centimeters and a height of 12 centimeters. It is melted and recast into a new cone with a base radius of 4 centimeters. What is the height of the new cone? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 1509,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the Fibonacci sequence defined by \\( F_1 = 1 \\), \\( F_2 = 1 \\), and \\( F_n = F_{n-1} + F_{n-2} \\) for \\( n \\geq 3 \\), find the value of \\( n \\) such that the sum of the first \\( n \\) Fibonacci numbers equals a quadratic function evaluated at its vertex. Specifically, let the quadratic function be \\( f(x) = x^2 + x - 2 \\). Find the value of \\( n \\) where the sum \\( F_1 + F_2 + \\cdots + F_n \\) is equal to \\( f(x) \\) evaluated at its vertex. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 1510,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has 72 oranges and wants to distribute them equally among his 8 workers. After distributing the oranges equally, he decides to give 5 more oranges to each worker. How many oranges will each worker have in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 1511,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate \\( 64^{2/3} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 1512,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a group of 50 students, 30 students are enrolled in a Math class, 25 students are enrolled in a Science class, and 10 students are enrolled in both classes. How many students are enrolled in neither class? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1513,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the rational expression \\(\\frac{2x^3 - 7x^2 + 5x - 3}{x^2 - 3x + 2}\\). Perform polynomial division to simplify the expression, and then solve for \\(x\\) in the equation \\(\\frac{2x^3 - 7x^2 + 5x - 3}{x^2 - 3x + 2} = 4\\).\n\n### Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 1514,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is organizing a charity event and needs to purchase balloons and decorations. She buys 50 balloons at $1.50 each and 20 sets of decorations at $10 each. The store offers a 15% discount on the total purchase if the bill exceeds $100. How much does Samantha pay after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "233.75",
"style": "rule"
}
|
numina_math
|
{
"index": 1515,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Harry, Ron, and Neville are having a race on their broomsticks. Assuming there are no ties, in how many different possible orders can they finish the race? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1516,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the exponential function \\( f(x) = 2^x \\). The function \\( g(x) \\) is a transformation of \\( f(x) \\) such that \\( g(x) = 2^{2x - 3} \\). Find the value of \\( g(4) \\) and express the result in terms of powers of 2. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32",
"style": "rule"
}
|
numina_math
|
{
"index": 1517,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a weekend trip. On Saturday, she plans to drive 120 miles to visit her friend, then drive another 80 miles to her favorite hiking spot. She drives at an average speed of 40 miles per hour and plans to take one 45-minute break. On Sunday, she will drive back home the same distance but at a speed of 50 miles per hour without any breaks. How many total hours will Sarah spend driving during the weekend trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9.75",
"style": "rule"
}
|
numina_math
|
{
"index": 1518,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In an arithmetic sequence, the first term is 12, and the common difference is 7. What is the sum of the first 20 terms in this sequence? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1570",
"style": "rule"
}
|
numina_math
|
{
"index": 1519,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A circular garden has a radius of 7 meters. The gardener wants to put a fence around the garden and needs to calculate the circumference of the garden to know how much fencing material to buy. He also wants to convert the circumference into centimeters for more precise measurement. If the gardener decides to subtract 200 centimeters from the total length of the fence to leave an entrance, what is the final length of the fencing material required in centimeters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4196",
"style": "rule"
}
|
numina_math
|
{
"index": 1520,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that $\\log_{b} 64 = 3$ and $\\log_{b} 2 = 1$, use the change of base formula to find $b$. Then, evaluate $\\log_{b} 16$ using the properties of exponents and logarithms. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 1521,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Michelle has a recipe that calls for 3/4 cup of sugar. She only has a 1/4 cup measuring cup. How many times does she need to fill the 1/4 cup measuring cup to get the exact amount of sugar needed for the recipe? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 1522,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is training for a marathon and wants to track her weekly running distance. She runs at a constant pace of 6 miles per hour. On Monday, she runs for 1.5 hours. On Wednesday, she increases her running time by 50% compared to Monday. On Friday, she runs 75% of the time she ran on Wednesday. On Sunday, she decides to run the same distance she ran on Monday and Wednesday combined. How many miles does Emily run in total for the week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "55.125",
"style": "rule"
}
|
numina_math
|
{
"index": 1523,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company produces 1,200 gadgets each month. 30% of these gadgets fail quality control checks and are discarded. Of the remaining gadgets, 20% are sold in bulk at a discounted rate, and the rest are sold at full price. If the company sells each gadget at full price for $50, how much revenue does the company generate from selling gadgets at full price each month? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33600",
"style": "rule"
}
|
numina_math
|
{
"index": 1524,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sam has 48 stickers which he wants to distribute equally among his 6 friends. After distributing the stickers, he wants to give 2 more stickers to each friend. How many stickers will Sam have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 1525,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Conor can chop 12 eggplants, 9 carrots, and 8 potatoes in a day. If he works 4 times a week, how many vegetables can he chop in 3 weeks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "348",
"style": "rule"
}
|
numina_math
|
{
"index": 1526,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "For how many integer values of \\( x \\) is \\( x^2 - 10x + 21 < 0 \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 1527,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe for a special fruit punch requires the use of three types of juice in the ratio of 3:2:5 (apple: orange: pineapple). If you need to make 10 liters of this fruit punch, how many liters of each type of juice are required? Additionally, if 10% of the total punch is lost during the preparation, how many liters of fruit punch will you actually have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 1528,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Annie works part-time at a local cafe. She earns $12 per hour and works 15 hours per week. How much will she earn in a month if she works 4 weeks in that month? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "720",
"style": "rule"
}
|
numina_math
|
{
"index": 1529,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A retailer sells a product for $150 after adding a 20% profit on its cost price. If the product is subject to a 10% sales tax, find the original cost price of the product before adding the profit and tax. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "125",
"style": "rule"
}
|
numina_math
|
{
"index": 1530,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mrs. Smith has two children, Anna and Ben. She wants to limit their combined screen time to no more than 3 hours each day. Today, Anna has already used her gadget for 1.5 hours, and Ben has used his for 45 minutes. How many more minutes can Ben use his gadget if Anna doesn't use her gadget anymore for the rest of the day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 1531,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A local bakery sells muffins in packs of 6 for $5 per pack and croissants in packs of 4 for $7 per pack. A customer wants to buy 8 packs of muffins and 5 packs of croissants. If they decide to distribute the total cost equally among 4 friends, how much will each friend have to pay? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18.75",
"style": "rule"
}
|
numina_math
|
{
"index": 1532,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, there are 30 students. Each student either plays basketball, soccer, or both. It is known that 18 students play basketball, 15 students play soccer, and 5 students play both sports. Using the principle of inclusion-exclusion, how many students play either basketball or soccer? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "28",
"style": "rule"
}
|
numina_math
|
{
"index": 1533,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( p = 3 \\) and \\( q = 2p + 1 \\), evaluate the expression \\( (q - 2)(q - 1) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 1534,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 3/4 cup of sugar, but you only have a 1/2 cup measuring tool. If you use the 1/2 cup measuring tool twice, how much more sugar do you need to meet the recipe's requirement? 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": 1535,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anna bought a laptop that was originally priced at $600. She received a discount of 15% and also had to pay an additional sales tax of 8% on the discounted price. What is the final price Anna paid for the laptop? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "550.80",
"style": "rule"
}
|
numina_math
|
{
"index": 1536,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A certain radioactive substance decays such that the amount remaining after each day is $\\frac{1}{4}$ of the amount from the previous day. If you start with a 256-gram sample, after how many days will the remaining substance be less than 1 gram? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1537,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If $\\frac{2}{3}$ of a number is $\\frac{5}{6}$ of another number, and the first number is 18, what is the second number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14.4",
"style": "rule"
}
|
numina_math
|
{
"index": 1538,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells cakes. Each cake costs $25. The bakery also offers a discount of $5 on every cake if a customer buys more than 3 cakes. A customer bought some cakes and paid $200 in total after the discount. How many cakes did the customer buy? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 1539,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The area of a rectangle is given by the formula \\( A = l \\times w \\). If the area \\( A \\) of the rectangle is \\( \\frac{75}{2} \\) square units and the length \\( l \\) is \\( \\frac{15}{2} \\) units, find the width \\( w \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1540,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the real solutions of the equation \\( x^3 - 3x + \\sqrt[3]{27} = 0 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.879",
"style": "rule"
}
|
numina_math
|
{
"index": 1541,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has three jars containing different numbers of candies. The first jar has twice as many candies as the second jar, and the third jar has 10 more candies than the second jar. If the total number of candies in all three jars is 58, how many candies are in each jar? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22",
"style": "rule"
}
|
numina_math
|
{
"index": 1542,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery makes a batch of cookies where the total weight of the batch is 48 kilograms. If 3/4 of the cookies are chocolate chip and the rest are oatmeal. The weight of the oatmeal cookies is 1/2 of the weight of the chocolate chip cookies. What is the weight of the oatmeal cookies? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 1543,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If $3^x = 81$ and $2^y = 16$, what is the value of $x \\cdot y$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 1544,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A florist has 25 roses and 18 tulips. During the morning, she sells 15 roses and 10 tulips. In the afternoon, she receives a new shipment of 12 roses and 8 tulips. How many flowers does she have now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "38",
"style": "rule"
}
|
numina_math
|
{
"index": 1545,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular grid has dimensions \\(3 \\times 4\\). You want to find the number of unique paths from the top-left corner to the bottom-right corner, moving only right or down. Additionally, how many of these paths pass through the point \\((2, 3)\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1546,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a marathon race, there were 45 runners in total. The number of runners who finished before Lisa is three times smaller than the number of runners who finished after her. At what place did Lisa finish? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 1547,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe calls for 3 cups of sugar to make 24 cookies. If you only want to make 18 cookies, how much sugar should you use? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.25",
"style": "rule"
}
|
numina_math
|
{
"index": 1548,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that \\( p \\) and \\( q \\) are the roots of the quadratic equation \\( x^2 - 5x + 6 = 0 \\), use Vieta's formulas to find the value of \\( p^3 + q^3 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35",
"style": "rule"
}
|
numina_math
|
{
"index": 1549,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify $\\frac{8 \\times 10^6}{4 \\times 10^2}$. (Your answer should be a single number, with no products or quotients.) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20000",
"style": "rule"
}
|
numina_math
|
{
"index": 1550,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A shipment of 72 identical boxes weighs a total of 864 kilograms. If the weight is evenly distributed among the boxes, and you remove one box, what is the average weight of the remaining boxes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 1551,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Dexter went to the mall and saw that Apple products are on sale. He wants to buy an iPhone 12 with a 15% discount and an iWatch with a 10% discount. The price tag shows that an iPhone 12 costs $800 while an iWatch costs $300. Upon checkout, he will receive a further 2% cashback discount on the total after applying the individual product discounts. How much would the items cost in total after the discounts and cashback? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "931",
"style": "rule"
}
|
numina_math
|
{
"index": 1552,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A digital music library contains 10 days of music and takes up 24,000 megabytes of disk space. On average, how many megabytes of disk space does one hour of music in this library take up? 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": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 1553,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company manufactures gadgets and incurs a fixed cost of \\$1000 each month. The production cost for each gadget is \\$20. If each gadget is sold for \\$50, how many gadgets must the company sell each month to break even? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "34",
"style": "rule"
}
|
numina_math
|
{
"index": 1554,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa is preparing for a marathon and runs at a constant pace of 6.5 miles per hour. She wants to convert her running speed to feet per second to better understand her pace. Given that 1 mile equals 5280 feet, how many feet per second does Lisa run? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9.5333",
"style": "rule"
}
|
numina_math
|
{
"index": 1555,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has a total of 120 cows and 150 sheep. If he decides to sell half of his cows and one-third of his sheep, how many animals does he have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "160",
"style": "rule"
}
|
numina_math
|
{
"index": 1556,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a survey of 150 people about their pet preferences, it was found that 90 people like dogs, 60 people like cats, and 30 people like both dogs and cats. Additionally, 20 people said they do not like either dogs or cats. How many people in the survey like only cats? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 1557,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A trapezoid has a top base of 8 centimeters, a bottom base of 15 centimeters, and a height of 6 centimeters. What is the area of the trapezoid in square centimeters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "69",
"style": "rule"
}
|
numina_math
|
{
"index": 1558,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $x$ be the integer such that $0 \\le x < 19$ and $7x \\equiv 1 \\pmod{19}$. What is $5^x \\pmod{19}$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1559,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma is currently three times as old as her brother James. In five years, she will be twice as old as James will be at that time. How old are Emma and James now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1560,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A radioactive substance decays such that the mass remaining after each hour is 80% of the mass from the previous hour. If the initial mass of the substance is 500 grams, how much mass remains after 5 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "163.84",
"style": "rule"
}
|
numina_math
|
{
"index": 1561,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily runs a lemonade stand where she sells lemonade at $5 per cup. She also sells cookies at $2 each. On a particular day, she sold 12 cups of lemonade and 15 cookies. How much revenue did Emily make that day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 1562,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The first term of an arithmetic progression is 5, and the common difference is 3. What is the 20th term of the arithmetic progression? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "62",
"style": "rule"
}
|
numina_math
|
{
"index": 1563,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Myrtle’s 3 hens lay 3 eggs each per day. She plans to be away for 7 days and asks her neighbor to take as many eggs as they would like. The neighbor takes 12 eggs. Upon her return, Myrtle collects the remaining eggs but accidentally drops 5 on her way into the house. How many eggs does Myrtle have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "46",
"style": "rule"
}
|
numina_math
|
{
"index": 1564,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many different ways can you select a committee of 3 people from a group of 7 people if the order of selection does not matter? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35",
"style": "rule"
}
|
numina_math
|
{
"index": 1565,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore received an order for 40 copies of a science textbook and 50 copies of a history textbook. Each science textbook costs $12.75 and each history textbook costs $15.90. What is the total cost of the order? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1305",
"style": "rule"
}
|
numina_math
|
{
"index": 1566,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the function \\( f(x) = \\frac{x+1}{x-2} \\). Determine the value of \\( x \\) that makes \\( f(x) \\) discontinuous, and explain why \\( f(x) \\) is discontinuous at that value. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 1567,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jessica bought 18.75 meters of fabric to make costumes for a play. She needs to divide the fabric evenly among 5 costumes. After cutting the fabric, she realized she needs an additional 0.75 meters for each costume. How much more fabric does Jessica need to buy in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.75",
"style": "rule"
}
|
numina_math
|
{
"index": 1568,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "For \\(\\triangle ABC\\), all its side lengths are integers. The perimeter of \\(\\triangle ABC\\) with a side of length \\(25\\) and a side length of \\(18\\) is at least what value? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "51",
"style": "rule"
}
|
numina_math
|
{
"index": 1569,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Stephanie is managing her monthly bills and needs to determine how much she still owes. Her electricity bill is $80, and she has paid $50 towards it. Her gas bill is $60, and she has paid half of it. She has a water bill of $45, and has made a $20 payment. Additionally, her internet bill is $35, and she has already paid $10. How much does Stephanie still need to pay to fully cover all her bills? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "110",
"style": "rule"
}
|
numina_math
|
{
"index": 1570,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A theater sells tickets for a play every day. On the first day, it sells 10 tickets. Each subsequent day, it sells 5 more tickets than the previous day. How many tickets are sold in total over the first 7 days? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "175",
"style": "rule"
}
|
numina_math
|
{
"index": 1571,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sophia works at a factory where she assembles toy cars. She assembles 8 toy cars per hour. If she works 7 hours a day and the factory operates 6 days a week, how many toy cars does Sophia assemble in two weeks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "672",
"style": "rule"
}
|
numina_math
|
{
"index": 1572,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The bookstore held a sale and reduced the price of a popular novel by 25%. After the discount, the novel costs $18. What was the original price of the novel? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 1573,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that \\(x = 2\\) is a root of the polynomial equation \\(2x^3 - 5x^2 + ax - 6 = 0\\), find the value of \\(a\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1574,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex bought 150 apples at $0.50 each and sold them at $0.75 each. Calculate his profit, and then find out how much money he has after spending $20 on supplies. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17.50",
"style": "rule"
}
|
numina_math
|
{
"index": 1575,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A classroom has 8 students. Their test scores out of 100 are as follows: 85, 90, 76, 88, 92, 81, 79, and 84. What is the average test score for the students in the classroom? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "84.375",
"style": "rule"
}
|
numina_math
|
{
"index": 1576,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: $\\frac{3\\sqrt{50} + 2\\sqrt{18}}{\\sqrt{2}}$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "21",
"style": "rule"
}
|
numina_math
|
{
"index": 1577,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, the teacher asks the students to find a two-digit number such that when its digits are reversed and the smaller number is subtracted from the larger number, the result is equal to the difference between the original two-digit number and its arithmetic mean. What is the original two-digit number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 1578,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces widgets at a rate given by the function \\( W(t) = 5t + 3 \\), where \\( t \\) represents time in hours and \\( W(t) \\) is the number of widgets produced. If the factory operates for 8 hours a day, and each widget requires 2.5 units of raw material, how many units of raw material are needed in a day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "107.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1579,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The decimal representation of \\(0.\\overline{7}\\) is a repeating decimal. Convert \\(0.\\overline{7}\\) to a fraction and simplify it to its lowest terms. What is the denominator of the simplified fraction? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 1580,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical tank of radius 5 meters is filled with water to a height of 8 meters. The tank has a leak, and water is leaking at a constant rate of 2 cubic meters per hour. A pump is used to add water to the tank at a rate of 1 cubic meter per hour. How long will it take for the water level to drop to 4 meters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "314.159",
"style": "rule"
}
|
numina_math
|
{
"index": 1581,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer plants a row of apple trees. Each year, the number of apple trees doubles. If the farmer starts with 4 apple trees and plants for 5 years, how many apple trees will the farmer have at the end of the 5 years? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "128",
"style": "rule"
}
|
numina_math
|
{
"index": 1582,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Bingley has 7 marbles. Kelly gives Bingley a third of her 21 marbles. Then Bingley gives half of his marbles to his friend. How many marbles does Bingley have remaining? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 1583,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Bucket X contains 3 more pieces of fruit than Bucket Y, and Bucket Y contains 5 more pieces of fruit than Bucket Z. If Bucket Z contains 7 pieces of fruit, how many pieces of fruit are there in all three buckets combined? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "34",
"style": "rule"
}
|
numina_math
|
{
"index": 1584,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from City A to City B at an average speed of 60 kilometers per hour and returns from City B to City A at an average speed of 40 kilometers per hour. If the total round trip takes 5 hours, what is the distance between City A and City B? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 1585,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "James is planning a budget for a small event. He has allocated $120 for decorations, $80 for food, and $50 for miscellaneous expenses. He ended up spending $45 less on decorations than he budgeted, and $20 more on food than he budgeted. After these adjustments, he donated half of the remaining miscellaneous budget to charity. How much of his budget is left after these expenses and donation? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 1586,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenna has 100 mL of a 50% saline solution. She evaporates some water from the solution, and the concentration of the solution increases to 70%. How much water was evaporated? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "28.57",
"style": "rule"
}
|
numina_math
|
{
"index": 1587,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria is training for a marathon and runs at a steady speed of 6.5 miles per hour. If she runs for 1 hour and 45 minutes, how many kilometers does she cover? (Note: 1 mile is approximately 1.60934 kilometers) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18.31",
"style": "rule"
}
|
numina_math
|
{
"index": 1588,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The decimal representation of a number is $0.36\\overline{3}$. Convert this repeating decimal to a fraction and simplify it. What is the numerator of the simplified fraction? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 1589,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a work project that she needs to complete in 72 hours. She decides to work on it in 6-hour shifts. How many shifts will she need to complete the project? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 1590,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the number of whole numbers \\( n \\) such that \\( \\lfloor \\sqrt{n} \\rfloor \\) is a perfect square and \\( 1 \\leq n \\leq 1000 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "960",
"style": "rule"
}
|
numina_math
|
{
"index": 1591,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 0.75 liters of juice every minute. Due to a machine upgrade, the production rate increased by 0.25 liters per minute. If the factory operates for 8 hours a day, how many liters of juice will it produce in one day after the upgrade? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "480",
"style": "rule"
}
|
numina_math
|
{
"index": 1592,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe for a cake requires 2.5 cups of flour, but you only have a measuring cup that measures in milliliters. If 1 cup is equivalent to 240 milliliters, how many milliliters of flour do you need for the recipe? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 1593,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the number 1011 from binary (base-2) to decimal (base-10). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 1594,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the angle between the hour hand and the minute hand at 3:27? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "58.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1595,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria goes to a store with $50. She buys a toy for $15 and a book for $12. After making these purchases, she decides to donate $5 to a charity. How much money does Maria have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 1596,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store offers a 25% discount on a jacket that costs $80. Additionally, there is a seasonal promotion offering an extra 10% discount on the already discounted price. What is the final price of the jacket after applying both discounts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "54",
"style": "rule"
}
|
numina_math
|
{
"index": 1597,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lydia is 15 years old and has a weekly allowance of $10. She wants to save enough money to buy a bicycle that costs $250. How many weeks will it take Lydia to save enough money to buy the bicycle if she saves all her allowance every week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 1598,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the value of \\( (x - 3)^2 \\) if \\( x = 7 \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 1599,
"name": "numina_math",
"split": "train"
}
|
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