prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "A car's fuel tank holds 60 liters of gasoline. If the car consumes fuel at a rate of 8 liters per 100 kilometers, how many kilometers can the car travel on a full tank? Then, if the car has already traveled 150 kilometers, how much fuel is left in the tank? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 9900,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah loves to drink fresh juice every day. She spends $5 on fresh juice each day. She has a discount card that gives her a 10% discount on her total juice spending every month. After applying the discount, how much does Sarah spend on fresh juice in a month with 30 days? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "135",
"style": "rule"
}
|
numina_math
|
{
"index": 9901,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is building a rectangular garden. He buys 8 bags of soil, each weighing 45 pounds. Later, he realizes he needs to remove 3 bags of soil to adjust the garden's height. Calculate the total weight of the soil remaining in pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "225",
"style": "rule"
}
|
numina_math
|
{
"index": 9902,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Express the fraction \\(\\frac{0.75}{0.125}\\) as a decimal. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6.0",
"style": "rule"
}
|
numina_math
|
{
"index": 9903,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a science experiment, the temperature of a substance is measured at different times. The relationship between the temperature \\( T \\) (in degrees Celsius) and the time \\( t \\) (in minutes) is given by the linear equation \\( T = 3t + 5 \\). If the temperature of the substance is measured to be 35 degrees Celsius, how many minutes have passed since the start of the experiment? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 9904,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A water tank is being filled with water from two hoses. Hose A can fill the tank in 3 hours, while Hose B can fill it in 6 hours. If both hoses are used together, how long will it take to fill 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": 9905,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex works at a factory where he earns $20 per hour. For any hours worked beyond 40 hours in a week, he earns overtime pay at a rate of 1.5 times his regular hourly wage. If Alex worked 50 hours in one week, how much total pay did he earn for that week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1100",
"style": "rule"
}
|
numina_math
|
{
"index": 9906,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "An aunt lives on the seventh floor of her building. It takes her 45 seconds to go from one floor to the next. How many minutes does it take her to go from the first floor to her home on the seventh floor? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.5",
"style": "rule"
}
|
numina_math
|
{
"index": 9907,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company has a total budget of $2400 to allocate for purchasing new office chairs and desks. Each chair costs $80 and each desk costs $120. If the company buys only chairs or only desks, how many ways can the budget be fully utilized? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 9908,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is making gift baskets for a charity event. Each basket contains 4 units of chocolate, 3 units of cookies, and 2 units of tea. The unit costs are $1.50 for chocolate, $2.00 for cookies, and $3.00 for tea. How much does it cost to create 10 gift baskets? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180.00",
"style": "rule"
}
|
numina_math
|
{
"index": 9909,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company produces a blend of two ingredients, A and B, where the cost of ingredient A is $5 per unit and the cost of ingredient B is $10 per unit. The total cost of the blend should not exceed $100. If the company decides to use twice as many units of ingredient A as ingredient B, how many units of each ingredient should they use to minimize the cost while staying within the budget constraints? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 9910,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A flower garden has a total of 105 flowers of various colors. The number of red flowers is twice the number of orange flowers. There are five fewer yellow flowers than red flowers. If there are 10 orange flowers, how many pink and purple flowers are there if they have the same amount and there are no other colors? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 9911,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A real estate agent sold a house for $300,000. She earned a 5% commission on the sale. After the sale, she invested her commission in a project that promised a 10% return on investment within a year. What was her total earnings from the commission and the investment return after one year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16500",
"style": "rule"
}
|
numina_math
|
{
"index": 9912,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is saving for a new computer that costs $1200. She has already saved 45% of the total amount. If she plans to save an additional $100 each month, how many more months will it take for her to have enough money to buy the computer? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 9913,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha bought a large pizza and cut it into 12 equal slices. She ate 3 slices and gave 4 slices to her friends. Later, she decided to cut the remaining pizza into smaller slices, each being half the size of the original slices. How many smaller slices did Samantha end up with? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 9914,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many different four-digit numbers can be formed using the digits 2, 3, 4, and 5, if the first digit must be 2 and no digit can be repeated? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 9915,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lucille is wondering who has the tallest house between her and her neighbors. Her family's house is 80 feet tall. One neighbor's house is 70 feet tall. Another neighbor's house is 99 feet tall. How much shorter is Lucille's house than the average height? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 9916,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria has a goal to read a certain number of pages each day for a month to prepare for her exams. She decides to read 15 pages every day. If the month has 30 days, how many pages will Maria have read by the end of the month? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "450",
"style": "rule"
}
|
numina_math
|
{
"index": 9917,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a road trip. She drives at a constant speed of 60 miles per hour. She plans to drive for 3 hours in the morning, take a 1-hour lunch break, then continue driving for another 4 hours. However, during the second part of her trip, she has to reduce her speed by 10 miles per hour for 2 hours due to road construction. How many total miles does she drive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "400",
"style": "rule"
}
|
numina_math
|
{
"index": 9918,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is offering a discount on a rectangular table that originally costs $500. The store applies a discount of 20%, and then an additional discount of 10% on the reduced price. If the perimeter of the table is 20 feet and the length of the table is twice its width, what is the final price of the table after both discounts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "360",
"style": "rule"
}
|
numina_math
|
{
"index": 9919,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "An equilateral triangle has sides each of length \\(3x\\) cm. If the perimeter of the triangle is \\(54\\) cm, what is the value of \\(x\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 9920,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "For how many positive integers \\( n \\) does the sum of the squares of the first \\( n \\) positive integers \\( 1^2 + 2^2 + \\cdots + n^2 \\) evenly divide \\( 3n^2 \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 9921,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The function \\( g(x) \\) satisfies \\( g(x+y) = g(x) + g(y) \\) for all real numbers \\( x \\) and \\( y \\). If \\( g(3) = 7 \\) and \\( g(5) = 11 \\), find \\( g(8) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 9922,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A circular garden has a circumference of 132 meters. If 1/4 of the circumference is to be decorated with lights, how many 0.5-meter long light strips are needed to cover this section? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "66",
"style": "rule"
}
|
numina_math
|
{
"index": 9923,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the smallest positive integer \\( n \\) such that \\( n \\) is divisible by 6 and the sum of the digits of \\( n \\) is divisible by 9. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 9924,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine the smallest positive integer \\( y \\) such that the product \\( 7! \\times y \\) is divisible by \\( 15^3 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 9925,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence defined by \\( a_n = 3n + 2 \\) for \\( n \\geq 1 \\). Find the sum of the first 10 terms of this sequence. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "185",
"style": "rule"
}
|
numina_math
|
{
"index": 9926,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A school plans a field trip and needs to arrange transportation using vans. Each van can carry a maximum of 12 students. If there are 150 students going on the trip, and the school wants to ensure that each van is filled to its maximum capacity whenever possible, how many vans will the school need to arrange? Additionally, how many students will be in the van that isn't full? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 9927,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 3/4 cup of sugar. If Lana is making a batch that is 3 times the original recipe and she only has 2 cups of sugar available, how much more sugar does she need to make the batch? 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": 9928,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In how many ways can 8 distinct people be arranged in a row if three specific people (let's call them A, B, and C) must always stand together? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4320",
"style": "rule"
}
|
numina_math
|
{
"index": 9929,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(x\\) and \\(y\\) be real numbers such that \\(x + y = 10\\). Find the minimum value of \\(|x - y|\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 9930,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice earns $15 per hour and works 40 hours a week. Bob earns a fixed salary of $600 per week. Calculate the difference in their monthly earnings, assuming a month has 4 weeks. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 9931,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells cookies in packs of 8 for $3 per pack. If a customer buys 5 packs of cookies, how much will the total cost be? Additionally, if the customer decides to buy 3 more individual cookies at $0.50 each, what will the new total cost be? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16.50",
"style": "rule"
}
|
numina_math
|
{
"index": 9932,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mark has twice as many apples as Tom and Tom has 15 apples. If Lucy has 5 more apples than Mark, how many apples do they have in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 9933,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x) = \\sqrt[3]{x + 2} \\). Find \\( f^{-1}(8) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "510",
"style": "rule"
}
|
numina_math
|
{
"index": 9934,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Suppose that the variable $x$ is inversely proportional to the variable $y$. Furthermore, consider an ellipse with foci at $(0, 0)$ and $(6, 0)$ and a major axis length of 10. If $x = 8$ when $y = 3$, find the distance between the center of the ellipse and the point where the circle, centered at $(3, 0)$ and passing through $(6, 4)$, intersects the ellipse's major axis. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 9935,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has 134 pieces of candy and wants to distribute them equally among her 5 friends. After giving each friend an equal amount of candy, how many pieces of candy does she have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 9936,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A number \\( N \\) in the form of \\( \\overline{567A8} \\) is divisible by 9. What is the missing digit \\( A \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 9937,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a factory produces 120 gadgets in 4 hours, how many gadgets will it produce in 10 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 9938,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 3/4 cup of sugar for each cake. If you have 6 cups of sugar, how many cakes can you make? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 9939,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah works 40 hours a week at her job and is paid $20 per hour. She is subject to a 15% tax on her earnings. How much money does Sarah take home in a month (4 weeks) after taxes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2720",
"style": "rule"
}
|
numina_math
|
{
"index": 9940,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there are 150 students in Grade 7 and 130 students in Grade 8. During a school event, 40 students from Grade 7 and 50 students from Grade 8 were absent. How many students were present at the event? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "190",
"style": "rule"
}
|
numina_math
|
{
"index": 9941,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A right triangle has legs of lengths 9 cm and 12 cm. What is the length of the hypotenuse? Express your answer in simplest radical form. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 9942,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Three friends, Alex, Ben, and Charlie, decide to split the cost of a dinner equally. The total bill, including tax and tip, comes to $144. If each friend pays the same amount, how much does each friend pay? Additionally, if Ben had a coupon that reduced his share by $12, how much does he end up paying? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 9943,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The first term of a geometric sequence is 2, and the sum of the first four terms is 30. Find the common ratio \\( r \\) of this sequence. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 9944,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sam has $60 and decides to buy some books. Each book costs $8. After buying the books, he still has $20 left. How many books did Sam buy? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 9945,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Divide the polynomial $3x^3 - 5x^2 + 2x - 7$ by $x - 2$ and use the Remainder Theorem to verify the remainder. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 9946,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is collecting stamps. She started with 15 stamps in her collection. Each month, she adds 7 new stamps to her collection. After 4 months, she decided to give 5 stamps to her friend. How many stamps does Emily 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": 9947,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the remainder when 435 is divided by 23? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "21",
"style": "rule"
}
|
numina_math
|
{
"index": 9948,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah wants to buy a new laptop that costs $899.99. She has saved $350.75 and she decides to save an additional $50 every week. How many weeks will it take Sarah 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": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 9949,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A construction company needs to purchase cement for a large project. They need 50 bags of cement for each of the 8 buildings they are constructing. Each bag of cement weighs 40 kilograms. How many kilograms of cement do they need in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16000",
"style": "rule"
}
|
numina_math
|
{
"index": 9950,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "An investor bought a stock priced at $\\$144$ per share. Over a year, the stock price increased by $15\\%$. After this increase, the investor bought 20 more shares. What is the total value of the investor's stock holdings now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3312",
"style": "rule"
}
|
numina_math
|
{
"index": 9951,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Julia has baked 50 cookies and wants to package them into boxes that can hold 8 cookies each. After filling as many boxes as possible, how many cookies will Julia have left over? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 9952,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a math class, the teacher decides to give a surprise quiz. The quiz consists of 5 questions, each worth 2 points. If a student answers a question correctly, they receive 2 points. If a student answers a question incorrectly, they receive 0 points. After the quiz, the teacher decides to calculate the class average score and the probability of a student scoring exactly 6 points. There are 10 students in the class, and their scores are as follows: 10, 8, 6, 6, 4, 4, 4, 2, 2, and 0. What is the class average score, and what is the probability of a student scoring exactly 6 points? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.2",
"style": "rule"
}
|
numina_math
|
{
"index": 9953,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenna has a jar with 100 coins. She spent $3.50 on a book, which she paid with coins. If each coin is worth $0.25, how many coins does she have left in the jar? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "86",
"style": "rule"
}
|
numina_math
|
{
"index": 9954,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that \\( x \\equiv 7 \\pmod{13} \\) and \\( y \\equiv 5 \\pmod{13} \\), find the value of \\( z \\) in the range \\( 0 \\le z < 13 \\) such that \\( xy \\equiv z \\pmod{13} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 9955,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a car's fuel efficiency is directly proportional to the speed at which it travels, and it gets 30 miles per gallon (mpg) at 50 miles per hour (mph), how many miles per gallon will it get at 60 mph? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 9956,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria takes a trip to visit her friend. She drives to her friend's house at an average speed of 60 miles per hour. On her way back, she drives at an average speed of 40 miles per hour due to traffic. If the total time for the round trip is 5 hours, what is the distance between Maria's house and her friend's house? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 9957,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many perfect squares are there between 1 and 10,000 that are also even numbers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 9958,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation \\( \\sqrt[3]{x} + \\sqrt{x} = 10 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 9959,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Li Ming is reading a book. On the first day, he read 72 pages, and on the second day, he read 88 pages. The total number of pages he read in the two days is exactly 40% of the total number of pages in the book. How many pages are there in total in the book? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "400",
"style": "rule"
}
|
numina_math
|
{
"index": 9960,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Ella wants to save money to buy a new bicycle that costs $240. She currently has $60. To save the remaining amount, she decides to save a fixed amount of money each week. If she wants to buy the bicycle in 10 weeks, how much should she save per week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 9961,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A fruit store received a shipment of fruits. The weight of the apples is 132 kilograms, which is 5/11 of the weight of the pears. The weight of the bananas is 5/6 of the weight of the pears. How many kilograms of bananas were received? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "242",
"style": "rule"
}
|
numina_math
|
{
"index": 9962,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a sequence of five consecutive numbers, the sum of the first two numbers is 23. What is the sum of all five numbers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "65",
"style": "rule"
}
|
numina_math
|
{
"index": 9963,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that the polynomial \\( P(x) = x^4 + 2x^3 + 5x^2 + 8x + 10 \\) has roots \\( \\alpha, \\beta, \\gamma, \\delta \\), and it is known that \\(\\alpha\\) and \\(\\beta\\) are complex conjugates, and \\(\\gamma\\) and \\(\\delta\\) are also complex conjugates. Determine the value of \\(\\alpha + \\beta\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-1",
"style": "rule"
}
|
numina_math
|
{
"index": 9964,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a monthly budget of $2000. She decides to allocate 30% of her budget to rent, 20% to groceries, 15% to transportation, and the remaining amount to savings. How much money does Sarah allocate to savings each month? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "700",
"style": "rule"
}
|
numina_math
|
{
"index": 9965,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that the degree measure of the sum of the interior angles of a convex polygon with $n$ sides is 1800 degrees, and knowing the relationship between the number of sides and the sum of interior angles for any convex polygon, determine the degree measure of the sum of the interior angles of a convex polygon with $n + 2$ sides. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2160",
"style": "rule"
}
|
numina_math
|
{
"index": 9966,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels at a constant speed of 15 miles per hour. If the cyclist starts riding at 8:00 AM and takes a 20-minute break every 2 hours, how many miles will the cyclist have covered by 2:00 PM, including the time spent on breaks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 9967,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah's initial savings account balance was $500. Over the first year, it increased by 12%. She then deposited an additional $150 into her account. During the second year, the total amount in her account increased by 8%. What is her final account balance at the end of the second year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "766.8",
"style": "rule"
}
|
numina_math
|
{
"index": 9968,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa is organizing a school event and bought 4 packs of balloons. Each pack contains 20 balloons. Before the event, 10 balloons burst. During the event, 35 balloons were used. How many balloons are left unused after the event? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35",
"style": "rule"
}
|
numina_math
|
{
"index": 9969,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The function \\( f(x) = 2x + 3 \\) represents the relationship between \\( x \\) and \\( f(x) \\). If \\( f(x) = 11 \\), solve for \\( x \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 9970,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A project requires a team to complete a task. If 5 workers can complete the task in 12 days, how many days will it take for 8 workers to complete the same task, assuming they all work at the same rate? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7.5",
"style": "rule"
}
|
numina_math
|
{
"index": 9971,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells cookies in boxes of different sizes. Each small box contains 4 cookies, and each large box contains 10 cookies. If a customer buys a total of 9 boxes and receives 68 cookies, how many small boxes and how many large boxes did the customer buy? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 9972,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Square $ABCD$ has side length $1$ unit. Points $E$ and $F$ are on sides $AB$ and $CB$, respectively, such that $AE = CF$. When the square is folded along the lines $DE$ and $DF$, sides $AD$ and $CD$ coincide and lie on diagonal $BD$. The length of segment $AE$ can be expressed in the form $\\sqrt{k}-m$ units. What is the integer value of $k+m$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 9973,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farm has a total of 120 acres of land. The land is divided into three parts. One-third of the land is used for growing corn, one-fourth of the remaining land is used for growing wheat, and the rest is used for growing soybeans. How many acres of land are used for growing soybeans? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 9974,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Julia has 600 books in her library. She decides to donate half of them to a local school. Then, she gives 30% of the remaining books to her friends. How many books does Julia have left in her library? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "210",
"style": "rule"
}
|
numina_math
|
{
"index": 9975,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Liam is a construction worker who works different hours on weekdays and weekends. On weekdays, he works 8 hours per day, and on weekends, he works 5 hours per day. If Liam works this schedule for 3 weeks, how many total hours does he work in those 3 weeks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 9976,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is buying eggs for a large family brunch. She needs to buy 10 dozen eggs. The price for a dozen eggs at Store A is $3.50, while Store B sells eggs individually for $0.30 each. How much money will Emily save by buying from Store A instead of Store B? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 9977,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Factor and simplify the expression: $4x^2 - 12x + 9 - (2x - 3)^2$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 9978,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells 3 dozen cookies for $15.00. At this rate, how much would 5 dozen cookies cost? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25.00",
"style": "rule"
}
|
numina_math
|
{
"index": 9979,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria wants to buy a new rug for her living room. She finds a rectangular rug that is 8 feet long and 5 feet wide. However, the store is having a 20% discount on all rugs. If the original price of the rug is $200, what is the discounted price of the rug, and what is the area of the rug in square feet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "160",
"style": "rule"
}
|
numina_math
|
{
"index": 9980,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(x, y, z\\) be positive real numbers such that \\(x + y + z = 1\\). Find the minimum value of\n\\[\n\\frac{1}{x} + \\frac{1}{y} + \\frac{1}{z}.\n\\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 9981,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jessica went shopping and bought 3 shirts, each costing $20. She also bought 2 pairs of jeans, each costing $35. The store offered a discount of $15 on her total bill. How much did Jessica spend altogether after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "115",
"style": "rule"
}
|
numina_math
|
{
"index": 9982,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 1500 widgets in 8 hours. If the production rate remains consistent, how many widgets will the factory produce in 10 hours? Additionally, if the factory decides to increase its production by 20% for the next 10 hours, how many widgets will be produced in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2250",
"style": "rule"
}
|
numina_math
|
{
"index": 9983,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has 3 fields. In the first field, he grows 1/2 of his total corn. In the second field, he grows 1/3 of his total corn. The rest of the corn is grown in the third field. If he has 240 bushels of corn in total, how many bushels of corn does he grow in each field? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 9984,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John received a $100 bill for his birthday. He decided to spend it on a few items: a $35 toy, a $22 book, and a $15 meal. After purchasing these items, he also gave $10 to charity. How much money does John 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": 9985,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A classroom has a total of 45 students. Each student receives 3 notebooks. If there are a total of 150 notebooks available, how many students will not receive notebooks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 9986,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The measure of one of two complementary angles is 5 less than three times the measure of the other angle. What are the measures of the two angles? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "66.25",
"style": "rule"
}
|
numina_math
|
{
"index": 9987,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A truck driver needs to transport goods from City A to City B. The total distance between the cities is 300 kilometers. The truck travels at a constant speed of 60 kilometers per hour. The weight of the goods is in the ratio of 4:5 for fragile items to non-fragile items. If the total weight of the goods is 900 kilograms, how long will it take for the truck to transport the goods from City A to City B? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 9988,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A delivery truck travels from City A to City B, a total distance of 360 kilometers. The truck drives at a constant speed of 60 kilometers per hour. After delivering goods in City B, the truck returns to City A at a speed of 45 kilometers per hour. How many hours does the entire round trip take? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 9989,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a resource management simulation, there are 7 types of resources needed to build a space station. Each type of resource has a different number of units available: Resource A (10 units), Resource B (8 units), Resource C (6 units), Resource D (5 units), Resource E (3 units), Resource F (2 units), and Resource G (1 unit). You need exactly 12 units to complete the space station. How many different combinations of resources can be selected to total exactly 12 units? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17",
"style": "rule"
}
|
numina_math
|
{
"index": 9990,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school cafeteria, 3/5 of the students chose pizza for lunch, and the rest chose pasta. If there are 450 students in total, how many more students chose pizza than pasta? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 9991,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In 15 years, Kate will be 5 times as old as she was 10 years ago. How old is Kate now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16.25",
"style": "rule"
}
|
numina_math
|
{
"index": 9992,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A sequence of integers starts with 5 and follows the rule that each subsequent number is obtained by adding 7 to the previous number. If the 10th term in the sequence is subtracted from the 15th term, what is the result? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35",
"style": "rule"
}
|
numina_math
|
{
"index": 9993,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation \\( \\sqrt{5x - 4} + 3 = 7 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 9994,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe for making 1 cake requires 3 cups of sugar and 4 cups of flour. If you have 12 cups of sugar, how many cakes can you make, and how much flour will you need in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 9995,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Ella wants to buy a new laptop that originally costs $1200. The store offers a 15% discount on all electronics. Additionally, there is a special promotional discount of 5% off the already discounted price for purchases made on weekends. How much will Ella pay for the laptop if she buys it on a Saturday? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "969",
"style": "rule"
}
|
numina_math
|
{
"index": 9996,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Factor the expression \\( 4x^3 + 8x^2 - 12x \\) and then evaluate it at \\( x = 2 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 9997,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\): \\( 3^{2x} = 27^{x+1} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-3",
"style": "rule"
}
|
numina_math
|
{
"index": 9998,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a small bakery, there are 3 types of cakes (chocolate, vanilla, and strawberry) and 4 types of drinks (coffee, tea, juice, and milk). If a customer wants to buy one type of cake and one type of drink, how many different combinations can the customer choose from? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 9999,
"name": "numina_math",
"split": "train"
}
|
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