prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "A store is having a sale where all items are discounted by 25%. If a customer buys an item originally priced at $80 and another item originally priced at $120, how much does the customer pay in total after the discount is applied? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 2400,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sally has a collection of nickels and dimes worth $2.20. She has 5 more nickels than dimes. How many of each coin does she have?\n\n### Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 2401,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is shopping for groceries. She buys 3 bags of apples, each containing 6 apples, and 4 bags of oranges, each containing 8 oranges. If the cost of each apple is $0.50 and the cost of each orange is $0.75, and she has a coupon that gives her a 10% discount on the total cost, what is the final amount Sarah has to pay? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "29.7",
"style": "rule"
}
|
numina_math
|
{
"index": 2402,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A class of 20 students took a math test. The class is divided into two groups: Group A with 12 students and Group B with 8 students. The average score of Group A was 75, and the average score of Group B was 85. What was the average score of the entire class? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "79",
"style": "rule"
}
|
numina_math
|
{
"index": 2403,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the polynomial expression and determine the degree of the resulting polynomial: \\( (3x^2 - 4x + 5) \\cdot (x - 2) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2404,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A 5-meter long wire weighs approximately 250 grams. If you have a wire of the same type that weighs 2000 grams, how long is the wire? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2405,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a survey, 5 students were asked how many hours they spent studying last week. Their responses were 10, 12, 14, 16, and 18 hours. After analyzing the data, it was found that the average (arithmetic mean) number of hours spent studying by these students is 2 hours more than the average number of hours spent by another group of 5 students. What is the total number of hours spent studying by the students in the second group? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 2406,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at an average speed of 60 miles per hour on a highway. Another car, which travels on the same highway, takes 1.5 hours less to cover the same distance at an average speed of 80 miles per hour. How far is the distance they both cover? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "360",
"style": "rule"
}
|
numina_math
|
{
"index": 2407,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Suppose that \\(x\\) and \\(y\\) are nonzero real numbers such that \\(\\frac{5x + y}{x - 4y} = -1\\). What is the value of \\(\\frac{x + 3y}{3x - y}\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2408,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Last year, Maria's grocery bill was $200 per month. This year, due to inflation, her grocery bill increased by 15%. To manage the increased cost, she decided to reduce her other monthly expenses by $30. What is Maria's total monthly expense this year if her other expenses last year were $300 per month? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "500",
"style": "rule"
}
|
numina_math
|
{
"index": 2409,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a library, the ratio of fiction books to non-fiction books is 4:7. If there are 180 more non-fiction books than fiction books, how many fiction books are there in the library? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "240",
"style": "rule"
}
|
numina_math
|
{
"index": 2410,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a certain country store, there are three kinds of bottled drinks. A cola, which costs $3, a juice for $1.5, and water for $1 per bottle. One day the store was able to sell 18 bottles of cola, 30 bottles of water, and 15 bottles of juice. How much did the shop earn? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "106.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2411,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence defined by \\( a_n = n^2 + 2n + 1 \\) for \\( n \\) ranging from 1 to 10. Calculate the sum of the terms in this sequence and simplify your answer. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "505",
"style": "rule"
}
|
numina_math
|
{
"index": 2412,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a math competition, there are three groups of participants. The number of participants in the first group is three times the number of participants in the second group. The number of participants in the second group is five more than half the number of participants in the third group. If the third group has 40 participants, how many participants are there in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "140",
"style": "rule"
}
|
numina_math
|
{
"index": 2413,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a farm, there are two types of animals: chickens and cows. The total number of legs of all the animals is 50 more than twice the number of heads. If each chicken has 2 legs and each cow has 4 legs, and the total number of animals is 25, how many cows are there? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 2414,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is planning her monthly budget. She spends 30% of her income on rent, 20% on groceries, 10% on transportation, 15% on savings, and the remaining $600 on other expenses. If Emily's total income is $x, find the value of $x. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2400",
"style": "rule"
}
|
numina_math
|
{
"index": 2415,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A line passes through the points \\((2, 3)\\) and \\((4, 7)\\). Find the equation of the line in slope-intercept form and determine the y-intercept. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-1",
"style": "rule"
}
|
numina_math
|
{
"index": 2416,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist rides a bike at a speed of 12 miles per hour. He plans a trip where he will ride for 3/4 of an hour at this speed. After that, he will ride for 2/3 of the distance he covered in the first part of his trip but at a speed of 9 miles per hour. How far will he ride in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 2417,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A local charity is organizing a fundraising event. They aim to collect 25% of their $20,000 goal from ticket sales and the rest from donations. If each ticket costs $50, how many tickets do they need to sell to meet their target from ticket sales, and how much money do they still need to raise from donations? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15,000",
"style": "rule"
}
|
numina_math
|
{
"index": 2418,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A school is organizing a field trip to a science museum. There are 15 students and 5 teachers attending the trip. If student tickets cost $2 each and teacher tickets cost $4 each, how much will the total cost of the museum tickets be? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 2419,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Kevin is planning to host a barbecue party and needs to buy meat and drinks for his guests. He buys 15 pounds of chicken at $4 per pound, 10 pounds of beef at $5 per pound, and 8 cases of soda at $12 per case. If he wants to split the total cost equally among his 8 friends, how much does each friend need to pay? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25.75",
"style": "rule"
}
|
numina_math
|
{
"index": 2420,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine the domain of the real-valued function \\( f(x) = \\sqrt{7 - \\sqrt{12 - \\sqrt{4x + 1}}} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "[-\\frac{1}{4},\\frac{143}{4}]",
"style": "rule"
}
|
numina_math
|
{
"index": 2421,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A concert ticket costs $45.50. After a 10% discount, how much will four tickets cost? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "163.8",
"style": "rule"
}
|
numina_math
|
{
"index": 2422,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Ethan is playing a game where he gains points for achievements and loses points for mistakes. He gains 10 points for each achievement and loses 5 points for each mistake. If Ethan has 8 achievements and 6 mistakes, how many points does he have in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 2423,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Subtract 0.75 from 1, then add the result to the sum of \\(\\frac{3}{5}\\) and \\(\\frac{7}{10}\\). What is the final result? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.55",
"style": "rule"
}
|
numina_math
|
{
"index": 2424,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is training for a marathon. She initially runs at a speed of 6 miles per hour for 4 hours. Over time, she increases her speed by 50% and her running duration by 25%. How far can she run now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 2425,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Chad sandwiches 2 crackers with a scoop of peanut butter. He has 5 of these cracker sandwiches every night before bed. A box of crackers has 4 sleeves, with each sleeve holding 28 crackers. How many nights will 5 boxes of crackers last him? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "56",
"style": "rule"
}
|
numina_math
|
{
"index": 2426,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden is 20 meters long and 15 meters wide. The garden owner wants to plant a border of flowers around the perimeter of the garden, leaving a 1-meter-wide walkway inside the border. What is the area of the walkway? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 2427,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a right triangle, one of the legs has a length of 7 units and the hypotenuse has a length of 25 units. Find the length of the other leg. If the length of the other leg is an integer, verify that it satisfies the Pythagorean theorem. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 2428,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The center of a circle is at the origin \\((0, 0)\\) and it passes through the point \\((6, 8)\\). Calculate the circumference of the circle. What is the sum of the coordinates of the center of the circle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2429,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation \\( \\log_2(8) = x \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2430,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial functions \\( P(x) = x^3 + 2x^2 - x + 5 \\) and \\( Q(x) = 2x^2 - 3x + 4 \\), find the degree of the polynomial \\( P(x) \\cdot Q(x) \\). Simplify the resulting polynomial and identify the leading coefficient of the term with the highest degree. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2431,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A certain bacteria culture grows exponentially. Initially, there are 500 bacteria. The number of bacteria doubles every 3 hours. How many bacteria will there be after 12 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8000",
"style": "rule"
}
|
numina_math
|
{
"index": 2432,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Julia is comparing the total weight of two boxes. Box A contains 4 bags, each weighing 7 pounds. Box B contains 3 bags, each weighing 9 pounds. Which box is heavier, and by how many pounds? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2433,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The vertex form of a parabola is given by \\( y = a(x - h)^2 + k \\). Convert the quadratic function \\( y = 2x^2 - 4x + 3 \\) into its vertex form and identify the vertex. Then, determine the value of \\( y \\) when \\( x = \\frac{7}{2} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{27}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2434,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company produces gadgets, and each gadget requires 3 hours of labor. Each hour of labor costs $15. If the company produces 200 gadgets in a month, what is the total labor cost? If the company decides to increase production by 50% the next month, what will be the new total labor cost? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13500",
"style": "rule"
}
|
numina_math
|
{
"index": 2435,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, 3/5 of the students are boys and the rest are girls. If there are 18 more boys than girls, how many students are there in total in the classroom? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "90",
"style": "rule"
}
|
numina_math
|
{
"index": 2436,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a part-time job where she works 6 hours every weekday (Monday through Friday). On weekends, she works twice as many hours each day as she does on a weekday. How many hours does Sarah work in total over a week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "54",
"style": "rule"
}
|
numina_math
|
{
"index": 2437,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The local library held a book fair where they sold 12 more than twice the number of mystery novels as they did science fiction novels. If the library sold 20 science fiction novels, how many mystery novels did they sell? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "52",
"style": "rule"
}
|
numina_math
|
{
"index": 2438,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A product initially costs $200. The price is first increased by 15%, and then the new price is decreased by 20%. What is the final price of the product? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "184",
"style": "rule"
}
|
numina_math
|
{
"index": 2439,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a wildlife reserve, a researcher is tracking the frequency of certain bird species. She counts 45 sparrows, 30 robins, and 25 blue jays in the first hour. In the second hour, she counts 40 sparrows, 35 robins, and 30 blue jays. In the third hour, she counts 50 sparrows, 25 robins, and 20 blue jays. What is the total number of birds counted by the researcher in the three hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 2440,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells cupcakes at $2.50 each. They bake 120 cupcakes every day. If they sell all the cupcakes for 5 days, how much revenue will they generate in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1500",
"style": "rule"
}
|
numina_math
|
{
"index": 2441,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A scientist is studying the behavior of a certain chemical reaction. The reaction starts at a temperature of 20°C and increases by 5°C every hour. After how many hours will the temperature of the reaction reach 65°C? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2442,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maya has a budget of $50 to spend on groceries. She buys a pack of rice for $12.50, a pack of beans for $8.75, and a carton of milk for $3.50. After buying these items, she decides to buy apples that cost $0.75 each. How many apples can she buy with the remaining budget? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33",
"style": "rule"
}
|
numina_math
|
{
"index": 2443,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the sum of the cube roots of two integers, \\(a\\) and \\(b\\), is equal to 9, and one of the integers is 8, what is the other integer? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "343",
"style": "rule"
}
|
numina_math
|
{
"index": 2444,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells a piece of cake for $2.50, a cookie for $1.25, and a muffin for $3.75. If a customer buys 3 pieces of cake, 4 cookies, and 2 muffins, what is the total cost of their purchase? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 2445,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a speed of 55 miles per hour. How far will the car travel in 3 hours and 45 minutes? Convert your answer to kilometers. (Use the conversion factor: 1 mile ≈ 1.60934 kilometers) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "332.51",
"style": "rule"
}
|
numina_math
|
{
"index": 2446,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The sum of the first \\( n \\) terms of an arithmetic sequence is given by \\( S_n = \\frac{n}{2} \\left(2a + (n-1)d\\right) \\), where \\( a \\) is the first term and \\( d \\) is the common difference. If the sum of the first 5 terms is 60 and the common difference \\( d \\) is 4, find the first term \\( a \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2447,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jessica went to a store to buy a dress originally priced at $120. The store was offering a 25% discount on all items. After the discount, Jessica had to pay an additional 10% sales tax on the discounted price. How much did Jessica pay in total for the dress? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "99",
"style": "rule"
}
|
numina_math
|
{
"index": 2448,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jane is currently 3 times as old as her younger brother, Bob. Four years ago, the absolute value of the difference between their ages was 15 years. How old is each of them now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2449,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The ratio of number A to number B is 4:5. If the sum of A and B is 180, find the values of A and B. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 2450,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sophia is organizing a fundraising event where each ticket costs $15. She sells 120 tickets. The total cost to organize the event is $800. If she wants to divide the remaining profit equally among 5 local charities, how much money will each charity receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "200",
"style": "rule"
}
|
numina_math
|
{
"index": 2451,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah and Tom are sharing candies in the ratio 3:5. If Tom received 20 more candies than Sarah, how many candies did they share 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": 2452,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A class of 25 students decided to buy a gift for their teacher. They collected $3.50 from each student. However, due to some students being absent, they only managed to collect $70. How many students were absent on the day the collection was made? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2453,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "James has 3 more than 2 times the number of Oreos that Jordan has. If there are 36 Oreos in total, how many Oreos does Jordan have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 2454,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation: $\\log_{2}(8x) = 5 - \\log_{2}(4)$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2455,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a gardener spends 15 minutes watering each plant, how many plants can he water in 4 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 2456,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a family, Jenny is 5 years older than her brother Sam. Sam is 3 years younger than their sister Emma. If Emma is 14 years old, how old is Jenny? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 2457,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah decided to bake cookies for a bake sale. She bought 3 packs of butter at $4 each and 5 packs of sugar at $3 each. If she started with $50, how much money does she have left after buying the ingredients? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "23",
"style": "rule"
}
|
numina_math
|
{
"index": 2458,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given a right triangle \\( \\triangle ABC \\) with \\( \\angle C = 90^\\circ \\). The lengths of legs \\( AC \\) and \\( BC \\) are 6 units and 8 units, respectively. Calculate the area of \\( \\triangle ABC \\). Then, using trigonometric relationships, find the length of the altitude from \\( C \\) to hypotenuse \\( AB \\). Express your answer as a decimal to the nearest tenth.\n\n### Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.8",
"style": "rule"
}
|
numina_math
|
{
"index": 2459,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the expression: \\( \\frac{2^5 + 2^3}{2^2} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2460,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily's car can travel 300 miles on a full tank of gas. If she uses 60% of the tank on a road trip and the remaining gas for her daily commute, how many miles can she travel with the remaining gas? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2461,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the area of the triangle formed by the intersection of the parabola \\( y = x^2 \\) and the line \\( y = x + 2 \\), and the y-axis. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2462,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A certain arithmetic sequence starts with the term \\( a = 5 \\). Each subsequent term in the sequence is obtained by adding a constant value \\( d = 3 \\). Find the sum of the first 20 terms of this sequence. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "670",
"style": "rule"
}
|
numina_math
|
{
"index": 2463,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Ali, Bonnie, Carlo, and Dianna are going to drive together to a nearby theme park. The car they are using has 4 seats: 1 Driver seat, 1 front passenger seat, and 2 back passenger seats. Only Bonnie and Carlo are capable of driving the car. How many possible seating arrangements are there? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2464,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A restaurant offers a special combo meal where customers can choose one main dish, one side dish, and one drink. There are 4 main dishes, 5 side dishes, and 3 drinks available. How many different combo meals can a customer create? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 2465,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation \\( x^2 - 6x + 5 = 0 \\) by completing the square. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2466,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jessica has $2500 in her savings account. She plans to buy a new laptop that costs $900. After purchasing the laptop, she wants to save an additional $200 each month. How many months will it take Jessica to have $5000 in her savings account again? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 2467,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A fruit vendor sells apples in packs. He sells 60% of his apples in the morning and 1/3 of the remaining apples in the afternoon. If he has 160 apples left after the afternoon sale, how many apples did he start with? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 2468,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the smallest prime number \\( p \\) such that there exists an integer \\( x \\) which satisfies the congruence \\( 2x \\equiv 5 \\pmod{p} \\), and \\( p \\) is also a divisor of 391. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17",
"style": "rule"
}
|
numina_math
|
{
"index": 2469,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa has a collection of 15 marbles. Her friend gives her 7 more marbles. Lisa then decides to give 5 marbles to her younger brother. How many marbles does Lisa have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17",
"style": "rule"
}
|
numina_math
|
{
"index": 2470,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells muffins in two different packages. A small package contains 4 muffins and costs $5, while a large package contains 10 muffins and costs $11. If a customer has $30 to spend and wants to buy a total of 24 muffins, how many of each type of package should they buy to use all their money exactly? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2471,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The function \\( f(x) = 3x + 5 \\) has an inverse function \\( f^{-1}(x) \\). If the output of the inverse function is 7, what was the original input to the function \\( f(x) \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{2}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 2472,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation \\( \\frac{2x + 3}{5} - \\frac{x - 2}{10} = 2 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2473,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Piper is planning a road trip where she will drive at a consistent speed of 60 miles per hour. She intends to cover a total distance of 360 miles. If she plans to make stops every 90 miles, how many stops will she make during her trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2474,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A baker has 60 cupcakes and wants to divide them equally into boxes. Each box should contain a fractional number of cupcakes, specifically \\(\\frac{3}{2}\\) cupcakes per box. How many boxes does the baker need to use? Additionally, if each box costs $0.50, what is the total cost for all the boxes used? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 2475,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, the student population has increased by 20% over the last year. If the student population last year was 450 students, how many students are there this year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "540",
"style": "rule"
}
|
numina_math
|
{
"index": 2476,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A certain recipe requires \\(\\frac{2}{3}\\) cup of sugar per serving. If you are preparing the recipe for 9 servings, how many cups of sugar will you need in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2477,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A salesman travels for 6 hours at an average speed of 45 miles per hour. If he wants to increase his total distance traveled by 20% in the same amount of time, what should be his new average speed in miles per hour? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "54",
"style": "rule"
}
|
numina_math
|
{
"index": 2478,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Expand the polynomial \\((x + 2y)^5\\) using the Binomial Theorem and determine the coefficient of the term \\(x^3 y^2\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2479,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sophia and her younger brother Leo are measuring the length of a room using a measuring tape. The length of the room is 30 feet more than twice the width. If the width of the room is 15 feet, what is the length of the room? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 2480,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom is currently three times as old as Jerry. Five years ago, Tom was four times as old as Jerry was at that time. How old is Tom now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 2481,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression \\( 5 \\times (7 + 3) - 4 \\times (9 - 2) \\) using the distributive property and basic arithmetic operations. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22",
"style": "rule"
}
|
numina_math
|
{
"index": 2482,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the smallest positive integer \\( n \\) such that the sum of its digits is divisible by 9, and \\( n \\) is also divisible by 12. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 2483,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a speed of 60 miles per hour on the highway, 45 miles per hour on local roads, and 30 miles per hour in city traffic. If the car spends 2 hours on the highway, 1.5 hours on local roads, and 1 hour in city traffic, what is the total distance traveled by the car? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "217.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2484,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mia, Emma, and Noah decided to pool their money to buy a birthday gift for their friend. Mia is twice as old as Emma, and Emma is 3 years younger than Noah. If Noah is 12 years old, how much money did each contribute if they all contributed an amount of money equal to their age in dollars? What is the total amount of money they collected? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "39",
"style": "rule"
}
|
numina_math
|
{
"index": 2485,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the decimal \\(0.75\\) to a fraction, simplify the fraction, and then express the simplified fraction as a percentage. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 2486,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the fraction \\(\\frac{7}{24}\\) to its decimal representation. Determine if the decimal representation is terminating or repeating, and if it is repeating, find the repeating sequence. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2487,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "David can mow a lawn in 4 hours. Lisa can mow the same lawn in one-fifth the time it takes David. Alex can mow the same lawn in 3 hours more than twice the amount of time it takes Lisa. How long will it take Alex to mow the lawn? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.6",
"style": "rule"
}
|
numina_math
|
{
"index": 2488,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify and solve for \\( x \\) in the equation:\n\\[\n\\frac{6x^2 - 12x}{3x} = 4\n\\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-2",
"style": "rule"
}
|
numina_math
|
{
"index": 2489,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has $120 that she wants to exchange for Euros. The exchange rate is $1 = €0.85. After exchanging her money, she spends €30 on souvenirs. How many Euros does Sarah have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
numina_math
|
{
"index": 2490,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In how many ways can a committee of 3 people be formed from a group of 8 people, if the order in which the people are chosen does not matter? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "56",
"style": "rule"
}
|
numina_math
|
{
"index": 2491,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the function \\( h(x) = 4x^3 - 2x + 7 \\), find the value of \\( h(2) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35",
"style": "rule"
}
|
numina_math
|
{
"index": 2492,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa wants to visit her friend who lives 3 miles away from her house. She plans to walk to her friend’s house and then take a bus back home. If she walks at a speed of 4 miles per hour and the bus travels at a speed of 30 miles per hour, how much total time will Lisa spend traveling? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.85",
"style": "rule"
}
|
numina_math
|
{
"index": 2493,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John and Sarah are participating in a charity walk. John walks at a speed of 3 miles per hour, while Sarah walks at a speed of 4 miles per hour. They both start walking from the same point at the same time. If they walk in opposite directions, how long will it take for them to be 21 miles apart? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2494,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mark is a baker who makes cookies in batches. Each batch contains 3 dozen cookies. One morning, he made 5 batches of cookies. He sold 60 cookies by midday. In the afternoon, he made another 2 batches of cookies and sold 30 more cookies. How many cookies does Mark have left at the end of the day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "162",
"style": "rule"
}
|
numina_math
|
{
"index": 2495,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car rental company charges a flat fee of $50 per day plus $0.20 per mile driven. If a customer rented a car for 3 days and drove a total of 150 miles, how much did the customer pay in total?\n\n### Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 2496,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria is designing a rectangular flower bed that measures 8 feet by 12 feet. She wants to surround the flower bed with a 2-foot-wide path. She needs to calculate the total area covered by the flower bed and the path together. What is the total area? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "96",
"style": "rule"
}
|
numina_math
|
{
"index": 2497,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company produces and sells a product. The cost to produce $x$ units of the product is given by the expression $5x^2 + 3x + 2$. The revenue from selling $x$ units is given by the expression $8x^2 + 2x + 1$. Simplify the expression for the profit (revenue - cost) and find the sum of the coefficients of the resulting polynomial. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2498,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A tank can hold a total of 500 liters of water. Tank A is filled with 40 liters more than twice the amount of water in Tank B. If the total amount of water in both tanks is 500 liters, how many liters of water are in Tank A? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "347",
"style": "rule"
}
|
numina_math
|
{
"index": 2499,
"name": "numina_math",
"split": "train"
}
|
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