prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "A rectangular garden has a length of 12 meters and a width of 7 meters. If a fence is to be built around the garden, what is the total length of the fence needed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "38",
"style": "rule"
}
|
numina_math
|
{
"index": 2500,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where every item is 25% off. If a customer buys 4 items originally priced at $32 each, how much does the customer pay after the discount is applied? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "96",
"style": "rule"
}
|
numina_math
|
{
"index": 2501,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A box contains 125 apples, which is 5 more than three times the number of oranges in the box. After distributing the apples equally among 7 children, how many apples will be left in the box? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2502,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that $x^2 + y^2 = 25$ and $2x + y = 10$, find the value of $x$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2503,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car is rented for a trip, and the rental company charges $20 per day and $0.15 per mile driven. If the trip lasts for 2 weeks and the car is driven for a total of 840 miles, what is the total cost of the rental? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "406",
"style": "rule"
}
|
numina_math
|
{
"index": 2504,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mary has 5 green crayons and 8 blue crayons of different shades. If she gives out 3 green crayons and 1 blue crayon to Becky, how many crayons does she have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2505,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah commutes to work by car at a constant speed of 45 miles per hour. If her total travel time to work is 1.5 hours, how far has she traveled in the first 30 minutes of her commute? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2506,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In $\\triangle ABC$, $\\angle A = 2x + 10^\\circ$, $\\angle B = 3x - 20^\\circ$, and $\\angle C = x + 30^\\circ$. Determine the value of $x$ and the measure of each angle in the triangle. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "26.67",
"style": "rule"
}
|
numina_math
|
{
"index": 2507,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from city A to city B at a constant speed. If it takes the car 3 hours to travel from city A to city B, and the distance between the two cities is 180 kilometers, find the equation of the car's speed as a function of time in the form \\(d(t) = mt + c\\). Then, determine how long it will take for the car to travel 300 kilometers at the same speed. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2508,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Define a binary operation \\(\\oplus\\) by \\(a \\oplus b = a^2 + b^2 - ab\\). Evaluate \\(5 \\oplus 3\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "19",
"style": "rule"
}
|
numina_math
|
{
"index": 2509,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice and Bob are painting a fence together. Alice can paint the entire fence by herself in 6 hours, while Bob can do it in 4 hours. If they work together, how long will it take them to finish painting the fence? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.4",
"style": "rule"
}
|
numina_math
|
{
"index": 2510,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( f(x) = 2^x \\) and \\( g(x) = \\log_2(x) \\), find the value of \\( f(g(16)) + g(f(3)) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "19",
"style": "rule"
}
|
numina_math
|
{
"index": 2511,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A laptop is originally priced at $1200. During a sale, a discount of 25% is applied to the laptop. What is the sale price of the laptop after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "900",
"style": "rule"
}
|
numina_math
|
{
"index": 2512,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two numbers, 48 and 72, are given. Find the Greatest Common Divisor (GCD) and the Least Common Multiple (LCM) of these two numbers. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "144",
"style": "rule"
}
|
numina_math
|
{
"index": 2513,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria loves making handcrafted candles, which she sells online. The cost to produce each candle is $4, including materials and labor. She sells each candle for $10. If Maria sells 250 candles in a month, how much profit does she make in that month? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1500",
"style": "rule"
}
|
numina_math
|
{
"index": 2514,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The length of a rectangle is increased by 25% and the width is increased by 40%. What is the percent change in the area of the rectangle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 2515,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there are 120 students in total. Each student is either in the Math Club or the Science Club or both. If 80 students are in the Math Club and 70 students are in the Science Club, how many students are in both clubs? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2516,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anna is preparing a fruit salad and needs to use $\\dfrac{3}{4}$ of a pound of strawberries for each salad bowl. She has $\\dfrac{9}{2}$ pounds of strawberries. How many salad bowls can she prepare? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2517,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A triangle has a base of 12 units and a height of 8 units. If the height of the triangle is increased by 25%, what is the percentage increase in the area of the triangle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 2518,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Three workers, Alice, Bob, and Charlie, are tasked with completing a job together. Alice can complete the job in 4 hours, Bob can complete it in 6 hours, and Charlie can complete it in 12 hours. If they work together, how long will it take for them to complete the job? Express your answer as a simplified fraction of an hour. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2519,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A polynomial \\( p(x) \\) leaves a remainder of \\( -2 \\) when divided by \\( x - 2 \\) and a remainder of \\( 5 \\) when divided by \\( x + 1 \\). Let \\( r(x) \\) be the remainder when \\( p(x) \\) is divided by \\( (x - 2)(x + 1) \\). Find \\( r(3) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-\\frac{13}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 2520,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A teacher has 36 students in her class. She wants to divide the students equally into groups for a group project. After forming the groups, she realizes that 4 students were absent. She decides to redistribute the present students equally among the formed groups. If each group now has 4 students, how many groups were originally formed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2521,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a local library, there are a total of 48 shelves filled with books. Each shelf contains the same number of books. It is known that 2/3 of the shelves are dedicated to fiction books, and the rest are dedicated to non-fiction books. If there are a total of 384 fiction books, how many books are there on each shelf? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2522,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x) = 2x^2 - 3x + 5 \\) and \\( g(x) = x^3 - 2x^2 + x \\). Find \\( f(g(x)) \\) and then simplify \\( f(g(2)) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2523,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The first term of a geometric series is 3, and the sum of the first four terms is 120. Find the common ratio of the series. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2524,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train travels a distance of 300 kilometers at a constant speed. If the train increases its speed by 20%, it will take 1 hour less to cover the same distance. What is the original speed of the train in kilometers per hour? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 2525,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice and Bob are working together to paint a fence. Alice can paint the entire fence in 6 hours, while Bob can paint it in 4 hours. If they work together for 2 hours and then Alice continues alone to finish the job, how much more time does Alice need to complete painting the fence? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2526,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria has $\\$75.60$ and wants to buy notebooks for her class. Each notebook costs $\\$3.45$. After buying the notebooks, she wants to donate the remaining money to the school fund. How many notebooks can Maria buy, and how much money will she donate to the school fund? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.15",
"style": "rule"
}
|
numina_math
|
{
"index": 2527,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Aaron is gathering can lids to take to the recycling center. He uses 3 equal-sized boxes of canned tomatoes and adds the lids he gets to the 14 can lids he already has. He is now taking 53 can lids to the recycling center. How many can lids did he get from each box? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 2528,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A gardener notices a pattern in the number of flowers blooming each day. On the first day, 3 flowers bloom. On the second day, 6 flowers bloom. On the third day, 9 flowers bloom, and so on, with the number of blooming flowers increasing by 3 each day. If the pattern continues, how many flowers will bloom on the 10th day? Additionally, find the total number of flowers that have bloomed by the end of the 10th day. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "165",
"style": "rule"
}
|
numina_math
|
{
"index": 2529,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(\\mathbf{u} = \\begin{pmatrix} 4 \\\\ 0 \\\\ -3 \\end{pmatrix}\\) and \\(\\mathbf{v} = \\begin{pmatrix} 1 \\\\ 2 \\\\ -1 \\end{pmatrix}\\). Find the projection of \\(\\mathbf{u}\\) onto \\(\\mathbf{v}\\) and determine its magnitude. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{7\\sqrt{6}}{6}",
"style": "rule"
}
|
numina_math
|
{
"index": 2530,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Rita is planning to buy a new television set that costs $1,200. She has already saved $850. She plans to save an additional $150 per month until she can afford the TV. How many more months does Rita need to save to buy the television? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2531,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a road trip and needs to buy fuel. She finds out that the average price of fuel is $3.50 per gallon. Her car has a fuel efficiency of 25 miles per gallon, and she plans to travel a total of 500 miles. If she has a budget that allows her to spend only 80% of the total fuel cost, how much money does she need to allocate for the trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "56",
"style": "rule"
}
|
numina_math
|
{
"index": 2532,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial function \\( g(x) = x^4 - 4x^3 + 6x^2 - 4x + 1 \\), determine if the function is symmetric about the y-axis, and evaluate \\( g(2) - g(-2) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-80",
"style": "rule"
}
|
numina_math
|
{
"index": 2533,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length that is 3 times its width. The perimeter of the garden is 64 meters. What are the dimensions of the garden? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 2534,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A marathon runner trains for a race by running different routes on different days of the week. On Monday, she runs 5 miles, on Tuesday she runs 8 miles, on Wednesday she runs 10 miles, on Thursday she runs 6 miles, and on Friday she runs 12 miles. She rests on the weekend. If she maintains this schedule for 4 weeks, how many miles does she run in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "164",
"style": "rule"
}
|
numina_math
|
{
"index": 2535,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store sells a gaming laptop at an original price of $1500. During a special sale, the laptop is offered at a 25% discount. After applying the discount, the store then offers an additional 10% discount on the already discounted price. What is the final price of the laptop after both discounts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1012.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2536,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two trains, Train A and Train B, are traveling towards each other from two different cities that are 300 miles apart. Train A is traveling at 50 miles per hour, while Train B is traveling at 70 miles per hour. If both trains start their journey at the same time, how long will it take for the two trains to meet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2537,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Three friends, Alex, Ben, and Chloe, together have $300. The ratio of the amount of money Alex has to the amount of money Ben has is 5:4. Alex has $30 more than Chloe. How much money does Chloe have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "87.85",
"style": "rule"
}
|
numina_math
|
{
"index": 2538,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A local bookstore is having a sale where the price of each book is $12. If John buys the first book at full price and each subsequent book at half the price of the previous book, how much will he spend if he buys 5 books in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "23.25",
"style": "rule"
}
|
numina_math
|
{
"index": 2539,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company has 200 employees. They plan to give a bonus to employees who have prime-numbered IDs. If 20% of the employees do not have prime-numbered IDs, how many employees will receive the bonus? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "160",
"style": "rule"
}
|
numina_math
|
{
"index": 2540,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a birthday party and has a budget of $500. She wants to buy party favors for 25 guests. Each party favor costs $15, and she also wants to buy a cake that costs $75. After purchasing the party favors and the cake, how much money will Sarah have left from her budget? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 2541,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where all items are discounted by 20%. If the store normally sells widgets at $50 each and gadgets at $30 each, what is the total price for buying 3 widgets and 4 gadgets during the sale? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "216",
"style": "rule"
}
|
numina_math
|
{
"index": 2542,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company sells a product for $23.75 per unit. In a recent month, they sold 1,234 units. They want to round their total revenue to the nearest hundred dollars. What is the rounded total revenue? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "29300",
"style": "rule"
}
|
numina_math
|
{
"index": 2543,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom is currently 12 years older than Jerry. In 8 years, Tom will be twice as old as Jerry was 4 years ago. How old are Tom and Jerry now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2544,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A young tree grows at a steady rate of 1.5 feet per year. When the tree was planted, it was already 4 feet tall. How tall will the tree be in 10 years? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "19",
"style": "rule"
}
|
numina_math
|
{
"index": 2545,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "David is on a weight loss program and aims to lose weight steadily over a period of time. He decides to start by losing 2 pounds in the first week and plans to increase his weight loss by 1 pound each subsequent week. If he follows this plan for 8 weeks, how much weight will he have lost in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "44",
"style": "rule"
}
|
numina_math
|
{
"index": 2546,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a library, the ratio of fiction to non-fiction books is 5:3. If there are 45 fiction books, how many non-fiction books are there, and what is the total number of books in the library? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
numina_math
|
{
"index": 2547,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery made 240 cookies in the first 4 hours of operation. In the next 2 hours, the bakery increased its production rate by 50%. How many cookies did the bakery make in total at the end of 6 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "420",
"style": "rule"
}
|
numina_math
|
{
"index": 2548,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In how many ways can I choose 4 representatives from a committee of 12 people? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "495",
"style": "rule"
}
|
numina_math
|
{
"index": 2549,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evelyn has a total of 200 candies. She decides to give 15% of her candies to her best friend, 25% to her classmates, and the remaining candies to her siblings. How many candies does Evelyn give to her siblings? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2550,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The average of the first 50 positive whole numbers is 25.5. If the sum of these numbers plus an additional number \\( x \\) is 1300, what is \\( x \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 2551,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A teacher has a class of 24 students. One-eighth of the students received an A on the math test, while one-third received a B. The rest received either a C or a D. If the number of students who received a C is twice the number of students who received a D, how many students received a D? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 2552,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A television originally costs $800. During a holiday sale, the store offers a 15% discount on the television. Additionally, the store has a policy where members get an extra 5% off on the discounted price. If John, who is a member, buys the television during the sale, what is the final price he pays for the television? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "646",
"style": "rule"
}
|
numina_math
|
{
"index": 2553,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation: $\\sqrt{3x + 7} = x - 1$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2554,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jane is organizing a charity event and plans to distribute gift bags. She starts with 5 gift bags and adds 3 more each hour for 4 hours. Then, she decides to give away 2 gift bags every hour for the next 3 hours. How many gift bags does Jane have left after these activities? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 2555,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The number of cells in a bacterial culture doubles every hour. If there were 500 cells initially, how many hours will it take for the culture to reach 16,000 cells? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2556,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the sum of the first 5 terms of the geometric series where the first term is 2 and the common ratio is 3. Express your answer using exponential notation where possible. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2557,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car's fuel efficiency is measured at 30 miles per gallon. If a road trip covers 450 miles, how many gallons of fuel does the car use? Additionally, convert this amount of fuel into ounces. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1920",
"style": "rule"
}
|
numina_math
|
{
"index": 2558,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x) = 3x^2 + 5x - 2 \\). If \\( x = 4 \\), find \\( f(x) \\) and then calculate \\( 25\\% \\) of the result. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2559,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Thomas is planning his monthly budget. He earns $3,500 per month. His fixed expenses include rent for $1,200, utilities for $300, and a car payment of $400. He also plans to save 20% of his income each month. How much money will Thomas have left for other expenses after paying his fixed expenses and saving 20% of his income? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "900",
"style": "rule"
}
|
numina_math
|
{
"index": 2560,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria is organizing a book club event. She has 12 mystery novels. She has 5 more romance novels than mystery novels. She has 8 more science fiction novels than romance novels. How many novels does she have in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "54",
"style": "rule"
}
|
numina_math
|
{
"index": 2561,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires mixing a solution that consists of water and sugar in a 3:1 ratio. If you have 12 cups of water, how much sugar do you need to add to maintain the ratio? After mixing the solution, you realize that you only need half of the solution for your recipe. How many cups of the mixed solution will you have left if you discard the rest? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2562,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the base five number \\( 243_5 \\) to its decimal (base ten) equivalent. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "73",
"style": "rule"
}
|
numina_math
|
{
"index": 2563,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two angles, Angle \\( X \\) and Angle \\( Y \\), are supplementary. The measure of Angle \\( X \\) is 30 degrees more than three times the measure of Angle \\( Y \\). What are the measures of Angle \\( X \\) and Angle \\( Y \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "37.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2564,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces widgets at a rate of 5 dozen per hour. If the factory operates 8 hours a day, how many widgets does the factory produce in a week? Assume the factory operates 5 days a week. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2400",
"style": "rule"
}
|
numina_math
|
{
"index": 2565,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the absolute value of the difference of the squares of 10 and 6, and then multiply that result by 2? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "128",
"style": "rule"
}
|
numina_math
|
{
"index": 2566,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A theater company offers two types of season tickets. The cost of a basic season ticket is $x$, while the cost of a premium season ticket is three times the cost of a basic season ticket. If the total revenue from selling 50 basic season tickets and 20 premium season tickets is $14,000, what is the cost of one basic season ticket? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "127.27",
"style": "rule"
}
|
numina_math
|
{
"index": 2567,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine the horizontal asymptote of the rational function \\( \\frac{(2x^2 + 3x - 5)}{(x^2 + 4x + 6)} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2568,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the remainder when the product of the first four prime numbers is divided by 11? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2569,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A new laptop costs $1,200. Due to depreciation, its value decreases by 10% every year. What will be the value of the laptop after 3 years? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "874.8",
"style": "rule"
}
|
numina_math
|
{
"index": 2570,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jack has saved up $1500 in his savings account. Every month, he deposits $200 into his account. Additionally, his account earns a fixed interest of $50 at the end of every month. How much money will Jack have in his account at the end of 6 months? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3000",
"style": "rule"
}
|
numina_math
|
{
"index": 2571,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a class, the average score of 5 students on a math test is 78. If three of the students scored 82, 75, and 79 respectively, what is the average score of the remaining two students? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "77",
"style": "rule"
}
|
numina_math
|
{
"index": 2572,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the factored form of a quadratic equation \\((x - 2)(x + 3)\\), find the standard form of the quadratic equation and identify its roots. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-3",
"style": "rule"
}
|
numina_math
|
{
"index": 2573,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria is planning a birthday party and has a budget of $300. She needs to purchase a cake that costs $45, decorations that cost $65, and party favors for 10 guests, each costing $8. If she also wants to reserve a space that costs $100, will she be able to stay within her budget? How much money will she have left or need additionally? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2574,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial \\( P(x) = x^2 + 6x + 8 \\), factorize it and use the factors to find the distance between the roots using the distance formula. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2575,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah earns a base salary of $2,500 per month. In addition to her base salary, she earns a 5% commission on her sales. If Sarah's sales for the month were $12,000, how much did she earn in total for that month after accounting for a 10% income tax on her total earnings? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2790",
"style": "rule"
}
|
numina_math
|
{
"index": 2576,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(x\\) be a positive real number with the property that \\(x + \\frac{1}{x} = 3\\). Determine the value of \\(x^4 + \\frac{1}{x^4}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "47",
"style": "rule"
}
|
numina_math
|
{
"index": 2577,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom of 50 students, the number of students who scored above the average is 5 more than twice the number of students who scored below the average. How many students scored above the average? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35",
"style": "rule"
}
|
numina_math
|
{
"index": 2578,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A plant grows 5 cm every week. If the plant is currently 20 cm tall, how tall will it be after 7 weeks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "55",
"style": "rule"
}
|
numina_math
|
{
"index": 2579,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Expand and simplify the polynomial expression \\((2x + 3)^5\\) using the Binomial Theorem. What is the coefficient of the \\(x^3\\) term in the expansion? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "720",
"style": "rule"
}
|
numina_math
|
{
"index": 2580,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A scientist is working with a substance that has a half-life of 3 years. She starts with 80 grams of the substance. She models the decay using the function \\( A(t) = A_0 \\left(\\frac{1}{2}\\right)^{\\frac{t}{3}} \\), where \\( A(t) \\) represents the amount of substance remaining after \\( t \\) years, and \\( A_0 \\) is the initial amount of the substance. How much of the substance remains after 9 years? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2581,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of 5 friends decided to have dinner at a seafood restaurant. They ordered 4 dozen oysters on the half shell for $18.00 a dozen, 3 pounds of steamed crab for $20.00 a pound, and 5 pounds of grilled salmon for $25.00 a pound. If they split the bill equally, how much will each person owe? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "51.4",
"style": "rule"
}
|
numina_math
|
{
"index": 2582,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Avianna bought red candles and blue candles in the ratio of 5:3 for her birthday party. If Avianna had 45 red candles, how many blue candles did she have? Additionally, what is the total number of candles she bought? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
numina_math
|
{
"index": 2583,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah uses 2 sheets of paper every day for her schoolwork. Each pack of paper contains 500 sheets and costs $4. If there are 30 days in a month, how much does she spend on paper in a year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2584,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a small apartment complex, there are 15 apartments, each with 3 windows. One evening, a maintenance worker noticed that 24 windows were lit. How many apartments had their lights turned off? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2585,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "During a charity event, a total of 7 different sponsors each pledge a donation based on the number of hours they volunteer. Each sponsor volunteers for 4 hours, and each hour of volunteering translates to a $50 donation. How much in total do the sponsors contribute? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1400",
"style": "rule"
}
|
numina_math
|
{
"index": 2586,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 3 cups of flour for every 2 cups of sugar. If you want to make a larger batch and you have 9 cups of flour, how many cups of sugar do you need? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2587,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces gadgets at a constant rate of 60 gadgets per hour. During an 8-hour shift, the factory must meet a quota of producing at least 500 gadgets. If the factory has already produced 360 gadgets in the first 6 hours, what is the minimum rate (in gadgets per hour) at which the factory needs to produce gadgets for the remaining 2 hours to meet the quota? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "70",
"style": "rule"
}
|
numina_math
|
{
"index": 2588,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the sum of the series:\n\\[\n\\sum_{k=1}^{5} \\sin \\left( k \\pi \\right).\n\\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2589,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jane has been saving money for a new laptop. She saves $15 every week for 20 weeks. After that, she decides to increase her savings and saves $25 every week for the next 12 weeks. How much money has Jane saved in total by the end of these 32 weeks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 2590,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, the average score of students in a math test is calculated. There are 12 boys and 8 girls in the class. The average score of the boys is 75, and the average score of the girls is 85. What is the overall average score of the class? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "79",
"style": "rule"
}
|
numina_math
|
{
"index": 2591,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires \\( \\frac{3}{4} \\) cup of sugar for every \\( \\frac{1}{2} \\) cup of milk. If you have 3 cups of sugar, how many cups of milk do you need to maintain the same proportion? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2592,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for $x$ in the equation $3^{2x + 1} = 27^{x - 1}$ using properties of exponents and substitution. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2593,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, the number of students in the Science Club is 18. The number of students in the Art Club is 12 more than one-third of the number of students in the Science Club. How many students are in the Art Club? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 2594,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the largest integer value of \\( n \\) such that \\( n^2 - 9n + 18 \\) is negative. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2595,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The number of students in Class A and Class B is in the ratio 4:5. If there are 18 more students in Class B than in Class A, how many students are there in total in both classes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "162",
"style": "rule"
}
|
numina_math
|
{
"index": 2596,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a road trip and wants to compare two different routes. Route A is 300 miles long and has an average speed limit of 50 miles per hour. Route B is 320 miles long with an average speed limit of 60 miles per hour. How much time will Sarah save if she takes Route B instead of Route A? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2597,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Cathy is planning a small dinner party and wants to serve a dessert that requires a mixture of nuts. The recipe calls for 3/4 cup of almonds, 2/3 cup of walnuts, and 1/2 cup of pecans. She decides to make a double batch of the dessert. How many cups of nuts does she need in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.83",
"style": "rule"
}
|
numina_math
|
{
"index": 2598,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a small town, the local library is open for a total of 40 hours per week. On weekdays (Monday to Friday), it is open for 6 hours each day. On weekends (Saturday and Sunday), it is open for an equal number of hours each day. How many hours is the library open on each weekend day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2599,
"name": "numina_math",
"split": "train"
}
|
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