prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "A publishing company sells notebooks at $5 each. If a school buys 40 notebooks at the regular price but receives a discount of $1 per notebook for every notebook bought beyond the initial 20, how much does the school pay in total for 40 notebooks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 9700,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Linda is three times as old as her niece Emma. Five years ago, Linda was four times as old as Emma was at that time. How old is Emma now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 9701,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma is planning a small party and needs to allocate her budget for different items. She wants to buy 3 packs of napkins priced at $1.25 each, 2 packs of cups priced at $2.50 each, and 4 packs of plates priced at $3.75 each. After buying these items, she has $15 left. How much money did Emma initially have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "38.75",
"style": "rule"
}
|
numina_math
|
{
"index": 9702,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a deck of 52 cards, what is the expected number of times you need to draw a card (with replacement) to get the first Ace? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 9703,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A teacher wants to distribute 144 pencils equally among her 12 students. After distributing the pencils, she gives 3 more pencils to each student from a reserve stock. How many pencils does each student have in the end? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 9704,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa is organizing a charity event where she needs to prepare gift bags. Each gift bag contains 5 items. She plans to prepare 12 gift bags. Additionally, she wants to make sure that every participant at the event also gets a bottle of water. If she expects 48 participants, how many total items (including gift bag items and water bottles) does she need to prepare? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "108",
"style": "rule"
}
|
numina_math
|
{
"index": 9705,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the functions \\( f(x) = \\log_2 x \\) and \\( g(x) = x^2 - 9x + 20 \\), find the value of \\( x \\) such that \\( f(g(x)) = 3 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 9706,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A class of students is divided into groups for a project. Each group must have the same number of students. When the students are divided into groups of 4, there are 3 students left over. When they are divided into groups of 5, there are 4 students left over. What is the smallest number of students in the class if there are between 20 and 100 students? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "39",
"style": "rule"
}
|
numina_math
|
{
"index": 9707,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 4 cups of flour for every 3 cups of sugar. If you want to make a batch that uses 18 cups of sugar, how many cups of flour will you need? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 9708,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store sells a product for $50. They decide to increase the price by 30%, but later they realize that it was too high and decide to decrease the new price 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": "52",
"style": "rule"
}
|
numina_math
|
{
"index": 9709,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A storm dropped 6 inches of rain in the first hour. In the next two hours, the storm dropped 3 inches of rain each hour. In the final hour of the storm, it dropped 2 inches of rain. What was the average rainfall per hour for the duration of the storm? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.5",
"style": "rule"
}
|
numina_math
|
{
"index": 9710,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice is collecting palindromic numbers for her math project. She has collected 5 numbers: 121, 343, 484, 676, and 989. She wants to know the total sum of these palindromic numbers and the average value of the numbers she has collected. What is the total sum, and what is the average value? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "522.6",
"style": "rule"
}
|
numina_math
|
{
"index": 9711,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a talent show, there are four different singing roles, three different dancing roles, and two different acting roles. Only singers can be assigned to singing roles, only dancers can be assigned to dancing roles, and only actors can be assigned to acting roles. If there are six singers, five dancers, and four actors auditioning for the talent show, in how many ways can the nine roles be assigned? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "259200",
"style": "rule"
}
|
numina_math
|
{
"index": 9712,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A carpenter is working on a project that requires wood measured in meters, but the wood he has is measured in centimeters. He has a piece of wood that is 350 centimeters long. He needs to cut it into pieces that are each 1.4 meters long. How many full pieces of 1.4 meters can he cut from the 350 centimeters long wood? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 9713,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train leaves City A heading towards City B at a constant speed of 60 miles per hour. Two hours later, a car leaves City A heading towards City B at a speed of 80 miles per hour. If the distance between City A and City B is 400 miles, how long after the train leaves City A will the car catch up to the train? Also, calculate the total distance the car will have traveled by the time it catches up to the train. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "480",
"style": "rule"
}
|
numina_math
|
{
"index": 9714,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular prism-shaped aquarium has a length of 120 centimeters, a width of 50 centimeters, and a height of 60 centimeters. Due to evaporation, the water level decreases by 5 centimeters every week. How many weeks will it take for the water level to drop to half of the aquarium's original height? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 9715,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A pharmaceutical company has developed a new drug that decays in the human body following an exponential decay model. The initial dose of the drug is 100 milligrams, and it decays by 20% each hour. How much of the drug remains in the body after 5 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32.768",
"style": "rule"
}
|
numina_math
|
{
"index": 9716,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A teacher has 45 students and wants to distribute them equally into several groups. Each group should have the same number of students, and there should be at least 5 groups. How many students will each group have if the teacher wants to maximize the number of groups? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 9717,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $f(x) = x^2 + 3x + 2$ and define the operation $\\diamond$ as \\((a \\diamond b) = f(a) + f(b)\\). If $a = 1$ and $b = -2$, find the value of \\((a \\diamond b)\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 9718,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is planning to build a garden that is 300 square feet larger than four times the size of her friend's garden. If her friend's garden is 200 square feet, what will be the size of Emily's garden? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1100",
"style": "rule"
}
|
numina_math
|
{
"index": 9719,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A large cake is divided equally among 15 people. One person eats their entire share, but then three more people each give half of their share to someone else. What percentage of the original cake does the recipient receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 9720,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company has 6 different projects, and it needs to assign a project leader for each. The CEO decides to randomly assign one of the six available senior managers to each project. What percentage of the possible assignments will result in the same manager leading both Project A and Project B? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16.67",
"style": "rule"
}
|
numina_math
|
{
"index": 9721,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation \\(\\log(x^2 - 4) - \\log(2x - 4) = \\log(3)\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 9722,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A function \\( g \\) is defined for positive integers as follows:\n\\[ g(n) = \\left\\{\n\\begin{array}{cl}\n3n + 2 & \\text{if } n \\leq 5, \\\\\ng(n - 3) & \\text{if } n > 5.\n\\end{array}\n\\right.\\]\nFind the value of \\( g(11) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17",
"style": "rule"
}
|
numina_math
|
{
"index": 9723,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many two-digit numbers are there such that when they are divided by 7, the remainder is 4? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 9724,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the sum of the series \\( \\sum_{n=1}^{10} \\frac{1}{n(n+1)} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{10}{11}",
"style": "rule"
}
|
numina_math
|
{
"index": 9725,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah starts her homework at 4:30 PM and finishes it at 6:45 PM. On the same day, her brother Tim starts his homework at 5:15 PM and finishes at 7:00 PM. How much time, on average, do Sarah and Tim spend on their homework? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 9726,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A water tank can hold 500 liters of water. If water flows into the tank at a rate of 25 liters per minute, how long will it take to fill the tank to three-quarters of its capacity? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 9727,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Teacher Wang prints out the excellent \"Book Reading Reflections\" of three students in the class. Each line can accommodate 25 words, and there are 32 lines in total. According to the school's new requirement, each line should accommodate 40 words. How many lines of \"Book Reading Reflections\" need to be printed to meet the new requirement? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 9728,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, the ratio of boys to girls is 3:4. If the total number of students is 35, how many boys are in the classroom? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 9729,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery makes 8 whole chocolate cakes every day. Each cake is cut into 12 slices, and each slice sells for $4. How much money does the bakery earn in a day from selling chocolate cake slices? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "384",
"style": "rule"
}
|
numina_math
|
{
"index": 9730,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A chef is preparing a large batch of soup and needs to convert the recipe quantities. The original recipe calls for 3 quarts of broth to make 6 servings. If the chef wants to make enough soup for 45 servings, how many gallons of broth are needed? (Note: 1 quart = 0.25 gallons) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5.625",
"style": "rule"
}
|
numina_math
|
{
"index": 9731,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory operates 24 hours a day. It takes 6 hours to produce one batch of widgets. If the factory works continuously for 5 days, how many batches of widgets does it produce in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 9732,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe calls for 3/4 cup of sugar. If you want to make half of the recipe, how much sugar do you need? Additionally, if you accidentally added 1/8 cup too much sugar, how much sugar should you remove to have the correct amount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{8}",
"style": "rule"
}
|
numina_math
|
{
"index": 9733,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bus schedule states that the bus leaves the station at 6:45 AM and arrives at its destination at 9:25 AM. If there are two stops along the way, and the total stopping time is 25 minutes, how much time does the bus spend traveling without stopping? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "135",
"style": "rule"
}
|
numina_math
|
{
"index": 9734,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mr. Johnson deposited $12,000 in a savings account with an annual interest rate of 3% for a period of 5 years. If the interest earned is subject to a 25% tax, how much total interest after tax will Mr. Johnson receive at the end of the 5-year period? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1350",
"style": "rule"
}
|
numina_math
|
{
"index": 9735,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenny has a total of $2,400 to buy supplies for her art store. She spent $1,000 on paint and $800 on brushes. If she needs to equally divide the remaining money to buy canvases and frames, how much money will she allocate to each? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 9736,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a certain arithmetic sequence, the ratio of the third term to the fifth term is 2:5. If the third term is 12, what is the fifth term? Round your answer to the nearest whole number if necessary. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 9737,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe for a cake requires 2/3 cup of sugar. If you want to make 9 cakes, 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": 9738,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car dealership increased the price of a car by 20% and then offered a discount of 15% on the new price. If the original price of the car was $25,000, what is the final price of the car after the increase and discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25500",
"style": "rule"
}
|
numina_math
|
{
"index": 9739,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex is organizing a competition in which he needs to distribute 120 prizes among participants. He decides to give 5 prizes to each participant. However, he realizes that he can only distribute the prizes in groups where the number of participants in each group is a divisor of 120. How many different group sizes are possible? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 9740,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mary had a collection of 500 marbles. She decided to give away some of her marbles to her friends. She gave 50 marbles to John, 75 marbles to Sarah, and 40 marbles to Mike. How many marbles does Mary have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "335",
"style": "rule"
}
|
numina_math
|
{
"index": 9741,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A population of bacteria decreases according to an exponential decay model. The population at time \\( t \\) is given by \\( P(t) = P_0 e^{-kt} \\), where \\( P_0 \\) is the initial population and \\( k \\) is a positive constant. Given that the population halves every 2 hours, and at \\( t = 0 \\) the population is \\( P_0 = 1000 \\), determine the population after 6 hours. Additionally, use trigonometric identities to find \\( \\sin(\\pi/4 - \\theta) \\) if \\( \\cos \\theta = \\frac{1}{2} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "125",
"style": "rule"
}
|
numina_math
|
{
"index": 9742,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the polynomial \\(P(x) = 3x^3 - 4x^2 + 2x - 7\\) at \\(x = -2\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-51",
"style": "rule"
}
|
numina_math
|
{
"index": 9743,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company produces two types of widgets, A and B. For every 3 widgets of type A, they produce 5 widgets of type B. If the company produced 120 widgets of type B, how many widgets did they produce in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "192",
"style": "rule"
}
|
numina_math
|
{
"index": 9744,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\): \\( \\frac{1}{x+3} + \\frac{2x}{x+3} - \\frac{4}{x+3} = 5 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-6",
"style": "rule"
}
|
numina_math
|
{
"index": 9745,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa sells homemade cookies for $5 each. Today, she sold 8 cookies and received an additional $10 from a satisfied customer. Later, she spent $15 on ingredients for her next batch of cookies and deposited $20 into her savings account. How much money is Lisa left with after making the deposit? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 9746,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In parallelogram $ABCD$, point $P$ is on diagonal $\\overline{AC}$ such that $\\overline{AP} : \\overline{PC} = 2 : 1$. The area of $\\triangle ABD$ is $54$ square units. Find the area of $\\triangle APD$. Express your answer in simplest radical form. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "43.2",
"style": "rule"
}
|
numina_math
|
{
"index": 9747,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires 60% of its ingredients to be flour, 30% to be sugar, and the remaining 10% to be butter. If the total weight of the ingredients is 500 grams, how many grams of each ingredient are needed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 9748,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Ethan is planning a birthday party and wants to give each of his 15 guests a goodie bag. Each goodie bag will contain 3 candies, 2 small toys, and 1 sticker. If candies cost $0.25 each, small toys cost $1.50 each, and stickers cost $0.75 each, how much will Ethan spend in total on the goodie bags? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "67.50",
"style": "rule"
}
|
numina_math
|
{
"index": 9749,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends went to a theme park and decided to split the total cost of a ticket equally. The total cost for the group was $240. If the average cost per person was $30, how many friends were in the group? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 9750,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation \\( \\frac{3}{4}x - \\frac{1}{2} = \\frac{1}{4}(2x + 4) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 9751,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: \\((2^3 \\cdot 5^2) - (3^2 \\cdot 2^2)\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "164",
"style": "rule"
}
|
numina_math
|
{
"index": 9752,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex is planning a road trip and needs to rent a car. The rental company charges a base fee of $50 plus $0.20 per mile driven. If Alex drives 300 miles on his trip, and the total trip takes 6 hours, what is the cost per hour of his trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18.33",
"style": "rule"
}
|
numina_math
|
{
"index": 9753,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bag contains a certain number of identical marbles. Each marble weighs 10 grams. After removing 7 marbles, the bag weighs 230 grams. After removing a total of 10 marbles, the bag weighs 200 grams. How many marbles were initially in the bag? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 9754,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In how many ways can 6 people be seated in a row of 8 chairs if two specific people, Alice and Bob, must not sit next to each other? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15120",
"style": "rule"
}
|
numina_math
|
{
"index": 9755,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the smallest positive integer that is a palindrome and is divisible by both 12 and 15? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "606",
"style": "rule"
}
|
numina_math
|
{
"index": 9756,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is packing boxes for a move. Each box can hold a maximum weight of 50 pounds. She has 8 items, and their weights in pounds are represented by the algebraic expressions: 2x, 3x - 2, 4x + 1, x + 5, 2x + 3, 3x - 4, x, and 2x - 1. If each box must be filled to its maximum capacity without exceeding it, and if x = 3 pounds, how many boxes will Samantha need to pack all her items? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 9757,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, there are 5 math tests throughout the semester. The scores of the first four tests are 78, 85, 90, and 87. To pass the class, a student must have an average score of at least 80. What is the minimum score the student must get on the fifth test to pass the class? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 9758,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a city park, there are 9 different benches arranged in a straight line, each spaced 10 meters apart. How many people must be seated on these benches to ensure that at least two people are seated no more than 20 meters apart? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 9759,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( x = a + 7 \\), evaluate the expression \\( (x - a + 3) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 9760,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Eva has saved up $50 in quarters. She wants to buy some snacks from a machine that accepts only quarters. Candy bars cost ¢25 each, pieces of chocolate cost ¢75 each, and packs of juice cost ¢50 each. If Eva buys 4 candy bars, 3 pieces of chocolate, and 2 packs of juice, how many quarters will she have left after her purchase? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "183",
"style": "rule"
}
|
numina_math
|
{
"index": 9761,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression $\\dfrac{3 \\times (8 - 3)}{2 + \\dfrac{12}{4}}$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 9762,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train travels from City A to City B at a constant speed of 60 miles per hour. After reaching City B, it immediately returns to City A at a constant speed of 40 miles per hour. If the entire round trip takes 5 hours, how far is City B from City A? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 9763,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is offering a 25% discount on a jacket. If the original price of the jacket is $80, what is the discounted price? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 9764,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Liam is saving money to buy a new video game that costs $45. He saves $12 each week. In addition, he finds $3 in coins every week. How many weeks will it take Liam to save enough money to buy the video game? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 9765,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the value of \\( \\frac{(72 - 18) \\times 5}{9} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 9766,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels 120 kilometers in 3 hours. If the car continues to travel at the same speed, how far will it travel in 7 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "280",
"style": "rule"
}
|
numina_math
|
{
"index": 9767,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A toy factory packages toys in boxes. Each box contains 12 toys. The factory produces 144 toys per hour. If the factory works for 8 hours a day, how many boxes can they fill in one day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "96",
"style": "rule"
}
|
numina_math
|
{
"index": 9768,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A local train service runs a shuttle between two towns. On a certain day, the train carried 75 passengers from Town A to Town B in the morning and 45 passengers from Town B to Town A in the afternoon. If the train made two additional round trips that day, carrying the same number of passengers as the first trip in each trip, calculate the total number of passengers transported between both towns. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "360",
"style": "rule"
}
|
numina_math
|
{
"index": 9769,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company offers a starting salary of $45,000 with an annual raise of $3,000. If an employee's salary follows this arithmetic sequence, how many years will it take for the employee's salary to reach $72,000? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 9770,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah wants to buy notebooks for her class. Each notebook costs $2.50, and she needs to purchase 24 notebooks. How much will Sarah spend in total for the notebooks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60.00",
"style": "rule"
}
|
numina_math
|
{
"index": 9771,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah and Mark are organizing a charity event. For every 2 tickets Sarah sells, Mark sells 3. Together, they sold a total of 60 tickets. How many tickets did each of them sell? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 9772,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex wants to save for a new bicycle that costs $600. He plans to save 10% of his monthly income each month. If Alex’s monthly income is $2000, how many months will it take for him to save enough to buy the bicycle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 9773,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is saving money to buy a new bicycle that costs $720. She decides to save a fixed amount of money every week from her part-time job. If she plans to save $15 per week and receives an additional $14 from her parents each week, how many weeks will it take Samantha to save enough money to buy the bicycle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 9774,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the maximum value of \\(k\\) such that the sum of the squares of \\(k\\) consecutive integers starting from 1 is less than 1000. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 9775,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there are 120 students. One-third of the students are in the science club, one-fourth are in the math club, and one-sixth are in the art club. How many students are not in any club? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 9776,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the rational expression \\(\\frac{n^2 + 2n + 1}{n+1}\\). Simplify this expression and then find the sum of the simplified form evaluated from \\(n = 1\\) to \\(n = 10\\). Finally, determine the remainder when this sum is divided by 7. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 9777,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a triangle \\( \\Delta ABC \\), the sides opposite angles \\( A \\), \\( B \\), and \\( C \\) are \\( a \\), \\( b \\), and \\( c \\) respectively. Given that \\( \\angle A = 60^\\circ \\), \\( \\angle B = 45^\\circ \\), and the side \\( c = 10 \\) units, find the length of side \\( a \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\sqrt{1900-1000\\sqrt{3}}",
"style": "rule"
}
|
numina_math
|
{
"index": 9778,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery produces 6 dozen cookies per hour. If the bakery operates for 8 hours a day, how many cookies will they produce in a 5-day workweek? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2880",
"style": "rule"
}
|
numina_math
|
{
"index": 9779,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Out of 200 students in a school, 1/4 of them are participating in a math competition. If 40% of the participants are girls, how many boys are participating in the competition? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 9780,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x) \\) be a function that takes a four-digit number \\( x \\) and returns the remainder when \\( x^2 \\) is divided by 10000. Determine if there exists a four-digit number \\( x \\) such that \\( f(x) \\) is a fixed point, i.e., \\( f(x) = x \\). If such a number exists, find it. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9376",
"style": "rule"
}
|
numina_math
|
{
"index": 9781,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a puzzle game, three friends - Alice, Bob, and Carol - each make a statement about a mysterious number, \\( N \\), which is an integer between 1 and 100. \n- Alice says: \"The number is a power of 2.\"\n- Bob says: \"The number is odd.\"\n- Carol says: \"The number is a multiple of 5.\"\n\nOnly one of these statements is true. What is \\( N \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 9782,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma has a recipe that requires 3/4 cup of sugar to make 18 cookies. How many cups of sugar does she need to make 54 cookies? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.25",
"style": "rule"
}
|
numina_math
|
{
"index": 9783,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jamie needs to fill a swimming pool with water. The pool has a volume of 20,000 liters. Jamie has a hose that dispenses water at a rate of 50 liters per minute. How many hours will it take to fill the pool completely? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6.67",
"style": "rule"
}
|
numina_math
|
{
"index": 9784,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, 60% of the students are girls, and the rest are boys. If there are 24 boys in the classroom, how many girls are there? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 9785,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John repairs 5 cars. Three of the cars take 40 minutes each to repair. The remaining two cars take 50% longer each to repair. He makes $20 per hour repairing cars. How much money does he make 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": 9786,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tom has only been getting 5 hours of sleep per night. He decides to increase his sleep time by 2/5. How many hours of sleep does he get per night after making this change? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 9787,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the least positive integer \\( x \\) such that \\( x \\equiv 3 \\pmod{5} \\) and \\( x \\equiv 4 \\pmod{7} \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 9788,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A water tank can hold 750 gallons of water. If each bucket used to fill the tank holds 25 gallons of water, how many buckets are needed to fill the tank completely? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 9789,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "During a school charity event, the teachers and students together collected 240 pounds of food. The teachers collected 3 times as much food as the students. How many pounds of food did the students collect? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 9790,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical tank has a height of 10 feet and a diameter of 6 feet. The tank is partially filled with water to a height of 4 feet. If water is added to fill the tank completely, what volume of water, in cubic feet, is needed to fill the tank? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "169.65",
"style": "rule"
}
|
numina_math
|
{
"index": 9791,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The first term of an arithmetic sequence is a Fibonacci number, and the common difference is also a Fibonacci number. If the first term of the sequence is \\( F_5 \\) and the common difference is \\( F_3 \\), find the sum of the first 10 terms of this arithmetic sequence. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "140",
"style": "rule"
}
|
numina_math
|
{
"index": 9792,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John has $50 and wants to buy some items. Each item costs $2.50. After purchasing the items, he wants to save 20% of the remaining money for future expenses. How many items can John buy, and how much money will he save? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 9793,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma's grandmother is 75 years old. Emma is 1/3 the age of her mother, and her mother is 1/2 the age of her grandmother. How old is Emma? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12.5",
"style": "rule"
}
|
numina_math
|
{
"index": 9794,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, the teacher wants to arrange the students into rows such that each row has either 5 or 7 students. If there are 38 students in total, how many rows have exactly 7 students if every seat is occupied? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 9795,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, the ratio of the number of boys to the number of girls is 3:4. If there are 21 boys, how many girls are there in the classroom? Also, find the total number of students in the classroom. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "49",
"style": "rule"
}
|
numina_math
|
{
"index": 9796,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah measured the lengths of four different fabric pieces she bought. The lengths were as follows: $\\frac{1}{2}$ meter, $\\frac{3}{4}$ meter, $\\frac{5}{6}$ meter, and $\\frac{1}{3}$ meter. She wants to divide each fabric length into $\\frac{1}{4}$ meter strips. After dividing, she plans to add up all the strips to determine the total number of strips she has. Calculate the total number of strips Sarah will have. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 9797,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa is planning her wedding and is budgeting for the flowers. Each bouquet costs $45, and she wants to have 20 bouquets for the venue. She also needs centerpieces for the tables, and each centerpiece costs $30. If she plans to have 15 tables, how much will Lisa need to budget for both the bouquets and the centerpieces? Additionally, if Lisa has already saved $500, how much more does she need to save to cover the total cost? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "850",
"style": "rule"
}
|
numina_math
|
{
"index": 9798,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore sells two types of book bundles: Bundle A and Bundle B. Bundle A contains 3 fiction books and 2 non-fiction books, and Bundle B contains 5 fiction books and 4 non-fiction books. If a customer buys a total of 26 fiction books and 18 non-fiction books, how many of each type of bundle did they purchase? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 9799,
"name": "numina_math",
"split": "train"
}
|
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