prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "Sophia is organizing a party and has bought 36 cupcakes. She wants to distribute the cupcakes equally among 6 children. How many cupcakes will each child get? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2300,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Betty has three jars with a different number of marbles in each. The first jar contains 45 marbles, the second jar contains 62 marbles, and the third jar contains an unknown number of marbles. Betty wants to distribute all the marbles equally among her 7 friends. If she finds out that after distributing the marbles equally, each friend gets exactly 21 marbles, how many marbles are there in the third jar? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2301,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah wants to divide her collection of 72 marbles equally among her 3 friends. After distributing the marbles, she decides to buy 5 more marbles for each friend. How many marbles will each friend have in total after Sarah buys the additional marbles? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "29",
"style": "rule"
}
|
numina_math
|
{
"index": 2302,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation \\( \\sqrt{5x + 6} + 2 = x \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{9+\\sqrt{89}}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2303,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where all items are 35% off. If an item originally costs $120, what is the sale price of the item after the discount? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "78",
"style": "rule"
}
|
numina_math
|
{
"index": 2304,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of 5 friends decides to take a photo together. They each want to stand in a line, but they all have different heights. In how many different ways can they arrange themselves in a line so that no one is standing in their original position as per their heights? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "44",
"style": "rule"
}
|
numina_math
|
{
"index": 2305,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Three friends, Alice, Bob, and Charlie, collectively have $300. The ratio of Alice's money to Bob's money is 5:4, and Alice has $50 more than Charlie. How much money does Charlie have? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 2306,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Calculate the product $\\left(\\frac{2}{4}\\right)\\left(\\frac{4}{6}\\right)\\left(\\frac{6}{8}\\right)\\cdots\\left(\\frac{2000}{2002}\\right)$. Express your answer as a common fraction. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{1001}",
"style": "rule"
}
|
numina_math
|
{
"index": 2307,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A research scientist needs to prepare a diluted solution using \\(5.4 \\times 10^{-3}\\) liters of a concentrated solution. They have a stock solution of \\(2.7 \\times 10^{-1}\\) liters. If they dilute the stock solution by dividing it into equal parts, how many parts will each part contain \\(5.4 \\times 10^{-3}\\) liters? Express the number of parts in scientific notation. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5.0\\times10^{1}",
"style": "rule"
}
|
numina_math
|
{
"index": 2308,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A chef uses a secret ingredient that costs $10 per ounce. He finds a new supplier and the price of the ingredient is now 20% cheaper. If he needs 50 ounces of this ingredient for a recipe, how much does he save with the new supplier compared to the original price? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 2309,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The seats of a theater are arranged in 30 rows with 12 seats per row. At the start of a show, 150 people are seated. During the show, 20 more people arrive and find seats, but 5 people leave early. How many empty seats are there after these changes? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "195",
"style": "rule"
}
|
numina_math
|
{
"index": 2310,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression \\(5(3 + 4) + 2(6 + 1)\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "49",
"style": "rule"
}
|
numina_math
|
{
"index": 2311,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A circle is inscribed within a rectangle with vertices at (1, 1), (1, 5), (7, 1), and (7, 5). The circle is tangent to all four sides of the rectangle. The Cookie Monster wants to know the radius of the circle and the area of the circle. What is the radius and the area of the circle? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4\\pi",
"style": "rule"
}
|
numina_math
|
{
"index": 2312,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma has a daily routine that includes 45 minutes of exercise, 1 hour and 15 minutes of reading, and 35 minutes of cooking. If she starts her routine at 6:00 PM, at what time will she finish all her activities? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8:35",
"style": "rule"
}
|
numina_math
|
{
"index": 2313,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, there are 3 times as many boys as girls. The total number of students is 32. How many boys and girls are there in the classroom? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 2314,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "At a party, there are three large bowls of fruit punch. Each bowl has the same amount of punch. The total amount of punch in the three bowls is 240 liters. If the punch needs to be poured into smaller cups, each holding 5 liters, how many cups can be filled? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 2315,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Use the Rational Root Theorem to find all the rational roots of the polynomial equation \\(2x^3 - 3x^2 - 8x + 12 = 0\\), and then factorize the polynomial completely. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2-\\frac{3}{2}-2",
"style": "rule"
}
|
numina_math
|
{
"index": 2316,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length given by the polynomial \\(3x + 5\\) meters and a width given by \\(x + 2\\) meters. If the area of the garden is 91 square meters, find the value of \\(x\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.68",
"style": "rule"
}
|
numina_math
|
{
"index": 2317,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular flower garden is 6 meters long and 4 meters wide. If you want to plant flowers in a pattern where each flower takes up a square plot of 0.5 meters by 0.5 meters, how many flowers can you plant in the garden? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "96",
"style": "rule"
}
|
numina_math
|
{
"index": 2318,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many numbers in the set {14, 25, 32, 17, 48, 23, 56, 19, 31} are greater than 20? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2319,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Under standard growth conditions, the bacterial strain E.coli has a doubling time of 20 minutes. If 1 single bacterial cell is used to start a culture grown under standard growth conditions, how many bacterial cells will there be after the culture is grown for 4 hours? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4096",
"style": "rule"
}
|
numina_math
|
{
"index": 2320,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Henry went to the beach and picked up 17 perfect shells and 52 broken shells. Out of those 52 broken shells, half of them were spiral. Out of the 17 perfect shells, 12 of them were not spiral. How many more broken spiral shells were there than perfect spiral shells? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "21",
"style": "rule"
}
|
numina_math
|
{
"index": 2321,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels from Point A to Point B at a speed of 15 km/h and returns from Point B to Point A at a speed of 10 km/h. If the entire trip took 5 hours, how far is Point B from Point A? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2322,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a constant speed of 60 miles per hour. How long will it take to cover a distance of 360 miles, and how much distance will it cover in 3.5 hours? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "210",
"style": "rule"
}
|
numina_math
|
{
"index": 2323,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( z \\) be a complex number such that \\( z = 3 + 4i \\). Compute the magnitude of \\( z \\cdot \\overline{z} \\), where \\( \\overline{z} \\) is the conjugate of \\( z \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 2324,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily decides to start a savings plan. She starts by saving $50 in the first week and decides to increase her savings by $10 each subsequent week. How much money will Emily have saved in total after 8 weeks? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "680",
"style": "rule"
}
|
numina_math
|
{
"index": 2325,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A square garden has an area of 144 square meters. John wants to install a fence around the garden, but he has only 50 meters of fencing material. Will he be able to enclose the entire garden with the fencing material he has? Justify your answer using appropriate calculations. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{yesjohnwillbeabletoenclosethegardenwiththefencingmaterialhehas.}",
"style": "rule"
}
|
numina_math
|
{
"index": 2326,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A theater has 300 seats arranged in an arithmetic sequence across 15 rows, with each row having 2 more seats than the previous row. How many seats are there in the first row? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2327,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the infinite series \\( S = \\sum_{n=1}^{\\infty} \\frac{1}{n!} \\). What is the probability that a randomly selected term from this series (where the terms are all the reciprocals of factorials from \\(1!\\) to \\(n!\\) for \\(n \\to \\infty\\)) is a fraction whose denominator is a prime number? Express your answer as a common fraction. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2328,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden's length is increased by 20%, and its width is increased by 15%. If the original dimensions of the garden are 50 feet by 40 feet, by what percentage does the area of the garden increase? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "38",
"style": "rule"
}
|
numina_math
|
{
"index": 2329,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Calculate the sum of all the two-digit integers that are prime and lie within a sequence of five consecutive integers. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "236",
"style": "rule"
}
|
numina_math
|
{
"index": 2330,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two cyclists, Alex and Brian, are training on a 20-mile circular track. Alex rides at a speed of 12 mph, while Brian rides at a speed of 8 mph. If they start at the same point and ride in the same direction, after how many hours will Alex be 10 miles ahead of Brian? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2331,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa, Mark, and Julia were tasked with sorting apples. Lisa sorted 15 apples in the morning and 20 in the afternoon. Mark sorted 10 apples in the morning and 25 in the afternoon. Julia sorted 12 apples in the morning and 18 in the afternoon. How many more apples did Julia sort than Lisa and Mark combined in the morning? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 2332,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily wants to save money by buying groceries in bulk. She has a choice between buying a pack of 12 cans of soup for $18, or buying individual cans that cost $1.75 each. If Emily needs 36 cans of soup for the next three months, how much money will she save by choosing the bulk option over buying individual cans? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9.00",
"style": "rule"
}
|
numina_math
|
{
"index": 2333,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the polynomial \\( P(x) = x^4 + ax^3 + bx^2 + cx + d \\) with rational coefficients. It is known that one of its roots is \\(\\sqrt{2} + 1\\). Given that the polynomial has a symmetrical property and uses the Rational Root Theorem, determine the polynomial \\( P(x) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "p(x)=x^4-6x^2+1",
"style": "rule"
}
|
numina_math
|
{
"index": 2334,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anahi bought a 600-page journal to document her travels. In the first month, she wrote on 120 pages. In the second month, she wrote on 25% of the remaining pages. Unfortunately, she spilled water on the journal, damaging 30% of the remaining empty pages she was yet to write on. Calculate the total number of empty pages available for her to write on now. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "252",
"style": "rule"
}
|
numina_math
|
{
"index": 2335,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mrs. Lim milks her cows twice a day. Yesterday morning, she got 68 gallons of milk, and in the evening, she got 82 gallons. This morning, she got 18 gallons fewer than she had yesterday morning. After selling some gallons of milk in the afternoon, Mrs. Lim has only 24 gallons left. How much was her revenue for the milk if each gallon costs $3.50? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "616",
"style": "rule"
}
|
numina_math
|
{
"index": 2336,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John wants to accumulate $\\$5000$ in his savings account in 4 years. He plans to invest a certain amount of money in an account that offers an annual interest rate of 5%, compounded annually. Additionally, he wants to make annual contributions of $\\$1000$ at the end of each year. How much should John invest initially to meet his goal? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "567.50",
"style": "rule"
}
|
numina_math
|
{
"index": 2337,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the circle with the equation \\( (x-3)^2 + (y-4)^2 = 25 \\) and the parabola with the equation \\( y = x^2 - 6x + 8 \\). Determine the values of \\( k \\) for which the line \\( y = kx + 2 \\) is tangent to the parabola and intersects the circle exactly once. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "k=-6+2\\sqrt{6}k=-6-2\\sqrt{6}",
"style": "rule"
}
|
numina_math
|
{
"index": 2338,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the least common multiple (LCM) of 6, 8, and 12. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 2339,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A jar contains 10 quarters, 15 nickels, and 20 pennies. If three coins are randomly selected from the jar, what is the probability that exactly two of the selected coins are quarters? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{105}{946}",
"style": "rule"
}
|
numina_math
|
{
"index": 2340,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two numbers, \\(x\\) and \\(y\\), have a greatest common divisor (GCD) of 12 and a least common multiple (LCM) of 180. If \\(x\\) is known to be 36, what is \\(y\\)? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 2341,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a circle with center \\(O\\) and radius 5, let \\(A\\) and \\(B\\) be points on the circle such that \\(\\angle AOB = 60^\\circ\\). Convert the polar coordinates of \\(A\\) and \\(B\\) to Cartesian coordinates, then use trigonometric identities to find the distance between points \\(A\\) and \\(B\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2342,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The length of a rectangle is three times its width. If the perimeter of the rectangle is 64 meters, what are the length and width of the rectangle? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{width} = 8 \\text{ meters}, \\text{length} = 24 \\text{ meters}",
"style": "rule"
}
|
numina_math
|
{
"index": 2343,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that \\( p, q, r, s \\) are the roots of a polynomial, and the following conditions are satisfied:\n\\[ p + q + r + s = 8 \\]\n\\[ pq + pr + ps + qr + qs + rs = 12 \\]\nFind the largest possible value of \\( s \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2344,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A runner completes a lap around a track in 2 minutes and 30 seconds. If the runner continues at the same pace, how many laps will they complete in 1 hour and 15 minutes? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2345,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Angela is a bike messenger in New York. She needs to deliver 8 times as many packages as meals. If she needs to deliver 27 meals and packages combined, how many meals does she deliver? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2346,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jessica has $45.75 in her bank account. She deposits $20.50 and then withdraws $35.25. How much money does Jessica have in her bank account after these transactions? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "31.00",
"style": "rule"
}
|
numina_math
|
{
"index": 2347,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah invested 1,000 USD in a savings account that pays compound interest annually at a rate of 4%. How much money will she have in the account at the end of 5 years? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1216.65",
"style": "rule"
}
|
numina_math
|
{
"index": 2348,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from Town A to Town B at an average speed of 50 miles per hour. On the return trip from Town B to Town A, due to traffic, the car travels at an average speed of 30 miles per hour. If the total travel time for the round trip is 8 hours, what is the distance between Town A and Town B? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 2349,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The scores of five students in a math test are given as follows: $72$, $85$, $90$, $88$, and $95$. Calculate the arithmetic mean of these scores. Then express the mean as a fraction in its simplest form. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{86}{1}",
"style": "rule"
}
|
numina_math
|
{
"index": 2350,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A map has a scale of 1:10,000, meaning that 1 inch on the map represents 10,000 inches in real life. If two cities are 2.5 inches apart on the map, what is the actual distance between the cities in miles? (Note: 1 mile = 63,360 inches) Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.4",
"style": "rule"
}
|
numina_math
|
{
"index": 2351,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A project manager is scheduling tasks for a team of workers. Each task takes 1.5 hours to complete. The team works 6 hours a day. If the project manager needs to complete a total of 30 tasks, how many days will it take to finish the project? Additionally, if the team is composed of 3 workers, and each worker is given an equal number of tasks, how many tasks does each worker complete? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 2352,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist is training for a race and plans to ride his bike at a constant speed. He knows that he can cover 60 kilometers in 4 hours. If he wants to increase his speed by 25%, how far will he travel in the same amount of time (4 hours) at the new speed? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 2353,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, there are 15 more boys than girls. The average age of the boys is 12 years, and the average age of the girls is 10 years. If the total number of students is 45, what is the combined average age of all the students in the classroom? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11.33",
"style": "rule"
}
|
numina_math
|
{
"index": 2354,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the inverse of the function: \\( f(x) = 3x + 4 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "f^{-1}(x)=\\frac{x-4}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 2355,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the excluded values for the rational expression \\(\\frac{5x^3 - 20x}{x^3 - 4x}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "02-2",
"style": "rule"
}
|
numina_math
|
{
"index": 2356,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A team of workers is repainting a warehouse. They paint 200 square meters each day. After 5 days of work, there are still 300 square meters left unpainted. What is the total area of the warehouse? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{thetotalareaofthewarehouseis1300squaremeters.}",
"style": "rule"
}
|
numina_math
|
{
"index": 2357,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria is reading a novel. She reads at a constant speed of 40 pages per hour. She starts reading at 2:00 PM and needs to finish the novel by 8:00 PM. If she has already read 60 pages before 2:00 PM and the novel has a total of 300 pages, how many hours will she have left to spare after finishing the novel? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2358,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial equation \\((x+3)(x^2 + ax + b) = x^3 + 4x^2 + cx + d\\), find the values of \\(a\\), \\(b\\), \\(c\\), and \\(d\\) by equating coefficients. Simplify the expressions when necessary and solve for \\(a\\) and \\(b\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "a=1b=4c=7d=12",
"style": "rule"
}
|
numina_math
|
{
"index": 2359,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden's length is twice its width. The perimeter of the garden is 60 meters. Find the area of the garden. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "200",
"style": "rule"
}
|
numina_math
|
{
"index": 2360,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( x = 3 \\), find the value of \\( y \\) in the expression \\( y = 2x^2 + 5x \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33",
"style": "rule"
}
|
numina_math
|
{
"index": 2361,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is planning a birthday party and has a budget of $200. She wants to buy party hats and balloons. Each party hat costs $2, and she plans to buy 20 of them. Balloons come in packs of 10, and each pack costs $5. After buying the party hats, how many packs of balloons can Emily buy without exceeding her budget? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32",
"style": "rule"
}
|
numina_math
|
{
"index": 2362,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Express $0.\\overline{36}$ as a fraction in its lowest terms and then compute the value of $\\left(0.\\overline{36}\\right)^{-1}$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{11}{4}",
"style": "rule"
}
|
numina_math
|
{
"index": 2363,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma wants to buy a new smartphone that costs $750. She finds a deal that offers a 15% discount. After applying the discount, she also has to pay a sales tax of 8% on the discounted price. How much will she pay in total for the smartphone? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "688.50",
"style": "rule"
}
|
numina_math
|
{
"index": 2364,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A baker has 120 cupcakes. He wants to divide them equally among 8 boxes. After filling the boxes, he decides to give away 3/4 of the boxes. How many boxes of cupcakes does the baker have left? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2365,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given a regular polygon where the sum of its interior angles is 540 degrees, find the number of sides of the polygon. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2366,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that the graphs of \\( y = k(x) \\) and \\( y = m(x) \\) intersect at \\((1, 3)\\), \\((3, 5)\\), and \\((5, 7)\\), find the intersection point of \\( y = k(\\sqrt{x}) \\) and \\( y = m(x) - 1 \\). Also, calculate 50% of the y-coordinate of the intersection point. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{novalidintersectionpointfound}",
"style": "rule"
}
|
numina_math
|
{
"index": 2367,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation for \\( x \\) in the interval \\( 0 \\leq x < 2\\pi \\):\n\\[ \\sin(2x) = 1 - 2\\cos^2(x) \\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{nosolutions}",
"style": "rule"
}
|
numina_math
|
{
"index": 2368,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert $270^\\circ$ to radians and compute its cosine value. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2369,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company produces and sells two types of products: A and B. The revenue from selling one unit of product A is $150, and from selling one unit of product B is $200. The cost to produce one unit of product A is $100, and the cost to produce one unit of product B is $120. Last month, the company sold 300 units of product A and 250 units of product B. What is the total profit earned by the company from both products last month? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "35000",
"style": "rule"
}
|
numina_math
|
{
"index": 2370,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the cost of 3 books and 5 pens is $27, and the cost of 2 books and 3 pens is $18, find the cost of one book and one pen. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 2371,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A blueprint of a house uses a scale where 1 inch represents 8 feet. If the living room measures 3 inches by 4 inches on the blueprint, what are the actual dimensions of the living room in feet? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24 \\text{ feet} \\times 32 \\text{ feet}",
"style": "rule"
}
|
numina_math
|
{
"index": 2372,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In triangle \\( \\triangle ABC \\), the perimeter is 24. The side lengths are such that \\( AB = AC \\) and \\( BC = 10 \\). If \\( A \\) is at the origin \\((0,0)\\) and \\( B \\) is at \\((x, 0)\\), find the coordinates of \\( C \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "(-\\frac{1}{7}\\frac{20\\sqrt{3}}{7})\\text{or}(-\\frac{1}{7}-\\frac{20\\sqrt{3}}{7})",
"style": "rule"
}
|
numina_math
|
{
"index": 2373,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression \\(\\frac{\\sqrt{18} + \\sqrt{50}}{\\sqrt{2} + \\sqrt{5}}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-\\frac{16}{3}+\\frac{8\\sqrt{10}}{3}",
"style": "rule"
}
|
numina_math
|
{
"index": 2374,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two angles are complementary, and one angle is 20 degrees less than twice the other angle. What are the measures of the two angles? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36.67 \\text{ degrees and } 53.34 \\text{ degrees}",
"style": "rule"
}
|
numina_math
|
{
"index": 2375,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression \\( \\frac{3 + \\sqrt{5}}{2 - \\sqrt{3}} \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6+3\\sqrt{3}+2\\sqrt{5}+\\sqrt{15}",
"style": "rule"
}
|
numina_math
|
{
"index": 2376,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the functions \\( f(x) = x^2 - 4 \\) and \\( g(x) = 2x + 1 \\), find the \\( x \\)-coordinates of the points where the graphs of \\( y = f(g(x)) \\) and \\( y = g(f(x)) \\) intersect. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{norealintersectionpoints}",
"style": "rule"
}
|
numina_math
|
{
"index": 2377,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A water tank is being filled by two pipes. Pipe A can fill the tank in 4 hours, and Pipe B can fill the tank in 6 hours. However, there is a leak in the tank that can drain one-sixth of the tank's capacity per hour. If all three (Pipe A, Pipe B, and the leak) are operating together, how long will it take to fill the tank completely? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2378,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the Fibonacci sequence defined by \\(F_1 = 1\\), \\(F_2 = 1\\), and \\(F_n = F_{n-1} + F_{n-2}\\) for \\(n \\geq 3\\). What is the remainder when \\(F_{100}\\) is divided by 8? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2379,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression \\(\\left(\\frac{27}{8}\\right)^{2/3} \\times \\sqrt[3]{\\frac{64}{81}}\\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{3}{\\sqrt{[}3]{3}}",
"style": "rule"
}
|
numina_math
|
{
"index": 2380,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a population of bacteria that doubles every hour. The initial population at time \\( t = 0 \\) is 100. However, every hour, there is a 10% chance that a disaster will strike, wiping out half of the current population. If a disaster occurs at any given hour, what is the expected population after 3 hours? Express your answer as a fraction. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{6331625}{10000}",
"style": "rule"
}
|
numina_math
|
{
"index": 2381,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Johnny has a collection of nickels and dimes that add up to a total value of $2.15. If the number of nickels is 7 more than twice the number of dimes, how many nickels and dimes does Johnny have? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\text{johnnyhas9dimesand25nickels.}",
"style": "rule"
}
|
numina_math
|
{
"index": 2382,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A laptop is initially priced at $800. During a special promotion, the store offers a 25% discount on the laptop. After applying the discount, an additional 10% sales tax is added. What is the final price of the laptop? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "660",
"style": "rule"
}
|
numina_math
|
{
"index": 2383,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two fair dice are rolled. What is the probability that the sum of the numbers shown is not 7? Express your answer as a common fraction in lowest terms. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{5}{6}",
"style": "rule"
}
|
numina_math
|
{
"index": 2384,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the equation of a circle, \\( (x - 3)^2 + (y + 2)^2 = 25 \\), and the point \\( P(7, y) \\) on the circle, find the value of \\( y \\). Simplify your answer involving radicals. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-5",
"style": "rule"
}
|
numina_math
|
{
"index": 2385,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( y \\) in the equation: \\( 5y - 3(2y - 4) = 2(y + 6) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2386,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John starts his homework at 3:45 PM and takes a break every 20 minutes. If he finishes his homework at 6:25 PM, how many breaks did he take? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2387,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maria is saving to buy a new laptop that costs $1,200. She already has $500 saved. She plans to save an additional $100 per month. How many months will it take Maria to save enough money to buy the laptop if she also receives a 5% discount on the laptop price at the time of purchase? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2388,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the sum of the infinite series \\( S = 0.\\overline{9} + 0.\\overline{99} + 0.\\overline{999} + \\ldots \\) Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\infty",
"style": "rule"
}
|
numina_math
|
{
"index": 2389,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the remainder when the polynomial \\( P(x) = x^4 + 3x^3 - 5x^2 + 2x + 7 \\) is divided by \\( x - 2 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "31",
"style": "rule"
}
|
numina_math
|
{
"index": 2390,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $\\mathbf{u}$ and $\\mathbf{v}$ be orthogonal vectors, and let $\\mathbf{w}$ be a vector such that $\\mathbf{w} = \\mathbf{u} \\times \\mathbf{v}$. If $\\|\\mathbf{u}\\| = 3$ and $\\|\\mathbf{v}\\| = 4$, find $\\mathbf{w} \\cdot (\\mathbf{u} + \\mathbf{v})$. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2391,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there are 50 students who participate in either the Math Club, the Science Club, or both. Out of these students, 30 are in the Math Club and 25 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": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2392,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial function \\( f(x) = x^6 - 2x^4 + x^2 - 3 \\), verify whether it is symmetric with respect to the y-axis and evaluate \\( f(-2) \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33",
"style": "rule"
}
|
numina_math
|
{
"index": 2393,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Rationalize the denominator and simplify the following expression:\n\\[\n\\frac{3}{\\sqrt{2} + 1}\n\\] Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3\\sqrt{2}-3",
"style": "rule"
}
|
numina_math
|
{
"index": 2394,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a community garden, 3/5 of the plots are designated for vegetables, and the rest are for flowers. If 1/3 of the vegetable plots are used for tomatoes, and there are 150 plots in total, how many plots are used for tomatoes? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2395,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Julia needs to paint a fence that is 150 meters long. She knows that she can paint at a rate of 12 square meters per hour. The fence is 2 meters tall. How many hours will it take Julia to paint the entire fence, and if she can only paint for 5 hours each day, how many days will it take her to complete the job? Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2396,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the repeating decimal $0.\\overline{428}$ to a fraction and simplify it. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{428}{999}",
"style": "rule"
}
|
numina_math
|
{
"index": 2397,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Compare the fractions $\\frac{15}{4}$ and $\\frac{23}{6}$. Which fraction is greater? Express each fraction as a mixed number and a decimal, then determine which is larger. Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{23}{6}",
"style": "rule"
}
|
numina_math
|
{
"index": 2398,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the functions \\( f(x) = x^2 + 3 \\) and \\( g(x) = 2x - 1 \\), find the value of \\( x \\) such that \\( (f \\circ g)(x) = 19 \\). Let's think step by step and output the final answer within \boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-\\frac{3}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2399,
"name": "numina_math",
"split": "train"
}
|
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