prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "Find the coefficient of \\( x^3 \\) in the expansion of \\( (2x + 3)(x^2 - x + 4) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 10700,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a circle with center \\( O \\) and radius \\( 5 \\). Points \\( P \\) and \\( Q \\) are diametrically opposite on the circle, and the line segment \\( PQ \\) is a diameter. A point \\( R \\) lies on the circle such that the line segment \\( PR \\) is perpendicular to \\( PQ \\). If \\( R \\) is reflected over the line \\( PQ \\) to obtain a point \\( S \\), find the area of the quadrilateral \\( PORQ \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{25}{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 10701,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma baked 60 cookies and wants to distribute them equally among her 4 friends. If she decides to keep 5 cookies for herself, how many cookies will each friend get? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 10702,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A square piece of cardboard with a side length of 24 centimeters is used to create a cylindrical container by rolling it along one of its edges, forming the lateral surface of the cylinder. A circular base is then made from the remaining cardboard. Determine the total area of the cardboard used to make the cylinder, including its base. Express your answer in square centimeters. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "621.86",
"style": "rule"
}
|
numina_math
|
{
"index": 10703,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the vector equations of two lines:\n\\[ \\mathbf{r}_1 = \\begin{pmatrix} 1 \\\\ 2 \\\\ a \\end{pmatrix} + t \\begin{pmatrix} 2 \\\\ 1 \\\\ 3 \\end{pmatrix} \\]\n\\[ \\mathbf{r}_2 = \\begin{pmatrix} 4 \\\\ b \\\\ 2 \\end{pmatrix} + u \\begin{pmatrix} -1 \\\\ 4 \\\\ 1 \\end{pmatrix} \\]\nFind the values of \\( a \\) and \\( b \\) such that the lines intersect. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-1",
"style": "rule"
}
|
numina_math
|
{
"index": 10704,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a number \\( x \\) when divided by 5 leaves a remainder of 3, what is the value of \\( x \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 10705,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A clothing store offers a sequential discount on a $120 jacket. First, they apply a 20% discount, and then they apply an additional 10% discount on the new price. How much does the jacket cost after both discounts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "86.40",
"style": "rule"
}
|
numina_math
|
{
"index": 10706,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A point \\(P\\) is located at \\((3, 4)\\) on the coordinate plane. A circle with center at the origin and radius 5 is drawn. A line is drawn from \\(P\\) and intersects the circle at point \\(Q\\) such that \\(PQ\\) is tangent to the circle. If the x-coordinate of \\(Q\\) is rational, find the decimal representation of the y-coordinate of \\(Q\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 10707,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces widgets at a consistent rate. Each widget requires 3 minutes of machine time to be completed. If the factory operates 8 hours a day and has 5 machines working simultaneously, how many widgets can the factory produce in a single day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "800",
"style": "rule"
}
|
numina_math
|
{
"index": 10708,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah can type at a rate of 40 words per minute. She needs to type a report that is 1,200 words long. If she takes a 5-minute break after every 20 minutes of typing, how long will it take her to complete the report? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 10709,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jon and his three friends went out for dinner and decided to split the bill equally. The total bill, including tax and tip, came to $120. If they also decided to leave a $15 tip on top of the total bill, how much does each person need to pay?\n\n### Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33.75",
"style": "rule"
}
|
numina_math
|
{
"index": 10710,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jebb receives a paycheck of $650, but he has to pay 10% of it as tax. How much is his take-home pay after the tax deduction? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "585",
"style": "rule"
}
|
numina_math
|
{
"index": 10711,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory increased its production efficiency and now produces 200 units per day, which is 25% more than its previous daily production. What was the factory's previous daily production? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "160",
"style": "rule"
}
|
numina_math
|
{
"index": 10712,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma deposits $5000 in a savings account that offers an annual compound interest rate of 4% for a period of 5 years. How much money will Emma have in her account at the end of the 5 years? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6083.26",
"style": "rule"
}
|
numina_math
|
{
"index": 10713,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is organizing a community event and needs to measure the space for placing tables. She has a rectangular area that is 60 meters long and 45 meters wide. She wants to place tables such that each table occupies 5 square meters. How many tables can she place in the area? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "540",
"style": "rule"
}
|
numina_math
|
{
"index": 10714,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A triangle has vertices at \\( A(2, 3) \\), \\( B(8, 7) \\), and \\( C(4, -1) \\). The triangle is reflected about a line \\( L \\) such that the image points are \\( A'(2, -3) \\), \\( B'(8, -7) \\), and \\( C'(4, 1) \\). What is the equation of the line \\( L \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 10715,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $p$ be a prime number. Consider the decimal expansion of $\\frac{1}{p}$, which may be either terminating or repeating. If the decimal expansion of $\\frac{1}{p}$ is repeating with a period $k$, show that $k$ is the smallest integer such that $10^k \\equiv 1 \\pmod{p}$. Find the period of the decimal expansion of $\\frac{1}{17}$ and verify if it satisfies the properties discussed. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 10716,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A sequence of numbers starts at 5 and increases by 3 each time. If the sequence continues in this pattern, how many terms will be in the sequence before it reaches or exceeds 50? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 10717,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The functions \\( f(x) = 2x + 3 \\) and \\( g(x) = \\frac{x}{2} - 1 \\) are given. If \\( h(x) = f(g(x)) \\), find the value of \\( x \\) for which \\( h(x) = 7 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 10718,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah wants to distribute $1200 equally among her three children, but she decides to give an additional 10% of the total amount to her eldest child. How much money will each child receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "540",
"style": "rule"
}
|
numina_math
|
{
"index": 10719,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice and Bob are playing a game where they roll a six-sided die and multiply the results of their rolls together. Alice rolls the die three times and Bob rolls the die four times. If the product of Alice's rolls is less than the product of Bob's rolls, by how much could Bob's product exceed Alice's product? Assume the maximum possible results for both Alice and Bob. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1080",
"style": "rule"
}
|
numina_math
|
{
"index": 10720,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma has two cats, one weighing 8 pounds and the other weighing 6 pounds. She also has a dog that weighs twice as much as the two cats combined. If she can carry a maximum of 50 pounds in her pet carrier, how much additional weight can she carry after placing all her pets in the carrier? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 10721,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a party and needs to buy ingredients. She bought 15 kilograms of flour and 8.5 kilograms of sugar. Flour costs $2.25 per kilogram, and sugar costs $3.10 per kilogram. How much did Sarah spend in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60.10",
"style": "rule"
}
|
numina_math
|
{
"index": 10722,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider all polynomials of the form \n\\[ P(x) = x^5 + a_4 x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0 \\]\nwhere \\(a_i \\in \\{0,1\\}\\) for all \\(0 \\le i \\le 4\\). Each polynomial \\(P(x)\\) can have complex roots. Find the number of such polynomials that have exactly one real root and four complex roots, where the complex roots are conjugate pairs. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 10723,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A gardener is planting trees along a rectangular garden plot that measures 60 meters in length and 40 meters in width. He plants a tree every 4 meters along the perimeter of the garden plot. How many trees does he plant in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 10724,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore is having a sale where all books are offered at a 25% discount. If the discounted price of a book is $15, what was the original price of the book? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 10725,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\): \\(\\frac{2x + 3}{5} = \\frac{x - 2}{3}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-19",
"style": "rule"
}
|
numina_math
|
{
"index": 10726,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A motorcyclist travels from Town X to Town Y at an average speed of 60 kilometers per hour. On the return journey, he travels at an average speed of 40 kilometers per hour. The total round trip takes 5 hours. What is the distance between Town X and Town Y? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 10727,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah bought a certain number of apples and oranges from the market. She bought twice as many apples as oranges. The total cost of the apples was $18, and the total cost of the oranges was $12. If each apple costs $1 and each orange costs $2, how many apples and oranges did Sarah buy? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 10728,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In triangle \\(ABC\\), \\(\\angle A = 60^\\circ\\) and \\(\\angle B = 45^\\circ\\). If the side opposite \\(\\angle A\\) is 12 units, find the lengths of the sides opposite \\(\\angle B\\) and \\(\\angle C\\). Express your answer as a decimal to the nearest tenth. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "23.2",
"style": "rule"
}
|
numina_math
|
{
"index": 10729,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the sum of the prime numbers less than the factorial of 5? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1583",
"style": "rule"
}
|
numina_math
|
{
"index": 10730,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the greatest number of consecutive integers such that the sum of the digits of none of them is divisible by $3$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 10731,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Carlos bought a new laptop for $960. The price included a 20% sales tax. What was the original price of the laptop before the tax was added? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "800",
"style": "rule"
}
|
numina_math
|
{
"index": 10732,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The ratio of the number of boys to the number of girls in a school is 3:5. If there are 120 girls, how many boys are there in the school? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
numina_math
|
{
"index": 10733,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex had $500 saved up. He spent $150 on a new jacket and then received $75 from his birthday. If he decides to convert all his remaining money into euros at an exchange rate of 1 USD = 0.85 EUR, how many euros will Alex have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "361.25",
"style": "rule"
}
|
numina_math
|
{
"index": 10734,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A robotics club is forming a committee of 4 members from 6 candidates (A, B, C, D, E, and F), but they want to ensure that either A or B (or both) is included in the committee. How many different ways can this committee be formed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 10735,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anna and Ben are planning a trip from Town A to Town B. Anna drives at a constant speed, covering the distance in 3 hours. Ben drives at a different constant speed and covers the same distance in 4 hours. If Anna drives 20 miles per hour faster than Ben, find 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": "240",
"style": "rule"
}
|
numina_math
|
{
"index": 10736,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lily is preparing for her final exams and has made a study schedule. She plans to study for 2 hours every weekday, and on weekends she increases her study time to 4 hours each day. If her exams are in 4 weeks, how many hours will Lily have studied by the time her exams start? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
numina_math
|
{
"index": 10737,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a constant speed of 60 miles per hour. If the car's speed decreases by a rate of \\( r \\) miles per hour every hour, how many hours will it take for the car's speed to be reduced to 15 miles per hour if \\( r = \\frac{1}{4} \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 10738,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A chemist has a 200 mL solution with a 30% concentration of hydrochloric acid. If 50 mL of water evaporates from the solution, what is the new concentration of the solution? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 10739,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist rides from town A to town B. For the first 3 hours, he rides at an average speed of 20 kilometers per hour. For the next 4 hours, he increases his speed and rides at an average speed of 25 kilometers per hour. Calculate the total distance traveled and the average speed for the entire journey. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22.86",
"style": "rule"
}
|
numina_math
|
{
"index": 10740,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 1234 widgets in a day. If the factory operates for 7 days a week, how many widgets does it produce in a week? Round the total number of widgets produced to the nearest hundred. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8600",
"style": "rule"
}
|
numina_math
|
{
"index": 10741,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the smallest positive integer \\( x \\) that leaves a remainder of \\( 3 \\) when divided by \\( 5 \\), a remainder of \\( 4 \\) when divided by \\( 7 \\), and a remainder of \\( 2 \\) when divided by \\( 9 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "263",
"style": "rule"
}
|
numina_math
|
{
"index": 10742,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store sells a winter coat at a discounted price, offering a 30% discount on the original price. After applying the discount, the price of the coat is $210. What was the original price of the coat? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 10743,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Eva is baking cookies for a party, and she needs to make 3 dozen cookies. If each batch she bakes yields 8 cookies, how many batches does she need to bake? Additionally, if it takes 15 minutes to bake one batch, how long will it take her to bake all the cookies? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 10744,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has a rectangular field and wants to plant crops in a specific pattern. He decides to plant a row of crops every 1.5 meters along the length of the field, which is 45 meters long. If he starts planting at one end and plants a row every 1.5 meters until he reaches the other end, how many rows of crops will he plant? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 10745,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is managing her weekly schedule. She dedicates 40% of her week to work, 30% to sleep, and the rest to leisure activities. If she has a total of 168 hours in a week, how many hours does she allocate to leisure activities? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50.4",
"style": "rule"
}
|
numina_math
|
{
"index": 10746,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Matt is playing basketball and scores points in two quarters. In the first quarter, he made 2-point shots three times and 3-point shots five times. In the second quarter, he made 2-point shots five times and 3-point shots twice. How many points did he score in total for both quarters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "37",
"style": "rule"
}
|
numina_math
|
{
"index": 10747,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A test is with a full score of 100 points. Five students in a group want to reach an average of 92 points. If everyone scores a different whole number, what is the lowest score among them? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "66",
"style": "rule"
}
|
numina_math
|
{
"index": 10748,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa owns a small bookstore. She decides to increase the price of each book by 15% to cover rising costs. If the original price of a book is $20, how much will a customer pay for 3 books after the price increase? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "69",
"style": "rule"
}
|
numina_math
|
{
"index": 10749,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A storage box in the shape of a rectangular prism has dimensions 8 cm by 6 cm by 10 cm. Inside the storage box, there are several smaller cubes each with an edge length of 2 cm. How many such cubes can fit inside the storage box if all the space is utilized perfectly? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 10750,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A square \\(ABCD\\) is inscribed in the region bound by the parabola \\(y = x^2 - 6x + 8\\) and the \\(x\\)-axis, such that one side of the square lies on the \\(x\\)-axis. Find the area of square \\(ABCD\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 10751,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces a certain type of widget and the production follows a specific pattern. In the first month, they produce 100 widgets. Each subsequent month, the number of widgets produced is 80% of the previous month's production, rounded to the nearest integer. After how many months will the total number of widgets produced exceed 400? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 10752,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice's monthly salary increased by 15%. After the raise, she decided to save 20% of her new salary every month. If she saves $300 each month, what was her salary before the raise? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1304.35",
"style": "rule"
}
|
numina_math
|
{
"index": 10753,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma baked a large cake and sliced it into 12 equal pieces. She gave 1/4 of the cake to her neighbor and ate 1/3 of the remaining pieces herself. How many pieces of cake does Emma have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 10754,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company needs to distribute 500 promotional gift boxes. Each box includes 2 branded mugs. The cost of producing each mug is $3.50. If the company has a budget of $4,000 for the mugs, will they stay within their budget? How much will they spend or exceed the budget by? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "500",
"style": "rule"
}
|
numina_math
|
{
"index": 10755,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a speed of 60 miles per hour. How long will it take the car to travel 240 miles? Express your answer in hours and minutes. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 10756,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A worker is paid according to the number of days he works and the number of hours he works each day. He works for 5 days, and each day he works 2 hours more than the previous day, starting with 4 hours on the first day. If he is paid $15 per hour, what is his total payment at the end of the 5 days? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 10757,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cube has a side length of \\( a \\) units. If a sphere is inscribed in the cube, find the surface area of the sphere. Express your answer in terms of \\( a \\) and simplify your expression if necessary. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\pia^2",
"style": "rule"
}
|
numina_math
|
{
"index": 10758,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has $12.50. She bought three items costing $2.75 each and then donated $1.50 to a charity. How much money does she have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.75",
"style": "rule"
}
|
numina_math
|
{
"index": 10759,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Maya and America share a collection of 80 books. Maya has four times as many books as America, but she decides to donate 10 books to the local library. After her donation, the combined total of books they have is now 70. How many books did Maya originally have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "64",
"style": "rule"
}
|
numina_math
|
{
"index": 10760,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sophia is hosting a charity bake sale. She decides to bake cookies and cupcakes. Each cookie batch makes 24 cookies and costs $6 to produce, while each cupcake batch makes 12 cupcakes and costs $8 to produce. If she bakes 5 batches of cookies and 7 batches of cupcakes, what is the total cost of production, and how many items will she have to sell in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "204",
"style": "rule"
}
|
numina_math
|
{
"index": 10761,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company packages its products in boxes, and each box contains 5 items. If the company produces 12 boxes of items, how many items are produced in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 10762,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sophie bought 5 gift baskets for her friends. Each gift basket costs $13.40. She also bought a card for $3.50 and wrapping paper for $4.60. If Sophie paid with a $100 bill, how much change did she receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24.90",
"style": "rule"
}
|
numina_math
|
{
"index": 10763,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many 4-digit numbers are divisible by both 2 and 3? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1500",
"style": "rule"
}
|
numina_math
|
{
"index": 10764,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\(f(x) = \\frac{x^2 - 1}{x - 1}\\). Evaluate \\(f(3)\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 10765,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice and Bob are organizing a charity event. They need to set up a total of 120 chairs in the hall. Alice sets up 3 chairs for every 2 chairs that Bob sets up. If they work together, how many chairs does each person set up? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 10766,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A school is planning a field trip and needs to rent buses. One bus company offers buses with 36 seats, and another offers buses with 48 seats. What is the smallest number of seats that can be rented such that all the students can fit into the buses without any seats left over, and the number of seats is a multiple of both 36 and 48? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "144",
"style": "rule"
}
|
numina_math
|
{
"index": 10767,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangle has a length of \\( \\sqrt[3]{8} \\) meters and a width of \\( \\sqrt[4]{16} \\) meters. What is the area of the rectangle in square meters? Simplify your answer completely. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 10768,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A contractor was hired to paint a building. He found that he could paint 200 square feet in 4 hours. If the contractor needs to paint a total of 3,000 square feet, how many hours will it take him to complete the job? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 10769,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenna is buying a new smartphone that costs $800. She plans to buy a protective case that costs 15% of the price of the smartphone and a screen protector that costs 5% of the price of the smartphone. After calculating the total cost, she decides to use a discount coupon of $50. What is the final amount Jenna has to pay for the smartphone, protective case, and screen protector after applying the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "910",
"style": "rule"
}
|
numina_math
|
{
"index": 10770,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many four-digit even numbers can be formed using the digits 2, 0, 1, and 5 exactly once? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 10771,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A tree grows at a constant rate of 2 feet per year. If the height of the tree was 5 feet when it was first planted, after how many years will the total height of the tree be 1 foot less than three times its original height? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.5",
"style": "rule"
}
|
numina_math
|
{
"index": 10772,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah wants to buy some pencils for her class. Each pencil costs $0.25. She has $20. If she buys 50 pencils, how much money will she have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7.50",
"style": "rule"
}
|
numina_math
|
{
"index": 10773,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Liam is organizing a charity event and needs to set up tables. Each table can seat 8 people, and he expects 120 people to attend the event. How many tables does he need to set up? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 10774,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( P(z) = z^6 - 1 \\) and \\( Q(z) = z^4 - 1 \\). Determine the product of all distinct complex roots of the equation \\( P(z) = Q(z) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-1",
"style": "rule"
}
|
numina_math
|
{
"index": 10775,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma wants to buy pens and notebooks for her school's annual charity event. The price of a pen is $1.50 each, but if she buys a pack of 10 pens, the price is $12. The price of a notebook is $3 each, but if she buys a pack of 5 notebooks, the price is $13. If Emma needs 30 pens and 15 notebooks, how much money would she save by buying in bulk instead of buying each item individually? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 10776,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah runs a store where she sells handcrafted jewelry. She initially priced a bracelet at $150. Due to slow sales, she decided to offer a 20% discount on the bracelet. Later, she further reduced the discounted price by an additional 10%. Calculate the final price of the bracelet after both discounts. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "108",
"style": "rule"
}
|
numina_math
|
{
"index": 10777,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jonathan enjoys walking and running for exercise, and he has three different exercise routines. On Mondays, he walks at 2 miles per hour. On Wednesdays, he walks at 3 miles per hour. And on Fridays, he runs at 6 miles per hour. On each exercise day, he travels 6 miles. What is the combined total time, in minutes, he spends exercising in a week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "360",
"style": "rule"
}
|
numina_math
|
{
"index": 10778,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha has a ribbon that is 36 inches long. She cuts the ribbon into pieces such that the length of each piece is a fraction of the total length. She cuts one piece that is $\\frac{1}{4}$ of the ribbon's length, another piece that is $\\frac{1}{3}$ of the ribbon's length, and a third piece that is $\\frac{1}{6}$ of the ribbon's length. How many inches of ribbon does Samantha have left after making these cuts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 10779,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is organizing a charity event and needs to prepare 300 gift bags. It takes her 8 minutes to prepare one gift bag. If she works 5 hours a day, how many days will it take her to prepare all the gift bags? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 10780,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, there are 15 students. Each student is asked to classify the following numbers as odd or even: 23, 14, 7, 42, 19, 8, 31, 20. How many odd numbers and how many even numbers are there? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 10781,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A certain species of bacteria doubles in number every 3 hours. If a petri dish initially contains 500 bacteria, how many bacteria will there be after 15 hours? Also, if 2000 bacteria are removed after the 15 hours, how many bacteria will remain? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14000",
"style": "rule"
}
|
numina_math
|
{
"index": 10782,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Liam is organizing a bake sale and wants to make 3 types of treats: cookies, brownies, and cupcakes. Each cookie batch requires 5 cups of flour, each brownie batch requires 3 cups of flour, and each cupcake batch requires 4 cups of flour. If Liam plans to make 2 batches of cookies, 4 batches of brownies, and 5 batches of cupcakes, how many more cups of flour does he need for the cupcakes compared to the brownies? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 10783,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah drives to her grandmother's house which is 120 miles away every month. If the cost of gas is $0.15 per mile, how much does she spend on gas in a year for these trips? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "432",
"style": "rule"
}
|
numina_math
|
{
"index": 10784,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma has 3/4 of a chocolate bar. She decides to give 1/3 of her chocolate bar to her friend Lucy. After giving some to Lucy, she eats 1/8 of the remaining chocolate. How much of the chocolate bar does Emma have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{7}{16}",
"style": "rule"
}
|
numina_math
|
{
"index": 10785,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Cassie is trimming her pet's nails. She has four dogs and eight parrots. Each dog has four nails on each foot, and each parrot has three claws on each leg, except for one parrot who has an extra claw on one leg. How many nails does Cassie need to cut in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "113",
"style": "rule"
}
|
numina_math
|
{
"index": 10786,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is trying to decide between three different gym membership plans. The first plan is a monthly membership costing $50 per month, with an additional $100 sign-up fee. The second plan is a quarterly membership costing $140 every three months, with a $50 sign-up fee. The third plan is an annual membership costing $500 per year, with no sign-up fee. If Sarah plans to use the gym for one year, which membership plan is the most cost-effective? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "500",
"style": "rule"
}
|
numina_math
|
{
"index": 10787,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is trying to decide between two different brands of chocolate bars. Brand A offers a 150-gram bar for $3.75, while Brand B offers a 120-gram bar for $3.00. Emily wants to know which brand offers the better value by comparing the price per gram. What is the price per gram in cents of the brand with the better value? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.5",
"style": "rule"
}
|
numina_math
|
{
"index": 10788,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two supplementary angles \\(A\\) and \\(B\\) have their measures in degrees such that \\(A\\) is twice the measure of \\(B\\). What are the measures of angles \\(A\\) and \\(B\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 10789,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two numbers, \\(a\\) and \\(b\\), have a greatest common divisor (GCD) of 12 and a least common multiple (LCM) of 180. If \\(a\\) is 36, what is \\(b\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 10790,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A teacher has a class of 24 students and wants to distribute 96 apples equally among them. After distributing the apples, the teacher gives an additional 3 apples to each student who scored above 90% on their last test. If 6 students scored above 90%, how many apples does each of these 6 students receive in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 10791,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a library, there are 150 books in total. 90 books are fiction, 70 books are non-fiction, and 50 books are both fiction and non-fiction. Using the Inclusion-Exclusion Principle, determine the number of books that are either fiction or non-fiction or both. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "110",
"style": "rule"
}
|
numina_math
|
{
"index": 10792,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah's monthly salary is $5000. She contributes 15% of her salary to her retirement fund, and her monthly expenses include $1200 for rent, $300 for groceries, and $200 for utilities. After accounting for her retirement contributions and monthly expenses, how much money does Sarah have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2550",
"style": "rule"
}
|
numina_math
|
{
"index": 10793,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there are 120 students. 40% of these students are in the sports club. Out of the students in the sports club, 75% are boys and the rest are girls. The number of girls in the sports club is 30% of the total number of girls in the school. How many girls are there in the school? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 10794,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bacteria colony starts with 500 bacteria and grows by 40% every hour. How many bacteria will there be after 5 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2689",
"style": "rule"
}
|
numina_math
|
{
"index": 10795,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the equations \\( \\frac{3a}{4} + \\frac{2b}{5} = 7 \\) and \\( 2a - b = 1 \\), solve for \\( a \\) and \\( b \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "73",
"style": "rule"
}
|
numina_math
|
{
"index": 10796,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is baking cookies for a school bake sale. She uses 1.5 cups of sugar for each batch of cookies. If she wants to make 8 batches, how much sugar does she need in total? Additionally, if she only has 10 cups of sugar at home, how much more sugar does she need to buy? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 10797,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Julia is planning a trip from San Francisco to Las Vegas. She drives at a constant speed of 65 miles per hour, taking 15-minute breaks every 2 hours. The total distance of the trip is 570 miles. Once she arrives in Las Vegas, she needs an additional 20 minutes to find her hotel. How many hours will she spend to complete the trip to the hotel? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10.1",
"style": "rule"
}
|
numina_math
|
{
"index": 10798,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Vinny starts his weight loss journey weighing 300 pounds and loses 5% of his weight each month. If Vinny continues to lose weight at this rate indefinitely, what will be his weight after an infinite number of months? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 10799,
"name": "numina_math",
"split": "train"
}
|
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