prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "Sarah has a collection of 80 books. She decides to donate 3/5 of her books to the local library. Out of the remaining books, she gives 1/4 to her friend. How many books does Sarah have left after these donations? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 10100,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A theater has 20 rows of seats. Each row has 3 more seats than the previous row. If the first row has 10 seats, how many seats are there in total in the theater? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "770",
"style": "rule"
}
|
numina_math
|
{
"index": 10101,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "An equilateral triangle $ABC$ shares a common side with square $BCDE$ as shown. Determine the measure of angle $CAD$.\n\n[asy]\nsize(100);\npair A, B, C, D, E;\nB = (0,0);\nC = (1,0);\nD = (1,1);\nE = (0,1);\nA = (0.5,0.866); // 0.866 is approximately sqrt(3)/2 for an equilateral triangle with side length 1\ndraw(A--B--C--D--E--cycle);\ndraw(A--C);\nlabel(\"$A$\", A, N);\nlabel(\"$B$\", B, SW);\nlabel(\"$C$\", C, SE);\nlabel(\"$D$\", D, NE);\nlabel(\"$E$\", E, NW);\n[/asy] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 10102,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In how many ways can you partition the integer 15 into three consecutive integers such that the product of these integers is maximized? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 10103,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe for a cake requires flour and sugar in the ratio of 3:2. If you want to make a larger batch of the cake and have 9 cups of flour, how many cups of sugar do you need? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 10104,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the expression \\(\\frac{\\sqrt[5]{a^{10}b^5}}{\\sqrt[4]{a^8b^4}}\\), simplify it and express the answer as a simplified fraction. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 10105,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a set \\( \\mathcal{S} \\) of distinct positive integers such that for every integer \\( x \\) in \\( \\mathcal{S} \\), the arithmetic mean of the set of values obtained by deleting \\( x \\) from \\( \\mathcal{S} \\) is an integer. Given that 1 belongs to \\( \\mathcal{S} \\) and that 2002 is the largest element of \\( \\mathcal{S} \\), what is the greatest number of elements that \\( \\mathcal{S} \\) can have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2002",
"style": "rule"
}
|
numina_math
|
{
"index": 10106,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation: \\(\\left(x^2 + 6x + 9\\right)^{\\frac{1}{2}} = 2x - 1\\) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 10107,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A chemist has 50 ounces of a 40% alcohol solution. He wants to dilute it to a 25% alcohol solution by adding water. How many ounces of water must he add to achieve this concentration? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 10108,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah's salary is $40,000 per year. She receives a 5% raise each year. How much will her salary be after 3 years? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "46305",
"style": "rule"
}
|
numina_math
|
{
"index": 10109,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires a ratio of 3 parts sugar to 5 parts flour. If a baker wants to make a batch with a total of 40 cups of these ingredients, how many cups of sugar and flour should be used to maintain the ratio? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 10110,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A pie recipe calls for \\(\\frac{1}{2}\\) cup of sugar, \\(\\frac{2}{3}\\) cup of flour, and \\(\\frac{1}{4}\\) cup of milk. If you want to make 6 pies, how much of each ingredient will you need in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.5",
"style": "rule"
}
|
numina_math
|
{
"index": 10111,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length of 12 meters and a width of 8 meters. If a similar garden has a width of 10 meters, what is its length? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 10112,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a group of employees can complete a project in 30 days working 8 hours per day, how many days will it take to complete the same project if the employees work 10 hours per day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 10113,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha wants to buy some flowers for her garden. She decides to buy 8 rose bushes costing $12 each and 5 tulip bulbs costing $3 each. If she has $150 with her, how much change will she get back after buying the flowers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "39",
"style": "rule"
}
|
numina_math
|
{
"index": 10114,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Three friends, Alex, Ben, and Charlie, are painting a fence together. Alex can paint the entire fence in 6 hours, Ben can paint it in 8 hours, and Charlie can paint it in 12 hours. If they work together, how long will it take them to paint the entire fence? Express your answer as a decimal to the nearest hundredth. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.67",
"style": "rule"
}
|
numina_math
|
{
"index": 10115,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there are 100 students enrolled in extracurricular activities. 45 students are part of the drama club, and 60 students are part of the sports club. If 20 students are part of both clubs, how many students are part of either the drama club or the sports club? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "85",
"style": "rule"
}
|
numina_math
|
{
"index": 10116,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends decides to start a weekly savings plan. Each friend saves $5 per day, and there are 7 friends in the group. How much money do they save collectively in one week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "245",
"style": "rule"
}
|
numina_math
|
{
"index": 10117,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a fraction is in the form \\(\\frac{a}{b}\\) where \\(a\\) and \\(b\\) are positive integers with no common factors other than 1, and the decimal representation of the fraction repeats every 6 digits, what is the smallest possible value of \\(b\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 10118,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two friends, Alice and Bob, are planning a road trip. Alice drives at an average speed of 60 miles per hour, while Bob drives at an average speed of 45 miles per hour. They leave their homes at the same time and meet at a point that is exactly halfway between their homes. If the total distance between their homes is 210 miles, how long does each drive before they meet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.75",
"style": "rule"
}
|
numina_math
|
{
"index": 10119,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice has been saving money in a piggy bank. She started with $50 and saves $10 every week. After 7 weeks, she decides to withdraw $15 to buy a book. If she continues to save $10 each week for another 5 weeks, how much money will she have saved by the end of this period? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "155",
"style": "rule"
}
|
numina_math
|
{
"index": 10120,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence of integers from \\(1\\) to \\(100\\) inclusive. Let \\(S\\) be the sum of all integers in this sequence that are divisible by \\(3\\). Find the value of \\(S\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1683",
"style": "rule"
}
|
numina_math
|
{
"index": 10121,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A student is asked to multiply a two-digit number by a single-digit number. The two-digit number is 47, and the single-digit number is 6. During the calculation, the student mistakenly subtracts 7 from 6 instead of multiplying. What should the correct product be? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "282",
"style": "rule"
}
|
numina_math
|
{
"index": 10122,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah bought a new laptop that was originally priced at $1,200. The store was having a sale where the price of the laptop was reduced by 20%. After applying the discount, Sarah had to pay a 5% sales tax on the discounted price. How much did Sarah pay for the laptop in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1008",
"style": "rule"
}
|
numina_math
|
{
"index": 10123,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the sequence of numbers defined by \\( a_n = 3^n + 2^n \\) for \\( n = 1, 2, 3, \\ldots \\). Find the greatest common divisor of the terms \\( a_6 \\) and \\( a_{9} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 10124,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore is having a sale where all books are 15% off. If Jenna buys 3 books priced at $12.50 each and 2 books priced at $18.75 each, what is the total amount Jenna pays after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "63.75",
"style": "rule"
}
|
numina_math
|
{
"index": 10125,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is making a fruit punch for a party. The recipe requires 3/4 cup of sugar, but she accidentally added 1/2 cup more. To correct the mistake, she decided to remove 1/4 cup of the mixture. How much sugar is in the punch now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 10126,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily runs a local bakery where she sells cupcakes. She buys ingredients to make a dozen cupcakes for $3.50 and sells each cupcake for $0.75. If she wants to make a profit of $150 in a week, how many dozens of cupcakes does she need to bake and sell? Additionally, if she spends 15 minutes baking each dozen, how many hours does she spend baking to reach her goal? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 10127,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the vertical asymptotes of the rational function \\(\\frac{2x^3 - 8x^2 + 6x}{x^2 - 4}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-2",
"style": "rule"
}
|
numina_math
|
{
"index": 10128,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lena needs to buy ingredients for a party. She has a recipe that calls for 3 quarts of milk, but the store sells milk in gallons. If 1 gallon is equivalent to 4 quarts, how many gallons of milk should Lena buy to meet the recipe's requirements? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 10129,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine the sum of the digits of the 100th term in the arithmetic sequence where the first term is 5 and the common difference is 3. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 10130,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The path of a ball thrown into the air follows a parabolic trajectory described by the equation \\( y = -2x^2 + 12x + 3 \\), where \\( y \\) is the height of the ball in meters and \\( x \\) is the horizontal distance from the point of release in meters. Determine the maximum height reached by the ball. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "21",
"style": "rule"
}
|
numina_math
|
{
"index": 10131,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a small town, there are two rival bakeries, Bakery A and Bakery B. Bakery A sells muffins at $2 each and croissants at $3 each. Bakery B sells muffins at $2.50 each and croissants at $2.50 each. One day, Bakery A sold a total of 50 items (muffins and croissants combined) and earned $120. On the same day, Bakery B sold a total of 40 items and earned $100. How many muffins and croissants did each bakery sell? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 10132,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist rides 3/4 of a trail that is 40 kilometers long and then takes a break. After the break, the cyclist completes the remaining distance. What percentage of the total trail does the cyclist ride after the break? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 10133,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Ginger is weaving mats out of colored straw. Each mat takes 20 red straws, 30 orange straws, and half as many green straws as orange straws. How many straws does she need to make 10 mats? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "650",
"style": "rule"
}
|
numina_math
|
{
"index": 10134,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In triangle \\( ABC \\), \\( AB = AC \\), and \\( \\angle A = 40^\\circ \\). If point \\( D \\) is on \\( BC \\) such that \\( BD = 6 \\) and \\( DC = 8 \\), verify if the triangle inequality theorem holds for triangle \\( ABD \\) and find the measure of \\( \\angle BDC \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "140",
"style": "rule"
}
|
numina_math
|
{
"index": 10135,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical water tank has a radius of 3 meters and a height of 10 meters. If the tank is currently filled to 75% of its capacity, what is the volume of the water in the tank in cubic meters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "212.06",
"style": "rule"
}
|
numina_math
|
{
"index": 10136,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company is planning a team-building event and wants to allocate the costs based on the percentages of participation. The total cost for the event is $1200. If 40% of the participants are from the Sales department, 30% are from the Marketing department, and the remaining 30% are from the Engineering department, how much will each department need to contribute to cover the total cost? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "360",
"style": "rule"
}
|
numina_math
|
{
"index": 10137,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car's fuel efficiency decreases by 2 miles per gallon every 5,000 miles driven. If the car initially has a fuel efficiency of 30 miles per gallon, what is its fuel efficiency after driving 20,000 miles? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22",
"style": "rule"
}
|
numina_math
|
{
"index": 10138,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that the ratio of two numbers \\(a\\) and \\(b\\) is \\(3:4\\) and their greatest common divisor (GCD) is 6, find the values of \\(a\\) and \\(b\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 10139,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the polynomial \\( P(x) = 2x^5 - 3x^3 + x^2 - 4x + 7 \\) and the polynomial \\( Q(x) = -x^4 + 5x^2 - 2 \\), determine the leading term and the coefficient of the leading term of the polynomial \\( R(x) = P(x) \\cdot Q(x) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-2",
"style": "rule"
}
|
numina_math
|
{
"index": 10140,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sam can swim at a speed of 2 meters per second in still water. However, when swimming in a river with a current that flows at 1 meter per second, his effective speed downstream (with the current) increases by the speed of the current, while his effective speed upstream (against the current) decreases by the speed of the current. If Sam swims 200 meters downstream and then returns the same distance upstream, how long does the entire swim take? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "266.67",
"style": "rule"
}
|
numina_math
|
{
"index": 10141,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces widgets at a constant rate. It takes 6 hours to produce 150 widgets. How many widgets can the factory produce in a 10-hour shift? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "250",
"style": "rule"
}
|
numina_math
|
{
"index": 10142,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a 3x3 magic square, the sums of the numbers in each row, column, and diagonal are the same. One of the numbers in the magic square is represented by \\( x \\), and it is known that the number directly below it is \\( 2x \\), while the number directly to the right of it is \\( 3x \\). If the number directly below \\( 2x \\) is \\( 4x \\), and the total sum of each row, column, and diagonal in the magic square is 45, find the value of \\( x \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 10143,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily earns $90 a day. Every day, she spends part of her pay and saves the rest. After 25 days of work, she spent $1800. How much did Emily save in 25 days? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "450",
"style": "rule"
}
|
numina_math
|
{
"index": 10144,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car rental company charges a base rate of $50 per day for renting a car. Additionally, there is a mileage charge of $0.20 per mile driven. If a customer rents a car for 3 days and drives 150 miles, what is the total cost for the rental? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "180",
"style": "rule"
}
|
numina_math
|
{
"index": 10145,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden is 20 meters long and 15 meters wide. The owner wants to put a fence around the garden, and the fencing is sold in yards. How many yards of fencing does the owner need to buy to completely enclose the garden? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "77",
"style": "rule"
}
|
numina_math
|
{
"index": 10146,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical object is dropped into a rectangular tank, causing the water level to rise. The tank has dimensions of 50 cm in length and 40 cm in width, and initially contains water to a height of 25 cm. After the cylindrical object is dropped in, the water level rises to 30 cm. The diameter of the cylinder is 20 cm. What is the height of the cylinder in centimeters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "31.85",
"style": "rule"
}
|
numina_math
|
{
"index": 10147,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a ribbon that is 3 meters long. She needs to cut it into pieces that are each 0.25 meters long for a craft project. She uses 4 pieces for each craft item she makes. After making 6 craft items, how much ribbon does she have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 10148,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is recording the number of books she reads each month. In January, she read 3 books. In February, she read 5 books. In March, she read 2 books. In April, she read 4 books. What is the average number of books Sarah read per month over these four months? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.5",
"style": "rule"
}
|
numina_math
|
{
"index": 10149,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a bag contains 0.75 kilograms of apples, 1.25 kilograms of oranges, and 2.5 kilograms of bananas, calculate the total weight of the fruits in the bag. Additionally, if the price per kilogram is $3.60, find the total cost of the fruits in the bag. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16.2",
"style": "rule"
}
|
numina_math
|
{
"index": 10150,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John has a budget of $150 to spend on new books. If each book costs $12.75, how many books can John buy without exceeding his budget? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 10151,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jane and Tom are siblings. Jane's age is 40% of Tom's age. If the sum of their ages is 70 years, how old are Jane and Tom? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 10152,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The school's art club currently has 36 members, which represents an increase of 1/5 from the original number of members. How many members were originally in the art club? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 10153,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two runners, A and B, start from opposite ends of a 400-meter track and run towards each other. Runner A runs at a speed of 6 meters per second, and runner B runs at a speed that is three times the speed of Runner A. How long will it take for the two runners to meet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16.67",
"style": "rule"
}
|
numina_math
|
{
"index": 10154,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A number leaves a remainder of 3 when divided by 7 and a remainder of 5 when divided by 11. What is the smallest positive integer that satisfies both of these conditions? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "38",
"style": "rule"
}
|
numina_math
|
{
"index": 10155,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mr. Wang needs to pack a batch of goods. The original plan was to pack 30 items per hour, and it would take 6 hours to complete. In reality, he packed 20% more items per hour than planned. How many hours earlier than planned did he finish packing this batch of goods? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 10156,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is organizing a charity event and needs to prepare gift bags. Each gift bag must contain 5 chocolates and 3 small toys. If Emily has bought 60 chocolates and 36 small toys, how many complete gift bags can she prepare? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 10157,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a certain town, there are 120 buildings. Among these buildings, 72 are residential, 50 are commercial, and 20 are both residential and commercial. How many buildings are either residential or commercial but not both? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "82",
"style": "rule"
}
|
numina_math
|
{
"index": 10158,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the infinite sum:\n\\[ \\sum_{n=1}^{\\infty} \\frac{1}{n(n+1)}. \\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 10159,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Scott, Mary, and Ken committed to raising $4,000 for their local children’s cancer hospital. Right now, Mary’s collection is five times what Ken has, but three times Scott’s funds. If Ken has $600, by how much have the three exceeded their goal? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 10160,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah drives to her grandmother's house, which is 120 km away, at an average speed of 60 km/h. On her way back, she encounters traffic and her average speed drops to 40 km/h. What is her average speed for the entire round trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 10161,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels for 2 hours at a speed that is 75% of its usual speed and then for 3 hours at its usual speed, covering a total distance of 210 miles. What is the car's usual speed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "46.67",
"style": "rule"
}
|
numina_math
|
{
"index": 10162,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A toy store offers three types of toys: cars, dolls, and action figures. Each type of toy comes in four different colors: red, blue, green, and yellow. Additionally, there are three different sizes available for each toy: small, medium, and large. If a customer wants to purchase one toy, what is the total number of different options they have? Additionally, if the store decides to offer a discount on all large red toys, how many discounted options are available? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 10163,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the exponential equation \\(2^{2x+1} = 8 \\times 2^{x-1}\\) for \\(x\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 10164,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex has a part-time job where he works on different projects each day. On Monday, he worked on Project A for 1 hour and Project B for 2 hours. On Tuesday, he worked on Project A for 2 hours and Project B for 3 hours. On Wednesday, he worked on Project A for 3 hours and Project B for 4 hours. If Alex continues this pattern for the rest of the week, how many total hours will he have worked by the end of Sunday? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "63",
"style": "rule"
}
|
numina_math
|
{
"index": 10165,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is offering a 15% discount on all items. If a customer buys a shirt originally priced at $40 and a pair of pants originally priced at $60, what is the total amount the customer pays after applying the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "85",
"style": "rule"
}
|
numina_math
|
{
"index": 10166,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangle is inscribed in a circle with a radius of 10 units. If one side of the rectangle is 12 units, find the area of the rectangle. Additionally, find the perimeter of the rectangle. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "56",
"style": "rule"
}
|
numina_math
|
{
"index": 10167,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train and a car start from two towns 300 kilometers apart and travel towards each other. The train travels at a speed of 70 kilometers per hour, while the car travels at a speed of 50 kilometers per hour. They start at the same time. How long will it take for the train and the car to meet, and at what distance from the train's starting point will they meet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "175",
"style": "rule"
}
|
numina_math
|
{
"index": 10168,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore sold 15 more than twice the number of mystery novels as it did science fiction novels. If the bookstore sold 40 science fiction novels, how many mystery novels did it sell? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "95",
"style": "rule"
}
|
numina_math
|
{
"index": 10169,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A hiker is walking along a trail that goes up and down. On the first leg of the trail, the hiker climbs 150 meters. Then the hiker descends 80 meters. After that, the hiker climbs another 50 meters and finally descends 120 meters. What is the net change in the hiker's elevation? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 10170,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bakery sells cakes and cupcakes. Each cake is cut into 10 slices, and each cupcake is one serving. On Saturday, the bakery sold 120 slices of cake and 75 cupcakes. How many cakes and cupcakes did the bakery sell in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "87",
"style": "rule"
}
|
numina_math
|
{
"index": 10171,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular rug measuring 8 feet by 5 feet is on sale with a 20% discount. If the original price of the rug is $200, what is the sale price after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "160",
"style": "rule"
}
|
numina_math
|
{
"index": 10172,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A gardener is planning to plant a rectangular flower bed. The width of the bed is 3 meters, and he wants the length to be twice the width. He also plans to place a pathway around the flower bed that is 1 meter wide. Calculate the total area occupied by the flower bed and the pathway. How much area is occupied solely by the pathway? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22",
"style": "rule"
}
|
numina_math
|
{
"index": 10173,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the smallest four-digit number which is a multiple of 23? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1012",
"style": "rule"
}
|
numina_math
|
{
"index": 10174,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cafeteria offers 4 types of sandwiches, 3 types of drinks, and 5 types of desserts. If a student decides to randomly choose one sandwich, one drink, and one dessert for their meal, how many different meal combinations can the student make? Furthermore, what is the probability that the student will choose a specific meal consisting of a ham sandwich, orange juice, and a chocolate cake? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{60}",
"style": "rule"
}
|
numina_math
|
{
"index": 10175,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has three times as many apples as Tom, and Tom has half as many apples as Emily. If Emily has 24 apples, how many apples does Sarah have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 10176,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A container holds a mixture of water and juice in the ratio 3:5. If 24 liters of the mixture are water, how much total mixture is there? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "64",
"style": "rule"
}
|
numina_math
|
{
"index": 10177,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a birthday party and needs to buy balloons. She needs 150 balloons in total. A pack of 30 balloons costs $5 and a pack of 50 balloons costs $7. What is the minimum amount of money Sarah has to spend to get at least 150 balloons? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "21",
"style": "rule"
}
|
numina_math
|
{
"index": 10178,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company needs to assemble 3000 units of a product in a 10-hour workday. Each worker can assemble 30 units per hour. How many workers must be hired to meet the production goal in one day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 10179,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "An eight-sided die has its faces numbered from 1 to 8. If you roll the die twice, what is the expected value of the sum of the results? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 10180,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is preparing for a marathon and decides to do a training session consisting of running and biking. He bikes 30 miles at a speed of \\(4x\\) miles per hour, then switches to running and runs 10 miles at a speed of \\(x\\) miles per hour. If the total time spent on biking and running is 3 hours and 30 minutes, find his running speed \\(x\\) in miles per hour. (You may use a calculator on this problem.) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 10181,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sam has $50. He spent $12 on a book, $15 on a meal, and $8 on a movie ticket. How much money does he have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 10182,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A ship left a port and headed due west, carrying 500 pounds of food for the journey. After one day of sailing, the sailors used 3/8 of the supplies. After another two days, they used 2/3 of the remaining supplies. Calculate how many pounds of food are left on the ship to last the sailors until they dock. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "104.17",
"style": "rule"
}
|
numina_math
|
{
"index": 10183,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John owns a small business and sold a batch of items for $600. He made a profit of 20% on the cost price. If the sales tax on the batch was 8%, what was the original cost price of the items before tax? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "462.97",
"style": "rule"
}
|
numina_math
|
{
"index": 10184,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(n) \\) denote the sum of all the positive divisors of the integer \\( n \\). Suppose \\( g(n) = 2^n + 1 \\). Find the sum of all integers \\( n \\) such that \\( 1 \\le n \\le 20 \\) and \\( f(n) = g(n) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 10185,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In rectangle \\(ABCD\\), \\(AB = 12\\) and \\(BC = 5\\). Point \\(P\\) is on \\(BC\\) such that \\(AP\\) is perpendicular to \\(BD\\). Find the length of \\(AP\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 10186,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah plans to walk from her home to the park. She walks 1/5 of the total distance and then realizes she still has 2 kilometers to go. How far is her home from the park? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.5",
"style": "rule"
}
|
numina_math
|
{
"index": 10187,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In $\\triangle ABC$, $AB = 10$, $BC = 8$, and $CA = 6$. A line parallel to $BC$ intersects $AB$ at $D$ and $AC$ at $E$, creating $\\triangle ADE$ similar to $\\triangle ABC$. The area of $\\triangle ADE$ is $\\frac{9}{25}$ of the area of $\\triangle ABC$. What is the length of $DE$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.8",
"style": "rule"
}
|
numina_math
|
{
"index": 10188,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, there are 25 students in the dance club and three times that number in the art club. Additionally, there are 10 boys and 15 girls in the theater club. If each student participates in only one club, how many students, in total, are there in the dance club, the art club, and the theater club? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "125",
"style": "rule"
}
|
numina_math
|
{
"index": 10189,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many positive integers less than 200 are multiples of either 3, 5, or 7? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "107",
"style": "rule"
}
|
numina_math
|
{
"index": 10190,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "To transmit a positive integer less than 1000, the Networked Number Node offers two options.\nOption 1: Pay $\\$$d to send each digit d. Therefore, 123 would cost $\\$$1 + $\\$$2 + $\\$$3 = $\\$$6 to transmit.\nOption 2: Encode the integer into binary (base 2) first, and then pay $\\$$d to send each digit d. Therefore, 123 becomes 1111011 and would cost $\\$$1 + $\\$$1 + $\\$$1 + $\\$$1 + $\\$$0 + $\\$$1 + $\\$$1 = $\\$$6.\nWhat is the largest integer less than 1000 that costs the same whether using Option 1 or Option 2? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "123",
"style": "rule"
}
|
numina_math
|
{
"index": 10191,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels at an average speed of 12 miles per hour. If they travel a total distance of 36 miles, how long does the trip take? Additionally, if the cyclist then travels back the same distance at an average speed of \\( \\sqrt{144} \\) miles per hour, what is the total time for the round trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 10192,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company makes a profit of $12,000 each month. The company plans to distribute 25% of this profit to its employees as a bonus and reinvest the remaining amount back into the business. If the company has 10 employees and the bonus is distributed equally among them, how much does each employee receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 10193,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a game, you can win different amounts of money based on the roll of a fair 6-sided die. If you roll a 1, you win $2. If you roll a 2, you win $4. If you roll a 3, you win $6. If you roll a 4, you win $8. If you roll a 5, you win $10. If you roll a 6, you win $12. Calculate the expected value of the amount of money you will win. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 10194,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha subscribes to an online learning platform that costs $25 per month. She also subscribes to a monthly magazine that costs $15 per month. If she decides to cancel her magazine subscription after 6 months, what will be her total spending on both subscriptions for the first year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "390",
"style": "rule"
}
|
numina_math
|
{
"index": 10195,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many digits are there in the smallest integer solution to the inequality\n\\[\\frac{7x + 1}{x - 3} < 5?\\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 10196,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, the number of students in Class A is 20 more than twice the number of students in Class B. If the total number of students in both classes is 140, how many students are in each class? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 10197,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels from Town A to Town B, a distance of 180 miles, at an average speed of 60 miles per hour. After reaching Town B, the car immediately returns to Town A at an average speed of 45 miles per hour. What is the total time taken for the round trip, and what is the average speed for the entire journey? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "51.43",
"style": "rule"
}
|
numina_math
|
{
"index": 10198,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A number \\( x \\) is equal to \\( 9 \\times 12 \\times 18 \\). What is the smallest positive integer \\( y \\) such that the product \\( xy \\) is a perfect cube? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 10199,
"name": "numina_math",
"split": "train"
}
|
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