prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "How many positive integers less than $100$ are divisible by both $6!$ and $7!$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 1100,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The perimeter of a rectangular garden is 62 meters. If the length of the garden is 5 meters more than twice the width, what are the dimensions of the garden? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "22.34",
"style": "rule"
}
|
numina_math
|
{
"index": 1101,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two cyclists, Alex and Jamie, start from points X and Y, respectively, and head towards each other. Alex starts from point X traveling at a speed of 18 kilometers per hour, while Jamie starts from point Y traveling at a speed of 14 kilometers per hour. If the distance between points X and Y is 96 kilometers, how long will it take for Alex and Jamie to meet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 1102,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the multiplicative inverse of \\(3 \\pmod{101}\\), as a residue modulo 101. (Give an answer between 0 and 100, inclusive.) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "34",
"style": "rule"
}
|
numina_math
|
{
"index": 1103,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A city's population is initially 200,000. The population grows by 5% each year. After how many years will the population be at least 300,000? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 1104,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In triangle \\( \\triangle XYZ \\), \\( \\angle Y \\) is a right angle. The lengths of \\( XY \\) and \\( YZ \\) are both integer values and the hypotenuse \\( XZ \\) has a length of 13 units. Find all possible integer values for \\( XY \\) and \\( YZ \\). What is the area of the triangle for each pair of values? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 1105,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is shopping for a new wardrobe. She finds a store offering a promotion of 25% off on all items. She wants to buy a dress originally priced at $80, a pair of shoes originally priced at $120, and a handbag originally priced at $60. How much will she pay in total after applying the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "195",
"style": "rule"
}
|
numina_math
|
{
"index": 1106,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Laura is planning her wedding. She expects 220 people to attend the wedding, but she has been told that approximately 5% typically don't show up. If she wants to ensure that there are enough seats for everyone who will attend, how many seats should she plan for? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "209",
"style": "rule"
}
|
numina_math
|
{
"index": 1107,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A water tank has a capacity of 500 liters. Currently, it is filled to 60% of its capacity. If 20% of the current water is used, how many liters of water will remain in the tank? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "240",
"style": "rule"
}
|
numina_math
|
{
"index": 1108,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length of 15 meters and a width of 10 meters. If you want to place a fence around the garden and then place an additional fence inside the garden along one of the diagonals, what is the total length of the fencing required? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "68.03",
"style": "rule"
}
|
numina_math
|
{
"index": 1109,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa is planning a road trip and is considering two different car rental options. Option A costs $120 for the rental and $0.40 per mile for gas, while Option B costs $180 for the rental and $0.30 per mile for gas. If she plans to drive 400 miles, how much will she save by choosing the cheaper option? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 1110,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Amelia needs to bake 6 cakes for a party. Each cake takes 3/4 of an hour to bake. If she can only use one oven at a time, how many hours will it take Amelia to bake all the cakes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1111,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jerry was asked by his mom to do grocery shopping. He needs to buy 2 liters of mustard oil that costs $13 per liter, 3 pounds of gluten-free penne pasta that costs $4 per pound, and 1 pound of pasta sauce that costs $5. If Jerry can keep the rest of the $50 after grocery shopping, how much money will he have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 1112,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Johnny wrote an essay with 150 words. Madeline wrote an essay that was double in length, and Timothy wrote an essay that had 30 words more than Madeline's. If one page contains 260 words, how many pages do Johnny, Madeline, and Timothy's essays fill together? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 1113,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jane is saving money for a new bicycle. She has already saved $150. Each week, she saves an additional $25. If the bicycle costs $500, how many more weeks will it take for Jane to save enough money to buy the bicycle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 1114,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the product of two integers is equal to \\(2^6 \\times 3^4 \\times 5^2 \\times 7\\), what are the possible pairs of integers \\((a, b)\\) such that \\(a\\) and \\(b\\) are positive integers, and each can be factored into the form \\(2^x \\times 3^y \\times 5^z \\times 7^w\\) where \\(x, y, z,\\) and \\(w\\) are non-negative integers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "210",
"style": "rule"
}
|
numina_math
|
{
"index": 1115,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A line passes through the points (2, 3) and (4, 7). Write the equation of this line in slope-intercept form, \\( y = mx + b \\), and determine the value of \\( m + b \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 1116,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe for a fruit punch requires that the ratio of apple juice to orange juice is 3:4. If you need to make 56 liters of fruit punch, how many liters of apple juice and orange juice do you need? Additionally, if the amount of apple juice is increased by 20%, by what percentage should the amount of orange juice be decreased to keep the total volume of the punch unchanged? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 1117,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A regular polygon has interior angles that sum to 3240 degrees. Determine the number of sides of this polygon, and subsequently, calculate the number of diagonals it has. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "170",
"style": "rule"
}
|
numina_math
|
{
"index": 1118,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In right triangle $\\triangle ABC$, where $\\angle C = 90^\\circ$, $AC = 5$ units, and $BC = 12$ units. Point $D$ lies on $\\overline{AB}$ such that the coordinates of $D$ are $(x, y)$. If $D$ is equidistant from $A$ and $B$, find the coordinates of $D$ and determine the distance from $D$ to point $C$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1119,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma and Liam live in two different cities. Emma's city is 15 kilometers west of Liam's city. Emma drives 3 times the distance east to meet Liam as Liam drives west. Together, they cover a total distance of 40 kilometers. How many kilometers does Liam drive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 1120,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A city has an initial population of 50,000 people. The population grows at a rate of 1,200 people per year, and 500 people move out of the city every year. After how many years will the city's population reach 60,000 people? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 1121,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A small company has 3 departments: Sales, Marketing, and IT. The company decides to allocate a total budget of $120,000 to these departments. The Sales department is to receive twice the amount given to the Marketing department, and the IT department is to receive $10,000 more than the Marketing department. How much money does each department receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "37500",
"style": "rule"
}
|
numina_math
|
{
"index": 1122,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical water tank has a diameter of 10 meters and a height of 6 meters. It is being filled with water at a constant rate. However, there is a leak in the tank that causes it to lose water at a rate proportional to the volume of water currently in the tank. Let \\( V(t) \\) be the volume of water in the tank at time \\( t \\), and the rate of water loss is given by \\( kV(t) \\) for some constant \\( k \\). Suppose the tank is initially empty and the filling rate is 50 cubic meters per hour. After 4 hours, the tank is observed to contain 500 cubic meters of water. Determine the constant \\( k \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.094",
"style": "rule"
}
|
numina_math
|
{
"index": 1123,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice buys 3/4 of a pound of almonds and 2/3 of a pound of cashews. If almonds cost $6 per pound and cashews cost $9 per pound, how much does Alice spend in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1124,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory operates 8 hours a day and produces widgets at a rate of 120 widgets per hour. Each widget is sold for $2.50. How much total revenue does the factory generate in a week (5 working days) if 10% of the widgets are defective and cannot be sold? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10800",
"style": "rule"
}
|
numina_math
|
{
"index": 1125,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the following expression and express your answer with positive exponents: \\( \\frac{0.1^{-3} \\cdot 0.2^{-2}}{0.5^{-4} \\cdot 0.4^{-1}} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "625",
"style": "rule"
}
|
numina_math
|
{
"index": 1126,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A savings account offers a compound interest rate of 5% per year, compounded annually. Jane deposits $1,000 into this account. After 5 years, she decides to withdraw all the money. Calculate the total amount in the account at the end of 5 years and find the logarithm base 10 of the total amount. Use the change of base formula to express your answer. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.106",
"style": "rule"
}
|
numina_math
|
{
"index": 1127,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a class of 30 students, 18 students play basketball, 12 students play soccer, and 6 students play both basketball and soccer. How many students do not play either basketball or soccer? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1128,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A particle moves along a path in space such that its position at time \\( t \\) is given by the vector function \\( \\mathbf{r}(t) = \\langle t^2, 2t, 3t - 4 \\rangle \\). At what time \\( t \\) is the particle 5 units away from the origin? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-1.693",
"style": "rule"
}
|
numina_math
|
{
"index": 1129,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah bought a sweater that was originally priced at $75. She used a discount coupon that gave her 15% off the original price. After applying the discount, she also had to pay a sales tax of 8% on the discounted price. How much did Sarah pay for the sweater in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "68.85",
"style": "rule"
}
|
numina_math
|
{
"index": 1130,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many numbers in the sequence $57, 5757, 575757, \\dots$ are prime? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 1131,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company distributes gift cards to its employees every month. The number of gift cards distributed each month follows a pattern where each month's distribution is twice the sum of the number of cards distributed in the previous two months. If the company distributed 10 gift cards in the first month and 6 gift cards in the second month, how many gift cards will be distributed in the 6th month? Additionally, if the total number of gift cards distributed over the first six months is evenly divisible by a certain integer \\(d\\), what is the largest possible value of \\(d\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "924",
"style": "rule"
}
|
numina_math
|
{
"index": 1132,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah spends 1/3 of her day working, 1/4 of her day sleeping, and the rest of the time on leisure activities. How many hours does she spend on leisure activities in a day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 1133,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Chloe bought chocolate-dipped strawberries at $50 a dozen. She then sold them for $30 for half a dozen during the Mother's Day celebration. How much is Chloe's profit if she sold 50 dozens? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "500",
"style": "rule"
}
|
numina_math
|
{
"index": 1134,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah needs to prepare lemonade for a school event. She plans to make 15 liters of lemonade. Each liter of lemonade requires 3 lemons and 200 grams of sugar. Lemons are sold in packs of 12 and sugar is sold in 1 kg bags. How many packs of lemons and bags of sugar does she need to buy? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 1135,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the matrices\n\\[\n\\mathbf{A} = \\begin{pmatrix} a & 1 & b \\\\ 2 & 2 & 3 \\\\ c & 5 & d \\end{pmatrix} \\quad \\text{and} \\quad \\mathbf{B} = \\begin{pmatrix} -5 & e & -11 \\\\ f & -13 & g \\\\ 2 & h & 4 \\end{pmatrix}\n\\]\nwhich are inverses of each other. Find the sum of all the elements \\(a, b, c, d, e, f, g, h\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "45",
"style": "rule"
}
|
numina_math
|
{
"index": 1136,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the prime numbers between 30 and 70. How many of these prime numbers have a remainder of 3 when divided by 7? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 1137,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A palindromic number is a number that reads the same forward as backward. For example, 343 and 1221 are palindromic numbers. If we want to find the smallest palindromic number greater than 10,000 that is also divisible by 3, what is this number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10101",
"style": "rule"
}
|
numina_math
|
{
"index": 1138,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Liam is thinking of a two-digit number. He says, \"If I divide the number by 5, the remainder is 2. If I divide the number by 7, the remainder is also 2.\" What is the smallest possible number that Liam could be thinking of? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "37",
"style": "rule"
}
|
numina_math
|
{
"index": 1139,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is currently three times as old as her daughter, Emma. Five years ago, Sarah was four times as old as Emma was at that time. How old are Sarah and Emma now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 1140,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate the polynomial \\( P(x) = 3x^2 - 4x + 7 \\) for \\( x = 5 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "62",
"style": "rule"
}
|
numina_math
|
{
"index": 1141,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe for a cake requires 3 cups of flour and 2 cups of sugar. If you have 15 cups of flour and an unlimited amount of sugar, how many cakes can you make? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1142,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Using only the digits 1, 2, and 3, how many positive five-digit integers can be made that are palindromes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "27",
"style": "rule"
}
|
numina_math
|
{
"index": 1143,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( \\frac{2}{x-3} + \\frac{3}{x+3} = 1 \\), solve 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": 1144,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Aunt Yang's flower shop sold 150 pots of tulips last month. Each pot of tulips costs 40 yuan. How much money did she make from selling tulips? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6000",
"style": "rule"
}
|
numina_math
|
{
"index": 1145,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, there are 10 students. Each student has 5 pencils. If 3 students lose 2 pencils each, and then the teacher distributes 4 more pencils to every student, how many pencils are there in total in the classroom at the end? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "84",
"style": "rule"
}
|
numina_math
|
{
"index": 1146,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is offering a 20% discount on a jacket. After the discount, the price of the jacket is $80. What was the original price of the jacket before the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 1147,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A transformation in the complex plane maps \\( z \\) to \\( w = 2z + 3 - 4i \\). If the complex number \\( z = 1 + 2i \\) is transformed, what is the resulting complex number \\( w \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1148,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah bought a laptop for $800 and needs to pay a sales tax of 8%. After paying the tax, she also wants to buy a software package that costs $150. If she uses a coupon that gives her a 10% discount on the software, how much does Sarah need to pay in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "999",
"style": "rule"
}
|
numina_math
|
{
"index": 1149,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, 60% of the students are boys, and the rest are girls. If there are 240 girls in the school, how many students are there in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "600",
"style": "rule"
}
|
numina_math
|
{
"index": 1150,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( z_1, z_2, z_3 \\) be the roots of the polynomial \\( P(z) = z^3 + az^2 + bz + c \\). Given that \\( |z_1| = 2 \\), \\( |z_2| = 3 \\), and \\( |z_3| = 4 \\), find the magnitude of the product of the roots, \\( |z_1 z_2 z_3| \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 1151,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sedrach has 13 apple pies. If every apple pie can be quickly divided into halves and every half an apple pie can be split into 5 bite-size samples, how many people can taste Sedrach's apple pie if he divides them all into bite-size samples? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "130",
"style": "rule"
}
|
numina_math
|
{
"index": 1152,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sandra is a shopkeeper who buys candies in bulk. She purchased 200 candies at $0.40 each. She plans to sell them in packs of 10 candies each at a 25% profit per pack. How much profit will Sandra make after selling all the candies? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 1153,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "At a sports store, the price of a tennis racket is $120, a basketball is $30, and a pair of running shoes is $80. The store offers a 15% discount on tennis rackets, a 10% discount on basketballs, and a 20% discount on running shoes. If a customer buys one of each item, how much do they spend in total after applying all the discounts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "193",
"style": "rule"
}
|
numina_math
|
{
"index": 1154,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A committee of 10 members needs to select a subcommittee of 3 members. How many different ways can the subcommittee be chosen? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 1155,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company wants to distribute a bonus of $12,000 among its employees in such a way that the ratio of the amount received by managers to the amount received by regular employees is 3:1. If there are 4 managers and 12 regular employees, how much does each manager and each regular employee receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "500",
"style": "rule"
}
|
numina_math
|
{
"index": 1156,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( n = 2^3 \\times 3^2 \\times 5^1 \\times 7^1 \\). Let \\( f(n) \\) be a function that, given an integer \\( n \\), returns an integer \\( k \\), where \\( k \\) is the smallest possible integer such that \\( k! \\) is divisible by \\( n \\). What is the value of \\( f(n) \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 1157,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe requires a mixture of ingredients weighing 1/3 pound, 1/6 pound, and 1/4 pound. Convert the total weight of these ingredients into ounces. (Note: 1 pound = 16 ounces) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 1158,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a clearance sale, and they offer a 20% discount on all items. If the customer buys items worth $200, and then the store offers an additional 10% discount on the discounted price, what is the final price the customer pays for the items? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "144",
"style": "rule"
}
|
numina_math
|
{
"index": 1159,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Liam has a collection of 36 books, and he wants to organize them into boxes. Each box can hold 6 books. How many boxes will Liam need? After organizing the books, Liam discovers that 12 of his books are old editions, and he decides to donate these. How many new edition books does he have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 1160,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Compute the sum \n\\[\n\\sum_{k=0}^{90} \\left( \\cos^2 k^\\circ + 2 \\cos^4 k^\\circ \\right).\n\\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "113.75",
"style": "rule"
}
|
numina_math
|
{
"index": 1161,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a speed of 60 miles per hour. How long will it take for the car to travel 180 miles? If the car then continues to travel another 60 miles at a reduced speed of 40 miles per hour, what is the total time taken for the entire journey? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1162,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If a triangle has two sides of lengths 6 units and 3 units, how many different integer lengths can the third side be? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1163,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sam, John, and Peter are three friends with different heights. Sam is 5 cm taller than John, and John is 7 cm taller than Peter. If Peter is 140 cm tall, how tall is Sam? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "152",
"style": "rule"
}
|
numina_math
|
{
"index": 1164,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Linda is currently 28 years old. Four years ago, she was three times as old as her younger brother, Tom. How old is Tom now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 1165,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends scored the following points in a game: 18, 22, 15, 25, and 20. What is their average score? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "20",
"style": "rule"
}
|
numina_math
|
{
"index": 1166,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A jar contains a total of 50 coins, consisting of nickels, dimes, and quarters. The number of nickels is twice the number of dimes, and the total value of the coins is $6.75. How many dimes are in the jar? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 1167,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find all integer roots of the polynomial \n\\[P(x) = x^3 - 6x^2 + 11x - 6\\]\nand then compute the sum of these roots. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 1168,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Nora is planning her weekly budget. She wants to allocate her resources for different activities. She decides to spend 20% of her budget on groceries, 30% on rent, and 15% on utilities. The rest of her budget is to be spent on entertainment. If Nora's total weekly budget is $500, how much money does she allocate to each activity, and how much does she spend on entertainment? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "175",
"style": "rule"
}
|
numina_math
|
{
"index": 1169,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length of 15 yards and a width of 10 yards. However, 1/5 of the garden is not used for planting. What is the total area available for planting? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 1170,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the fraction \\(\\frac{3}{8}\\) into a decimal, multiply it by 24, and then subtract 5 from the result. What is the final value? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 1171,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mia is planning a birthday party and needs to buy party favors. She buys 7 packs of party favors and pays with a $50 bill. She receives $15 in change. How much did each pack of party favors cost? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1172,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Carlos is saving money to buy a new bicycle that costs $300. He currently has $150 saved up. If his savings increase by 20% each month, how many months will it take for Carlos to save enough money to buy the bicycle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 1173,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels at a constant speed of 15 miles per hour. His friend, who started the journey at the same time, travels at half the speed of the cyclist. If the friend wishes to catch up with the cyclist after 2 hours, how many more miles does he need to travel, and what would his required speed be to catch up in the next 2 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7.5",
"style": "rule"
}
|
numina_math
|
{
"index": 1174,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 2400 units of a product each month. Each unit requires 3.5 hours of labor to produce. If the factory operates for 25 days a month and each worker works 7 hours a day, how many workers are needed to produce the units? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 1175,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "At the school fair, Sally sells cupcakes for $3 each. She sells 5 cupcakes in the morning and 7 cupcakes in the afternoon. Later, she spends $6 on supplies for her baking. How many dollars does Sally have left after buying the supplies? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 1176,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the geometric sequence where the first term is given by \\(a\\) and the common ratio is \\(r\\). The fourth term of the sequence is given by \\(6!\\), and the magnitude of the complex number \\(z\\) is given by \\(|z| = 720\\). If \\(z = a \\cdot r^3\\), find the first term \\(a\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "720",
"style": "rule"
}
|
numina_math
|
{
"index": 1177,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the sum of all single-digit multiples of 2 and 3? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "32",
"style": "rule"
}
|
numina_math
|
{
"index": 1178,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A baker has a certain number of cookies. If he divides the cookies equally among 7 friends, he will have 3 cookies left over. If he divides the cookies equally among 5 friends, he will have 1 cookie left over. What is the smallest number of cookies the baker could have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "31",
"style": "rule"
}
|
numina_math
|
{
"index": 1179,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two workers, Alex and Ben, are painting a fence. Alex can paint the entire fence by himself in 10 hours, while Ben can paint the same fence by himself in 15 hours. They decide to work together to paint the fence. However, after working together for 2 hours, Alex has to leave. How much longer will it take Ben to finish painting the fence on his own? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 1180,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels 300 kilometers in 5 hours. At the same rate, how many kilometers will the car travel in 8 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "480",
"style": "rule"
}
|
numina_math
|
{
"index": 1181,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A city park has a square playground with a side length of 60 meters. The city plans to divide the playground into smaller square sections, each with a side length of 15 meters. How many smaller square sections will the playground be divided into? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "16",
"style": "rule"
}
|
numina_math
|
{
"index": 1182,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore bought a shipment of 120 novels for $1,200. The store sold 50 of these novels for $15 each, 30 for $20 each, and the remaining novels for $10 each. Calculate the bookstore's profit from this shipment. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "550",
"style": "rule"
}
|
numina_math
|
{
"index": 1183,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is collecting marbles. She currently has 15 red marbles and 20 blue marbles. She then buys a pack that contains twice as many green marbles as the total number of red and blue marbles she already has. How many marbles does Emily have in total now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "105",
"style": "rule"
}
|
numina_math
|
{
"index": 1184,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cylindrical tank with a height of 12 meters has the same volume as a conical tank. If the ratio of the base areas of the cylinder to the cone is 3:4, what is the height of the conical tank in meters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "27",
"style": "rule"
}
|
numina_math
|
{
"index": 1185,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In an isosceles triangle \\( \\triangle ABC \\), \\( AB = AC = 10 \\) units and \\( BC = 12 \\) units. Calculate the area of \\( \\triangle ABC \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48",
"style": "rule"
}
|
numina_math
|
{
"index": 1186,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are $5.5$ cm, $7.3$ cm, and $8.2$ cm. What is the area of the square in square centimeters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "27.5625",
"style": "rule"
}
|
numina_math
|
{
"index": 1187,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Tim has 30 fewer apples than Martha, and Harry has half as many apples as Tim. If Martha has 68 apples, how many apples does Harry have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "19",
"style": "rule"
}
|
numina_math
|
{
"index": 1188,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A class consists of 12 students. The students' final grades are as follows: 85, 90, 75, 80, 95, 70, 85, 80, 90, 75, 85, and 95. The teacher decides to give an extra 5 points to each student's grade. What is the new class average? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "88.75",
"style": "rule"
}
|
numina_math
|
{
"index": 1189,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lena is planning a road trip that will take her across several states. Her car averages 25 miles per gallon of gas, and her fuel tank can hold up to 12 gallons. If she plans to drive 300 miles each day for 5 days, how many gallons of gas will she need in total for the entire trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 1190,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Convert the decimal number \\( 731 \\) to base 6 and then find the sum of the digits of the resulting base 6 number. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 1191,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is organizing a book sale. She has 4 boxes of books. Each box contains 7 books. Additionally, she receives a donation of 15 more books. How many books does Sarah have in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "43",
"style": "rule"
}
|
numina_math
|
{
"index": 1192,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "There are two positive integers \\( c \\) for which the equation \\( 3x^2 + 4x + c = 0 \\) has rational solutions. What is the sum of those two values of \\( c \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 1193,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular park has a length of 15 meters and a diagonal of 17 meters. Find the width of the park. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 1194,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two workers, A and B, can complete a task together in 6 hours. Worker A alone can complete the task in 10 hours. How long would it take Worker B to complete the task alone? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 1195,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bookstore is having a sale where customers can buy 5 books for $10 each and receive a 20% discount on the total purchase. Additionally, they can buy 3 magazines for $4 each without any discount. If a customer buys both the books and the magazines, how much will they spend in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "52",
"style": "rule"
}
|
numina_math
|
{
"index": 1196,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jane runs a small bakery. She buys flour in bulk, spending $120 for 50 pounds of flour. Each loaf of bread requires 1 pound of flour and she adds another $0.50 worth of ingredients per loaf. She sells each loaf for $5. If Jane bakes and sells 100 loaves of bread, what is her total profit? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "210",
"style": "rule"
}
|
numina_math
|
{
"index": 1197,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John earns $15 per hour working at a bookstore. If he works 8 hours each day for 5 days a week, how much will he earn in 4 weeks? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2400",
"style": "rule"
}
|
numina_math
|
{
"index": 1198,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a group of 50 students, each student is born in one of the 12 months of the year. What is the minimum number of students that must be in the group to ensure that at least 5 students share the same birth month? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "49",
"style": "rule"
}
|
numina_math
|
{
"index": 1199,
"name": "numina_math",
"split": "train"
}
|
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