prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "Rose and Kylie are playing a game. Here are the rules:\n1. There are $14$ marbles placed in a row.\n2. The players take turns removing either $1$ or $2$ marbles each turn.\n3. Whoever picks the last marble wins the game.\nRose starts first and is followed by Kylie. To ensure her victory, how many marbles must Rose take away in the first turn? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2600,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends decided to travel to a city located 500 miles away. They traveled part of the way by car at an average speed of 60 miles per hour and the rest of the way by train at an average speed of 80 miles per hour. If the total travel time was 8 hours, how many miles did they travel by train? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 2601,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A digital clock displays the time in a 24-hour format. What is the sum of the digits of the time displayed at 19:34? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "17",
"style": "rule"
}
|
numina_math
|
{
"index": 2602,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A concert hall hosted a band performance and sold 150 tickets at $30 each. For the second performance, twice as many tickets were sold at the same price. How much total revenue did the concert hall generate from both performances? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13500",
"style": "rule"
}
|
numina_math
|
{
"index": 2603,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist rides his bike uphill at a speed of 10 miles per hour and downhill at a speed of 25 miles per hour. If the hill is 5 miles long, how long does it take the cyclist to ride up and down the hill? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.7",
"style": "rule"
}
|
numina_math
|
{
"index": 2604,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sam is training for a marathon and runs at a constant speed. He runs 5 miles in 40 minutes. If he increases his speed by 20%, how many minutes will it take him to run the same 5 miles at the increased speed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33.33",
"style": "rule"
}
|
numina_math
|
{
"index": 2605,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A gardener planted 15 rose bushes this month. Last month, she planted 5 fewer rose bushes than this month. How many rose bushes did the gardener plant in total over the two months? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 2606,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice left her house at 8 a.m. and cycled to her friend's house at a constant speed of 12 kilometers per hour. She arrived at her friend's house at 10 a.m. How far is Alice's house from her friend's house? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 2607,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice invested $1200 in two different mutual funds. She allocated one-third of her investment to Fund A and the remaining amount to Fund B. After one year, Fund A had increased by 50%, while Fund B had decreased by 20%. What is the total value of Alice's investment after one year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1240",
"style": "rule"
}
|
numina_math
|
{
"index": 2608,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mr. Ha owns 7 more silver dollars than Mr. Phung. Mr. Phung has 20 more silver dollars than Mr. Chiu has. If Mr. Chiu has 45 silver dollars, how many silver dollars do the three have in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "182",
"style": "rule"
}
|
numina_math
|
{
"index": 2609,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "There are 12 teachers in a school. If there are three times as many students as teachers in the school, how many students are there in the school? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 2610,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\(x\\): \\(3x - 5 = 2(x + 4)\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 2611,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a clearance sale where all items are marked down by 25%. If a customer buys a shirt originally priced at $40, a pair of jeans originally priced at $60, and a jacket originally priced at $100, how much does the customer pay in total after the discounts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 2612,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah loves painting and has decided to paint a mural on a wall in her neighborhood. The wall is 12 feet high and 20 feet wide. She plans to paint 5 flowers per square foot of the wall. How many flowers will she paint in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1200",
"style": "rule"
}
|
numina_math
|
{
"index": 2613,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "David plans to save for a new laptop that costs $960. He wants to save an equal amount of money each week for 24 weeks. If he already has $240 saved up, how much should he save per week to reach his goal? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2614,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A right triangle has one leg that is 5 units long and its hypotenuse is 13 units long. Find the length of the other leg. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2615,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression: \\(\\sqrt{\\left(\\sqrt{16} + \\sqrt{4}\\right)^2}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2616,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah wants to buy 3/4 of a pound of almonds. The price of almonds is $8 per pound. After buying the almonds, she realizes she only has $2 left in her wallet. How much money did Sarah initially have before buying the almonds? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2617,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A baker has 64 cupcakes. He decides to give away 8 of them to a friend. After giving them away, he divides the remaining cupcakes equally into boxes of 4. How many boxes of cupcakes does he have now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 2618,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah saved 2 and 3/4 times more money than last year. Last year she saved $500. This year she wants to donate 25% of her savings to a charity. How much money will she donate to the charity this year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "343.75",
"style": "rule"
}
|
numina_math
|
{
"index": 2619,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school cafeteria, the ratio of the number of students who prefer pizza to those who prefer burgers is 5:3. If a total of 64 students were surveyed, how many students prefer pizza? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2620,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer has three fields. Each field has 6 rows of corn, with each row containing 15 corn plants. The farmer decides to plant an additional 120 corn plants evenly across the three fields. How many corn plants are there in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "390",
"style": "rule"
}
|
numina_math
|
{
"index": 2621,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The speed of a train is 60% faster than the speed of a car. If the speed of the car is 50 miles per hour, what is the speed of the train? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 2622,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find all values of \\( x \\) such that the equation \\( 3^{2x} = 81^{x-1} \\) holds true. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
numina_math
|
{
"index": 2623,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah wants to buy a laptop that costs $1,500. She finds two options for payment. In Option A, the store offers a 10% discount on the laptop's price but charges a 5% sales tax on the discounted price. In Option B, the store offers no discount but charges a 5% sales tax on the original price. Which option should Sarah choose to pay less, and how much will she save? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "157.50",
"style": "rule"
}
|
numina_math
|
{
"index": 2624,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah buys 5 apples and 3 oranges. Each apple costs $1.20, and each orange costs 50% more than an apple. If she pays with a $20 bill, how much change does she receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8.60",
"style": "rule"
}
|
numina_math
|
{
"index": 2625,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Laura had a 5-liter container of juice. She poured out 1/5 of the juice into a glass for her brother and later gave away 1/4 of the remaining juice to her friend. How much juice does Laura have left in the container? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2626,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A bag contains 8 red balls, 6 blue balls, and 4 green balls. If one ball is randomly selected from the bag, what is the probability of selecting a red ball, and what percentage does this probability represent?\n\n### Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "44.44",
"style": "rule"
}
|
numina_math
|
{
"index": 2627,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( a \\) and \\( b \\) be the roots of the quadratic equation \\( x^2 - 6x + 5 = 0 \\). Suppose \\( a^2 + b^2 = p \\) and \\( a^3 + b^3 = q \\). Compute the value of \\( p + q \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "152",
"style": "rule"
}
|
numina_math
|
{
"index": 2628,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many distinct ways can the letters in the word \"BALLOON\" be arranged? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1260",
"style": "rule"
}
|
numina_math
|
{
"index": 2629,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends went out for dinner and decided to split the bill equally among themselves. The total bill came out to be $360. If the group initially consisted of 5 friends, but one more friend joined them at the last minute, how much less would each person have to pay compared to the original arrangement? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2630,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Three friends, Alice, Ben, and Carol, decide to share the cost of a dinner equally. The total cost of the dinner is $90. After paying, they realize they have forgotten to include a tip of 20%. How much more does each friend need to pay to cover the tip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2631,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Suppose \\( f(x) = 3x^2 + 5x \\) and \\( g(x) = 4x^3 - 2x + 1 \\). Find the degree of the polynomial \\( f(x) \\cdot g(x) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2632,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A number \\(N\\) has the prime factorization \\(2^3 \\times 3^2 \\times 5\\). If this number is divided by another number \\(M\\) which has the prime factorization \\(2 \\times 3 \\times 5\\), what is the ratio \\( \\frac{N}{M} \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2633,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation \\( \\sqrt{x + 6} = 5 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "19",
"style": "rule"
}
|
numina_math
|
{
"index": 2634,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa is organizing a charity bake sale and needs to buy ingredients. She plans to bake 20 cakes and each cake requires 3 bags of flour, 2 bags of sugar, and 1 bag of baking powder. If each bag of flour costs $5, each bag of sugar costs $3, and each bag of baking powder costs $2, how much will she spend in total on ingredients for the cakes? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "460",
"style": "rule"
}
|
numina_math
|
{
"index": 2635,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A smartphone originally costs $800. During a sale, the store offers a 25% discount on the smartphone. After the sale, the store decides to increase the discounted price by 10%. What is the final price of the smartphone? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "660",
"style": "rule"
}
|
numina_math
|
{
"index": 2636,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Julie wants to give her favorite cousin a $2345 mountain bike for his birthday. So far, she has saved $1500. Since the birthday is still a few weeks away, Julie has time to save even more. She plans on mowing 20 lawns, delivering 600 newspapers, and walking 24 of her neighbors’ dogs. She is paid $20 for each lawn, 40 cents per newspaper, and $15 per dog. After purchasing the bike, how much money will Julie have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "155",
"style": "rule"
}
|
numina_math
|
{
"index": 2637,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe calls for 3 cups of flour for every 2 cups of sugar. If you want to make a batch that uses 9 cups of flour, how many cups of sugar do you need? Also, if each cup of flour weighs 120 grams, how many grams of flour will you need in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1080",
"style": "rule"
}
|
numina_math
|
{
"index": 2638,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a regular pentagon, each interior angle is equal. If the measure of each angle is increased by 25% of its original measure, what is the new measure of each angle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "135",
"style": "rule"
}
|
numina_math
|
{
"index": 2639,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A certain type of bacteria doubles in number every 3 hours. If you start with 5 bacteria, how many bacteria will there be after 24 hours? Express your answer in the simplest form and write it as a rational expression. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1280",
"style": "rule"
}
|
numina_math
|
{
"index": 2640,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jessica invested $750 in a savings account that offers a simple annual interest rate of 3.5%. If she leaves the money in the account for 4 years, how much interest will she earn? Round your answer to the nearest hundredth. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "105",
"style": "rule"
}
|
numina_math
|
{
"index": 2641,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A clothing store is having a sale where all items are 25% off. If a jacket originally costs $80 and a pair of jeans originally costs $60, how much will a customer pay for both items after the discount is applied? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "105",
"style": "rule"
}
|
numina_math
|
{
"index": 2642,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a mythical kingdom, 3 cloves of garlic can repel 2 vampires, 8 vampire bats, or 3 wights. How many cloves of garlic are needed to repel 30 vampires, 12 wights, and 40 vampire bats? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72",
"style": "rule"
}
|
numina_math
|
{
"index": 2643,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends went out to dinner and decided to split the bill equally. The total bill, including tax and tip, came to $172.50. If there were 5 friends in the group, how much did each friend pay on average? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "34.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2644,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "What is the product of $(-8)(-5)$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2645,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels 300 miles in 5 hours. A bike travels 60 miles in 3 hours. What is the ratio of the car's speed to the bike's speed? If the car continues to travel at the same speed for 8 hours, how far will it travel? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "480",
"style": "rule"
}
|
numina_math
|
{
"index": 2646,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression and find the value of \\(x\\): \\((\\sqrt[3]{8})^{4x} = 16\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2647,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A number \\( N \\) in base 5 is represented as \\( 4321_5 \\). Convert \\( N \\) to its decimal form, and then find the largest prime factor of the decimal number. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "293",
"style": "rule"
}
|
numina_math
|
{
"index": 2648,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A swimming pool has a maximum capacity of 1500 gallons of water. If 850 gallons of water are already in the pool, how many more gallons of water can be added to the pool before reaching its full capacity? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "650",
"style": "rule"
}
|
numina_math
|
{
"index": 2649,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A train travels from City A to City B at a speed of 60 km/h and returns from City B to City A at a speed of 40 km/h. If the total travel time for the round trip is 5 hours, how far is City A from City B? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 2650,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a coordinate plane, five points $P_1, P_2, P_3, P_4,$ and $P_5$ are placed such that none of them lie on the same line. Each point is either red, blue, or green. You know that in any group of four points, at least two points are of the same color. Additionally, the distance between any two points of the same color is at most 5 units. Given these conditions, what is the maximum possible distance between any two points among the five points? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5\\sqrt{2}",
"style": "rule"
}
|
numina_math
|
{
"index": 2651,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah and Mark are organizing a charity marathon. They need to distribute water bottles equally among the participants. Sarah has collected 120 water bottles, and Mark has collected 3 times as many as Sarah. They expect 60 participants. How many water bottles will each participant receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2652,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Susan has a ribbon that is 3.6 meters long. She wants to cut it into pieces that are each 0.45 meters long. How many pieces of ribbon will she have, and how much ribbon, if any, will be left over?\n\n### Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2653,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company has a server that processes tasks at different rates during the day. From 9:00 AM to 12:00 PM, it processes tasks at a rate of 10 tasks per hour. From 12:00 PM to 3:00 PM, it processes tasks at a rate of 20 tasks per hour. From 3:00 PM to 6:00 PM, it processes tasks at a rate of 15 tasks per hour. Calculate the total number of tasks the server processes from 9:00 AM to 6:00 PM. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "135",
"style": "rule"
}
|
numina_math
|
{
"index": 2654,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe calls for 250 grams of flour to make one batch of cookies. If you want to make enough cookies for a party and you need to make 12 batches, how many kilograms of flour do you need to buy? (Note: 1 kilogram = 1000 grams) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 2655,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A father is currently three times as old as his son. Five years ago, the average of their ages was 20 years. How old is the father now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "37.5",
"style": "rule"
}
|
numina_math
|
{
"index": 2656,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah and John plan to go on a road trip. They drive 120 miles to their first destination. After resting, they drive another 180 miles to their second destination. If their car consumes fuel at a rate of 30 miles per gallon, and fuel costs $4 per gallon, how much did they spend on fuel for the entire trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 2657,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store offers a discount of 20% on all items during a sale. If the original price of a jacket is $75, how much will the jacket cost after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 2658,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "James is planning to buy new furniture for his living room. He budgets $1,200 for a sofa and $800 for a dining table. If he wants to buy these items during a sale where everything is 25% off, how much money will he spend on both items after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1500",
"style": "rule"
}
|
numina_math
|
{
"index": 2659,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex cycles a distance of 45 miles. He completes this distance in 3 hours. On another day, he cycles an additional 32 miles in 2 hours. What is his average speed over the entire distance? Express your answer as a mixed number. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15\\frac{2}{5}",
"style": "rule"
}
|
numina_math
|
{
"index": 2660,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "During a community event, a local bakery decided to donate cookies to three different schools. The bakery started by donating 60 cookies to School A, then they donated 1.5 times the number of cookies they gave to School A to School B. Finally, they donated the same number of cookies to School C as they did to School B. How many cookies did the bakery donate in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "240",
"style": "rule"
}
|
numina_math
|
{
"index": 2661,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The number of books in the library is directly proportional to the number of shelves it has. If the library has 10 shelves and holds 2000 books, how many shelves would be needed to hold 3500 books? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 2662,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A painter can paint a wall of 100 square meters in 5 hours. Another painter can paint the same wall in 3 hours. If both painters work together, how long will it take them to paint the wall? Express your answer in hours. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.875",
"style": "rule"
}
|
numina_math
|
{
"index": 2663,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that \\( x + \\frac{1}{x} = 3 \\), find the value of \\( x^2 + \\frac{1}{x^2} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2664,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, 25% of the students are left-handed. If there are 32 students in the classroom, how many students are left-handed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2665,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the following expression: $\\frac{6 \\sqrt{8} + 3 \\sqrt{18}}{3 \\sqrt{2}}$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2666,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily is buying ingredients for a cake. She needs 1.5 pounds of flour, 0.75 pounds of sugar, and 0.25 pounds of cocoa powder. If flour costs $2.40 per pound, sugar costs $1.80 per pound, and cocoa powder costs $3.60 per pound, what is the total cost of the ingredients? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5.85",
"style": "rule"
}
|
numina_math
|
{
"index": 2667,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma is traveling to Europe and needs to exchange her US dollars for euros. If the exchange rate is 1 US dollar = 0.85 euros, and she exchanges $500, how many euros will she receive? Additionally, if she spends 150 euros on souvenirs, how many euros does she have left? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "275",
"style": "rule"
}
|
numina_math
|
{
"index": 2668,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alice decides to buy 8 identical chairs for her new apartment. Each chair costs $45. If she finds a discount coupon that reduces the total cost by $60, how much will she pay in the end? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 2669,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, there are 40 students. Each student studies either Mathematics or Science or both. If 30 students study Mathematics and 25 students study Science, how many students study both subjects? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 2670,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a constant speed. If the car covers a distance of 120 miles in \\( t \\) hours and its speed is increased by 10 miles per hour, it would take 1 hour less to cover the same distance. Find the original speed of the car. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 2671,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John is arranging books on his shelf. The height of the books is measured in centimeters and follows an arithmetic sequence with a common difference of 2 cm. The heights of the first three books are 10 cm, 12 cm, and 14 cm. If John arranges 5 books in this pattern, what is the average height of the books? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 2672,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given the quadratic expression $3x^2 - 12x + k$, find the value of $k$ such that the expression represents a perfect square trinomial. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 2673,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jennifer and Mark are splitting the cost of a gift for their friend. Jennifer contributes twice as much as Mark. Together, they spend a total of $90. How much does each person contribute? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "60",
"style": "rule"
}
|
numina_math
|
{
"index": 2674,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is planning to build a small garden and she needs to buy soil bags. Each soil bag costs $5. She plans to buy enough soil bags to fill 3 garden beds, with each garden bed requiring 4 soil bags. How much will Samantha spend on soil bags 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": 2675,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A family had 10 eggs, but the mother used 5 of them to make an omelet. Then, 2 chickens laid 3 eggs each. How many eggs does the family have now? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 2676,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah used to receive 15 emails a day. After changing her email address, she now receives 40 emails a day. Assuming the number of emails from her contacts has not changed, how many emails per week is she receiving that are not intended for her? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "175",
"style": "rule"
}
|
numina_math
|
{
"index": 2677,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The first term of a geometric sequence is \\(2\\), and the common ratio is \\(5\\). What is the smallest \\(n\\) for which the \\(n\\)th term of the sequence is divisible by \\(10,000\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2678,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A survey was conducted among 50 students to find out the number of hours they study per week. The data collected is as follows: 5, 7, 8, 6, 9, 10, 7, 6, 8, 5, 7, 9, 10, 6, 8, 7, 9, 6, 8, 10, 7, 9, 8, 6, 7, 9, 10, 8, 6, 7, 9, 8, 10, 6, 7, 8, 6, 7, 9, 10, 8, 7, 6, 9, 8, 7, 10, 6, 7, 9. Find the mean, median, and mode of the number of hours the students study per week. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 2679,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two trains, Train A and Train B, are moving towards each other from two towns that are 500 kilometers apart. Train A starts from Town X and travels at a constant speed of 60 kilometers per hour. Train B starts from Town Y and travels at a constant speed of 40 kilometers per hour. If both trains start at the same time, how long will it take for the two trains to meet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2680,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jennifer earned $120 from a yard sale. She decided to split the money equally among her three children and then give an additional $10 to each child. How much money did each child receive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 2681,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider a piecewise function that defines the cost \\( C(x) \\) for shipping a package based on its weight \\( x \\) (in pounds) as follows:\n\\[ \nC(x) = \n\\begin{cases} \n10 & \\text{if } 0 < x \\leq 2 \\\\\n5x & \\text{if } 2 < x \\leq 10 \\\\\n50 + 2(x - 10) & \\text{if } x > 10 \n\\end{cases}\n\\]\nCalculate the cost of shipping a package that weighs 12 pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "54",
"style": "rule"
}
|
numina_math
|
{
"index": 2682,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces 12,000 widgets in a 30-day month. If each worker produces the same number of widgets per day and there are 50 workers in the factory, how many widgets does each worker produce on average per day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 2683,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many trailing zeros are there in the number \\( (50!)^2 \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 2684,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A square has a perimeter of 32 cm. Inside this square, a circle is inscribed such that it is tangent to all four sides of the square. What is the radius of the inscribed circle? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
numina_math
|
{
"index": 2685,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let \\( f(x) = 2^x \\) and \\( g(x) = \\log_2(x) \\). Find the value of \\( x \\) where the graphs of \\( f \\) and \\( g \\) intersect. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 2686,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of 6 friends went on a weekend trip and decided to share the expenses equally. They spent $120 on fuel, $180 on food, $90 on lodging, and $60 on entertainment. How much will each friend need to contribute to cover the total expenses? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "75",
"style": "rule"
}
|
numina_math
|
{
"index": 2687,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A company has 120 employees. 70% of the employees work in the marketing department, and 40% of those in marketing are working remotely. If the remaining employees are equally divided among two other departments, how many employees are working remotely in the marketing department, and how many employees are in each of the other two departments? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 2688,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a garden, there are 24 apple trees. Each tree produces 50 apples every month. If each apple has 10 seeds, how many seeds will there be in total after 6 months? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "72000",
"style": "rule"
}
|
numina_math
|
{
"index": 2689,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a collection of 60 marbles. She decides to give away some of her marbles to her friends. She gives 1/5 of her marbles to her friend John, 1/4 of what remains to her friend Amy, and 1/2 of what is left after that to her friend Mike. How many marbles does Sarah have left after giving the marbles to her friends? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 2690,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha has a piece of fabric that measures 3.87 meters in length. She needs to cut it into 7 equal pieces for a sewing project. After cutting, she plans to round the length of each piece to the nearest tenth of a meter. What will be the length of each piece after rounding? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.6",
"style": "rule"
}
|
numina_math
|
{
"index": 2691,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the system of nonlinear equations:\n\\[\nx^2 + y^2 + z^2 = 35\n\\]\n\\[\nxy + yz + zx = 20\n\\]\nFind the sum of all possible integer values of \\( x, y, \\) and \\( z \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 2692,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\( a = 4 \\), \\( b = 8 \\), and \\( c = 2 \\), what is the value of the expression \\(\\frac{(a^2 + b^2 + c^2)}{(a + b + c)}\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
numina_math
|
{
"index": 2693,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a road trip and needs to visit three different cities. She starts from her home and drives 120 miles to the first city. From there, she drives another 150 miles to the second city. Finally, she drives 200 miles to the third city. After visiting the third city, she returns home by driving the same distances in reverse order. How many miles in total does Sarah drive on her road trip? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "940",
"style": "rule"
}
|
numina_math
|
{
"index": 2694,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two cyclists, C and D, are 180 kilometers apart. Cyclist C starts cycling towards Cyclist D at a speed of 20 km/h, while Cyclist D starts cycling towards Cyclist C at a speed of 15 km/h. If they start at the same time, how long will it take for the two cyclists to meet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5.14",
"style": "rule"
}
|
numina_math
|
{
"index": 2695,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma sells handmade bracelets at a local craft fair. She sells each bracelet for $15. She spends $3 per bracelet on materials. If Emma sells 20 bracelets, how much profit does she make? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "240",
"style": "rule"
}
|
numina_math
|
{
"index": 2696,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mary has $120. She spends $45 on groceries and plans to buy a new dress for $80 next week. How much money will she need to save to afford the dress? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 2697,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A taxi service charges a flat fee of $3 for picking up a customer, plus $2.50 per mile traveled. If a customer takes a ride that covers 12 miles, how much will the total fare be? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "33",
"style": "rule"
}
|
numina_math
|
{
"index": 2698,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a chemistry lab, there are 3 types of chemicals: A, B, and C. Chemical A costs $15 per gram, Chemical B costs $10 per gram, and Chemical C costs $20 per gram. A scientist used 5 grams of Chemical A, 8 grams of Chemical B, and 3 grams of Chemical C for an experiment. How much did the total cost of the chemicals used in the experiment amount to? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "215",
"style": "rule"
}
|
numina_math
|
{
"index": 2699,
"name": "numina_math",
"split": "train"
}
|
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