prompt
listlengths 1
1
| reward_model
dict | data_source
stringclasses 1
value | extra_info
dict |
|---|---|---|---|
[
{
"content": "Find the area in the plane defined by the absolute value inequality \\( |x| + |y| \\leq 5 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 9600,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangular garden has a length of 20 units and a width of 15 units. A walking path of uniform width surrounds the garden. The total perimeter of the garden and the walking path together is 120 units. What is the width of the walking path? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "6.25",
"style": "rule"
}
|
numina_math
|
{
"index": 9601,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "James is planning a party and wants to buy decorations. He buys a pack of balloons for $4.75, a banner for $6.30, and a pack of streamers for $3.20. James also needs to buy 8 sets of party favors, each set costing $5.50. After buying all these items, how much money will James have left if he initially had $100? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "41.75",
"style": "rule"
}
|
numina_math
|
{
"index": 9602,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation $|5x - 4| + 6 = 10$ and find the product of all possible values of $x$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 9603,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A family of four decides to buy a large pizza and share it equally. If the pizza costs $28 and they also buy two bottles of soda costing $3 each, what is the total cost for each family member? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8.50",
"style": "rule"
}
|
numina_math
|
{
"index": 9604,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Two painters, Alice and Bob, are hired to paint a house. Alice can paint the entire house in 6 hours, while Bob can paint the same house in 8 hours. If they work together, how long will it take them to paint the entire house? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3.43",
"style": "rule"
}
|
numina_math
|
{
"index": 9605,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the Fibonacci sequence $F_0, F_1, F_2, \\ldots$ defined by $F_0 = 0$, $F_1 = 1$, and $F_{n+2} = F_{n+1} + F_n$ for $n \\geq 0$. Find the sum of the infinite series\n\\[\n\\sum_{n=0}^{\\infty} \\frac{F_n}{2^{n+1}}.\n\\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 9606,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, there are 25 students who each have a unique favorite fruit. The teacher wants to distribute 100 different fruits such that each student gets at least one fruit and no two students get the same type of fruit. However, the teacher can only ensure this under the condition that at least one fruit type is given to more than one student. How many different types of fruit must there be to guarantee that at least one fruit type is given to more than one student? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 9607,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A cyclist travels from Town X to Town Y at an average speed of 18 kilometers per hour. On the return trip from Town Y to Town X, the cyclist travels at an average speed of 12 kilometers per hour. The entire round trip takes 5 hours. How far is it from Town X to Town Y? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 9608,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A toy store buys action figures at $50 each. The store wants to make a profit of $15 on each action figure after applying a 25% discount. What should the selling price be before the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "86.67",
"style": "rule"
}
|
numina_math
|
{
"index": 9609,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many positive $4$-digit numbers are divisible by $6$ but not by $9$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1000",
"style": "rule"
}
|
numina_math
|
{
"index": 9610,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A staircase has 10 steps, and each step is 2 inches taller than the previous step. If the first step is 4 inches tall, what is the total height of the staircase? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "130",
"style": "rule"
}
|
numina_math
|
{
"index": 9611,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex and Jamie are saving up for a vacation that costs $4,800. They decide to save together and share the monthly savings equally. If they plan to save the amount in 2 years, how much should each person save per month? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "100",
"style": "rule"
}
|
numina_math
|
{
"index": 9612,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends went on a hike and found a pile of fruits in the forest. One by one, the friends picked up the fruits and carried them away. In all, there were 4 friends. The first friend picked up 5 fruits. The second friend picked up 2 more fruits than the first friend. The third friend picked up twice as many fruits as the second friend. The fourth friend picked up 3 fewer fruits than the third friend. How many fruits were there in the original pile of fruits? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "37",
"style": "rule"
}
|
numina_math
|
{
"index": 9613,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "James has a part-time job as a customer service representative where he assists customers over the phone. He handles each call for an average of 45 minutes and works 5 days a week, handling 10 calls per day. If he gets paid $0.10 per minute of call time, how much does he earn in a week? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "225",
"style": "rule"
}
|
numina_math
|
{
"index": 9614,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Four numbers, \\( a, b, c, \\) and \\( d \\), are such that \\( a + b = 15 \\), \\( b + c = 20 \\), \\( c + d = 25 \\), and \\( d + a = 30 \\). Use logical deduction and elimination methods to find the values of \\( a, b, c, \\) and \\( d \\). What is the value of \\( a \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 9615,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emily went to a store and bought art supplies for $20 and 2 skirts that cost the same amount of money. She spent a total of $50. How much did Emily pay for each of the skirts? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "15",
"style": "rule"
}
|
numina_math
|
{
"index": 9616,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve for \\( x \\) in the equation: \\( (x+3)(x-2) = x^2 + 2x + 3 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-9",
"style": "rule"
}
|
numina_math
|
{
"index": 9617,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A baker prepared a batch of cookies. After selling 3/4 of the batch, she baked an additional 60 cookies, which brought the total number of cookies back to the original amount. How many cookies did the baker originally have in the batch? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "80",
"style": "rule"
}
|
numina_math
|
{
"index": 9618,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah bought 5 gift boxes for $15 each and sold all of them for $20 each. She then used $50 of the money earned to buy more supplies. How much profit did Sarah make in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 9619,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Evaluate: \\(\\left| \\frac{25^2 - 15^2}{5^2 - 3^2} \\right|\\) Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "25",
"style": "rule"
}
|
numina_math
|
{
"index": 9620,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In trapezoid $ABCD$, the bases $AB$ and $CD$ are parallel, and $AB$ is twice the length of $CD$. A circle is inscribed in the trapezoid, touching all four sides. If the height of the trapezoid is 6 units and the area of the trapezoid is 72 square units, find the lengths of $AB$ and $CD$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 9621,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the modular inverse of \\( 17 \\) modulo \\( 312 \\). Express your answer as an integer from \\( 0 \\) to \\( 311 \\), inclusive. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "257",
"style": "rule"
}
|
numina_math
|
{
"index": 9622,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory produces toy cars at a rate of 1.25 units per hour. How many toy cars does the factory produce in a week if it operates 8 hours a day for 5 days? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 9623,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "John decided to refurbish his living room. He initially budgeted $500 for the project. He spent $150 on paint, $200 on new furniture, and $75 on decorations. However, he realized he also needed to buy new curtains which cost an additional $80. How much over or under budget was John after making all his purchases? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 9624,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A painter needs to mix a special color of paint using red and blue paint in the ratio of 3:2. If he needs a total of 25 liters of this special color, how many liters of red paint and blue paint does he need? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "10",
"style": "rule"
}
|
numina_math
|
{
"index": 9625,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "The temperature in degrees Fahrenheit (F) can be converted to degrees Celsius (C) using the formula \\( F = \\frac{9}{5}C + 32 \\). If the temperature in Celsius is 25 degrees, what is the temperature in Fahrenheit? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "77",
"style": "rule"
}
|
numina_math
|
{
"index": 9626,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the rational expression \\(\\frac{4x^3 - 8x^2 + 12x}{2x^2 - 4x}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2(\\frac{x^2-2x+3}{x-2})",
"style": "rule"
}
|
numina_math
|
{
"index": 9627,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In how many ways can 8 people be seated in a row of chairs if two of the people, Alice and Bob, refuse to sit next to each other? Find the remainder when the number of such arrangements is divided by 1000. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "240",
"style": "rule"
}
|
numina_math
|
{
"index": 9628,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a survey of 40 students about their preferences for three different sports—basketball, soccer, and tennis—it was found that:\n- 18 students like basketball,\n- 22 students like soccer,\n- 15 students like tennis,\n- 9 students like both basketball and soccer,\n- 7 students like both basketball and tennis,\n- 6 students like both soccer and tennis,\n- 4 students like all three sports.\n\nHow many students do not like any of the three sports? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 9629,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A garden shop is selling bags of soil. Each bag contains 25 kilograms of soil. A landscaper needs to buy enough soil to fill a garden that requires 300 kilograms of soil. How many more bags of soil does the landscaper need if he already has 7 bags? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 9630,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Kevin is training for a marathon and needs to run a total of 15 miles. He has already run 8 miles. If he runs at a consistent pace and it takes him 10 minutes to run 1 mile, how many more minutes does he need to finish his training? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "70",
"style": "rule"
}
|
numina_math
|
{
"index": 9631,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "An electronics store has a laptop originally priced at $800. During a sale, the price of the laptop is reduced by 20%. If a customer has a discount coupon that gives an additional 10% off the sale price, what is the final price of the laptop? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "576",
"style": "rule"
}
|
numina_math
|
{
"index": 9632,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A charity raffle is being held, and there are 12 different prizes to be won. The organizers want to randomly draw 4 winners from the 50 people who bought tickets. In how many ways can the 4 winners be selected if one person cannot win more than one prize? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "230300",
"style": "rule"
}
|
numina_math
|
{
"index": 9633,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A charity organization raised a total of $10,000. They decided to allocate 30% of the funds to building a new community center and 25% of the remaining funds to educational programs. The rest of the money is to be used for healthcare initiatives. How much money will be allocated to healthcare initiatives? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5250",
"style": "rule"
}
|
numina_math
|
{
"index": 9634,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is saving money to buy a new laptop. She saves $10 every day and plans to save this amount consistently for 6 months. If she spends 1/4 of her savings on other expenses every month, how much money will she have saved by the end of 6 months? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1350",
"style": "rule"
}
|
numina_math
|
{
"index": 9635,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A factory's production rate decreases by 10% every month. If the factory produced 1000 units in January, how many units will it produce in May of the same year? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "656",
"style": "rule"
}
|
numina_math
|
{
"index": 9636,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A farmer sells fresh produce at a local market. He buys apples at a cost price of $1.50 per pound. He wishes to make a profit of 40% on each pound of apples sold. To attract more customers, he decides to offer a discount of 10% on the selling price. What is the final selling price per pound of apples after the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1.89",
"style": "rule"
}
|
numina_math
|
{
"index": 9637,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If \\(x = 5\\) and \\(y = 8\\), find the value of \\(2x + 3y - (x \\cdot y) + \\frac{y}{x}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-4.4",
"style": "rule"
}
|
numina_math
|
{
"index": 9638,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A tank is filled with water to 60% of its capacity. After 200 liters of water are added, the tank becomes full. What is the total capacity of the tank in liters? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "500",
"style": "rule"
}
|
numina_math
|
{
"index": 9639,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jenny is organizing a community event and needs to buy bottled water for the participants. Each bottle holds 500 milliliters of water. Jenny estimates that each participant will drink 1.5 liters of water during the event. If there are 200 participants, how many bottles of water should Jenny buy, and how much will it cost if each bottle costs $0.50? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "300",
"style": "rule"
}
|
numina_math
|
{
"index": 9640,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A model train set uses a scale ratio of 1:87 to represent real-life trains. If the actual length of a train is 522 feet, what is the length of the model train to the nearest whole number? Additionally, if the model train is 6 feet long, what is the actual length of the real train to the nearest whole number? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "522",
"style": "rule"
}
|
numina_math
|
{
"index": 9641,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a theme park, the entrance fee is $10 for adults and $6 for children. Each ride ticket costs $3 for everyone. If a family consisting of 2 adults and 3 children visit the park and each member goes on 4 rides, how much will the family spend in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "98",
"style": "rule"
}
|
numina_math
|
{
"index": 9642,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A gaming tournament has rounds where each round's score is rounded up to the nearest integer if it's a decimal. In the first round, a player scores 5.7 points. In the second round, the player scores 6.3 points. In the third round, the player scores 8.9 points. After the third round, the player loses 4 points due to a penalty. What is the player's total score after three rounds and the penalty? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18",
"style": "rule"
}
|
numina_math
|
{
"index": 9643,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given vectors \\(\\mathbf{u} = \\begin{pmatrix} 1 \\\\ 2 \\\\ 1 \\end{pmatrix}\\), \\(\\mathbf{v} = \\begin{pmatrix} 2 \\\\ -1 \\\\ 3 \\end{pmatrix}\\), and \\(\\mathbf{w} = \\begin{pmatrix} 0 \\\\ 1 \\\\ -1 \\end{pmatrix}\\), find the determinant of the matrix \\(\\mathbf{A}\\) whose columns are these vectors. Additionally, verify if \\(\\mathbf{u}\\) is a unit vector and calculate the dot product \\(\\mathbf{u} \\cdot \\mathbf{v}\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 9644,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the absolute value equation: $|4x - 5| = 9$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "-1",
"style": "rule"
}
|
numina_math
|
{
"index": 9645,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Anna and Brian start from two towns, Town A and Town B, which are 150 km apart. They start biking towards each other at the same time. Anna bikes at a speed of 25 km/h, and Brian bikes at a speed of 35 km/h. How long will it take for them to meet? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.5",
"style": "rule"
}
|
numina_math
|
{
"index": 9646,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A 2000-meter road is being paved. In the first 8 days, 30% of the road is completed. At this rate, how many more days will it take to complete the road? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "19",
"style": "rule"
}
|
numina_math
|
{
"index": 9647,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex can paint a fence in 8 hours. Jordan can paint the same fence in 12 hours. If Alex and Jordan work together, how long will it take them to paint the entire fence? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4.8",
"style": "rule"
}
|
numina_math
|
{
"index": 9648,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A gardener is designing a circular flower bed. The circumference of the flower bed is twice the sum of its radius and the radius of another circular flower bed that has a radius of 5 meters. What is the radius of the first flower bed? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.34",
"style": "rule"
}
|
numina_math
|
{
"index": 9649,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Julia wants to buy a set of books. The prices of the books are $12.50, $15.75, $9.25, and $18.50. However, she has a discount coupon that reduces the total price by $7.50. How much will Julia pay for the books after using the discount coupon? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "48.50",
"style": "rule"
}
|
numina_math
|
{
"index": 9650,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Find the units digit of the expansion of \\((3x + 4)^5\\) when \\(x = 2\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
numina_math
|
{
"index": 9651,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a constant speed of 60 miles per hour. How long will it take for the car to travel 150 miles if it stops for a total of 30 minutes during the journey? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 9652,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Pam has 10 bags of apples. Each of her bags has as many apples as 3 of Gerald's bags. If Gerald's bags have 40 apples each, how many apples does Pam have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1200",
"style": "rule"
}
|
numina_math
|
{
"index": 9653,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Xiaoming needs to walk up from the 1st floor to the 5th floor and then back down to the 2nd floor. If there are 18 steps per floor, how many steps does Xiaoming take in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "126",
"style": "rule"
}
|
numina_math
|
{
"index": 9654,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha decides to buy a new smartphone that costs $800. She also wants to buy a protective case for $50 and a screen protector for $20. Additionally, she has to pay a sales tax of 7% on the total purchase. How much will Samantha spend in total on her new smartphone and accessories? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "930.90",
"style": "rule"
}
|
numina_math
|
{
"index": 9655,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a math competition, each participant earns points for solving problems correctly. In the first round, a participant earned 902 points, in the second round 804 points, in the third round 700 points, in the fourth round 609 points, in the fifth round 508 points, in the sixth round 403 points, in the seventh round 307 points, in the eighth round 201 points, and in the ninth round 106 points. What is the total number of points earned by the participant? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "4540",
"style": "rule"
}
|
numina_math
|
{
"index": 9656,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom, the teacher has 48 candies and wants to distribute them equally among a certain number of students such that each student receives a whole number of candies. If the number of students is a factor of 48 and is also a multiple of 3, how many ways can the teacher distribute the candies? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
numina_math
|
{
"index": 9657,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is planning a road trip and wants to calculate how long the trip will take. She will be driving a total distance of 480 miles. She plans to drive at an average speed of 60 miles per hour, but she also needs to account for three 30-minute breaks along the way. How long, in hours, will the entire trip take? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9.5",
"style": "rule"
}
|
numina_math
|
{
"index": 9658,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Suppose that $a$ and $b$ are positive integers for which $a$ has $3$ factors and $b$ has $a$ factors. If $b$ is divisible by $a$, then what is the least possible value of $b$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "8",
"style": "rule"
}
|
numina_math
|
{
"index": 9659,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A square sheet of metal with a side length of 30 centimeters is used to make a cone by cutting a sector from the square and then rolling the remaining part into a cone. The radius of the cone's base is equal to the side length of the square. Find the height of the cone in simplest radical form. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 9660,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a constant speed of 60 miles per hour. If the car's speed increases by 25% after every hour of travel, how many miles will the car have traveled in 3 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "228.75",
"style": "rule"
}
|
numina_math
|
{
"index": 9661,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If 4 machines can produce 120 widgets in 3 hours, how many widgets will 7 machines produce in 5 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "350",
"style": "rule"
}
|
numina_math
|
{
"index": 9662,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A rectangle has a length that is three times its width. The line passing through the origin and the point \\((3, 6)\\) intersects the length of the rectangle at its x-intercept and the width of the rectangle at its y-intercept. Calculate the area of the rectangle. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "108",
"style": "rule"
}
|
numina_math
|
{
"index": 9663,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Jennifer has been tracking her reading habits. She finishes reading 3 books each week. She decided to continue this for 8 weeks. Before starting this routine, she already had 15 books read. If she wants to have a total of 50 books read, how many more books does she need to read to reach her goal? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "11",
"style": "rule"
}
|
numina_math
|
{
"index": 9664,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Given that \\( x \\) and \\( y \\) are integers such that \\( \\gcd(3x + 4y, 60) = 1 \\), what are the possible integer values of \\( x \\) and \\( y \\) if \\( x \\) is constrained to be between 0 and 10 inclusive? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "7",
"style": "rule"
}
|
numina_math
|
{
"index": 9665,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a triangle, the measures of the three angles are expressed as $x$, $2x$, and $\\sqrt{(x+30)^2 - 900}$. Find the value of $x$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "39.275",
"style": "rule"
}
|
numina_math
|
{
"index": 9666,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A recipe for fruit punch requires 3 parts of orange juice, 2 parts of apple juice, and 1 part of grape juice. If you have 12 liters of orange juice, how many liters of apple juice and grape juice are needed to maintain the same ratio? Also, what is the total volume of the fruit punch? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "24",
"style": "rule"
}
|
numina_math
|
{
"index": 9667,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Alex has a balance of -$45.75 in his bank account. He decides to deposit $120 into his account. After making the deposit, he wants to withdraw as many $5 bills as possible. How many $5 bills can Alex withdraw? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 9668,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many different four-letter arrangements can be formed using the six letters \\(A, B, C, D, E,\\) and \\(F\\), if the first letter must be \\(C\\), one of the other letters must be \\(B\\), and no letter can be used more than once in the arrangement? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 9669,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A car travels at a constant speed of 60 miles per hour. If the car travels for 3/5 of an hour, how far does it travel in that time? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "36",
"style": "rule"
}
|
numina_math
|
{
"index": 9670,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sophia has a recipe that requires 3/4 cup of sugar. She only has a 1/3 cup measuring cup. How many times does she need to use the 1/3 cup measuring cup to get the exact amount of sugar required for the recipe? Convert your answer into a decimal. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.25",
"style": "rule"
}
|
numina_math
|
{
"index": 9671,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is a factory worker who assembles toy cars. She can assemble 5 toy cars per hour. If she works 6 hours a day and needs to meet a target of assembling 180 toy cars in a week (5 working days), what percentage of her daily target does she need to meet each day? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "83.33",
"style": "rule"
}
|
numina_math
|
{
"index": 9672,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many whole numbers between 1 and 200 are multiples of 15? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "13",
"style": "rule"
}
|
numina_math
|
{
"index": 9673,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A population of bacteria doubles every hour. Initially, there are 100 bacteria. If we assume that the growth can be modeled continuously and described by an exponential function, what will be the population of bacteria after 12 hours? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "409600",
"style": "rule"
}
|
numina_math
|
{
"index": 9674,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah has a collection of 60 marbles. She decides to give 2/5 of her marbles to her friend. After giving away the marbles, she decides to further divide the remaining marbles equally among 4 other friends. How many marbles does each of the 4 friends get? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9",
"style": "rule"
}
|
numina_math
|
{
"index": 9675,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A store is having a sale where all items are discounted by 20%. If a customer purchases 4 items priced at $25, $40, $60, and $75 respectively, what is the total amount the customer will save due to the discount? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "40",
"style": "rule"
}
|
numina_math
|
{
"index": 9676,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A map scale indicates that 2 inches on the map corresponds to 5 miles in reality. If a river is represented as 7.5 inches long on the map, what is the actual length of the river in miles? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "18.75",
"style": "rule"
}
|
numina_math
|
{
"index": 9677,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Consider the number 12. In how many ways can you partition 12 into distinct positive integers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "14",
"style": "rule"
}
|
numina_math
|
{
"index": 9678,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "A group of friends decides to buy a video game console together. If each person contributes $50$, they fall short by $80$. If each person contributes $60$, they end up with $40$ extra. How much does the video game console cost? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "680",
"style": "rule"
}
|
numina_math
|
{
"index": 9679,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "On a map, a scale of 1:1000 is used. If the distance between two cities is 7.5 centimeters on the map, what is the actual distance between the two cities in kilometers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "0.075",
"style": "rule"
}
|
numina_math
|
{
"index": 9680,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Solve the equation for \\(x\\): \\( \\log_2 (8x) = \\log_4 (64) \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
numina_math
|
{
"index": 9681,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Lisa is planning a birthday party and needs to buy supplies. She buys 5 packs of balloons at $3 each, 3 packs of streamers at $4 each, and 10 party hats at $2 each. Calculate the total amount Lisa spends on the party supplies. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "47",
"style": "rule"
}
|
numina_math
|
{
"index": 9682,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a 3x3 magic square, the sum of the numbers in each row, column, and diagonal is equal to a constant \\( S \\). Five of the numbers in the magic square are represented by the variables \\( a \\), \\( b \\), \\( c \\), \\( d \\), and \\( e \\), and they are placed as shown below. Determine the value of \\( S \\).\n\n\\[\n\\begin{array}{|c|c|c|}\n\\hline\na & 20 & b \\\\\n\\hline\n15 & c & d \\\\\n\\hline\ne & 25 & 30 \\\\\n\\hline\n\\end{array}\n\\] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "120",
"style": "rule"
}
|
numina_math
|
{
"index": 9683,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many even numbers between 1 and 1000 are divisible by both 4 and 5? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 9684,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a school, the number of boys is three times the number of girls. If the total number of students is 120, how many boys and how many girls are there in the school? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 9685,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Emma is organizing a charity event and needs to order t-shirts. The cost for each t-shirt is $15. The supplier offers a 20% discount on the total cost if Emma orders 50 or more t-shirts. Emma calculates that she needs exactly 50 t-shirts. How much will she save by ordering 50 t-shirts at once with the discount compared to ordering them individually? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "150",
"style": "rule"
}
|
numina_math
|
{
"index": 9686,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Sarah is organizing a juice-tasting event. She bought three different bottles of juice. The bottles contain the following volumes of juice: 1.5 liters, 600 milliliters, and 850 milliliters. How many liters of juice did Sarah buy in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "2.95",
"style": "rule"
}
|
numina_math
|
{
"index": 9687,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "If the least common multiple (LCM) of two numbers is 72 and their greatest common divisor (GCD) is 6, and one of the numbers is $\\frac{1}{3}$ of the other, find the two numbers. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "12",
"style": "rule"
}
|
numina_math
|
{
"index": 9688,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Simplify the expression $\\left(2a + 3b\\right)^2 - 4ab$ using the given values: $a = 2, b = 3$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "109",
"style": "rule"
}
|
numina_math
|
{
"index": 9689,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha wants to buy a new laptop that costs $950 and a printer that costs $150. In her state, the sales tax rate is 8%. How much will Samantha pay in total, including the sales tax? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "1188",
"style": "rule"
}
|
numina_math
|
{
"index": 9690,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Compute: \\( 97 \\times 103 \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "9991",
"style": "rule"
}
|
numina_math
|
{
"index": 9691,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mia owns a farm with sheep and ducks. Together, there are 50 animals. If the total number of legs is 140, how many sheep and ducks does Mia have on her farm? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "30",
"style": "rule"
}
|
numina_math
|
{
"index": 9692,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a classroom of 50 students, each student is asked to pick a number between 1 and 100 inclusive. If exactly 12 students chose prime numbers and the remaining students chose non-prime numbers, how many students picked a number that is not prime? Also, how many students chose a number greater than 50 and less than or equal to 75 inclusive that is not prime? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "19",
"style": "rule"
}
|
numina_math
|
{
"index": 9693,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Samantha is planning a trip to Europe and needs to convert her money into euros. She has $500. The current exchange rate is 1 USD to 0.85 EUR. She also needs to pay a flat conversion fee of $10. After converting her money, how many euros will Samantha have? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "416.5",
"style": "rule"
}
|
numina_math
|
{
"index": 9694,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Mary had 89 stickers. She used 3 large stickers on the front page of her journal and 7 stickers each to 6 other pages of her journal. How many stickers does Mary have remaining? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "44",
"style": "rule"
}
|
numina_math
|
{
"index": 9695,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "In a puzzle game, there are four types of tokens: stars, moons, suns, and planets. There are 5 stars, twice as many moons as stars, 3 times as many suns as moons, and 4 times as many planets as suns. How many tokens are there in total? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "165",
"style": "rule"
}
|
numina_math
|
{
"index": 9696,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "How many positive perfect squares less than 10000 have a ones digit of 1, 4, 5, 6, or 9? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "50",
"style": "rule"
}
|
numina_math
|
{
"index": 9697,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Let $S$ be the set of integers $n > 1$ for which $\\frac{1}{n}$ has a repeating decimal expansion of period 6. Given that 7 is prime, how many positive integers are in $S$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
numina_math
|
{
"index": 9698,
"name": "numina_math",
"split": "train"
}
|
[
{
"content": "Determine the probability that a randomly chosen even number from 1 to 1000 is a perfect cube. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
{
"ground_truth": "\\frac{1}{100}",
"style": "rule"
}
|
numina_math
|
{
"index": 9699,
"name": "numina_math",
"split": "train"
}
|
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