prompt listlengths 1 1 | reward_model dict | data_source stringclasses 1
value | extra_info dict |
|---|---|---|---|
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A rectangular garden has a length that is twice its width. The area of the garden is 200 square meters. What are the dimensions of the garden, and what is the ratio of the length to the perimeter of the garden?\... | {
"ground_truth": "10\\sqrt{5}",
"style": "rule"
} | numina_math | {
"index": 100,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Maria is training for a marathon and tracks her running time each day. She plans to run a total of 10 hours this week. If Maria decides to split her running time equally over 7 days and runs at a constant speed,... | {
"ground_truth": "1.5",
"style": "rule"
} | numina_math | {
"index": 101,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Simplify the expression \\(3(x + 4)(x - 2) - 2(x^2 - 4)\\).\n**Solution**: 1. **Distribute the terms inside the parentheses:**\n \\[\n 3(x + 4)(x - 2) - 2(x^2 - 4)\n \\]\n\n2. **First, expand the binomial ... | {
"ground_truth": "\\pm2\\sqrt{\\frac{3+\\sqrt{5}}{2}}\\pm2\\sqrt{\\frac{3-\\sqrt{5}}{2}}",
"style": "rule"
} | numina_math | {
"index": 102,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Sarah runs a small business selling handmade candles. She sells each candle for $15. Last week, she sold 30 candles. Her total cost to make the candles was $270. What was Sarah's profit for the week?\n**Solution... | {
"ground_truth": "112.5",
"style": "rule"
} | numina_math | {
"index": 103,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Evaluate the expression: \\( \\left(\\frac{256}{16}\\right)^{\\frac{3}{4}} \\).\n**Solution**: 1. **Simplify the fraction inside the parentheses:**\n \\[\n \\frac{256}{16}\n \\]\n We know that \\( 256 = ... | {
"ground_truth": "23",
"style": "rule"
} | numina_math | {
"index": 104,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A group of 8 friends is planning to sit around a circular table for a dinner party. If two specific friends insist on sitting next to each other, how many distinct seating arrangements are possible?\n**Solution*... | {
"ground_truth": "2520",
"style": "rule"
} | numina_math | {
"index": 105,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A baker has \\( \\frac{3}{4} \\) of a cake left. He wants to divide this remaining cake equally among \\( 2 \\frac{1}{2} \\) customers. How much cake will each customer get?\n**Solution**: To solve this problem,... | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | numina_math | {
"index": 106,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A company needs to purchase materials for a project. They require 500 meters of a special cable. The cost of the cable is $0.75 per foot. Calculate the total cost of the cable in dollars. (Note: 1 meter = 3.2808... | {
"ground_truth": "20250",
"style": "rule"
} | numina_math | {
"index": 107,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A company hires new employees in two phases. In the first phase, they hire employees in an arithmetic sequence, starting with 4 employees and increasing by 3 employees each subsequent month for 5 months. In the ... | {
"ground_truth": "225",
"style": "rule"
} | numina_math | {
"index": 108,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Maria is making a batch of cookies. The recipe calls for 2 cups of sugar for every 3 cups of flour. If she wants to make a larger batch using 12 cups of flour, how many cups of sugar will she need?\n**Solution**... | {
"ground_truth": "31",
"style": "rule"
} | numina_math | {
"index": 109,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Consider the lines given by the equations \\( y = 2x + 1 \\) and \\( y = -\\frac{1}{2}x + 3 \\). Determine the coordinates of their intersection point.\n**Solution**: To find the intersection point of the lines ... | {
"ground_truth": "(\\frac{33}{14}\\frac{1}{25})",
"style": "rule"
} | numina_math | {
"index": 110,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: In a geometric sequence, the first term is \\( 16 \\) and the common ratio is \\( \\frac{1}{4} \\). Find the greatest common divisor of the numerator and the denominator of the \\( 10^{th} \\) term when expresse... | {
"ground_truth": "4",
"style": "rule"
} | numina_math | {
"index": 111,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Emma is organizing a charity event and needs to prepare gift bags for the attendees. She plans to give each attendee a gift bag containing a set of items. For the first 50 attendees, she includes 5 items in each... | {
"ground_truth": "160",
"style": "rule"
} | numina_math | {
"index": 112,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A square garden has a total area of 144 square meters. If the garden is divided into smaller square plots such that the side length of each smaller square plot is 3 meters, how many smaller square plots can be c... | {
"ground_truth": "4",
"style": "rule"
} | numina_math | {
"index": 113,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A manufacturer produces two types of widgets: A and B. Widget A costs $15 each to produce, and Widget B costs $20 each. The manufacturer can either produce 40 Widget As or 25 Widget Bs in a day. If the manufactu... | {
"ground_truth": "600",
"style": "rule"
} | numina_math | {
"index": 114,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A bakery sells cookies in boxes of 24. They estimate that they will need approximately 960 cookies for an upcoming event. If they have already prepared 520 cookies, how many more boxes of cookies will they need ... | {
"ground_truth": "5",
"style": "rule"
} | numina_math | {
"index": 115,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Alex is painting a large rectangular wall. He can paint 150 square feet per hour. The wall is 12 feet high and 30 feet wide. He spends 2 hours painting the wall each day. How many days will it take Alex to finis... | {
"ground_truth": "8",
"style": "rule"
} | numina_math | {
"index": 116,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Simplify the expression \\(\\frac{2x^2 - 8}{x + 2} - \\frac{6x^2 - 12}{x - 2}\\).\n**Solution**: To simplify the given expression, we need to perform polynomial simplification and combine like terms. We will als... | {
"ground_truth": "\\frac{3x^2+12x-32}{(x+2)(x+4)(x-2)}",
"style": "rule"
} | numina_math | {
"index": 117,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A rectangular lawn measures 50 feet by 30 feet. In the center of the lawn, there is a square flower bed with a side length of 10 feet. If you want to install a fence around the remaining grass area and the cost ... | {
"ground_truth": "150",
"style": "rule"
} | numina_math | {
"index": 118,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Emma has a subscription service for online streaming that costs $12 per month. She also has a gym membership that costs $30 per month. If Emma decides to keep both subscriptions for a year, how much will she spe... | {
"ground_truth": "14",
"style": "rule"
} | numina_math | {
"index": 119,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Sarah has a monthly budget of $2,500. This month, she spent $1,200 on rent, $300 on groceries, $150 on utilities, and $200 on entertainment. How much money does Sarah have left in her budget for the month?\n**So... | {
"ground_truth": "13",
"style": "rule"
} | numina_math | {
"index": 120,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Emily is planning a road trip and needs to rent a car. The car rental company charges $50 per day plus $0.25 for each mile driven. If Emily rents the car for 5 days and drives 300 miles, how much will she have t... | {
"ground_truth": "0.40",
"style": "rule"
} | numina_math | {
"index": 121,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Given the function \\( f(x) = \\frac{3x - 5}{2} \\), find the inverse function \\( f^{-1}(x) \\). Verify your result by showing that \\( f(f^{-1}(x)) = x \\).\n**Solution**: To find the inverse function \\( f^{-... | {
"ground_truth": "g(f^{-1}(11))=1",
"style": "rule"
} | numina_math | {
"index": 122,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Compare the two values $\\frac{2}{3}$ and $0.\\overline{666}$ and determine which is greater. Express your answer as a common fraction and a repeating decimal.\n**Solution**: First, let's convert the repeating d... | {
"ground_truth": ">",
"style": "rule"
} | numina_math | {
"index": 123,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Simplify the expression \\( \\frac{4^3 \\times 2^2 + 6^2}{2^3 + 3^2} \\).\n**Solution**: 1. **Evaluate the exponents and perform the multiplications in the numerator:**\n \\[\n 4^3 = 64\n \\]\n \\[\n 2... | {
"ground_truth": "\\frac{n-2}{n+2}",
"style": "rule"
} | numina_math | {
"index": 124,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Find the center and radius of the circle with the equation \\(x^2 + y^2 - 6x + 8y - 11 = 0\\).\n**Solution**: To find the center and radius of the circle, we need to rewrite the given equation in the standard fo... | {
"ground_truth": "18\\pi",
"style": "rule"
} | numina_math | {
"index": 125,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A company manufactures and sells widgets. The cost to produce each widget is $20, and the company sells each widget for $50. The company wants to maximize its profit by selling a certain number of widgets. If th... | {
"ground_truth": "50",
"style": "rule"
} | numina_math | {
"index": 126,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Given two vectors \\(\\mathbf{a} = \\begin{pmatrix} 1 \\\\ 2 \\\\ 3 \\end{pmatrix}\\) and \\(\\mathbf{b} = \\begin{pmatrix} 4 \\\\ 5 \\\\ 6 \\end{pmatrix}\\), find the dot product \\(\\mathbf{c} \\cdot \\mathbf{... | {
"ground_truth": "2\\sqrt{34}",
"style": "rule"
} | numina_math | {
"index": 127,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A local bookstore is having a clearance sale. They have a total of 150 books, which they have divided into two categories: novels and textbooks. The novels are priced at $8 each, and the textbooks are priced at ... | {
"ground_truth": "-20",
"style": "rule"
} | numina_math | {
"index": 128,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Consider the numbers 4, 6, 8, 9, and 10. Multiply these numbers together. What is the sum of the composite numbers in the product?\n**Solution**: To solve this problem, we first need to multiply the given number... | {
"ground_truth": "\\text{novalidnegativeintegersolution}",
"style": "rule"
} | numina_math | {
"index": 129,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Simplify the expression: \\(\\frac{2 + \\sqrt{5}}{3 - \\sqrt{2}}\\).\n**Solution**: To simplify the expression \\(\\frac{2 + \\sqrt{5}}{3 - \\sqrt{2}}\\), we will rationalize the denominator by multiplying the n... | {
"ground_truth": "14-4\\sqrt{6}",
"style": "rule"
} | numina_math | {
"index": 130,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A store is having a sale where all items are 25% off. If a customer buys a jacket originally priced at $80, a pair of shoes originally priced at $60, and a hat originally priced at $20, how much money does the c... | {
"ground_truth": "120",
"style": "rule"
} | numina_math | {
"index": 131,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Solve for \\(x\\) in the equation \\(\\sqrt{3x + 7} - \\sqrt{x - 1} = 2\\).\n**Solution**: To solve the equation \\(\\sqrt{3x + 7} - \\sqrt{x - 1} = 2\\), we will first isolate one of the square roots and then s... | {
"ground_truth": "17+2\\sqrt{13}",
"style": "rule"
} | numina_math | {
"index": 132,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Jessica wants to buy 3 notebooks and 2 pens. Each notebook costs $1.75 and each pen costs $0.95. How much money will Jessica spend in total?\n**Solution**: Step 1: Calculate the total cost of the notebooks.\n- N... | {
"ground_truth": "4",
"style": "rule"
} | numina_math | {
"index": 133,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Sarah has 60 marbles. She decides to give $\\frac{1}{3}$ of her marbles to her friend Lisa and $\\frac{1}{4}$ of the remaining marbles to her cousin Tom. How many marbles does Sarah have left after giving some t... | {
"ground_truth": "34",
"style": "rule"
} | numina_math | {
"index": 134,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A cyclist travels to a town 60 miles away at an average speed of 15 miles per hour. After a short break, the cyclist returns to the starting point at an average speed of 10 miles per hour. How much total time di... | {
"ground_truth": "10",
"style": "rule"
} | numina_math | {
"index": 135,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Given the polynomial \\( P(x) = x^4 - 4x^3 + 6x^2 - 4x + 1 \\), find the roots of \\( P(x) \\) and verify that they satisfy the polynomial equation.\n**Solution**: To find the roots of the polynomial \\( P(x) = ... | {
"ground_truth": "1.75",
"style": "rule"
} | numina_math | {
"index": 136,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A regular pentagon and a regular hexagon are inscribed in the same circle. Calculate the probability that a randomly chosen interior angle from one of these polygons is greater than $120^\\circ$.\n**Solution**: ... | {
"ground_truth": "\\frac{1}{8}",
"style": "rule"
} | numina_math | {
"index": 137,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: In a classroom, the ratio of boys to girls is 3:5. If there are 32 students in total, how many boys and how many girls are there in the classroom?\n**Solution**: Let's denote the number of boys as \\( B \\) and ... | {
"ground_truth": "80",
"style": "rule"
} | numina_math | {
"index": 138,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Convert the decimal number 3456 to base 6. What are the steps and the final result of this conversion?\n**Solution**: To convert the decimal number 3456 to base 6, follow these steps:\n\n1. **Divide the number b... | {
"ground_truth": "81",
"style": "rule"
} | numina_math | {
"index": 139,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Let \\( z = 3 + 4i \\) and \\( w = 1 - 2i \\). Compute the complex number \\( z \\cdot w \\) and then find the magnitude of the resulting complex number.\n**Solution**: First, we need to multiply the complex num... | {
"ground_truth": "1",
"style": "rule"
} | numina_math | {
"index": 140,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Two workers, Alice and Bob, are painting a house. Alice can paint the house alone in 6 hours, while Bob can paint it alone in 4 hours. If they start painting together but Alice stops after 2 hours, how long will... | {
"ground_truth": "5.53",
"style": "rule"
} | numina_math | {
"index": 141,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: What is the remainder when \\( 12345 \\) is divided by \\( 7 \\)?\n**Solution**: To find the remainder when \\( 12345 \\) is divided by \\( 7 \\), we can use modular arithmetic. We can break down the problem ste... | {
"ground_truth": "2",
"style": "rule"
} | numina_math | {
"index": 142,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A factory produces two types of widgets: A and B. The probability that a randomly chosen widget is of type A is 0.7, and the probability that a randomly chosen widget is of type B is 0.3. The quality control dep... | {
"ground_truth": "0.5714",
"style": "rule"
} | numina_math | {
"index": 143,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Samantha spends 30% of her monthly income on rent, 20% on groceries, 15% on transportation, and saves the remaining amount. If her monthly income is $4000, how much does she save each month?\n**Solution**: 1. Ca... | {
"ground_truth": "1170",
"style": "rule"
} | numina_math | {
"index": 144,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A local bakery sells two types of cakes: vanilla and chocolate. Each vanilla cake sells for $15, while each chocolate cake sells for $20. The bakery sold twice as many vanilla cakes as chocolate cakes in a week.... | {
"ground_truth": "30",
"style": "rule"
} | numina_math | {
"index": 145,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Let \n\\[\\mathbf{M} = \\begin{pmatrix} 1 & 2 & 2 \\\\ 2 & 1 & -2 \\\\ a & b & c \\end{pmatrix}.\\]\nIf $\\mathbf{M} \\mathbf{M}^T = 10 \\mathbf{I}$, find the values of $a$, $b$, and $c$.\n\nNote: For a matrix $... | {
"ground_truth": "(abcd)=(1001)",
"style": "rule"
} | numina_math | {
"index": 146,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A car rental service charges a base fee of $50 per day plus $0.25 per mile driven. If a customer rents a car for 3 days and drives a total of 200 miles, how much will the customer have to pay in total?\n**Soluti... | {
"ground_truth": "116",
"style": "rule"
} | numina_math | {
"index": 147,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: In a market, the price of apples is directly proportional to the weight. If 4 kilograms of apples cost $12, how much will 7 kilograms of apples cost? Additionally, if the price of apples increases by 1/3, what w... | {
"ground_truth": "7.50",
"style": "rule"
} | numina_math | {
"index": 148,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Compute the value of the expression: \\((2^3 \\cdot 5) + (4 \\cdot 3^2) - (6 \\cdot 2^2)\\).\n**Solution**: Let's break down the expression step by step, applying arithmetic operations, properties of exponents, ... | {
"ground_truth": "506208",
"style": "rule"
} | numina_math | {
"index": 149,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Express $\\frac{5}{12}$ as a decimal, and then identify the repeating decimal sequence. Round the repeating decimal to the nearest thousandth.\n**Solution**: To express $\\frac{5}{12}$ as a decimal, we perform t... | {
"ground_truth": "297",
"style": "rule"
} | numina_math | {
"index": 150,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A gardener is planning to plant a row of flowers. She starts with 10 flowers already planted. Each day, she plants 3 more flowers. After 5 days, she decides to remove 2 flowers. How many flowers are left in the ... | {
"ground_truth": "192",
"style": "rule"
} | numina_math | {
"index": 151,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A recipe calls for $\\frac{3}{4}$ cup of sugar. If you want to make half the recipe, how much sugar do you need? Express your answer as a fraction.\n**Solution**: To find how much sugar you need for half the rec... | {
"ground_truth": "\\frac{17}{24}",
"style": "rule"
} | numina_math | {
"index": 152,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A library has a total of 625 books. The librarian decides to distribute these books evenly across 5 sections. After distributing the books, she realizes she needs to move half of the books from the first section... | {
"ground_truth": "6",
"style": "rule"
} | numina_math | {
"index": 153,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A quadratic polynomial \\( P(x) \\) has roots at \\( x = 2 \\) and \\( x = -3 \\). The sum of the coefficients of the polynomial is required to be 5. Write the polynomial \\( P(x) \\) and find the value of the c... | {
"ground_truth": "x^2-4x+3",
"style": "rule"
} | numina_math | {
"index": 154,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Given the system of equations \\( y = x^2 + 4x + 3 \\) and \\( y = -2x + 1 \\), find the coordinates of the points where the two parabolas intersect.\n**Solution**: To find the points where the two parabolas int... | {
"ground_truth": "0",
"style": "rule"
} | numina_math | {
"index": 155,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Simplify the expression \\(3(x + 4)(x - 2) - 2(x^2 - 4)\\).\n**Solution**: 1. **Distribute the terms inside the parentheses:**\n \\[\n 3(x + 4)(x - 2) - 2(x^2 - 4)\n \\]\n\n2. **First, expand the binomial ... | {
"ground_truth": "288",
"style": "rule"
} | numina_math | {
"index": 156,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Triangle \\(ABC\\) has vertices at \\(A(2, 3)\\), \\(B(-1, 1)\\), and \\(C(4, -2)\\). Reflect triangle \\(ABC\\) over the line \\(x = 1\\) to form triangle \\(A'B'C'\\). Calculate the area of triangle \\(A'B'C'\... | {
"ground_truth": "p'(-34)q'(-68)r'(-92)",
"style": "rule"
} | numina_math | {
"index": 157,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Jenna is planning a road trip. She drives the first leg of her journey for 1.5 hours at a speed of 60 mph, then takes a break for lunch for 30 minutes. After lunch, she drives for another 2 hours at a speed of 5... | {
"ground_truth": "4.35",
"style": "rule"
} | numina_math | {
"index": 158,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Consider the transformation of the function \\( f(x) \\) defined by \\( y = f(x) \\) to \\( y = f(x - 3) + 2 \\). Suppose the point \\((5, 7)\\) lies on the graph of \\( y = f(x) \\). If the function \\( g(x) = ... | {
"ground_truth": "(-30)(00)(-1.53\\sqrt{3})",
"style": "rule"
} | numina_math | {
"index": 159,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Two trains, Train A and Train B, are traveling towards each other from two different cities that are 300 miles apart. Train A travels at a speed of 40 miles per hour, while Train B travels at a speed of 60 miles... | {
"ground_truth": "12:26",
"style": "rule"
} | numina_math | {
"index": 160,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Given that \\(f(x) = 2x^2 - x + 4\\) and \\(g(x) = 3x - 5\\), find the value of \\(f(g(2)) + g(f(2))\\).\n**Solution**: 1. **Evaluate \\(g(2)\\):**\n \\[\n g(2) = 3(2) - 5 = 6 - 5 = 1\n \\]\n\n2. **Substit... | {
"ground_truth": "6",
"style": "rule"
} | numina_math | {
"index": 161,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Express $0.\\overline{45} + 0.\\overline{8}$ as a common fraction.\n**Solution**: To solve this problem, we need to convert the repeating decimals to fractions and then add them together. Here's the step-by-step... | {
"ground_truth": "\\frac{9}{11}",
"style": "rule"
} | numina_math | {
"index": 162,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Consider the telescoping series \\( \\sum_{n=1}^{10} \\left( \\frac{1}{n(n+1)} \\right) \\). Find the sum of this series.\n**Solution**: First, let's simplify the general term of the series:\n\\[ \\frac{1}{n(n+1... | {
"ground_truth": "\\frac{10}{11}",
"style": "rule"
} | numina_math | {
"index": 163,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A triangle \\(ABC\\) has vertices \\(A(0, 6)\\), \\(B(4, 2)\\), and \\(C(6, 8)\\). A line segment from \\(A\\) intersects line segment \\(\\overline{BC}\\) at \\(D\\) such that the length of \\(\\overline{AD}\\)... | {
"ground_truth": "\\sqrt{61}",
"style": "rule"
} | numina_math | {
"index": 164,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Sarah owns a small bakery. She makes and sells cookies. Each cookie sells for $1.50. The ingredients for each cookie cost $0.75, and each batch of cookies requires $5 for additional overhead costs (electricity, ... | {
"ground_truth": "105",
"style": "rule"
} | numina_math | {
"index": 165,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Alex bought a book for $15 and a pen for $3. He gave the cashier a $20 bill. How much change did Alex receive?\n**Solution**: 1. First, we need to determine the total cost of the items Alex bought.\n \\[\n \... | {
"ground_truth": "5.50",
"style": "rule"
} | numina_math | {
"index": 166,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Sarah is training for a marathon and runs at a constant speed of 6 miles per hour. On Monday, she ran for 2 hours and on Tuesday, she ran for 1.5 hours. On Wednesday, she plans to run enough miles to make her to... | {
"ground_truth": "9",
"style": "rule"
} | numina_math | {
"index": 167,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A farmer has a plot of land that needs to be divided into smaller sections for planting. Each section is 20 square meters. If the farmer has already divided 5 sections and still has 100 square meters left to div... | {
"ground_truth": "6",
"style": "rule"
} | numina_math | {
"index": 168,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A cylindrical water tank has a radius of 1.5 meters and a height of 3 meters. If the tank is currently filled to 60% of its capacity, how many more liters of water are needed to fill the tank completely? (Note: ... | {
"ground_truth": "2",
"style": "rule"
} | numina_math | {
"index": 169,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Evelyn is planning her study schedule for the week. She has 5 subjects to study, and she wants to allocate a total of 20 hours for studying. She decides to spend twice as much time on Mathematics as on History, ... | {
"ground_truth": "1",
"style": "rule"
} | numina_math | {
"index": 170,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Let $h(x) = 2x + 5$ and $k(x) = x^2 - 4x + 7$. Find $h(k(3))$.\n**Solution**: 1. First, we need to evaluate $k(3)$.\n \\[\n k(x) = x^2 - 4x + 7\n \\]\n Substituting $x = 3$:\n \\[\n k(3) = 3^2 - 4(3)... | {
"ground_truth": "6",
"style": "rule"
} | numina_math | {
"index": 171,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: What is the smallest positive integer that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and a remainder of 4 when divided by 5?\n**Solution**: To solve this problem, we need to ... | {
"ground_truth": "53",
"style": "rule"
} | numina_math | {
"index": 172,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Jane and Tom are comparing the money they have saved. Jane has saved $550, while Tom has saved $420. They both decide to save an additional $150 each. After adding the additional amount, how much more money does... | {
"ground_truth": "90",
"style": "rule"
} | numina_math | {
"index": 173,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Solve the equation: \\(3(x - 4) + 5 = 2x + 7\\).\n**Solution**: 1. Distribute the 3 on the left side:\n \\[\n 3(x - 4) + 5 = 2x + 7 \\implies 3x - 12 + 5 = 2x + 7\n \\]\n \n2. Simplify the left side:\n ... | {
"ground_truth": "6",
"style": "rule"
} | numina_math | {
"index": 174,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Solve the equation: \\(3(x - 4) + 5 = 2x + 7\\).\n**Solution**: 1. Distribute the 3 on the left side:\n \\[\n 3(x - 4) + 5 = 2x + 7 \\implies 3x - 12 + 5 = 2x + 7\n \\]\n \n2. Simplify the left side:\n ... | {
"ground_truth": "13",
"style": "rule"
} | numina_math | {
"index": 175,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Let \\(\\mathbf{A}\\) be a \\(2 \\times 2\\) matrix such that \\(\\mathbf{A} \\mathbf{v} = \\lambda \\mathbf{v}\\) for some eigenvalue \\(\\lambda\\) and for all two-dimensional vectors \\(\\mathbf{v}\\). If \\(... | {
"ground_truth": "2\\pi",
"style": "rule"
} | numina_math | {
"index": 176,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: The length of the top base of a trapezoid is 10 cm less than twice the length of the bottom base. The height of the trapezoid is 8 cm. If the area of the trapezoid is 96 square cm, find the lengths of the top ba... | {
"ground_truth": "70",
"style": "rule"
} | numina_math | {
"index": 177,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A model train set uses a scale of 1:50. If the actual length of the train is 1000 feet, and each year the length of the model train increases by 10% of the previous year's length, what will be the length of the ... | {
"ground_truth": "12.08",
"style": "rule"
} | numina_math | {
"index": 178,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Alice drives from Town X to Town Y, a distance of 150 miles, at an average speed of 50 miles per hour. On her return trip from Town Y to Town X, she encounters heavy traffic and averages only 30 miles per hour. ... | {
"ground_truth": "42.86",
"style": "rule"
} | numina_math | {
"index": 179,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A factory produces widgets and gadgets. Each widget takes 8 minutes to produce, while each gadget takes 10 minutes. Last week, the factory produced 60% of its time making widgets and the rest making gadgets. If ... | {
"ground_truth": "22.5",
"style": "rule"
} | numina_math | {
"index": 180,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Sarah is planning her monthly budget. She has allocated $150 for groceries, $75 for transportation, $100 for entertainment, and $200 for miscellaneous expenses. She also saves twice as much as her entertainment ... | {
"ground_truth": "480",
"style": "rule"
} | numina_math | {
"index": 181,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Consider the polynomial function \\( f(x) = x^3 - 4x^2 - 7x + 10 \\). Determine the x-intercepts of the graph of \\( f(x) \\) by factoring the polynomial and solving for \\( x \\).\n**Solution**: First, we need ... | {
"ground_truth": "c=2-4\\sqrt{2}\\text{or}c=2+4\\sqrt{2}",
"style": "rule"
} | numina_math | {
"index": 182,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: The volume of a sphere is given by the formula \\( V = \\frac{4}{3} \\pi r^3 \\). A sphere has a volume of \\( 36\\pi \\) cubic units. If the volume of the sphere is increased by 50%, what will be the new radius... | {
"ground_truth": "113.04",
"style": "rule"
} | numina_math | {
"index": 183,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Given a parabola in vertex form \\(y = a(x - h)^2 + k\\), where the vertex is at \\( (h, k) \\). If the vertex of the parabola is the midpoint of the line segment joining the points \\( (2, 3) \\) and \\( (6, 7)... | {
"ground_truth": "5",
"style": "rule"
} | numina_math | {
"index": 184,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Simplify the expression: $(3x - 4)(3x + 4) - (2x - 5)^2$\n**Solution**: 1. Apply the Difference of Squares Formula to the first part of the expression:\n \\[\n (3x - 4)(3x + 4) = (3x)^2 - (4)^2 = 9x^2 - 16\n... | {
"ground_truth": "x^2-9x+5",
"style": "rule"
} | numina_math | {
"index": 185,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Find the domain of the function \\( f(x) = \\frac{\\sqrt{x + 3}}{x^2 - 4x + 3} \\).\n**Solution**: To determine the domain of the function \\( f(x) = \\frac{\\sqrt{x + 3}}{x^2 - 4x + 3} \\), we need to consider ... | {
"ground_truth": "(-21)\\cup(3\\infty)",
"style": "rule"
} | numina_math | {
"index": 186,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A restaurant offers 4 types of appetizers, 5 types of main courses, and 3 types of desserts. If a customer wants to order a meal consisting of one appetizer, one main course, and one dessert, how many different ... | {
"ground_truth": "15",
"style": "rule"
} | numina_math | {
"index": 187,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Given the system of linear equations:\n\\[ \n2x + 3y = 12 \n\\]\n\\[ \n4x - y = 2 \n\\]\nSolve for \\(x\\) and \\(y\\) using the elimination method.\n**Solution**: To solve the system of equations using the elim... | {
"ground_truth": "\\frac{9}{7}",
"style": "rule"
} | numina_math | {
"index": 188,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A delivery driver covers 300 miles on his route in 5 hours. On another day, he covers 450 miles in 7.5 hours. What is his average speed in miles per hour for both days combined?\n**Solution**: To find the averag... | {
"ground_truth": "4",
"style": "rule"
} | numina_math | {
"index": 189,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A number is 5 more than twice its divisor. If the divisor is 7, what is the number?\n**Solution**: Let's define the number as \\( N \\) and its divisor as \\( D \\).\n\nGiven:\n1. The divisor \\( D \\) is 7.\n2.... | {
"ground_truth": "6",
"style": "rule"
} | numina_math | {
"index": 190,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A team of workers is paving a highway. Each day, they pave 0.5 kilometers more than 1/70 of the entire highway. It takes them 70 days to complete the highway. What is the total length of the highway?\n**Solution... | {
"ground_truth": "8.4",
"style": "rule"
} | numina_math | {
"index": 191,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Find the range of the function \\(f(x) = -x^2 + 4x + 5\\).\n**Solution**: Step 1: Identify the quadratic expression and its properties.\nThe given function is \\(f(x) = -x^2 + 4x + 5\\). This is a quadratic func... | {
"ground_truth": "(-\\infty3]",
"style": "rule"
} | numina_math | {
"index": 192,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A particle moves along a path described by the parametric equations \\( x(t) = t^2 + 2t \\) and \\( y(t) = 3t + 4 \\). At what point does the particle cross the parabola defined by \\( y = 2x + 1 \\)?\n**Solutio... | {
"ground_truth": "(00)",
"style": "rule"
} | numina_math | {
"index": 193,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: If the measure of one angle is \\( (3x + 10)^\\circ \\) and it is complementary to another angle measuring \\( (2x + 5)^\\circ \\), find the value of \\( x \\) and the measures of both angles.\n**Solution**: Ste... | {
"ground_truth": "\\text{first angle: } 43.75 \\text{ degrees, second angle: } 136.25 \\text{ degrees}",
"style": "rule"
} | numina_math | {
"index": 194,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A bookstore is having a sale where every book is sold at a 25% discount. If the original price of each book is $20, how much would 8 books cost during the sale?\n**Solution**: 1. First, find the amount of discou... | {
"ground_truth": "225",
"style": "rule"
} | numina_math | {
"index": 195,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Sarah has a collection of 30 books. She donates 10 books to a local library. Later, she buys 15 more books from a bookstore. She then decides to give away a third of her current collection to her friends. How ma... | {
"ground_truth": "12",
"style": "rule"
} | numina_math | {
"index": 196,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Samantha is designing a two-part garden. The first part is a rectangular vegetable patch measuring 8 feet by 12 feet, and the second part is a rectangular flower bed measuring 5 feet by 10 feet. If Samantha need... | {
"ground_truth": "32",
"style": "rule"
} | numina_math | {
"index": 197,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Sarah is organizing a charity event and needs to prepare gift bags. She plans to include 5 items in each bag, and she has bought 8 different types of items. If she prepares 40 gift bags, how many items does she ... | {
"ground_truth": "42 \\text{ toys and } 28 \\text{ books}",
"style": "rule"
} | numina_math | {
"index": 198,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A gardener has 3 identical roses, 4 identical tulips, and 5 identical daisies. He wants to plant them in a row in his garden. How many different ways can he arrange the flowers?\n**Solution**: To solve this prob... | {
"ground_truth": "8640",
"style": "rule"
} | numina_math | {
"index": 199,
"name": "numina_math",
"split": "train"
} |
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