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 farmer has a rectangular field whose length is given by the polynomial expression \\(3x + 2\\) meters and the width is \\(x - 1\\) meters. If \\(x = 4\\), calculate the area of the field in square meters.\n**S... | {
"ground_truth": "30",
"style": "rule"
} | numina_math | {
"index": 0,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A company has a 60-minute meeting scheduled, and it was found that only 40% of the employees attended. If 24 employees were present, how many employees were there in total? How many more employees were absent th... | {
"ground_truth": "20",
"style": "rule"
} | numina_math | {
"index": 1,
"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 ribbon that is 3/4 of a yard long. She cuts off a piece that is 1/3 of the total length of the ribbon. After that, she uses 1/2 of the remaining ribbon to wrap a gift. How many yards of ribbon does s... | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | numina_math | {
"index": 2,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: If a car can travel 60 miles in 1 hour and a bicycle can travel the same distance in 4 hours, how long will it take for them to travel 60 miles together, assuming they can combine their speeds?\n**Solution**: 1.... | {
"ground_truth": "15",
"style": "rule"
} | numina_math | {
"index": 3,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Find the slope of the line that passes through the points \\((4, \\frac{1}{2})\\) and \\((-\\3, \\frac{5}{4})\\).\n**Solution**: To find the slope \\(m\\) of the line passing through two points \\((x_1, y_1)\\) ... | {
"ground_truth": "0",
"style": "rule"
} | numina_math | {
"index": 4,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Samantha is saving money to buy a new bicycle. She decides to save money by putting aside a fixed amount each week. In the first week, she saves $10. In the second week, she saves $15. In the third week, she sav... | {
"ground_truth": "110",
"style": "rule"
} | numina_math | {
"index": 5,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Given the numbers \\(2^5 \\cdot 3^3 \\cdot 5^2\\) and \\(2^3 \\cdot 3^4 \\cdot 7\\), find their greatest common divisor (GCD).\n**Solution**: To find the greatest common divisor (GCD) of the numbers \\(2^5 \\cdo... | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | numina_math | {
"index": 6,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Two water tanks, Tank A and Tank B, are being filled simultaneously. Tank A is filled at a rate of 12 liters per minute, while Tank B is filled at a rate of 8 liters per minute. If Tank B takes 15 minutes longer... | {
"ground_truth": "12",
"style": "rule"
} | numina_math | {
"index": 7,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: John has a total budget of $150 to buy some new books. Each book costs $15. After buying as many books as he can afford, he wants to save the remaining money. How many books can John buy, and how much money will... | {
"ground_truth": "0",
"style": "rule"
} | numina_math | {
"index": 8,
"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 least common multiple (LCM) of 48 and 180? Additionally, find the greatest common divisor (GCD) of the same two numbers.\n**Solution**: To solve this problem, we need to find both the least common mu... | {
"ground_truth": "(6180)(1860)(3036)",
"style": "rule"
} | numina_math | {
"index": 9,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: In an isosceles triangle \\( \\triangle ABC \\), \\(\\angle BAC = 30^\\circ\\), and the equal sides \\( AB \\) and \\( AC \\) each have a length of 10 units. Find the length of the base \\( BC \\).\n**Solution**... | {
"ground_truth": "\\frac{10\\sqrt{3}}{3}",
"style": "rule"
} | numina_math | {
"index": 10,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A bag contains 10 red balls and 10 blue balls. You draw 5 balls from the bag without replacement. What is the expected number of red balls you draw? Express your answer as a common fraction.\n**Solution**: We ca... | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | numina_math | {
"index": 11,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Given $f(x) = 3x - 7$, find $f^{-1}(f(f(x)))$.\n**Solution**: To find the inverse function $f^{-1}(x)$ for $f(x) = 3x - 7$, we start by setting $y = f(x)$:\n\\[ y = 3x - 7 \\]\n\nNext, solve for $x$ in terms of ... | {
"ground_truth": "3",
"style": "rule"
} | numina_math | {
"index": 12,
"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 3 cups of sugar for every 5 cups of flour. If a baker wants to make a batch that uses 12 cups of flour, how many cups of sugar will they need? Additionally, if the baker only has a tablespoon ... | {
"ground_truth": "0.45",
"style": "rule"
} | numina_math | {
"index": 13,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: In an equilateral triangle \\( \\triangle ABC \\), a circle is inscribed, touching each side of the triangle exactly once. If the radius of the inscribed circle is \\( \\sqrt{3} \\) cm, find the side length of t... | {
"ground_truth": "79",
"style": "rule"
} | numina_math | {
"index": 14,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A line intersects the parabola \\( y = x^2 - 4x + 3 \\) at two points. If the line passes through the vertex of the parabola, what is the equation of the line and at what points does it intersect the parabola?\n... | {
"ground_truth": "2x-3",
"style": "rule"
} | numina_math | {
"index": 15,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A sequence is defined such that the \\( n \\)-th term is given by the formula \\( a_n = \\frac{2n + 3}{n + 1} \\). Find the sum of the first five terms of this sequence. Express your answer as a fraction in simp... | {
"ground_truth": "8.45",
"style": "rule"
} | numina_math | {
"index": 16,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A chemistry lab has a 50% alcohol solution and a 30% alcohol solution. How many liters of each solution should be mixed together to obtain 20 liters of a 40% alcohol solution?\n**Solution**: 1. Let's denote the ... | {
"ground_truth": "x = 62.5 \\text{ ml}, y = 187.5 \\text{ ml}",
"style": "rule"
} | numina_math | {
"index": 17,
"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": "2",
"style": "rule"
} | numina_math | {
"index": 18,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: How many different 4-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 if repetition of digits is allowed?\n**Solution**: To determine how many different 4-digit numbers can be formed using the digi... | {
"ground_truth": "12",
"style": "rule"
} | numina_math | {
"index": 19,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: At a fruit market, the price of bananas is $0.50 each, and the price of oranges is $0.75 each. If Lisa buys 8 bananas and 6 oranges, what is the total cost of her purchase?\n**Solution**: 1. Calculate the cost o... | {
"ground_truth": "10.00",
"style": "rule"
} | numina_math | {
"index": 20,
"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:\n\\[ \n\\begin{cases}\nx^2 + y^2 = 20 \\\\\n2x + 3y = 10\n\\end{cases}\n\\]\nFind the values of \\(x\\) and \\(y\\) that satisfy both equations.\n**Solution**: Step 1: Solve the se... | {
"ground_truth": "x\\approx2.13y\\approx5.46",
"style": "rule"
} | numina_math | {
"index": 21,
"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 bakery and sells her famous muffins. She buys ingredients for $120. Each muffin costs her $1 to make, and she sells each muffin for $4. If she makes 50 muffins, how much profit does she make?\... | {
"ground_truth": "210",
"style": "rule"
} | numina_math | {
"index": 22,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Sarah is driving to her friend's house which is 300 miles away. She plans to travel at an average speed of 60 miles per hour. However, she knows that due to traffic, she will only be able to travel at 75% of her... | {
"ground_truth": "2.5",
"style": "rule"
} | numina_math | {
"index": 23,
"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^2 + 4x + 5)(2x - 3) \\).\n**Solution**: To simplify the expression \\( (3x^2 + 4x + 5)(2x - 3) \\), follow these steps:\n\n1. **Distribute each term in the first polynomial by eac... | {
"ground_truth": "f(x)=2x^2-7x-15",
"style": "rule"
} | numina_math | {
"index": 24,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Emily starts her homework at 4:15 PM and spends 45 minutes on math, 30 minutes on science, and 25 minutes on history. At what time does she finish her homework?\n**Solution**: To find out when Emily finishes her... | {
"ground_truth": "80",
"style": "rule"
} | numina_math | {
"index": 25,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A small business manufactures custom T-shirts. The fixed cost for operating the business is $500 per month. Additionally, the variable cost per T-shirt is $8. They sell each T-shirt for $20. If the business sell... | {
"ground_truth": "250",
"style": "rule"
} | numina_math | {
"index": 26,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Convert the repeating decimal $0.\\overline{36}$ into its simplest fractional form.\n**Solution**: To convert the repeating decimal $0.\\overline{36}$ into a fraction, follow these steps:\n\n1. Let \\( x = 0.\\o... | {
"ground_truth": "2",
"style": "rule"
} | numina_math | {
"index": 27,
"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) = 2x^4 + 3x^3 - 11x^2 + 6x - 3 \\), use the Rational Root Theorem to identify all possible rational roots and determine the actual rational roots of the polynomial. Then, factorize ... | {
"ground_truth": "\\{-11-7711\\}",
"style": "rule"
} | numina_math | {
"index": 28,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: There are two sets of animals in a zoo: Set A consists of lions and Set B consists of tigers. The total number of animals in both sets combined is 50. The number of lions is twice the number of tigers. How many ... | {
"ground_truth": "72",
"style": "rule"
} | numina_math | {
"index": 29,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Emily has a total of 60 candies. She decides to distribute them among her three friends, Sarah, John, and Leo, in such a way that each friend gets a different fraction of the total candies. Sarah gets \\( \\frac... | {
"ground_truth": "50",
"style": "rule"
} | numina_math | {
"index": 30,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A triangle in the coordinate plane has its vertices at points \\( A(2, 3) \\), \\( B(5, 11) \\), and \\( C(7, 8) \\). Calculate the area of the triangle formed by these points.\n**Solution**: To find the area of... | {
"ground_truth": "1",
"style": "rule"
} | numina_math | {
"index": 31,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: John and Sara are working together to complete a project. John can complete the project on his own in 10 hours, while Sara can complete it on her own in 15 hours. If they work together, how many hours will it ta... | {
"ground_truth": "2.5",
"style": "rule"
} | numina_math | {
"index": 32,
"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": "x\\text{-intercepts:}2\\pmi",
"style": "rule"
} | numina_math | {
"index": 33,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A company had 500 employees last year. This year, the number of employees increased by 20%. Next year, the company plans to reduce the number of employees by 15% of this year's total. How many employees will the... | {
"ground_truth": "184",
"style": "rule"
} | numina_math | {
"index": 34,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A staircase has 15 steps, and the height of each step increases by a consistent amount as you go up. The first step is 7 inches high, and the last step is 21 inches high. How much does the height of each step in... | {
"ground_truth": "24",
"style": "rule"
} | numina_math | {
"index": 35,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: A line passes through the points (2, 3) and (4, 7). Find the equation of the line in slope-intercept form (y = mx + b).\n**Solution**: To find the equation of the line that passes through the points (2, 3) and (... | {
"ground_truth": "\\frac{8}{3}x-\\frac{7}{3}",
"style": "rule"
} | numina_math | {
"index": 36,
"name": "numina_math",
"split": "train"
} |
[
{
"content": "Here are 3 similar examples to help solve the problem:\n\n**Example 1**:\n**Problem**: Evaluate the sum \\[\\sum_{n=1}^\\infty \\frac{1}{(n+1)(n+2)}\\].\n**Solution**: To solve this infinite series, we'll start by decomposing the rational function into partial fractions. The given term is \\[\\fra... | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | numina_math | {
"index": 37,
"name": "numina_math",
"split": "train"
} |
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