idx int64 0 61 | prompt stringlengths 868 2.58k | answers sequencelengths 1 1 | gt stringlengths 1 53 |
|---|---|---|---|
24 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve the problem, we need to convert the repeating decimal \\(0.\\overline{1331}\\) into a fraction. Let's denote \\(x = 0.\\overline{1331}\\). Then, we can write:\n\n\\[10000x = 1331.\\overline{1331}\\]\n\nSubtracting \\(x = 0.\\overline{1331}\\) from this equation, we get:\n\n\\[10000x - x = 1331.\\overline{... | 1030 |
4 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve this problem, we need to find the coordinates of the point \\( P \\) on the line \\( y = -x + 6 \\) such that \\( P \\) is equidistant from the points \\( A(10, -10) \\) and \\( O(0, 0) \\).\n\n1. Let \\( P \\) be the point \\((x, y)\\). Since \\( P \\) lies on the line \\( y = -x + 6 \\), we can write \\... | (8,-2) |
27 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve this problem, let's denote the three consecutive integers as \\( n-1 \\), \\( n \\), and \\( n+1 \\).\n\n1. The product of these three integers is given by:\n \\[\n (n-1) \\cdot n \\cdot (n+1) = 120\n \\]\n\n2. The mean of these three integers is:\n \\[\n \\text{Mean} = \\frac{(n-1) + n + (n+1)}... | 6 |
18 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve this problem, we need to set up a system of equations based on the given conditions. Let's denote the two-digit number as \\(10a + b\\), where \\(a\\) and \\(b\\) are the digits of the number. Here, \\(a\\) is the tens digit and \\(b\\) is the units digit.\n\nThe problem gives us two conditions:\n1. The s... | 143 |
40 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve this problem, we need to find the quadratic polynomial \\(P(x) = ax^2 + bx + c\\) that satisfies the given inequalities and the condition \\(P(11) = 181\\).\n\nGiven the inequalities:\n\\[x^2 - 2x + 2 \\le P(x) \\le 2x^2 - 4x + 3\\]\nwe can infer that \\(P(x)\\) must be a linear combination of the polynom... | 406 |
42 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve this problem, we need to understand the geometric properties of the square and the regular heptagon.\n\n1. **Square Properties**: Each internal angle of a square is \\(90^\\circ\\).\n2. **Regular Heptagon Properties**: Each internal angle of a regular heptagon is \\(\\frac{(7-2) \\times 180^\\circ}{7} = \... | \frac{270}7\text{ degrees} |
10 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve the problem, we need to evaluate the expression \\(441 + 2(21)(19) + 361\\). Let's break it down:\n\n1. First, calculate \\(2(21)(19)\\).\n2. Then, add the result to 441 and 361.\n\nLet's do this step-by-step using Python to ensure accuracy.\n```python\n# Step-by-step calculation\nterm1 = 441\nterm2 = 2 *... | 1600 |
2 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve the problem, we need to determine the $x$-intercept ($a$), the $y$-intercept ($b$), and the slope ($m$) of the line given by the equation $\\frac{x}{4} + \\frac{y}{12} = 1$. Then, we will compute the value of $a + b + m$.\n\n1. **Find the $x$-intercept ($a$):**\n The $x$-intercept is the value of $x$ wh... | 13 |
41 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve this problem, we need to determine the probability of obtaining face \\( F \\) on an unfair six-sided die and then use this information to find the probability of obtaining a sum of 7 when two such dice are rolled. We will then use the given probability to find the fraction \\( \\frac{m}{n} \\) and determ... | 29 |
20 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve the problem $(1+2i)6-3i$, we need to follow these steps:\n\n1. First, we need to multiply the complex number $(1+2i)$ by 6.\n2. Then, we need to subtract $3i$ from the result obtained in step 1.\n\nLet's break it down and solve it step-by-step using Python and SymPy.\n\n```python\nimport sympy as sp\n\n# ... | 6+9i |
7 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To determine the degree of the polynomial \\( p(x) \\), we need to analyze the expression:\n\n\\[ p(x) = \\frac{(x - b)(x - c)}{(a - b)(a - c)} + \\frac{(x - a)(x - c)}{(b - a)(b - c)} + \\frac{(x - a)(x - b)}{(c - a)(c - b)}. \\]\n\nFirst, let's simplify the expression. We can observe that the polynomial \\( p(x)... | 0 |
50 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve this problem, we need to determine the value of \\( b \\) such that the line passing through the points \\((-5, 4)\\) and \\((-1, 3)\\) has a direction vector of the form \\(\\begin{pmatrix} -7 \\\\ b \\end{pmatrix}\\).\n\n1. **Find the direction vector of the line:**\n\n The direction vector of the lin... | \frac{7}{4} |
1 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve this problem, we can use a system of equations. Let's define:\n- \\( d \\) as the number of dimes.\n- \\( n \\) as the number of nickels.\n\nFrom the problem, we know the following:\n1. Hillary has a total of 11 coins, so \\( d + n = 11 \\).\n2. The total value of the coins is 75 cents. Since dimes are wo... | 7 |
56 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"To solve this problem, we need to understand the pattern of the sum of the first $N$ positive odd numbers. The $n$-th positive odd number can be represented as $2n - 1$. The sum of the first $N$ positive odd numbers is given by:\n\n$$\n1 + 3 + 5 + \\cdots + (2N - 1) = N^2\n$$\n\nThis is a well-known result from th... | 11 |
12 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
2. Perform a self-evaluation:
- You may include reasoning to verify correctness.
- However, your final self-... | [
"The given sequence is a geometric sequence with the first term \\( a = \\frac{1}{4} \\) and common ratio \\( r = \\frac{1}{2} \\).\n\nThe sum of the first \\( n \\) terms of a geometric sequence is given by the formula:\n\\[ S_n = a \\frac{1 - r^n}{1 - r} \\]\n\nGiven that the sum of the first \\( n \\) terms is \... | 8 |
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