idx int64 0 5k | prompt stringlengths 228 4.87k | answers sequencelengths 16 16 | gt dict |
|---|---|---|---|
325 | <|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The product of 600×50 has $\_\_\_\_\_\_$ zeroes at the end. Let's think step by step and output the final answer within \boxed{}<|im_end|>
<|im_start|>assistant
| [
"To find the number of trailing zeroes in the product of \\(600 \\times 50\\), we should first calculate the product and then determine the number of trailing zeroes. The number of trailing zeroes in a number is determined by how many times the number can be divided by 10. Since \\(10 = 2 \\times 5\\), we need to c... | {
"ground_truth": "4",
"style": "rule"
} |
3,422 | "<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["To find the total sum of the diameters of all subsets of \\( S \\) whose diameter is 91, we need t(...TRUNCATED) | {
"ground_truth": "9 \\times 91 \\times 2^{90}",
"style": "rule"
} |
3,908 | "<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["### Step 1: Verify Statement 1\nThe set $\\left\\{\\frac{-1 + \\sqrt{5}}{2}, \\frac{-1 - \\sqrt{5}(...TRUNCATED) | {
"ground_truth": "3, 4",
"style": "rule"
} |
4,279 | "<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["To find the radius \\( r \\) of the circle inscribed in triangle \\( ABC \\) with sides \\( AB = 6(...TRUNCATED) | {
"ground_truth": "2",
"style": "rule"
} |
1,707 | "<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["$\\text{To evaluate the expression } 5x^{y-1} + 2y^{x+1} \\text{ when } x = 3 \\text{ and } y = 4,(...TRUNCATED) | {
"ground_truth": "647",
"style": "rule"
} |
3,495 | "<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["### Reasoning\n\n1. First, we need to determine the function \\(f(x)\\).\n2. We can start by subst(...TRUNCATED) | {
"ground_truth": "f(-1) = 1",
"style": "rule"
} |
3,056 | "<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["### Step 1: Find the value of \\( k \\)\n\nFor a function \\( f(x) = 3^x - k \\cdot 3^{-x} \\) to (...TRUNCATED) | {
"ground_truth": "[\\frac{1}{4}, \\frac{1}{3})",
"style": "rule"
} |
682 | "<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["To **solve the given determinant**, we need to evaluate the expression using cofactor expansion or(...TRUNCATED) | {
"ground_truth": "6x^2 + 36x + 48",
"style": "rule"
} |
4,581 | "<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["The function $y = 2^{|x|}$ has a different behavior depending on the sign of $x$. Specifically:\n\(...TRUNCATED) | {
"ground_truth": "1",
"style": "rule"
} |
1,438 | "<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["A native from the Tanga-Tanga tribe could get 2 drums, 3 wives, and one leopard skin for 111 arrow(...TRUNCATED) | {
"ground_truth": "20, 9, 44",
"style": "rule"
} |
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