prompt stringlengths 293 4.93k | answers sequencelengths 4 4 | gt stringlengths 1 350 | rewards sequencelengths 4 4 |
|---|---|---|---|
<|im_start|>system
Please provide a detailed, step-by-step explanation of your reasoning. Enclose your full thought process within <think> and </think> tags. Finally, present your final answer enclosed in \boxed{...}.<|im_end|>
<|im_start|>user
Given that one solution to the system of linear equations $x - 2y = m$ is $\begin{cases} x = 2 \ y = 1 \end{cases}$, find the value of $m$.<|im_end|>
<|im_start|>assistant
| [
"<think>\nOkay, so I have this problem here where I need to find the value of m in the equation x - 2y = m. And it's given that one solution to this system of equations is x = 2 and y = 1. Hmm, let me think about how to approach this.\n\nFirst, let me recall what a system of linear equations is. It's a set of two o... | 0 | [
true,
true,
true,
true
] |
<|im_start|>system
Please provide a detailed, step-by-step explanation of your reasoning. Enclose your full thought process within <think> and </think> tags. Finally, present your final answer enclosed in \boxed{...}.<|im_end|>
<|im_start|>user
Bully Dima placed 38 wooden toothpicks in a rectangle shape of \(3 \times 5\). Then he simultaneously ignited two adjacent corners of this rectangle marked in the diagram below.
It is known that one toothpick burns in 10 seconds. How many seconds will it take for the whole structure to burn?
(The fire spreads from each burned toothpick to all adjacent unburned toothpicks at a constant speed.)<|im_end|>
<|im_start|>assistant
| [
"<think>\nOkay, so there's this problem where Bully Dima put 38 wooden toothpicks in a rectangle shape of 3x5. Then he ignited two adjacent corners. We need to figure out how long it takes for the whole structure to burn. Each toothpick burns in 10 seconds, and the fire spreads from each burned toothpick to all adj... | 65 | [
false,
false,
false,
false
] |
<|im_start|>system
Please provide a detailed, step-by-step explanation of your reasoning. Enclose your full thought process within <think> and </think> tags. Finally, present your final answer enclosed in \boxed{...}.<|im_end|>
<|im_start|>user
Find the sum \( S_{n} = \sin \alpha \cdot \sin ^{2} \frac{\alpha}{2} + 2 \sin \frac{\alpha}{2} \cdot \sin ^{2} \frac{\alpha}{4} + \cdots + 2^{n-1} \cdot \sin \frac{\alpha}{2^{n-1}} \cdot \sin ^{2} \frac{\alpha}{2^{n}} \).<|im_end|>
<|im_start|>assistant
| [
"<think>\nOkay, let me try to figure out how to find the sum \\( S_{n} = \\sin \\alpha \\cdot \\sin ^{2} \\frac{\\alpha}{2} + 2 \\sin \\frac{\\alpha}{2} \\cdot \\sin ^{2} \\frac{\\alpha}{4} + \\cdots + 2^{n-1} \\cdot \\sin \\frac{\\alpha}{2^{n-1}} \\cdot \\sin ^{2} \\frac{\\alpha}{2^{n}} \\). Hmm, so each term in t... | 1 | [
false,
false,
false,
false
] |
"<|im_start|>system\nPlease provide a detailed, step-by-step explanation of your reasoning. Enclose (...TRUNCATED) | ["<think>\nOkay, so I need to find the real number m such that set B is a subset of set A. The sets (...TRUNCATED) | 1 \text{ or } 3 | [
false,
false,
false,
false
] |
"<|im_start|>system\nPlease provide a detailed, step-by-step explanation of your reasoning. Enclose (...TRUNCATED) | ["<think>\nOkay, let me try to figure out this problem step by step. So, we have the numbers 1 throu(...TRUNCATED) | 12 | [
false,
false,
false,
false
] |
"<|im_start|>system\nPlease provide a detailed, step-by-step explanation of your reasoning. Enclose (...TRUNCATED) | ["<think>\nOkay, so I have this problem here about an ellipse, and I need to find the value of |PQ| (...TRUNCATED) | 2\sqrt{2} | [
true,
false,
false,
false
] |
"<|im_start|>system\nPlease provide a detailed, step-by-step explanation of your reasoning. Enclose (...TRUNCATED) | ["<think>\nOkay, let's tackle this geometry problem step by step. So, we have triangle ABC and a poi(...TRUNCATED) | 14 | [
false,
false,
false,
false
] |
"<|im_start|>system\nPlease provide a detailed, step-by-step explanation of your reasoning. Enclose (...TRUNCATED) | ["<think>\nAlright, so I need to find the intersection of sets A and B. Let me start by recalling wh(...TRUNCATED) | \{x|2<x\leq4\} | [
false,
false,
false,
false
] |
"<|im_start|>system\nPlease provide a detailed, step-by-step explanation of your reasoning. Enclose (...TRUNCATED) | ["<think>\nAlright, let's see. The problem is about solving the quadratic equation \\(x^2 - (2A)x + (...TRUNCATED) | A = 5 | [
false,
false,
false,
false
] |
"<|im_start|>system\nPlease provide a detailed, step-by-step explanation of your reasoning. Enclose (...TRUNCATED) | ["<think>\nOkay, so I need to figure out the first term in this geometric sequence: 12, 24, a, b, 38(...TRUNCATED) | \frac{3}{4} | [
false,
false,
false,
false
] |
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