id int64 1 41k | question stringlengths 61 1.07k | generation_model stringclasses 1
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value | pass_rate float64 0.13 0.88 | expected_answer int64 1 83.3k | accepted_formated stringlengths 1k 210k | rejected_formated stringlengths 1.73k 3.64M | license stringclasses 1
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1 | Consider the equation $[x] \cdot [y] = x + y$. Find the equations of the two lines on which all non-integer solutions of this equation lie, and express your answer in the form $y = mx + b$. Provide the sum of the slopes and y-intercepts of these lines. | gpt-oss-120 | tir | 0.875 | 4 | <|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competitor. The final answer must be a non-negative integer between 0 and 99999. You must place the final integer answer inside \boxed{}.<|end|><|start|>user<|message|>Consider the equation $[x] \cdot [y] = x + y$. Find the equati... | <|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competitor. The final answer must be a non-negative integer between 0 and 99999. You must place the final integer answer inside \boxed{}.<|end|><|start|>user<|message|>Consider the equation $[x] \cdot [y] = x + y$. Find the equati... | cc-by-4.0 |
2 | Consider the equation $[x] \cdot [y] = x + y$. Find the equations of the two lines on which all non-integer solutions of this equation lie, and express your answer in the form $y = mx + b$. Provide the sum of the slopes and y-intercepts of these lines. | gpt-oss-120 | tir | 0.875 | 4 | <|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competitor. The final answer must be a non-negative integer between 0 and 99999. You must place the final integer answer inside \boxed{}.<|end|><|start|>user<|message|>Consider the equation $[x] \cdot [y] = x + y$. Find the equati... | <|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competitor. The final answer must be a non-negative integer between 0 and 99999. You must place the final integer answer inside \boxed{}.<|end|><|start|>user<|message|>Consider the equation $[x] \cdot [y] = x + y$. Find the equati... | cc-by-4.0 |
3 | Consider the equation $[x] \cdot [y] = x + y$. Find the equations of the two lines on which all non-integer solutions of this equation lie, and express your answer in the form $y = mx + b$. Provide the sum of the slopes and y-intercepts of these lines. | gpt-oss-120 | tir | 0.875 | 4 | <|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competitor. The final answer must be a non-negative integer between 0 and 99999. You must place the final integer answer inside \boxed{}.<|end|><|start|>user<|message|>Consider the equation $[x] \cdot [y] = x + y$. Find the equati... | <|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competitor. The final answer must be a non-negative integer between 0 and 99999. You must place the final integer answer inside \boxed{}.<|end|><|start|>user<|message|>Consider the equation $[x] \cdot [y] = x + y$. Find the equati... | cc-by-4.0 |
4 | Consider the equation $[x] \cdot [y] = x + y$. Find the equations of the two lines on which all non-integer solutions of this equation lie, and express your answer in the form $y = mx + b$. Provide the sum of the slopes and y-intercepts of these lines. | gpt-oss-120 | tir | 0.875 | 4 | <|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competitor. The final answer must be a non-negative integer between 0 and 99999. You must place the final integer answer inside \boxed{}.<|end|><|start|>user<|message|>Consider the equation $[x] \cdot [y] = x + y$. Find the equati... | <|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competitor. The final answer must be a non-negative integer between 0 and 99999. You must place the final integer answer inside \boxed{}.<|end|><|start|>user<|message|>Consider the equation $[x] \cdot [y] = x + y$. Find the equati... | cc-by-4.0 |
5 | Consider the equation $[x] \cdot [y] = x + y$. Find the equations of the two lines on which all non-integer solutions of this equation lie, and express your answer in the form $y = mx + b$. Provide the sum of the slopes and y-intercepts of these lines. | gpt-oss-120 | tir | 0.875 | 4 | <|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competitor. The final answer must be a non-negative integer between 0 and 99999. You must place the final integer answer inside \boxed{}.<|end|><|start|>user<|message|>Consider the equation $[x] \cdot [y] = x + y$. Find the equati... | <|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competitor. The final answer must be a non-negative integer between 0 and 99999. You must place the final integer answer inside \boxed{}.<|end|><|start|>user<|message|>Consider the equation $[x] \cdot [y] = x + y$. Find the equati... | cc-by-4.0 |
6 | "Consider the equation $[x] \\cdot [y] = x + y$. Find the equations of the two lines on which all no(...TRUNCATED) | gpt-oss-120 | tir | 0.875 | 4 | "<|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competito(...TRUNCATED) | "<|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competito(...TRUNCATED) | cc-by-4.0 |
7 | "Consider the equation $[x] \\cdot [y] = x + y$. Find the equations of the two lines on which all no(...TRUNCATED) | gpt-oss-120 | tir | 0.875 | 4 | "<|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competito(...TRUNCATED) | "<|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competito(...TRUNCATED) | cc-by-4.0 |
8 | "In triangle \\(ABC\\), let \\(D\\) be on \\(BC\\) such that \\(AD\\) bisects \\(\\angle BAC\\). \\((...TRUNCATED) | gpt-oss-120 | tir | 0.5 | 1 | "<|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competito(...TRUNCATED) | "<|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competito(...TRUNCATED) | cc-by-4.0 |
9 | "In triangle \\(ABC\\), let \\(D\\) be on \\(BC\\) such that \\(AD\\) bisects \\(\\angle BAC\\). \\((...TRUNCATED) | gpt-oss-120 | tir | 0.5 | 1 | "<|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competito(...TRUNCATED) | "<|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competito(...TRUNCATED) | cc-by-4.0 |
10 | "In triangle \\(ABC\\), let \\(D\\) be on \\(BC\\) such that \\(AD\\) bisects \\(\\angle BAC\\). \\((...TRUNCATED) | gpt-oss-120 | tir | 0.5 | 1 | "<|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competito(...TRUNCATED) | "<|start|>system<|message|>You are a world-class International Mathematical Olympiad (IMO) competito(...TRUNCATED) | cc-by-4.0 |
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