{"status": "success", "data": {"description_md": "Let $x$ and $y$ be positive integers such that the range of $\\{x, y, x+y\\}$ is $7$. Given that the mean of the same set is an integer, find the minimum possible value of $x$.\n\nNote that the range of a list is defined to be the positive difference between its largest and smallest elements.", "description_html": "<p>Let <span class=\"katex--inline\">x</span> and <span class=\"katex--inline\">y</span> be positive integers such that the range of <span class=\"katex--inline\">\\{x, y, x+y\\}</span> is <span class=\"katex--inline\">7</span>. Given that the mean of the same set is an integer, find the minimum possible value of <span class=\"katex--inline\">x</span>.</p>&#10;<p>Note that the range of a list is defined to be the positive difference between its largest and smallest elements.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Mock Euclid 2025 - Problem 2 Part C", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}