{"status": "success", "data": {"description_md": "Let $n$ be a positive integer. If for any distinct $x_1,x_2,\\ldots,x_n \\in \\mathbb{R}$, we can always find $1 \\le i < j \\le n$ such that $$\\dfrac{x_ix_j + 1}{x_j - x_i} \\ge \\sqrt{3}$$ what is the minimum value of $n$?\n\n$\\textbf{(A)}~4\\qquad\\textbf{(B)}~5\\qquad\\textbf{(C)}~6\\qquad\\textbf{(D)}~7\\qquad\\textbf{(E)}~8$", "description_html": "<p>Let <span class=\"katex--inline\">n</span> be a positive integer. If for any distinct <span class=\"katex--inline\">x_1,x_2,\\ldots,x_n \\in \\mathbb{R}</span>, we can always find <span class=\"katex--inline\">1 \\le i &lt; j \\le n</span> such that <span class=\"katex--display\">\\dfrac{x_ix_j + 1}{x_j - x_i} \\ge \\sqrt{3}</span> what is the minimum value of <span class=\"katex--inline\">n</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}~4\\qquad\\textbf{(B)}~5\\qquad\\textbf{(C)}~6\\qquad\\textbf{(D)}~7\\qquad\\textbf{(E)}~8</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2024 Mock AMC 12 - Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/2024_mock_amc12-p24", "prev": "/problem/2024_mock_amc12-p22"}}