{"status": "success", "data": {"description_md": "Let $n$ be a positive integer such that $\\frac 12 + \\frac 13 + \\frac 17 + \\frac 1n$ is an integer. Which of the following statements is '''not''' true:\n\n$\\mathrm{(A)}\\ 2\\ \\text{divides\\ }n<br>\\qquad\\mathrm{(B)}\\ 3\\ \\text{divides\\ }n<br>\\qquad\\mathrm{(C)}\\ 6\\ \\text{divides\\ }n<br>\\qquad\\mathrm{(D)}\\ 7\\ \\text{divides\\ }n<br>\\qquad\\mathrm{(E)}\\ {n > 84}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let  <span class=\"katex--inline\">n</span>  be a positive integer such that  <span class=\"katex--inline\">\\frac 12 + \\frac 13 + \\frac 17 + \\frac 1n</span>  is an integer. Which of the following statements is &#8216;&#8217;&#8216;not&#8217;&#8217;&#8217; true:</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 2\\ \\text{divides\\ }n\\qquad\\mathrm{(B)}\\ 3\\ \\text{divides\\ }n\\qquad\\mathrm{(C)}\\ 6\\ \\text{divides\\ }n\\qquad\\mathrm{(D)}\\ 7\\ \\text{divides\\ }n\\qquad\\mathrm{(E)}\\ {n &gt; 84}</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2002 AMC 12B Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12B_p05", "prev": "/problem/02_amc12B_p03"}}