{"status": "success", "data": {"description_md": "Let $n$ be a positive integer such that $\\frac{1}{2}+\\frac{1}{3}+\\frac{1}{7}+\\frac{1}{n}$ is an integer. Which of the following statements is '''not''' true?\n\n$\\mathrm{(A) \\ } 2\\text{ divides }n\\qquad \\mathrm{(B) \\ } 3\\text{ divides }n\\qquad \\mathrm{(C) \\ } 6\\text{ divides }n\\qquad \\mathrm{(D) \\ } 7\\text{ divides }n\\qquad \\mathrm{(E) \\ } n>84$", "description_html": "<p>Let  <span class=\"katex--inline\">n</span>  be a positive integer such that  <span class=\"katex--inline\">\\frac{1}{2}+\\frac{1}{3}+\\frac{1}{7}+\\frac{1}{n}</span>  is an integer. Which of the following statements is &#8220;'not&#8221;&#8217; true?</p>\n<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>\n<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": 1, "problem_name": "2002 AMC 10B Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc10B_p08", "prev": "/problem/02_amc10B_p06"}}