{"status": "success", "data": {"description_md": "How many positive integers $n$ satisfy the following condition:\n$$(130n)^{50} > n^{100} > 2^{200}$$\n\n$\\mathrm{(A) \\ } 0\\qquad \\mathrm{(B) \\ } 7\\qquad \\mathrm{(C) \\ } 12\\qquad \\mathrm{(D) \\ } 65\\qquad \\mathrm{(E) \\ } 125$", "description_html": "<p>How many positive integers <span class=\"katex--inline\">n</span> satisfy the following condition:<br/>&#10;<span class=\"katex--display\">(130n)^{50} &gt; n^{100} &gt; 2^{200}</span></p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A) \\ } 0\\qquad \\mathrm{(B) \\ } 7\\qquad \\mathrm{(C) \\ } 12\\qquad \\mathrm{(D) \\ } 65\\qquad \\mathrm{(E) \\ } 125</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2005 AMC 10A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc10A_p14", "prev": "/problem/05_amc10A_p12"}}