{"status": "success", "data": {"description_md": "For how many (not necessarily positive) integer values of $n$ is the value of $4000\\cdot \\left(\\tfrac{2}{5}\\right)^n$ an integer?\n\n$\\textbf{(A) }3 \\qquad\n\\textbf{(B) }4 \\qquad\n\\textbf{(C) }6 \\qquad\n\\textbf{(D) }8 \\qquad\n\\textbf{(E) }9 \\qquad$", "description_html": "<p>For how many (not necessarily positive) integer values of  <span class=\"katex--inline\">n</span>  is the value of  <span class=\"katex--inline\">4000\\cdot \\left(\\tfrac{2}{5}\\right)^n</span>  an integer?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }3 \\qquad\n\\textbf{(B) }4 \\qquad\n\\textbf{(C) }6 \\qquad\n\\textbf{(D) }8 \\qquad\n\\textbf{(E) }9 \\qquad</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": "2018 AMC 10A Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10A_p08", "prev": "/problem/18_amc10A_p06"}}