{"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$\\textbf{(A) }3 \\qquad<br>\\textbf{(B) }4 \\qquad<br>\\textbf{(C) }6 \\qquad<br>\\textbf{(D) }8 \\qquad<br>\\textbf{(E) }9 \\qquad$\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>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>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }3 \\qquad\\textbf{(B) }4 \\qquad\\textbf{(C) }6 \\qquad\\textbf{(D) }8 \\qquad\\textbf{(E) }9 \\qquad</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": "2018 AMC 12A Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc12A_p08", "prev": "/problem/18_amc12A_p06"}}