{"status": "success", "data": {"description_md": "For all integers $n \\geq 9,$ the value of\n\n$$\\frac{(n+2)!-(n+1)!}{n!}$$is always which of the following?\n\n$\\textbf{(A) } \\text{a multiple of 4} \\qquad \\textbf{(B) } \\text{a multiple of 10} \\qquad \\textbf{(C) } \\text{a prime number} \\qquad \\textbf{(D) } \\text{a perfect square} \\qquad \\textbf{(E) } \\text{a perfect cube}$\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 all integers  <span class=\"katex--inline\">n \\geq 9,</span>  the value of</p>&#10;<p> <span class=\"katex--display\">\\frac{(n+2)!-(n+1)!}{n!}</span> is always which of the following?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } \\text{a multiple of 4} \\qquad \\textbf{(B) } \\text{a multiple of 10} \\qquad \\textbf{(C) } \\text{a prime number} \\qquad \\textbf{(D) } \\text{a perfect square} \\qquad \\textbf{(E) } \\text{a perfect cube}</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": "2020 AMC 12B Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12B_p07", "prev": "/problem/20_amc12B_p05"}}