{"status": "success", "data": {"description_md": "Let $a<b<c$ be three integers such that $a,b,c$ is an arithmetic progression and $a,c,b$ is a geometric progression.  What is the smallest possible value of $c$?\n\n$\\textbf{(A) }-2\\qquad<br>\\textbf{(B) }1\\qquad<br>\\textbf{(C) }2\\qquad<br>\\textbf{(D) }4\\qquad<br>\\textbf{(E) }6\\qquad$\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>Let  <span class=\"katex--inline\">a&lt;b&lt;c</span>  be three integers such that  <span class=\"katex--inline\">a,b,c</span>  is an arithmetic progression and  <span class=\"katex--inline\">a,c,b</span>  is a geometric progression.  What is the smallest possible value of  <span class=\"katex--inline\">c</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }-2\\qquad\\textbf{(B) }1\\qquad\\textbf{(C) }2\\qquad\\textbf{(D) }4\\qquad\\textbf{(E) }6\\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": 3, "problem_name": "2014 AMC 12A Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc12A_p15", "prev": "/problem/14_amc12A_p13"}}