{"status": "success", "data": {"description_md": "There are exactly $N$ distinct rational numbers $k$ such that $|k|<200$ and $$5x^2+kx+12=0$$ has at least one integer solution for $x$.  What is $N$?\n\n$\\textbf{(A) }6\\qquad<br>\\textbf{(B) }12\\qquad<br>\\textbf{(C) }24\\qquad<br>\\textbf{(D) }48\\qquad<br>\\textbf{(E) }78\\qquad$\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>There are exactly  <span class=\"katex--inline\">N</span>  distinct rational numbers  <span class=\"katex--inline\">k</span>  such that  <span class=\"katex--inline\">|k|&lt;200</span>  and  <span class=\"katex--display\">5x^2+kx+12=0</span>  has at least one integer solution for  <span class=\"katex--inline\">x</span> .  What is  <span class=\"katex--inline\">N</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }6\\qquad\\textbf{(B) }12\\qquad\\textbf{(C) }24\\qquad\\textbf{(D) }48\\qquad\\textbf{(E) }78\\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 19", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc12A_p20", "prev": "/problem/14_amc12A_p18"}}