{"status": "success", "data": {"description_md": "Joy has $30$ thin rods, one each of every integer length from $1$ cm through $30$ cm. She places the rods with lengths $3$ cm, $7$ cm, and $15$ cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?\n\n$\\textbf{(A)}\\ 16\\qquad\\textbf{(B)}\\ 17\\qquad\\textbf{(C)}\\ 18\\qquad\\textbf{(D)}\\ 19\\qquad\\textbf{(E)}\\ 20$", "description_html": "<p>Joy has  <span class=\"katex--inline\">30</span>  thin rods, one each of every integer length from  <span class=\"katex--inline\">1</span>  cm through  <span class=\"katex--inline\">30</span>  cm. She places the rods with lengths  <span class=\"katex--inline\">3</span>  cm,  <span class=\"katex--inline\">7</span>  cm, and  <span class=\"katex--inline\">15</span>  cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 16\\qquad\\textbf{(B)}\\ 17\\qquad\\textbf{(C)}\\ 18\\qquad\\textbf{(D)}\\ 19\\qquad\\textbf{(E)}\\ 20</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": "2017 AMC 10A Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc10A_p11", "prev": "/problem/17_amc10A_p09"}}