{"status": "success", "data": {"description_md": "A bee starts flying from point $P_0$. She flies $1$ inch due east to point $P_1$. For $j \\ge 1$, once the bee reaches point $P_j$, she turns $30^{\\circ}$ counterclockwise and then flies $j+1$ inches straight to point $P_{j+1}$. When the bee reaches $P_{2015}$ she is exactly $a \\sqrt{b} + c \\sqrt{d}$ inches away from $P_0$, where $a$, $b$, $c$ and $d$ are positive integers and $b$ and $d$ are not divisible by the square of any prime. What is $a+b+c+d$ ?\n\n$\\textbf{(A)}\\; 2016 \\qquad\\textbf{(B)}\\; 2024 \\qquad\\textbf{(C)}\\; 2032 \\qquad\\textbf{(D)}\\; 2040 \\qquad\\textbf{(E)}\\; 2048$\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>A bee starts flying from point  <span class=\"katex--inline\">P_0</span> . She flies  <span class=\"katex--inline\">1</span>  inch due east to point  <span class=\"katex--inline\">P_1</span> . For  <span class=\"katex--inline\">j \\ge 1</span> , once the bee reaches point  <span class=\"katex--inline\">P_j</span> , she turns  <span class=\"katex--inline\">30^{\\circ}</span>  counterclockwise and then flies  <span class=\"katex--inline\">j+1</span>  inches straight to point  <span class=\"katex--inline\">P_{j+1}</span> . When the bee reaches  <span class=\"katex--inline\">P_{2015}</span>  she is exactly  <span class=\"katex--inline\">a \\sqrt{b} + c \\sqrt{d}</span>  inches away from  <span class=\"katex--inline\">P_0</span> , where  <span class=\"katex--inline\">a</span> ,  <span class=\"katex--inline\">b</span> ,  <span class=\"katex--inline\">c</span>  and  <span class=\"katex--inline\">d</span>  are positive integers and  <span class=\"katex--inline\">b</span>  and  <span class=\"katex--inline\">d</span>  are not divisible by the square of any prime. What is  <span class=\"katex--inline\">a+b+c+d</span>  ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\; 2016 \\qquad\\textbf{(B)}\\; 2024 \\qquad\\textbf{(C)}\\; 2032 \\qquad\\textbf{(D)}\\; 2040 \\qquad\\textbf{(E)}\\; 2048</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": 5, "problem_name": "2015 AMC 12B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/15_amc12B_p24"}}