{"status": "success", "data": {"description_md": "Let $a$, $b$, $c$, $d$, and $e$ be positive integers with $a+b+c+d+e=2010$ and let $M$ be the largest of the sums $a+b$, $b+c$, $c+d$ and $d+e$. What is the smallest possible value of $M$?\n\n$\\textbf{(A)}\\ 670 \\qquad \\textbf{(B)}\\ 671 \\qquad \\textbf{(C)}\\ 802 \\qquad \\textbf{(D)}\\ 803 \\qquad \\textbf{(E)}\\ 804$\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</span> ,  <span class=\"katex--inline\">b</span> ,  <span class=\"katex--inline\">c</span> ,  <span class=\"katex--inline\">d</span> , and  <span class=\"katex--inline\">e</span>  be positive integers with  <span class=\"katex--inline\">a+b+c+d+e=2010</span>  and let  <span class=\"katex--inline\">M</span>  be the largest of the sums  <span class=\"katex--inline\">a+b</span> ,  <span class=\"katex--inline\">b+c</span> ,  <span class=\"katex--inline\">c+d</span>  and  <span class=\"katex--inline\">d+e</span> . What is the smallest possible value of  <span class=\"katex--inline\">M</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 670 \\qquad \\textbf{(B)}\\ 671 \\qquad \\textbf{(C)}\\ 802 \\qquad \\textbf{(D)}\\ 803 \\qquad \\textbf{(E)}\\ 804</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": "2010 AMC 12B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12B_p15", "prev": "/problem/10_amc12B_p13"}}