{"status": "success", "data": {"description_md": "A subset $B$ of the set of integers from $1$ to $100$, inclusive, has the property that no two elements of $B$ sum to $125$. What is the maximum possible number of elements in $B$?\n\n$\\mathrm{(A)} 50 \\qquad \\mathrm{(B)} 51 \\qquad \\mathrm{(C)} 62 \\qquad \\mathrm{(D)} 65 \\qquad \\mathrm{(E)} 68$", "description_html": "<p>A subset  <span class=\"katex--inline\">B</span>  of the set of integers from  <span class=\"katex--inline\">1</span>  to  <span class=\"katex--inline\">100</span> , inclusive, has the property that no two elements of  <span class=\"katex--inline\">B</span>  sum to  <span class=\"katex--inline\">125</span> . What is the maximum possible number of elements in  <span class=\"katex--inline\">B</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)} 50 \\qquad \\mathrm{(B)} 51 \\qquad \\mathrm{(C)} 62 \\qquad \\mathrm{(D)} 65 \\qquad \\mathrm{(E)} 68</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": 4, "problem_name": "2005 AMC 10B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/05_amc10B_p24"}}