{"status": "success", "data": {"description_md": "Consider sets $\\mathcal{A}$ and $\\mathcal{B}$. Set $\\mathcal{A}$ contains $12$ elements, exactly $4$ of which are also in $\\mathcal{B}$. If the union of $\\mathcal{A}$ and $\\mathcal{B}$ contains $24$ elements, find the number of elements in $\\mathcal{B}$ but not $\\mathcal{A}$.\n\n$\\textbf{(A)}~20\\qquad\\textbf{(B)}~12\\qquad\\textbf{(C)}~24\\qquad\\textbf{(D)}~8\\qquad\\textbf{(E)}~0$", "description_html": "<p>Consider sets <span class=\"katex--inline\">\\mathcal{A}</span> and <span class=\"katex--inline\">\\mathcal{B}</span>. Set <span class=\"katex--inline\">\\mathcal{A}</span> contains <span class=\"katex--inline\">12</span> elements, exactly <span class=\"katex--inline\">4</span> of which are also in <span class=\"katex--inline\">\\mathcal{B}</span>. If the union of <span class=\"katex--inline\">\\mathcal{A}</span> and <span class=\"katex--inline\">\\mathcal{B}</span> contains <span class=\"katex--inline\">24</span> elements, find the number of elements in <span class=\"katex--inline\">\\mathcal{B}</span> but not <span class=\"katex--inline\">\\mathcal{A}</span>.</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}~20\\qquad\\textbf{(B)}~12\\qquad\\textbf{(C)}~24\\qquad\\textbf{(D)}~8\\qquad\\textbf{(E)}~0</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2024 Mock AMC 10 - Problem 7", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}