{"status": "success", "data": {"description_md": "Consider the following $100$ sets of $10$ elements each:\n$$\\begin{align*}\n&\\{1,2,3,\\ldots,10\\}, \\\\\n&\\{11,12,13,\\ldots,20\\},\\\\\n&\\{21,22,23,\\ldots,30\\},\\\\\n&\\vdots\\\\\n&\\{991,992,993,\\ldots,1000\\}.\n\\end{align*}$$\nHow many of these sets contain exactly two multiples of $7$?\n\n$\\textbf{(A)}\\ 40\\qquad\\textbf{(B)}\\ 42\\qquad\\textbf{(C)}\\ 43\\qquad\\textbf{(D)}\\ 49\\qquad\\textbf{(E)}\\ 50$", "description_html": "<p>Consider the following  <span class=\"katex--inline\">100</span>  sets of  <span class=\"katex--inline\">10</span>  elements each:<br/>\n <span class=\"katex--display\">\\begin{align*}\n&amp;\\{1,2,3,\\ldots,10\\}, \\\\\n&amp;\\{11,12,13,\\ldots,20\\},\\\\\n&amp;\\{21,22,23,\\ldots,30\\},\\\\\n&amp;\\vdots\\\\\n&amp;\\{991,992,993,\\ldots,1000\\}.\n\\end{align*}</span> <br/>\nHow many of these sets contain exactly two multiples of  <span class=\"katex--inline\">7</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 40\\qquad\\textbf{(B)}\\ 42\\qquad\\textbf{(C)}\\ 43\\qquad\\textbf{(D)}\\ 49\\qquad\\textbf{(E)}\\ 50</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": "2022 AMC 10B Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10B_p09", "prev": "/problem/22_amc10B_p07"}}