{"status": "success", "data": {"description_md": "Consider the following $100$ sets of $10$ elements each:\n\n$$\\{1,2,3,\\ldots,10\\},$$\n\n$$\\{11,12,13,\\ldots,20\\},$$\n\n$$\\{21,22,23,\\ldots,30\\},$$\n\n$$\\vdots$$\n\n$$\\{991,992,993,\\ldots,1000\\}$$\n\nHow many of these sets contain exactly two multiples of $7$?\n\n$\\textbf{(A)}\\ 40\\qquad\\textbf{(B)}\\ 42\\qquad\\textbf{(C)}\\ 43\\qquad\\textbf{(D)}\\ 49\\qquad\\textbf{(E)}\\ 50$\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>Consider the following <span class=\"katex--inline\">100</span> sets of <span class=\"katex--inline\">10</span> elements each:</p>&#10;<p><span class=\"katex--display\">\\{1,2,3,\\ldots,10\\},</span></p>&#10;<p><span class=\"katex--display\">\\{11,12,13,\\ldots,20\\},</span></p>&#10;<p><span class=\"katex--display\">\\{21,22,23,\\ldots,30\\},</span></p>&#10;<p><span class=\"katex--display\">\\vdots</span></p>&#10;<p><span class=\"katex--display\">\\{991,992,993,\\ldots,1000\\}</span></p>&#10;<p>How many of these sets contain exactly two multiples of <span class=\"katex--inline\">7</span>?</p>&#10;<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>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2022 AMC 12B Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12B_p07", "prev": "/problem/22_amc12B_p05"}}