{"status": "success", "data": {"description_md": "Consider the following $100$ sets of $10$ elements each:\n\n$$\n\\begin{aligned}\n&\\{11,12,13,...,20\\}\\\\\n&\\{21,22,23,...,30\\}\\\\\n&\\vdots\\\\\n&\\{991,992,993,...,1000\\}.\n\\end{aligned}\n$$\n\nHow many of these sets contain exactly two multiples of $7$?\n\n$\\textbf{(A)}\\ 40\\qquad\\textbf{(B)}\\ 42\\qquad\\textbf{(C)}\\ 43\\qquad\\textbf{(D)}\\ 49\\qquad\\textbf{(E)}\\ 50$", "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\">&#10;\\begin{aligned}&#10;&amp;\\{11,12,13,...,20\\}\\\\&#10;&amp;\\{21,22,23,...,30\\}\\\\&#10;&amp;\\vdots\\\\&#10;&amp;\\{991,992,993,...,1000\\}.&#10;\\end{aligned}&#10;</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;", "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"}}