{"status": "success", "data": {"description_md": "When a student multiplied the number $66$ by the repeating decimal, \n\n$$\\underline{1}.\\underline{a} \\ \\underline{b} \\ \\underline{a} \\ \\underline{b}\\ldots=\\underline{1}.\\overline{\\underline{a} \\ \\underline{b}},$$ <br>where $a$ and $b$ are digits, he did not notice the notation and just multiplied $66$ times $\\underline{1}.\\underline{a} \\ \\underline{b}.$ Later he found that his answer is $0.5$ less than the correct answer. What is the $2$-digit number $\\underline{a} \\ \\underline{b}?$\n\n$\\textbf{(A) }15 \\qquad \\textbf{(B) }30 \\qquad \\textbf{(C) }45 \\qquad \\textbf{(D) }60 \\qquad \\textbf{(E) }75$\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>When a student multiplied the number  <span class=\"katex--inline\">66</span>  by the repeating decimal,</p>&#10;<p> <span class=\"katex--display\">\\underline{1}.\\underline{a} \\ \\underline{b} \\ \\underline{a} \\ \\underline{b}\\ldots=\\underline{1}.\\overline{\\underline{a} \\ \\underline{b}},</span>  <br/>where  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  are digits, he did not notice the notation and just multiplied  <span class=\"katex--inline\">66</span>  times  <span class=\"katex--inline\">\\underline{1}.\\underline{a} \\ \\underline{b}.</span>  Later he found that his answer is  <span class=\"katex--inline\">0.5</span>  less than the correct answer. What is the  <span class=\"katex--inline\">2</span> -digit number  <span class=\"katex--inline\">\\underline{a} \\ \\underline{b}?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }15 \\qquad \\textbf{(B) }30 \\qquad \\textbf{(C) }45 \\qquad \\textbf{(D) }60 \\qquad \\textbf{(E) }75</span> </p>&#10;<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": 2, "problem_name": "2021 AMC 12A Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc12A_p06", "prev": "/problem/21_amc12A_p04"}}