{"status": "success", "data": {"description_md": "A finite sequence of three-digit integers has the property that the tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term. For example, such a sequence might begin with the terms $247, 475$, and $756$ and end with the term $824$. Let $S$ be the sum of all the terms in the sequence. What is the largest prime factor that always divides $S$? \n\n$\\mathrm{(A)}\\ 3\\qquad \\mathrm{(B)}\\ 7\\qquad \\mathrm{(C)}\\ 13\\qquad \\mathrm{(D)}\\ 37\\qquad \\mathrm{(E)}\\ 43$", "description_html": "<p>A finite sequence of three-digit integers has the property that the tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term. For example, such a sequence might begin with the terms <span class=\"katex--inline\">247, 475</span>, and <span class=\"katex--inline\">756</span> and end with the term <span class=\"katex--inline\">824</span>. Let <span class=\"katex--inline\">S</span> be the sum of all the terms in the sequence. What is the largest prime factor that always divides <span class=\"katex--inline\">S</span>?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ 3\\qquad \\mathrm{(B)}\\ 7\\qquad \\mathrm{(C)}\\ 13\\qquad \\mathrm{(D)}\\ 37\\qquad \\mathrm{(E)}\\ 43</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2007 AMC 10A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc10A_p23", "prev": "/problem/07_amc10A_p21"}}