{"status": "success", "data": {"description_md": "Bernardo chooses a three-digit positive integer $N$ and writes both its base-$5$ and base-$6$ representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base-$10$ integers, he adds them to obtain an integer $S$. For example, if $N=749$, Bernardo writes the numbers $10444$ and $3245$, and LeRoy obtains the sum $S=13,689$. For how many choices of $N$ are the two rightmost digits of $S$, in order, the same as those of $2N$?\n\n$\\textbf{(A)}\\ 5\\qquad\\textbf{(B)}\\ 10\\qquad\\textbf{(C)}\\ 15\\qquad\\textbf{(D)}\\ 20\\qquad\\textbf{(E)}\\ 25$\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": "

Bernardo chooses a three-digit positive integer N and writes both its base- 5 and base- 6 representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base- 10 integers, he adds them to obtain an integer S . For example, if N=749 , Bernardo writes the numbers 10444 and 3245 , and LeRoy obtains the sum S=13,689 . For how many choices of N are the two rightmost digits of S , in order, the same as those of 2N ?

\\textbf{(A)}\\ 5\\qquad\\textbf{(B)}\\ 10\\qquad\\textbf{(C)}\\ 15\\qquad\\textbf{(D)}\\ 20\\qquad\\textbf{(E)}\\ 25

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2013 AMC 12B Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12B_p24", "prev": "/problem/13_amc12B_p22"}}