2013 AMC 10A Problems/Problem 21

Revision as of 20:25, 7 February 2013 by Countingkg (talk | contribs) (Created page with "==Problem== A group of <math>12</math> pirates agree to divide a treasure chest of gold coins among themselves as follows. The <math>k^{\text{th}}</math> pirate to take a share...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

A group of $12$ pirates agree to divide a treasure chest of gold coins among themselves as follows. The $k^{\text{th}}$ pirate to take a share takes $\frac{k}{12}$ of the coins that remain in the chest. The number of coins initially in the chest is the smallest number for which this arrangement will allow each pirate to receive a positive whole number of coins. How many coins does the $12^{\text{th}}$ pirate receive?


$\textbf{(A)}\ 720\qquad\textbf{(B)}\ 1296\qquad\textbf{(C)}\ 1728\qquad\textbf{(D)}\ 1925\qquad\textbf{(E)}\ 3850$

Solution