AMC 12 2005a Problem 19

A faulty car odometer proceeds from digit $3$ to digit $5$, always skipping the digit $4$, regardless of position. For example, after traveling one mile the odometer changed from $000039$ to $000050$. If the odometer now reads $002005$, how many miles has the car actually traveled?

$\textbf{(A) } 1404 \textbf{(B) } 1462 \textbf{(C) } 1604 \textbf{(D) } 1605 \textbf{(E) } 1804$