Let \(S\) be the set of all positive integers having at most \(4\) digits and such that each of the digits is \(0\) or

[Vincen]

Let \(S\) be the set of all positive integers having at most \(4\) digits and such that each of the digits is \(0\) or \(1.\) What is the greatest prime factor of the sum of all the numbers in \(S?\)

A. 11
B. 19
C. 37
D. 59
E. 101

Answer: E

Source: Official Guide