AMC 10A/12A 2024 (Problem 18/11)

Number TheoryMedium

There are exactly

K

positive integers

5\le b\le2024

such that the base-

b

integer

2024_b

is divisible by

16

(where

16

is in base ten). What is the sum of the digits of

K

\text{(A)}\;16

\text{(B)}\;17

\text{(C)}\;18

\text{(D)}\;20

\text{(E)}\;21