If \(a\) and \(b\) are positive integers, is \(10^a + b\) divisible by \(3?\)

[VJesus12]

If \(a\) and \(b\) are positive integers, is \(10^a + b\) divisible by \(3?\)

(1) \(\dfrac{b}2\) is an odd integer.

(2) The remainder of \(\dfrac{b}{10}\) is \(b.\)

Answer: E

Source: GMAT Club Tests