Question 8

Given that $a$ and $b$ are natural numbers that satisfy $a = 2 \times b$ and $b$ is divisible by $5$.

How many of the following four statements are true based on the information above?

$(1)$ $a$ is an even number

$(2)$ The unit digit of $a$ is always $0$

$(3)$ $a + b$ is divisible by $5$

$(4)$ $3a + 2b$ is an odd number