What's the digit "a" in this number? a and b are digits in a four-digit natural number 7a5b. If 7a5b is divisible by 18, how many different possible values can "a" have?

Since it is divisible by $18$, $7a5b$ must be divisible by $9$ and $2$.  Using divisibility rules, 
$$b \text{ must be even}$$ 
$$7+a+5+b \text{ must be divisible by 9}$$
So if $b$ is even it is of the form $2k$ for some integer $k$.  So then $7+a+5+2k=9m$.   Now use cases for $b$.  For example, when $b=2$, 
$$7+a+5+2=14+a$$
So $a$ must be 4 since $14+4=18=9\cdot2$.
Now, what about $a=4,6,8,10$?  You can try them on your own.
