In the number $6 a 78 b$, $a$ is the digit of the thousands place and $b$ is the digit of the units place. If $6 a 78 b$ is divisible by 45, then the value of $a+b$ is:
(a) 5
(b) 6
(c) 7
(d) 8
(e) 9
The number is divisible by 5 and 9.

Every number divisible by 5 ends in 0 or 5. Thus, $b=0$ or $b=5$.

Every number divisible by 9 has the sum of its digits as a multiple of 9.

Therefore, we have that $6+a+7+8+0=21+a$ or $6+a+7+8+5=26+a$ are multiples of 9. Hence, $a=6$ or $a=1$, respectively. From this, we get: $a+b=6+0=6 \quad$ or $a+b=1+5=6$.