What is the sum of 2-digit numbers that are divisible by either 5 or 7?

Number of two-digit numbers divisible by 5 = 10, 15, 20,......95

Number of two-digit numbers divisible by 7 = 14, 21, 28,.....98

Number of two-digit numbers divisible by 35 = 35, 70

Using $$S_{n}=\ \dfrac{n}{2}\left(2a+\left(n-1\right)d\right)$$

Sum of the numbers divisible by 5 $$=\dfrac{18}{2}\left(10+95\right)=9\times105=945$$

Sum of the numbers divisible by 7 $$=\dfrac{13}{2}\left(14+98\right)=13\times56=728$$

We need to subtract the numbers divisible by both 5 and 7 $$=35+70=105$$. 

So total $$=945+728-105=1568$$