Official solution
\[ \because \] 91 = 13 \[ \times \] 7
So the required numbers are either divisible by
7 or 13.
SA
= sum of numbers between 100 and 200 which are divisible by 7.
\[ \Rightarrow \] SA = 105 + 112 + ..... + 196
SA = \[{{14} \over 2}\left[ {105 + 196} \right]\] = 2107
SB
= Sum of numbers between 100 and 200 which are divisible by 13.
SB = 104 + 117 + ....... + 195
SB = \[{8 \over 2}\left[ {104 + 195} \right]\] = 1196
SC = Sum of numbers between 100 and 200 which are divisible by 7 and 13.
SC = 182
Sum of numbers divisible by
7 or 13 = Sum of no. divisible by
7 + sum of the no. divisible by 13 -- Sum of the
numbers divisible by 7 and 13
= 2107 + 1196 - 182
= 3121