Official solution
According to this question, any number between 1 to 100 should be divisible by 2 or 5 but not by 2\[ \times \]5 = 10.
Possible numbers between 1 to 100 divisible by 2 are 2, 4, 6, .... , 100
This is an A.P where first term = 2, last term = 100 and total terms = 50.
\[ \therefore \] Sum of the numbers divisible by 2
= \[{{50} \over 2}\left[ {2 + 100} \right]\]
= 25\[ \times \]102
= 2550
Possible numbers between 1 to 100 divisible by 5 are 5, 10, 15, .... , 100
\[ \therefore \] Sum of the numbers divisible by 5
= \[{{20} \over 2}\left[ {5 + 100} \right]\]
= 10\[ \times \]105
= 1050
And possible numbers between 1 to 100 divisible by 10 are 10, 20, 30, .... , 100
\[ \therefore \] Sum of the numbers divisible by 10
= \[{{10} \over 2}\left[ {10 + 100} \right]\]
= 5\[ \times \]110
= 550
\[ \therefore \] Required sum = 2550 + 1050 - 550 = 3050