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