How many even integers 'n', where, $$ 100 \leq n \leq 200 $$, are divisible neither by 7 nor by 9?

Total even integers between 100 and 200 = $$\frac{200-100}{2}\ \ +\ \ 1\ =\ 51$$
Even integers divisible by 7 = Number of multiple of 14.
There are 7 integers which are of form 14k(112,126,...) between 100-200
Even integers divisible by 9 = Number of multiple of 18.
There are 6 integers which are of form 18k(108,126,...) between 100-200
Even integers divisible by both 7 and 9 = No. of multiple of LCM(14,18) = No. of multiple of 126k = 1
So, Required answer = 51-(7+6)+1 = 39.
Option C is the answer.