What is the largest five digit number exactly divisible by 88?

Correct option is D

To check the divisibility of 88, the number should be divisible by 8 and 11 both.
Divisibility rule of 11: the given number can only be completely divided by 11 if the difference of the sum of digits at odd position and sum of digits at even position in a number is 0 or 11.
Divisibility rule of 8: If the last three digits of a given number are zeros or if the number formed by the last three digits is divisible by 8, then such a number is divisible by 8. 
By checking these divisibilty rules,
99968 is the correct answer.