If W is the set of all the integers between 69 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
Choose the correct choice from the following answers.
A) 20 B) 32 C) 33 D) 34 E) 35

Rationale: "multiples of 2 from 69 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 68 = [ 99 / 2 ] - [ 68 / 2 ] = 49 - 34 = 15 multiples of 3 from 69 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 68 = [ 99 / 3 ] - [ 68 / 3 ] = 33 - 23 = 10 multiples of 2 and 3 bothi . e . 6 from 69 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 68 = [ 99 / 6 ] - [ 68 / 6 ] = 16 - 11 = 5 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 15 + 10 - 5 = 20 answer option a"
Answer: A