how many integers between 100 and 200 , inclusive , can not be evenly divided by 3 nor 5 ?
"the total numbers between 100 and 200 , inclusive , is 101 . 3 * 34 = 102 and 3 * 66 = 198 so the number of multiples of 3 is 33 . 5 * 20 = 100 and 5 * 40 = 200 so the number of multiples of 5 is 21 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 13 = 195 so the number of multiples of 15 is 7 . thus the total number is 101 - 33 - 21 + 7 = 54 . the answer is e ."
subtract(200, add(add(multiply(const_2, const_100), multiply(add(const_3, const_4), const_10)), const_2))