How many positive integers less than or equal to 1000 are multiples of 3 or 4 but not 5?

There are: 1000 / 3==333  + 1000 / 4==250  -  1000 / 12 ==83  -  1000 / 15 ==67  -  1000 / 30==33

 

333  +  250  -  83  -  67  -  33 ==400 such integers