divisible by 5 AND 3 means divisible by 15
so find the multiples of 15 between 100 and 150. There are only three: 15*7=105, 15*8=120, 15*9=135
between 100 and 150 (not including 100 or 150, I assume ) there are 49 integers, only 3 of them are visible by both 5 and 3, so 46 integers are not divisible by 5 and 3.
the answer is 46.
