1. Count up positive integers that are less than or equals 1000. Including 1000 is for grouping shown below. The count of integers: A=1000
2. Divide the integers into 10-member-groups in a manner like { 1,2,3,4,5, ...,10}, {11,12,13. ...,20} ...{991,992,993 ...1000}. The count of groups: B=A÷10=1000÷10=100
3. Count odd integers in one group that are not the multiple of 5. The count: C=(10÷2)-1=4
4. The total number of positive integers that are less than 1000, odd, and not the multiple of 5: D=BxC=100x4=400
Therefore, the answer is: 400