Name: Abdu
Who is asking: Student
Level: Secondary
Question:
How many positive integers less than 1,001 are divisible by either 2 or 5 or both?
Hi Abdu,
Try a smaller problem.
How many positive integers less than 11 are divisible by either 2 or 5 or both?
The positive integers less than 11 are
1,2,3,4,5,6,7,8,9,10
Half of them are divisible by 2
2,4,6,8,10
One fifth of them are divisible by 5
5,10
These lists both include 10 which is divisible by 2 and 5. When counting the number of integers in the two lists combined we can only count the 10 once. Thus the number of positive integers less than 11 are divisible by either 2 or 5 or both is 5 + 2  1 = 6.
Now try your problem with 1,001 rather than 11.
When you are done with that how about this problem:
How many positive integers less than 1,001 are divisible by either 2 or 5 but not both?
Penny
