Find the number of all the 3-digit numbers which are divisible by 2 but not divisible by 10.
I am totally confused here-- I was trying to sort out all numbers divisible by 2, and then cancel the ones divisible by 10. However there must be an easier way.
That's exactly how to do it but I'm not sure why you are being troubled by it.
How many even $3$ digit numbers are there? Is that a hard question? The first $3$ digit number is $100$ and the last is $999$. The first even one is $100$ and the last even one is $998$. Every other number is even. How many total are there?
How many $3$ digit numbers are divisible by $10$? Same reasoning. The first $3$ digit number is $100$ and the last is $999$ and the first divisible by $10$ is $100$ and the last is $990$. Every 10th number is divisible by $10$. How many total are there.
And every number divisible by $10$ is even. So just subtract the second answer from the first.