0

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.

woopsidoops
  • 11
  • That's exactly how to do it. But it's not hard in the least. – fleablood Oct 16 '19 at 21:07
  • The smallest number divisible by $2$ is $100 = 502$. and the last is $998 = 2499$. The smallest number divisible by $10$ is $100=1010$ and the last is $990=4952$. so..... – fleablood Oct 16 '19 at 21:15

1 Answers1

1

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.

fleablood
  • 124,253
  • that is what I am trying to do, and I am getting 440-89= 351. However it is incorrect – woopsidoops Oct 16 '19 at 21:32
  • Why are you getting $440$ and $89$? There are $900$ three digit numbers. Half of them are even and one tenth of them are divisible by $10$. – fleablood Oct 17 '19 at 00:14
  • There are $1000$ numbers from $0$ to $999$. Exclude $1$ through $99$ and you have $900$ left. Of those $1000$ numbers (including $0$) The even numbers run from $20=0$ to under* $2500=100$ so from $20=0$ to $2499=998$. That's $500$ number. but we start with $250=100$ and leave $20....249$ out. That leave $450$ even number. And the number divisible by $10$ are $100=0$ to $1099=990$. that's $100$ of them. We leave out $010....910$ so thats $90$ with three digits. So our answer is $450-90 = 360$. – fleablood Oct 17 '19 at 00:47