The problem
How many positive integers from 100-999 are divisible by 7.
I want to confirm if my approach is the best approach in finding the answer.
The smallest integer that can be divided by 7 is
105+112+119+126+133+140+147+154+161+168+175+182+18 9+196
there are 14 numbers divisible by 7 from the range 100-200 so from 100-900 would be 9*14 = 126 numbers there is still 99 numbers unaccounted for
but the answer in my textbook states 128 numbers in total. How is that possible?
Thank You guys for the reply, I was doing it the long way =/.
but one thing can I do [999-100]/7 I still got the same answer if I rounded down
There are 1 more thing that is confusing me.
same problem as before but finding the integers that are divisible by 3 or 4
I found all the numbers divisble by 3 which is 300 and divisble by 4 which is 225, but the answer is 450.
and when they ask is not divisible by either 3 or 4, do I count the numbers that are divisible by 1-9 excluding 3 and 4? but the answer is 450 as well.
and when they ask is divisible by 3 and not 4, how would I approach this
Im really sorry for all these questions but as some of you may experience, my professor is not the very best at teaching and every lesson, I find myself reading the textbook and have a puzzled look. I also have a final coming up so any help would be appreciated.
Thank You again in advance.
Use the Inclusion-Exclusion Principle.
Meaning find the number divisible by 3, find the number divisible by 5, and then subtract the number divisible by 3 AND 5, i.e. 15.