Inclusive vs exclusive range

GRE Quant Problem Solving
1

Hi all, my test is coming up and while I know how to solve for this type of question, I find myself not sure about the specifics. I know when it says inclusive we do N-M+1 for any number m-n. However, what if a question says:

  1. “what is the sum of multiples of 4 between 12-108” I take the (med)( total of amount numbers) do we just do (108-12/4) +1 or just (108-12/4)? I’ve seen this question as being inclusive… I can’t find many questions like it for reference but in my notes I don’t have inclusive or exclusive written. would they ever give me this and say exclusive or will it always be inclusive?

  2. same issue with: what is the number of odd numbers between 4-199? do we just do (199-5/2)+1

  3. for sum of consecutive integers I have been doing n(n+1)/2

2

To do the sum of consecutive numbers, use （a_1+a_n)n/2 , where n is the total amount of the numbers in sequence; a_1 is the first number, a_n is the last number
in 99% cases, it is inclusive

to find the total odd/even numbers between[4,199], you could use (199-4+1)/2 as well

3

First of all, If they want you to take 12 and 108 into account, they’ll explicitly mention it. The question will be “What is the sum of multiples of four between 12 and 108 both inclusive?”. Secondly, you do need to add 1. If they don’t mention the word inclusive, you need to exclude the extreme terms.

4

yes you need to add 1