Can a shorter IQ test be devised that provides a more approximate measure of IQ? Disclaimer: I am not a student of psychology, just an interested guy - but here goes anyway...

IQ tests usually contain dozens of questions and take considerable time. I think this is because such tests have to differentiate between a great diversity of intelligence levels.

Now, I wonder if a test could be devised such that you answer a fraction of a number of questions associated with the usual IQ test, and the test result is yes, your IQ is between 100 and 120, or no, your IQ is outside of this range.

This could be useful, if someone is intelligent, but has problems with attention, or in some kind of survey setting, where people don't have a lot of time.
Yes, what you say is entirely possible. If precision is not as much of an issue, it is possible to devise a test (of anything, not just a test of IQ) which would return a score of, say, 115 plus or minus 10 points. It could also return a yes/no answer to a question such as "is the score inside the range 100..120.

One person who explore such question is Laurencelle, 2015, Le différentiel de sélection multiple [in french] The Quantitative Methods for Psychology, 11(3), 174-188. doi http://dx.doi.org/10.20982/tqmp.11.3.p174