If 30 is divided by half and 10 is added to the result, then what is f

The ambiguity is because of the phrasing 'divided by half'. The GMAT will never use phrasing like this, because it's not completely clear (as your question demonstrates)!

If a problem says 'divided by 1/2' or 'divided by one half', you should do what Afc0892 suggested and divide the number by the fraction 1/2.

If a problem says 'divided in half', you should divide the number by 2.

But 'divided by half' isn't really correct grammar, and it's not something you'd see on the GMAT. In general, the GMAT rarely or never will attempt to trick you with ambiguous language - it actually tries to be extremely clear. A problem that wasn't clear would quickly be weeded out in the experimental stages, because a lot of high-scorers would miss it by simply having a different (valid) interpretation of it. The GMAT also isn't really trying to play dirty tricks on you; it wants to give you problems that can be solved by reasoning through them, not just by knowing a single language trick.

That said, there are a couple of pieces of wording that people very often misinterpret (even though they do have one clear correct interpretation) - here are a few of those: https://www.manhattanprep.com/gre/blog/ ... cks-traps/ (this is a GRE article, but you'll see very similar things on the GMAT!)