If you have an idea approximately when you will hear back from Job "B", I would tell Job "A" (if they contact you first) that you would let them know on a specific date (you will be hearing back from "B"). Let them know you need the time to render a decision. This also gives you the opportunity of getting some "what if" questions out of the way, such as salary, vacation time, insurance, and when these would kick in.

Good luck & hope that "B" comes through for you!

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We're off to never never land