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Article:

Successful Job Transitions, III: Starting a New Job

Get permission to ask questions

Avoid the awkwardness of asking one too many questions by saying up front that you understand a lot of questions can be trying. If you sense that is becoming the case, simply ask: "I sense that another question will annoy you, right?"

Most people will say, "No" which is your cue to go ahead -- ask another question! If they say, "Yes" innocently ask who you might talk to get your other questions answered.