Yes, although your use of "a minute" makes it sound possibly sarcastic.
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Anonymous Is "all of" being used in the right context in the following sentence:The news report was so inaccurate. I wasted all of a minute listening to it.I would not say that this is a correct use of "all of a/an". It's not quite right. The implication is "only a certain amount of time" and/or "an inadequate amount of time".