"Having been" is really just a specific example of the "having + past participle" construction.
Having eaten, we retired to the living room.
Having painted the entire house himself, he needed a bath.
This is a perfectly good usage, but you won't see it often on the GMAT. What you're likely to see is something like this:
The movie having been shown first was not funny.
What does this mean? If we are trying to specify our subject, we should say "the movie that was shown first," or even just "the movie shown first." The only way that "having been" would add value here would be as an adverbial modifier:
The movie, having been shown first, set the tone for the entire festival.
Here we're saying that the movie set the tone *as a result* of its being shown first, so the "having been" modifier makes sense.
Another troublesome usage looks like this:
I talked with a co-worker having a break at the same time that I was.
Here, "having" is used to introduce a noun modifier. In fact, everything after "having" is part of the noun modifier, and that's the problem! We can't say "I was" because there's no verb for "was" to refer back to. This is part of the general trouble the GMAT gets us into with -ing words--being, having, flourishing, doubling, etc. They can be used in many different ways, but readers often treat them incorrectly as verbs, when there are several other ways they can be used. Take a look:
1) Verb: Are you having a good time?
2) Noun: Having an MBA will improve my resume.
3) Noun modifier: The man having a heart attack was on the 7th floor.
4) Adverb: My daughter stayed in her room having a fit.
So there are lots of legitimate ways of using having, and we could create an identical list for other -ing words, but you're right to be nervous. The GMAT tends to use these words in trap answers. Don't cross off an answer just because you see -ing, but exercise caution and think about what purpose the word/phrase is serving. Also, "having" and "being" are probably more common in wrong answers than in right ones, so if you're left guessing, pick something else.
Dmitry Farber | Manhattan GMAT Instructor | New York
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