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I was working on a GMAT question:

The least possible value for the mean of the numbers of hours of TV reported for the week is [choices].

It a single choice question. But in the phrase "the least possible value" which word does least modify? possible or value?

If it modifies possible, it means the value that is the most impossible. If it modifies value, it means the least value among all possible ones. Which one does the phrase actually mean?

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Strictly speaking, it doesn't make sense that you could modify the word possible with least (or most).

Something either is possible or it isn't.

Colloquially, people do sometimes make this mistake. But what they are really trying to express is the idea of something that is the least or most probable or likely.

You can say the least number of possibilities—but that's something different.

So, I would assume that least is modifying value in the GMAT question because it doesn't make sense for it to be modifying possible.

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least is a superlative and thus is predicated against a set of things or possibilities.

You are being asked to identify the least (of) {the possible values}.

So it's {least}{possible value}.

BTW, an impossible value is not a "least possible" value. The least possible percentage of oxygen in the air that is needed for us to remain conscious is not zero percent oxygen.

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