GMAT Sentence Correction (SC) | slim/fat/ chance

Hi,

what if in an SC question, we are asked to choose between

slim vs less chance

or

fat vs greater chance

what will be the right option?

Since chance is a unit of measure(probability) ideally it should be greater or less(depending on the question). But colloquially slim\fat chance is also considered right. What is the GMAT for or against this?

Also
in place of lesser, if we're given an option to choose between
lesser vs lower
lesser vs smaller

greater vs cooler
greater vs higher
greater
...

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