For this question let's think about the negative context clue "not". we're being told there is "not" some measure of sense in what the politician said.

"many", "plenty", "lot of" and "big" don't match this negative construction very well but "much" does work because we can say "there is not much sense".

When something lacks quantity or substance, we often use "not much" to describe it.

So in this case, to properly fill in the blank with the correct negative term, the missing word should be choice d - "much".

The full sentence with the blank filled makes logical sense as "there is not much sense in what that politician has just said."