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Count If Value In Range 1 Greater Than Value In Range 2

I have two ranges that show parts of a question to be answered and those parts already answered (aa6:aa55 and ab6:ab55). I would like to count those elements where the value in column AA is greater than the corresponding value in column AB, showing questions with parts still to be answered. Currently I have a formula comparing the two and am counting the occurrences of true or false. This seems to be overkill and I am sure that there is an array formula that can do the same thing more efficiently, unfortunately I cannot figure it out.

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