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IPMAT Indore 2023 - QA (SA) Q8 Explanation
December 6, 2024
From 5! onwards, every term will be a have multiple of 15.
Reason: Each term will have a minimum of one 3 and one 5 as its factors.
Thus, 15 will be a factor of every term from 5! onwards, thus we will not get any remainder (or zero remainder) when they are divided by 15.
∴ Thus, only the sum of first 4 terms of the expression will give the final remainder.
Adding first 4 terms, we get
= 1! + 2! +3! +4! = 1 + 2+ 6 +24 = 33.
So, when 33 is divided by 15, the reminder obtained will be 3. Ans