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Number theory Difficulty 5.0 AIME, harder Find the answer United Kingdom

Given the integers from $1$ to $25$ , Ajibola wants to remove a few and then split those that remain into two groups so that the products of the integers in each group are equal. Ajibola removes the smallest possible number of integers in order to achieve this. What is the sum of the numbers which Ajibola removes?

(A) $75$ (B) $79$ (C) $81$ (D) $83$ (E) $89$

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