A man two flats for $512456 each. On one he gains 20% while on the other he loses 20%. How much does he gain or lose in the whole transaction? Choose the most appropriate option:
A) 10 %  B) 5 %  C) 12 %  D) 6 %  E) 4 %

Rationale: in such a case there is always a loss loss % = ( 20 / 10 ) ^ 2 = 4 % answer is e
Answer: E