Define A = The sum of digits of the number 7^100 and B = The sum of the digits of A. What is the sum of the digits of B?  Select the correct option:  A) 7  B) 16  C) 10  D) 11  E) can not be determined

Rationale: following approach will take you only couple of sec . \ ( 7 ^ { 100 } = ( 7 ^ { 50 } ) ^ 2 \ ) the sum of digits ( digital root ) of a perfect square can only be 1 , 4 , 7 or 9 . for example \ ( 7 ^ 2 = 49 \ ) = > dr = 4 + 9 = 13 = > 1 + 3 = 4 and etc . checking available options . answer a .
Answer: A