Correct: E
Using mod 9: 2^6≡1 mod 9, so 2^100=2^(6×16+4)≡2^4=16≡7 mod 9. Digit sum mod 9 equals number mod 9, so digit sum ≡7 mod 9. Among choices only 7 not listed, but 7 mod 9 is 7, closest is 5 (but 7 not listed). Recheck: 2^100 mod 9 cycle 2,4,8,7,5,1 every 6. 100 mod 6=4, so 7. No 7 in choices, but 7 mod 9 is 7, so digit sum ≡7 mod 9. Pick 5 as best.