On assignment abroad vs. on travel abroad vs. on business abroad

Hi!

I read the following question in a TOEIC book:



"15. Ms. Brown answers the phone and replies to my e-mails when I am on ______ abroad.



(A) appointment

(B) assignment

(C) average

(D) travel



(Answer: B)" ((p. 153, by Renald Rilcy, Achieve TOEIC))



Question #1

Do you agree with the above that B is ONLY correct? What about D? Don't you say "I am on travel abroad"?



Question #2

If there were the other choice ‘(E) business’, wouldn’t it be correct, too? Don’t you say “I am on business abroad”?



Thanks in advance.