"My sister travels a lot, so she saw a lot."
Translation:Моя сестра багато подорожує, отже вона бачила багато.
‘Отже’ is ‘hence, so, as a result’. It marks a logical conclusion from something:
Ти чув про це, отже ти знаєш — You have heard about it, hence you know.
Отже ти чув про це? — So you have heard about it, haven't you? (There is no evident prelude in this sentence, the conclusion is made from the context. It's like ‘I've heard that you heard, hence I'm asking’)
While it seems sometimes similar ‘Отож’ is not a logical conclusion but a closing remark (as a result; in the end; that is why) or a way to say ‘that's the point‘:
Я прочитав цю книгу. Отож думаю, що читати далі. — I have read this book. And now (that's why) I'm thinking what to read next.
Ти чув про це. Отож розкажи й мені! — You've heard about it. So tell me too!
(А): Ця книга була цікавою! (Б): Отож! — (A): This book was interesting! (B): I told you that!