They lived on the outskirts of the city.
Words that are similar in meaning to each other are known as 'synonyms', and words that are quite unlike each other in terms of meaning are known as 'antonyms'. In this case, we have to find the word which is NOT a synonym of the phrase 'on the outskirts'. Options A), B) and C) are very closely related to not just each other, but also the phrase 'on the outskirts' itself, and are hence ruled out. This leaves us with Option D) - 'In the middle of', which is the correct answer. 'In the middle of' itself refers to a central location; and thus we see how the word changes the meaning of the original sentence and is thus wrong.