"I live in a city."
Translation:Я живу в городе.
Its quite complicated to explain..cause in english you dont have any situation like this.. I am from Sovakia and for me it makes sense,it is called "origin" - a word from which words alike are derivative(s?) So in slovak origin for город is a word "mesto" (coincidentally it means city-город :D ). So if origin is "v meste" (i dont know how it works in russian but in this are our languages suchlike,so i can partially use it), it means "в городе", you must give it a right form (i think in interwiew they will understand you without any problem,but here on duolingo you better be gramatically correct :)
Actually, in English, this is more complicated.
If you said в город to a Russian, this would start the same reaction as if a Russian said "I live in city" to you.
You would explain that, sometimes, the preposition "in" needs the definite article, but not for all nouns. For example, there are fixed combinations like "in town", "in church", "in school". By adding the definite article, that would change the meaning of the words.
All in all, prepositions need special modifications, be it case endings in Russian or (definite) articles in English to sound natural.
одном means "one" or "single". What you seem to have said is "I live in one city". GoogleTranslate translated your sentence as "I live in the same city", which may be the idiom for в одном город.
I think that you are trying to use одном like the article "a" - but there are no articles in Russian. Without anything else before it, Город already means "a city" or "the city".