If synonyms are counted once, how many daily-used words there are in the English Language?

English is famous for its synonyms. As a English learner, I am thoroughly conquered by that. When preparing for an English exam which requires me to remembering 6000 words , I find that there are so many words with almost the same meaning. for xample ,garbage / junk / rubbish /trash ,baggage / luggage , curious / peculiar / weird / odd / eccentric / bizarre ,etc . If we count each group as a words ,how many everyday used words there are in English? ( If counted like this, there may be only 1500~2000 words in the 6000 vacabulary for my exam. But it is sufficient to read original English articles with few words obstacles. )