Of the 200 members of a certain association, each member who speaks German also speaks English, and 70 of the members speak only Spanish. If no member speaks all three languages, how many of the members speak two of the 3 languages?
Venn diagram is the best way to solve this question. So here are the tips for it:
From the stem if 70 speaks only Spanish and no student speaks three languages, max # of students who speaks two languages is 200-70=130.
Note that if ALL who speaks German speaks English means that no student speaks ONLY German, but not vise-versa, meaning that there may be the students who speak English only.
Also note there may be the students among 200 who speak no English, German or Spanish.
So, basically we need to determine the number of students who speak only English and the number of students who doesn't speak any languages and subtract this from 130 (as we already subtracted only Spanish and know that there are no only German).
(1) 60 speaks ONLY English, max # of students who speaks two languages is 200-70-60=70. But we don't know how this 70 is split: don't know how many don't speak any of the languages. Not sufficient.
(2) 20 don't speak any of the language. Clearly insufficient.
(1)+(2) 70-20(any languages)=50 (# of students who speak two languages).
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