my ans is A...only 1) is enough to ans the q's
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 members speak two of the three languages?
1) 60 of the members speak only English
2) 20 of the members do not speak any of the 3 languages
Use the Venn formula:
AuBuC = Only A + Only B + Only C + (A&B + A&C + B&C) - 2(A&B&C)
The question asks for the value (A&B + A&C + B&C)
200 - (none of the languages) = 70 + 0 + English + (German&English + German&Spanish + Spanish&English) - 2(0)
So, 200 - (none of the languages) = 70 + English + (German&English + German&Spanish + Spanish&English)
Now if we only knew the number of persons that ONLY spoke english and those who didn't speak any of the languages then we could answer. You need both 1) and 2) to get this info.
EG + Eonly + ES + 70 + None = 200
Or, EG + ES = 130 - (Eonly + None)
i. Eonly = 60
INSUFF as we don't know "None"
ii. None = 20
INSUFF as we don't know Eonly
EG + ES = 130 - (60+20) = 50
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