Set Theory -

[Mank]

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?

(1) 60 of the members speak only English
(2) 20 of the members do not speak any of the three languages

Thanks

[Rahul@gurome]

Solution:
It is given that each member who speaks German also speaks English.
It means that the set of people who speak German is contained in the set of people who speak English.
Since no member speaks all the three languages, there cannot be any member who speaks German and Spanish because if a member speaks German, he speaks English as well and in such a case he will ultimately be speaking 3 languages.
But there might be some members who speak English and Spanish

First consider statement (1) alone.
It says 60 of the members speak only English.
We need more data to determine the number of members who speak 2 of the 3 languages.
So (1) alone is not sufficient.

Next consider (2) alone.
20 of the members do not speak any of the three languages.
But this does not give us any information about the number of people speaking 2 of the three languages.
Or (2) alone is not sufficient.

Next combine both the statements together and check.
So we have 60 speak English only, 70 speak Spanish only, 20 speak neither of the 3 languages and 200 is the total number of people.
Let the number of people who speak German be x and the number of people who speak both English and Spanish be y .
So x+ y is the number of people who speak 2 of the 3 languages.
Or 60+x+y+70+20 = 200.
Or x+y is 50.

The correct answer is hence (C).

[Mank]

Thanks a lot...