GMATPrep Question - Need expert help

[voodoo_child]

Of the 200 members of certain association, each member who speaks german also speaks english. and 70 members speak only spanish. no member speaks all 3 languages. how many of the members speaks 2 of 3 languages ?
1. 60 members speaks only english
2. 20 members do not speak any of the three languages

OA = C
I was able to compute the solution :
(u = Union and n = Intersection)
E u G u S = E + G + S - (E n S) - (S n E) - (S n G) + (E n G n S) + {Who speak 0 languages}
E n S = G
(E n G n S) = 0
{Who speak 0 languages} = 20
E= 60
S=70

Therefore, people speaking two languages = 200-150 = 50


My question is that if every member who speaks English also speaks German (or vice-versa), they cannot speak Spanish because members who speak all 3 languages = 0. For instance, if in a room, I have 100 people of which 50 speak English and Spanish, and 0 who speak all three languages. It means that I will have only 50 people who speak two languages. I cannot have anyone from (English / German) group speak Spanish because he will end up speaking three languages. Any thoughts?

Thanks

[Mike@Magoosh]

My question is that if every member who speaks English also speaks German (or vice-versa), they cannot speak Spanish because members who speak all 3 languages = 0. For instance, if in a room, I have 100 people of which 50 speak English and Spanish, and 0 who speak all three languages. It means that I will have only 50 people who speak two languages. I cannot have anyone from (English / German) group speak Spanish because he will end up speaking three languages. Any thoughts?

First of all, be very careful . . saying

a) every member who speaks English also speaks German

vs.

b) every member who speaks German also speaks English

are two wildly different things. If only (a) is true, it would be impossible to have 50 people who spoke Spanish and English, under the condition that no one speaks all three, because all those people who knew English would thereby have to know German. Under this condition, you could have English & German speakers, Spanish & German speakers, just German speakers, just Spanish speakers, and folks who don't speak any of the three.

If only (b) is true, you can have 50 people who spoke Spanish and English, but there could also be a number of German & English speakers, so the number of folks who speak two languages could be more than 50. Under this condition, you could have Spanish & English, German & English, just English, just Spanish, and folks who don't speak any of the three.

If (a) and (b) are simultaneously true, and no one speaks all three, then the only allowable categories are (1) English & German speakers, (2) Spanish speakers (3) folks who do not speak any of the three languages. Again, it would be impossible to have any who spoke English & Spanish or German & Spanish.

BTW, in your paragraph, when you said "of which 50 speak English and Spanish", did you mean "of which 50 speak English and German"? That would have made most of what you said correct.

Do keep in mind, though, that (a) alone vs (b) alone vs. (a) + (b) constitute three very different conditions.

Does all this make sense? Let me know if I can answer any further questions.

Mike