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mberkowitz · Fri Oct 10, 2008 2:35 pm

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

is the best way to solve using venn diagram or equation?

thanks.

oa is c

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kris610 · Fri Oct 10, 2008 6:49 pm

Interesting question. I'm not sure if a venn diagram would be easier, albeit you can use variables.

G = German Speakers

X = Only English

S = Spanish only = 70 (Given)

Y = Spanish and English

Now, G + X + Y + S + Neither = 200

G + Y is what you want -- G will give you overlap between German and English speakers and Y gives you Spanish and English. There can be no German and Spanish as there is no one who speaks all the 3.

Now A tells you X = 60. Not sufficient

B tells you 'Neither' but you don't know X.

Put them together you get G + Y.

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raju232007 · Sat Oct 11, 2008 2:47 am

I think Venn diagram is the best method to be applied for 3 set problems...
I came across the explanation for this problem somewhere in this forum...But I have a few doubts..

How is P(German & Spanish) & P(German)=0

Can someone explain this question using a Venn Diagram approach?

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kris610 · Sat Oct 11, 2008 7:26 am

Anyone who speaks German speaks English and nobody speaks all the three.

So, anyone who speaks German doesn't speak Spanish.

Hence intersection of German and Spanish will be 0.

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Hate Standardized Tests · Tue Nov 25, 2008 2:49 pm

can someone walk through how each statement is sufficient or not sufficient?

And if I was to solve this, can't I just do the following?

If there are 200 members in the association and 20 are neighter, then we know that 180 speaks at least ONE of te three languages.

We can then subtract 60 who speak only English and 70 who speak only Spanish from 180 and get 50 who speak at least TWO of the languages?

THx in advance for your thoughts.

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raajan_p · Tue Nov 25, 2008 8:39 pm

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thechamp · Tue Jan 13, 2009 8:51 pm

In this example, is the info provided in 2) not redundant? We have a total of 200 people. It is not hard and fast that we have to have some people who speak neither of the three languages, right?
Tot. 200
LESS
Spanish only 70
English only 60
German only NA
All 3 lang. 0
-----------------------
Tot.for 2 Lang. 70

Why do we need 2) at all? Am I missing something?