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.

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?

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.

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.

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?

Yes, this is exactly how I approached this sum as well.

Hope its correct.

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?

raajan_p wrote:

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?

Yes, this is exactly how I approached this sum as well.

Hope its correct.

Yes, it is the right way to do it given the problem. If the problem didn't state that all germans speak english and didn't specify that no one speaks all 3 than it would change everything.

My opinion, easiest way to solve this is venn diagram.

1. Draw a circle for english
2. Draw german inside of english
3. Draw a spanish that overlaps with english but does not touch German (coz we've told that no one speaks all 3)

Now, shade the portion of the circle where data is given and you'll find that the inner german circle and the english to spanish overlap is the only remaining and since both represent 2 languages, that's your answer.

200 - 60 - 70 - 20 = 50

I am sorry but I still haven't understood why we need #2 which states "No one speaks all three languages". In that case the answer would be 70.

thechamp wrote:I am sorry but I still haven't understood why we need #2 which states "No one speaks all three languages". In that case the answer would be 70.

Consider,
8 aspects in all

none language
E only
G only
S only
ES
EG
GS
EGS

And fill,

Note here SG = 0 , as no speaks all languages..
And subtract the SUM from 200

Answer C

Hope this helps

mmslf75 wrote:

thechamp wrote:I am sorry but I still haven't understood why we need #2 which states "No one speaks all three languages". In that case the answer would be 70.

Consider,
8 aspects in all

none language
E only
G only
S only
ES
EG
GS
EGS

And fill,

Note here SG = 0 , as no speaks all languages..
And subtract the SUM from 200

Answer C

Hope this helps

this explanation was a life saver! i think i'll use the listing method more often so much easier when they give you a total and there are a bunch of compenents...so many that a chart wont do it justice.