language association

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mberkowitz: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Sun Jul 20, 2008 10:47 am; Location: new york city; Thanked: 1 times

by mberkowitz » Fri Oct 10, 2008 1:35 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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Source: Beat The GMAT — Data Sufficiency | Fri Oct 10, 2008 1:35 pm

kris610: Master | Next Rank: 500 Posts; Posts: 198; Joined: Fri Mar 09, 2007 8:40 pm; Thanked: 7 times

by kris610 » Fri Oct 10, 2008 5:49 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: Master | Next Rank: 500 Posts; Posts: 133; Joined: Sat Dec 29, 2007 2:43 am; Thanked: 12 times

by raju232007 » Sat Oct 11, 2008 1:47 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: Master | Next Rank: 500 Posts; Posts: 198; Joined: Fri Mar 09, 2007 8:40 pm; Thanked: 7 times

by kris610 » Sat Oct 11, 2008 6:26 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: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Thu Nov 13, 2008 10:57 am

by Hate Standardized Tests » Tue Nov 25, 2008 1:49 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: Senior | Next Rank: 100 Posts; Posts: 75; Joined: Wed Aug 27, 2008 7:19 am; Location: Orlando; Thanked: 6 times

by raajan_p » Tue Nov 25, 2008 7:39 pm

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.

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thechamp: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Mon Jul 14, 2008 3:42 pm

by thechamp » Tue Jan 13, 2009 7:51 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?

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sjd00d: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Jan 05, 2009 11:04 pm; Thanked: 2 times

by sjd00d » Tue Jan 13, 2009 9:34 pm

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

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thechamp: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Mon Jul 14, 2008 3:42 pm

by thechamp » Wed Jan 14, 2009 6:46 pm

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.

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mmslf75: Legendary Member; Posts: 503; Joined: Sun Aug 09, 2009 9:53 pmFollowed by: 2 members; Thanked: 31 times

by mmslf75 » Sun Jan 03, 2010 4:36 am

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

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missrochelle: Master | Next Rank: 500 Posts; Posts: 117; Joined: Wed Jun 09, 2010 7:02 am

by missrochelle » Mon Aug 30, 2010 6:01 pm

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.

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