Of the 200 members of a certain association, each member who

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Re: DS: Sets [#permalink]

25 Jan 2008, 10:15

X= 50

I think that it is the only way to solve this problem.

Do you think there is another way to solve it?

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Data Suff problem on Sets [#permalink]

09 Jun 2009, 20:55

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 languages.

Answer: C.

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Re: Data Suff problem on Sets [#permalink]

10 Jun 2009, 00:43

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The fastest way (at least for me) to solve this is to draw the three circle Venn diagram. Lets see what is given.

Total Members (t) = 200
German Speaking Only (g) = 0 (as everyone who speaks German also speaks English)
Spanish Speaking Only (s) = 70
English only (e) = not given
English and German (eg) = not given
English and Spanish (es) = not given
German and Spanish (gs) = not given
English, German and Spanish (egs) = not given
Not English, German and Spanish (Notegs) = not given
Put all of these in the venn diagram.
Asking eg+es+gs=?

Lets look at statement 1.
English only (e) = 60 Not Sufficient.

Lets look at statement 2
Not English, German and Spanish (Notegs) = 20 Not sufficient

Both of them together Sufficient:

200-0-70-60-20-0=50

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Venn.jpg [ 22.1 KiB | Viewed 1473 times ]

Last edited by nookway on 10 Jun 2009, 14:26, edited 1 time in total.

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Re: Data Suff problem on Sets [#permalink]

10 Jun 2009, 06:59

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the following are the only formations that result from the problem statement.

200 = E' + E'S' + E'G' + S' + No of ppl who donot speak any language.

E' represents only english
E'S' represnts only english and spanish accoringly..

combing one and two,

200 = 60 + e's' + e'g' + 70 + 20..

the value of e's' + e'g' means the no of people studying speaking 2 languages.

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Re: GMATPrep: Of the 200 members of a certain assocation... [#permalink]

06 May 2011, 12:43

it is 200 - ( 20 + 60 + 70) = 50

hence C
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Re: GMATPrep: Of the 200 members of a certain assocation... [#permalink]

07 May 2011, 18:00

I've done the following, could someone please opine about the Venn Diagram and the solution. I've a feel I'm doing something wrong.

E - G - both = 60

Only E + Only S + Both = 180 (because G is inside E)

Only E = 60, only S = 70

=> both S & E = 180 - 130 = 50

=> E = 110

=> 110 - 50 - G = 60

=> G = 0

So people speaking 2 languages = 50

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Venn.png [ 9.8 KiB | Viewed 340 times ]

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Re: GMATPrep: Of the 200 members of a certain assocation... [#permalink]

08 May 2011, 13:42

Used venn diagram for this.

1. Not sufficient

as we dont know whether there are any people that speak neither G,E and S.

2. Not Sufficient

as we dont know anything about the english only.

together , we know the english only and neither count.
sufficient to find the people who can talk 2 languages.

Answer is C.

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Re: Data Suff problem on Sets [#permalink]

23 Nov 2011, 16:37

nookway wrote:

The fastest way (at least for me) to solve this is to draw the three circle Venn diagram. Lets see what is given.

Total Members (t) = 200
German Speaking Only (g) = 0 (as everyone who speaks German also speaks English)
Spanish Speaking Only (s) = 70
English only (e) = not given
English and German (eg) = not given
English and Spanish (es) = not given
German and Spanish (gs) = not given ---> 0
English, German and Spanish (egs) = not given ---> 0
Not English, German and Spanish (Notegs) = not given
Put all of these in the venn diagram.
Asking eg+es+gs=?

Lets look at statement 1.
English only (e) = 60 Not Sufficient.

Lets look at statement 2
Not English, German and Spanish (Notegs) = 20 Not sufficient

Both of them together Sufficient:

200-0-70-60-20-0=50

Is my logic Correct? Since everyone who speaks German must speak English and no one speaks 3 languages that means that:

0 --->ppl who speak German and spanish

0---> ppl who speak only German

0 ----> ppl who speak all three languages.

Therefore the result is the number of people who Speak (German and English) and (Spanish and English) since people who speak all languages is 0.

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Re: Of the 200 members of a certain association, each member who [#permalink]

23 Nov 2011, 21:04

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Gordon wrote:

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 3 languages, how many of the members speak 2 of the 3 languages?

1.) 60 members speak only english
2.) 20 membes do not speak any of the 3 languages.

Please explain your calculation.

Responding to a pm:

I like to analyze every sentence of the question as I read it. Sometimes, it leads me to the answer by the time I read the question stem at the end. This is one of those questions.
Let me explain.

Of the 200 members of a certain association, each member who speaks german also speaks english,

It tells me that there is no one who speaks only German.

and 70 of the members speak only spanish.

70 people speak only Spanish. If now I know how many people speak only English, I will get how many people speak only one language.

If no member speaks all 3 languages,

no one speaks all 3 languages

how many of the members speak 2 of the 3 languages?

200 = Members who speak no language + members who speak only 1 language + [highlight]members who speak exactly 2 languages[/highlight] + members who speak 3 languages (=0)

We need to know the highlighted number.

1.) 60 members speak only english
Now I know how many people speak only one language but I don't know how many speak no language.

2.) 20 membes do not speak any of the 3 languages.
Now I know how many people speak no language but I don't know how many speak only one language.

Both statements together, give me all the information I need. I mark (C) here and move on but I will show the calculation below.

200 = 20 + (60 + 70 + 0) + [highlight]members who speak exactly 2 languages[/highlight] + 0
[highlight]members who speak exactly 2 languages[/highlight] = 50
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Re: Of the 200 members of a certain association, each member who [#permalink]

24 Nov 2011, 04:19

VeritasPrepKarishma wrote:

200 = Members who speak no language + members who speak only 1 language + [highlight]members who speak exactly 2 languages[/highlight] + members who speak 3 languages (=0)

wow.. Thanks so much! I have totally forgot this formula.. which is common sense basically...

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Re: Of the 200 members of a certain association, each member who [#permalink]

09 Dec 2011, 14:02

Attachment:

G1.jpg [ 14.85 KiB | Viewed 192 times ]

Based on this image, you can solve the question easily.
We need to find the number of areas which have overlap (G with E - and- S with E)
Taking 2 statements into consideration, we can find this number.

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Re: Of the 200 members of a certain association, each member who [#permalink]

13 Dec 2011, 21:51

Wow! this question just added a new twist to regular 3-bubble Venn diagram. I am glad I read it!
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Re: Of the 200 members of a certain association, each member who [#permalink] 13 Dec 2011, 21:51

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