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

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 3 languages?

Venn diagram is the best way to solve this question. So here are the tips for it:
From the stem if 70 speaks only Spanish and no student speaks three languages, max # of students who speaks two languages is 200-70=130.
Note that if ALL who speaks German speaks English means that no student speaks ONLY German, but not vise-versa, meaning that there may be the students who speak English only.
Also note there may be the students among 200 who speak no English, German or Spanish.

So, basically we need to determine the number of students who speak only English and the number of students who doesn't speak any languages and subtract this from 130 (as we already subtracted only Spanish and know that there are no only German).

(1) 60 speaks ONLY English, max # of students who speaks two languages is 200-70-60=70. But we don't know how this 70 is split: don't know how many don't speak any of the languages. Not sufficient.

(2) 20 don't speak any of the language. Clearly insufficient.

(1)+(2) 70-20(any languages)=50 (# of students who speak two languages).

Answer: C.
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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

1) English only = 60. Spanish only = 70. English+German = x. English + Spanish = y. Can't solve. Insufficient.

2) Can't solve either as we only know Spanish only = 70 and None = 20.

Using both:

(German + English) + (English only) + (English + Spanish) + (Spanish only) + None = 200
(German + English) + (English + Spanish) = 200 - 60 - 70 - 20 = 30

Ans C

Note:
1) German only = 0 since each memeber who speaks german also speaks english
2) German + Spanish = 0 for the same reason.

Yes using Venn Diagram is best.

Total = 200

Only Spanish = 70

Statement 1

Only English = 60

insufficient

Statement 2

None = 20

insufficient

both satements

200 - 20 = 180 speak at least one language.

since 70 speak only Spanish and 60 speak only English and since each member who speaks German also speaks English (but not the other way around) then:

180 - 70 - 60 = 50

no more then 50 people can speak German and they have to speak also English.

either way they speak two languages (even if its English and Spanish).

the answer is 50.

sufficient

the answer is (C)

Venn Diagram

Green = only Spanish = 70

Blue = only English = 60

Red = three languages = 0

since 20 members speak none then 200-20 = 180

that leaves 180-60-70 = 50 for the yellow and gray.

since both the yellow and gray represents member with two languages then the answer is 50.

i got the ans the first time, but now not able to undertsand . is this diag correct?
how to get 50 from this??

arjtryarjtry, in your diagram:

-all of the zeros are in the right place;
-you correctly have 60 only speaking English, and 70 only speaking Spanish;
-the only mistake is in the overlap of German and English, where you've also written 60; we have no information about how many people speak both German and English. Put a y there instead. Then the question asks for x+y. If we know that 0 people speak none of the three languages, we know that 180 people must be represented in the diagram, so 60+y+0+0+x+0+70 = 180, and x+y = 50. Since x+y is exactly what we're asked for, we have sufficient information. There is no way to actually find the value of either x or y here- we don't have enough information- but luckily we don't need to find x or y; we only need to find x+y.
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thanks Ian, but
how do we interpret the info that each german speaks english?
is it just a red herring?

No, that's important information. If everyone who speaks German also speaks English, then you must have zero people who only speak German. In addition, since no one speaks all three languages, no one speaks both German and Spanish. So this fact is the reason for two of the zeros in your diagram.
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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.

Number who speak exactly two of three languages = (Total - Those who speak none - Those who speak exactly 1 lang - those who speak all 3 languages)

(1) Not sufficient since it does not tell us how many dont speak any language
(2) Not sufficient since we cannot conclude from this how many speak just one language (we know about english but not spanich)

(1) + (2) Sufficient

Total = 200
Speak none = 20
Speak exactly 1 = 60 (E) + 70 (S) + 0 (G, as all who speak german also speak english)
Speak all three = 0
Hence exactly two = 50

Answer = (C)
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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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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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I still dont get it Bunuel, I'll put forward my explanation and please correct me where i am making a mistake. I'll Share a diagram with my explanation.

According to the information in the question, I created the following diagram. We know that All german speakers spoke English BUT NOT ALL ENGLISH SPEAKERS SPOKE GERMAN. So, the Orange region is the ONLY GERMAN SPEAKING segment..

Since, NO ONE SPOKE JUST GERMAN, AND EVERY GERMAN SPEAKER SPOKE ENGLISH WE CAN PUT THE ORANGE OVAL INSIDE THE GREEN BIGGER OVAL WHICH DENOTES THE ENGLISH SPEAKERS, SO THE ALL GREEN area denotes ONLY THE ENGLISH SPEAKERS. (Not the German + English Speakers)

The red denotes ONLY SPANISH SPEAKING people and Blue denotes people who spoke 2 languages, and the only 2 languages possible here are Spanish and English, since no one speaks all three languages.

Now we need to determine the size of the BLUE region.

Statement 1: I think statement 1 tells us the size of the GREEN, ONLY the green region and we still dont know the size of the orange region. NOTE that 200 = Orange+Green+Blue+Red+White (Universe, who speak no language). So insufficient, since we just have the value of Green and the red region.
we have,

200= Orange+60+Blue+70+White
70= Orange+Blue+White. So Not Sufficient.




Statement 2: again, we know 200= Orange+Green+Blue+Red+White
Here we know Red= 70, White= 20

so, 200= Orange+Green+Blue+70+20
110= Orange+Green+Blue. Not sufficient.


St (1)+(2),

We know Green= 60, Red=70, White= 20, However regions Orange and Blue are unknown.

200= Orange+Green+Blue+Red+White
200= Orange+60+Blue+70+20
200= 150+Orange+Blue
200-150= Orange+Blue
50= Orange+Blue.

Now since we dont know what Orange is, we cannot know the value of Blue. If the Statement 1 was, Only 60 Speak English, then we could have presumed that 60 includes all English speaking individuals including the German+english, however, Statement 1 says, 60 ONLY speak english and not german, and so it tells us about the Green region.

So, IMO answer E, tell me where I am wrong, Bunuel. Thanks

Two of the 3 languages is the sum of Orange (English and German) and Blue (English and Spanish) and it's 50, as you've correctly written, so the answer is C, not E,
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Hi

Posting the topic so that people following different threads will be able to get the concept

There is a basic formula for this question
please refer to the diagram attached
Hope this helps

TOTAL - NEITHER = TOTAL THREE - ONLY TWO - 2(ALL THREE)

Answer: Option C

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There could be two Venn diagrams. (refer attachment)

Why are we not considering the second case?

Am I missing something?