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# A social club has 200 members. Everyone in the club who

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A social club has 200 members. Everyone in the club who [#permalink]

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13 Sep 2010, 10:01
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A social club has 200 members. Everyone in the club who speaks German also speaks English. 70 members only speak Spanish. If no one speaks all 3 languages, how many speak 2 out of 3 languages?

(1) 60 only speak English
(2) 20 don't speak any of the 3 languages
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13 Sep 2010, 10:17
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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).

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16 Sep 2010, 00:19
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Of the 200 members of a certain asociation, 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?

A) 60 of the memebrs speak only English.
B) 20 of the members do not speak any of the languages.
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16 Sep 2010, 00:33
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

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16 Sep 2010, 02:34
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shrouded1 wrote:
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

Thanks Shrouded 1. I was confused with the German (who speak Spanish) part. Thanks for the explanation.
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01 Sep 2011, 00:51
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from the info:
E=G
y=those who speak 2/3 lang
n=who dont speak any lang

200=E+G+70-y+n

A) E=G=60. we still don't know 'n', so INSUFFICIENT.
B) n=20, but we don't know E or G.

C) sufficient to calculate y.
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Re: A social club has 200 members. Everyone in the club who [#permalink]

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14 Feb 2014, 04:05
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08 Mar 2015, 12:26
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Re: A social club has 200 members. Everyone in the club who [#permalink]

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08 Mar 2015, 22:18
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Bunuel 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 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).

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
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Re: A social club has 200 members. Everyone in the club who [#permalink]

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09 Mar 2015, 03:25
Paur wrote:
Bunuel 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 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).

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 [color=#0000ff]BLUE region. [/color]

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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A social club has 200 members. Everyone in the club who [#permalink]

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09 Mar 2015, 21:47
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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)
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File comment: SOLUTION

Untitled.png [ 25.43 KiB | Viewed 1782 times ]

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Re: A social club has 200 members. Everyone in the club who [#permalink]

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11 Mar 2015, 06:51
+1 for C.
Number of people left after removing Spanish speaking people = 170.
Among 170, there are people who speak German & English (since anyone who speaks German also speaks English), People who speak only English, and people who dont speak any of the languages (it is not explicitly mentioned in the question that all of them speak at least a language.).
Combining 1 and 2, we can get the answer. Sufficient.
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Re: A social club has 200 members. Everyone in the club who [#permalink]

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11 Mar 2015, 06:52
+1 for C.
Number of people left after removing Spanish speaking people = 170.
Among 170, there are people who speak German & English (since anyone who speaks German also speaks English), People who speak only English, and people who dont speak any of the languages (it is not explicitly mentioned in the question that all of them speak at least a language.).
Combining 1 and 2, we can get the answer. Sufficient.
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Re: A social club has 200 members. Everyone in the club who [#permalink]

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18 May 2015, 00:37
Paur wrote:
Bunuel 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 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).

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

THIS IS HARD
the main point is there is no person speaking Spanish and German because there is no person speaking 3 language.

so the ven diagram is like that, color one
Re: A social club has 200 members. Everyone in the club who   [#permalink] 18 May 2015, 00:37
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