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

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Manager
Joined: 24 Dec 2005
Posts: 95
Of the 200 members of a certain association, each member who [#permalink]

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12 Mar 2006, 23:40
1
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55% (hard)

Question Stats:

70% (02:12) correct 30% (02:04) wrong based on 174 sessions

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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 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-social-club-has-200-members-everyone-in-the-club-who-100935.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Aug 2012, 04:59, edited 1 time in total.
Manager
Joined: 22 Feb 2006
Posts: 123
Location: Oxford

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13 Mar 2006, 01:34
C

The member who speak 2 of three languages are = German Speakers + English and Spanish Speakers....

and using the conditions given we know that 200 people are divided in the below mutual sets...

Engilsh only (60)
Spanish only(70)
German + English
English + Spanish
None of above(20)

so the ones who speak (German + English) or (English + Spanish) = 200-60-70-20
=50

So we need both options to get the answer...

Last edited by Rocky on 13 Mar 2006, 21:51, edited 1 time in total.
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Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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13 Mar 2006, 04:37
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.
Manager
Joined: 24 Dec 2005
Posts: 95

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13 Mar 2006, 05:18
That nets to 50 . You wrote 30. typo I guess. ywilfred you are as articulate as always. Thanks
Manager
Joined: 22 Feb 2006
Posts: 123
Location: Oxford

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13 Mar 2006, 21:51
Yes, It was a typo... corrected it.... sorry....
Manager
Joined: 08 Feb 2006
Posts: 126

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20 Apr 2006, 22:41
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 members speaks all 3 languages, how many of the members speak 2 of the 3 languages?

1) 60 of the members speak only English.

2) 20 of the members do not speak any of the 3 languages.
Senior Manager
Joined: 15 Mar 2005
Posts: 418
Location: Phoenix

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20 Apr 2006, 22:48
jlui4477 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 members speaks all 3 languages, how many of the members speak 2 of the 3 languages?

1) 60 of the members speak only English.

2) 20 of the members do not speak any of the 3 languages.

Out of 200, 70 speak only Spanish. Therefore, 130 speak English only, or a combination of two languages, or none of these languages.

From 1, 60 speak English only. Thus, 70 speak German and English, and Spanish and English, or none of these languages. Not sufficient.

From 2, 20 don't speak any of these languages. Also, 70 speak only Spanish. Thus, 110 speak Only English or German and English. Since we don't know how many people speak only English, this too isn't sufficient.

Combining 1 and 2, the answer is 50. Hence C.
_________________

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Senior Manager
Joined: 23 May 2005
Posts: 266
Location: Sing/ HK

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20 Apr 2006, 22:50
Also got C by using Venn Diagram. However if i didn't consider possibilty statement (2), would've made the mistake of choosing A. Yikes
Manager
Joined: 04 Apr 2006
Posts: 60
Location: Land Of Opportunities

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21 Apr 2006, 02:32
sm176811/ Hermione
Can you pl explain how you got this using venn diagram.
VP
Joined: 29 Apr 2003
Posts: 1403

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22 Apr 2006, 23:57

x + y + 60 + 70 + 20 = 100 (where x and y are ppl speaking German and English, English and spanish respectively)

so x + y = 50....!
Intern
Joined: 28 Aug 2007
Posts: 13
GMATPrep: Of the 200 members of a certain assocation... [#permalink]

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12 Oct 2007, 12:09
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?

(1) 60 of the members speak only English
(2) 20 of the members do not speak any of the three languages

Is it best to use a Venn Diagram to solve this?

I think I got thrown off by the statement ' each member who speaks German also speaks English' --- I assume that it cannot work in reverse (i.e., that each member who speaks English also speaks Spanish) - correct?
VP
Joined: 08 Jun 2005
Posts: 1145

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12 Oct 2007, 12:46
1
KUDOS
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).

sufficient

VP
Joined: 09 Jul 2007
Posts: 1100
Location: London

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12 Oct 2007, 15:20
I could not draw Venn for it, but foud it easy to do the following

we know
200 people
Spanish only 70, so we have 130 left
no member speaks 3 languages
we need to find German speakers who speak Enlgish

1. English speakers only 60, so 130-60=70 nonspeakers and E and G together
2. No language speakers 20, so 70-20=50 EandG

so C
VP
Joined: 08 Jun 2005
Posts: 1145

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12 Oct 2007, 22:31
1
KUDOS
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.

Attachments

untitled.JPG [ 12.48 KiB | Viewed 8016 times ]

VP
Joined: 09 Jul 2007
Posts: 1100
Location: London

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13 Oct 2007, 01:25
KillerSquirrel wrote:
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.

nice work, KillerSquirrel, forgot that overlap can be 0.
Manager
Joined: 13 Jul 2007
Posts: 121

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13 Oct 2007, 11:50
KillerSquirrel,

I have couple of questions - used Venn diagram

1. Till I read St2 I did not think that there would be ppl who cannot speak either language so I came with Ans A.

G - only German
S - only Spanish
E - only ENglish
a - GE
b- GS
c SE
d - all 3 =0

G + A + B + C + E + 70 = 200
Now G = 0 as whoever speaks G also speaks E
Sicne d = 0, b also is 0 (otherwise there would be ppl who can speak 3 lang)

Since E = 60

A + B + C = 70 and thats how I came w/ A.

In many problems like these we don't hv neither case? How can be sure of that.
VP
Joined: 08 Jun 2005
Posts: 1145

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13 Oct 2007, 13:21
lnaik wrote:
KillerSquirrel,

I have couple of questions - used Venn diagram

1. Till I read St2 I did not think that there would be ppl who cannot speak either language so I came with Ans A.

G - only German
S - only Spanish
E - only ENglish
a - GE
b- GS
c SE
d - all 3 =0

G + A + B + C + E + 70 = 200
Now G = 0 as whoever speaks G also speaks E
Sicne d = 0, b also is 0 (otherwise there would be ppl who can speak 3 lang)

Since E = 60

A + B + C = 70 and thats how I came w/ A.

In many problems like these we don't hv neither case? How can be sure of that.

http://www.gmatclub.com/forum/t52560
http://www.gmatclub.com/forum/t50919
http://www.gmatclub.com/forum/t51534

I just enclosed three random problems I found using search. All of them use the neither option, so you assumption is wrong.

CEO
Joined: 29 Mar 2007
Posts: 2559
Re: GMATPrep: Of the 200 members of a certain assocation... [#permalink]

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13 Oct 2007, 23:09
slsu 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?

(1) 60 of the members speak only English
(2) 20 of the members do not speak any of the three languages

Is it best to use a Venn Diagram to solve this?

I think I got thrown off by the statement ' each member who speaks German also speaks English' --- I assume that it cannot work in reverse (i.e., that each member who speaks English also speaks Spanish) - correct?

S1:
Insufficient. I really wanted to answer Suff. for this question, but I then realized that it doesn't say anywhere that everyone speaks at least one of the languages. If they did then im pretty sure this would be sufficient.

200-60-70= 70. But among these 70 we don't know who doesn't speak any of the languages.

S2: Insuff.

Together we know who doesn't speak any of the three languages. So we have 50 people left.

C.
SVP
Joined: 21 Jul 2006
Posts: 1510

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25 Jan 2008, 06:12
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.

Thanks
CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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25 Jan 2008, 06:30
"C" seems to be right.

200=70(only Spanish)+60(only English)+20(do not speak any of the three languages)+0(no member speaks all three languages)+x(two languages)
x=50
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Re: DS: Sets   [#permalink] 25 Jan 2008, 06:30

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