# Thread: GMAT Prep Set theory Problem

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## GMAT Prep Set theory Problem

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.

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Any takers?

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Emphasis is that nobody speaks all three language.
Combining I and II

So, there cant be Sp and English speaker as we know some germans speak english.

Draw a venn diagram and you will see Spanish circle standing alone while German one is enclosed in English.
So we need to find how many people speak German.
200 - 20 = 60 + 70 + German [they speak English as well]
German = 180 - 130

C.

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Originally Posted by mbawannabe
Emphasis is that nobody speaks all three language.
Combining I and II

So, there cant be Sp and English speaker as we know some germans speak english.

Draw a venn diagram and you will see Spanish circle standing alone while German one is enclosed in English.
So we need to find how many people speak German.
200 - 20 = 60 + 70 + German [they speak English as well]
German = 180 - 130

C.
IMO the bolded text is not correct. Since all members who spk English(E) do not spk German(G), there would be some members who would spk both English and Spanish (S). Moreover, the Q stem is asking about how many members speak two of the three languages. Symbolically we need to find out the value of

N(S & G only) + N(S & E only) + N(G & E only) ........where N denotes no of memebrs.

Given .....N(S & G only) = 0.... &.... N(S & G & E) = 0

St 1 & St 2:

N(S or G or E) = N(only S) + N(only G) + N(only E) + N (G&E only) + N(S&E only) + N (S&G only) + N (S & G & E)

200-20 .........= ...70 ......+ ...0........ + .....60.... + N(G & E only) + N(S& E only) + .......0 ........+ .........0.......

N(S &E only) + N(G & E only) = 50 ........SUFF

Ans IMO C

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Originally Posted by B-Guru
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.
Can someone help to explain and solve this DS problem again .... thanks ....

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Originally Posted by winjeemat
IMO the bolded text is not correct. Since all members who spk English(E) do not spk German(G), there would be some members who would spk both English and Spanish (S). Moreover, the Q stem is asking about how many members speak two of the three languages. Symbolically we need to find out the value of

N(S & G only) + N(S & E only) + N(G & E only) ........where N denotes no of memebrs.

Given .....N(S & G only) = 0.... &.... N(S & G & E) = 0

St 1 & St 2:

N(S or G or E) = N(only S) + N(only G) + N(only E) + N (G&E only) + N(S&E only) + N (S&G only) + N (S & G & E)

200-20 .........= ...70 ......+ ...0........ + .....60.... + N(G & E only) + N(S& E only) + .......0 ........+ .........0.......

N(S &E only) + N(G & E only) = 50 ........SUFF

Ans IMO C
How did you conclude that N(S & G only) = 0....

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Originally Posted by gmatcraze
How did you conclude that N(S & G only) = 0....
He comes to conclusion that (S&G)=0 because in the problem it says everyone who speaks german speaks english. And Their is no one who speaks all the three.

If S&G !=0 then it will contradict the given data. So 50 is correct

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IMO c

Both statements are needed