Overlapping Sets

[naveenhv]

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.

[force5]

IMO- c

A and B are insufficient.
combining.

total 180
German and english-= x
English and spanish= ES
German and spanish= GS

English only = 60
spanish only = 70
hence 180= 2languages+130
2 languages = 50

hence C

[Stendulkar]

S = Only Spanish
E = Only English
G = Only german

a = spanish + german
b = german + english
c = spanish + english

d = all three

We have to find a + b + c

From information given in the question stem, S = 70, d = 0,G = 0 and a= 0 ( because it is given that everyone who speaks german has to speak english so noone speaks only german and no one speaks german and spanish)

So now we have : S + E + G + a + b + c + d = Students who speak atleast one language.

Therefore, 70 + E + b + c + = Students who speak atleast one language..... (i)

Statement 1 : E = 60

Hoever we do not know how many do not speak any language. There we cannot solve (i)

Statement 2 : RHS of (i) is given but no other info...therefore insufficient.

Combining :

70 + 60 + B + C = 180

B+ C = 50...Sufficient..

This method looks lengthy....but if u use Venn Diagram it becomes very easy..

[Stendulkar]

S = Only Spanish
E = Only English
G = Only german

a = spanish + german
b = german + english
c = spanish + english

d = all three

We have to find a + b + c

From information given in the question stem, S = 70, d = 0,G = 0 and a= 0 ( because it is given that everyone who speaks german has to speak english so noone speaks only german and no one speaks german and spanish)

So now we have : S + E + G + a + b + c + d = Students who speak atleast one language.

Therefore, 70 + E + b + c + = Students who speak atleast one language..... (i)

Statement 1 : E = 60

Hoever we do not know how many do not speak any language. There we cannot solve (i)

Statement 2 : RHS of (i) is given but no other info...therefore insufficient.

Combining :

70 + 60 + B + C = 180

B+ C = 50...Sufficient..

This method looks lengthy....but if u use Venn Diagram it becomes very easy..

[atulmangal]

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.

+1 for C

No need to over think..

we need combination of 2 languages, straight away check the possible combinations and infavourable quantities

G + E ---> fav
E + S ---> fav
E only---> Not Fav
NO lang ---> Not fav

so need to find NOT FAV to get the fav combo...Op A and Op B gives that together hence Op C

[champmag]

Yes the question becomes very simple with the use of venn diagram.

+1 for C.