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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

by swerve » Fri Jan 25, 2019 9:42 am

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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.

The OA is C

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by fskilnik@GMATH » Sun Jan 27, 2019 6:40 am

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swerve wrote: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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Following the Venn diagram shown ("overlapping sets"), it is easy to bifurcate each statement alone.

Conclusion: we are already sure the correct answer is (C) or (E)!

$$? = x + y$$
$$\left( {1 + 2} \right)\,\,\left\{ \matrix{
\,E \cup G \cup S = 200 - 20 = 180 \hfill \cr
\,E \cup G \cup S = 60 + 70 + x + y \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = x + y\,\,\, = \,\,\,180 - \left( {60 + 70} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {\rm{C}} \right)$$


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by deloitte247 » Sun Jan 27, 2019 12:35 pm

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70 members speak Spanish and no member speaks three languages = 200 - 70 = 130
All members that speak German also speak English but not English speaks German i.e there are members that speak more of the three Languages.
We need to find the numbers of members that speak no language from 130 at all and subtract it from 130.

Statement 1
Only 60 speak English
Maximum number of members who speaks 2 languages = 130 - 60 = 70 , but there is no information on members that speak more of the three Languages, hence statement 1 is INSUFFICIENT.

Statement 2
20 don't speak any of the three languages
Maximum number of members who speak 2 languages = 130 -20 = 110
But no information on members that speak English only hence statement 2 is INSUFFICIENT.

Both statement together
From statement 1 , 70 members comprises of those that speak English only and those that speak English only and those that don't speak any of the three Languages.
From statement 2, 20 members don't speak any of the three Languages .
Total numbers of members that speak two out of three Languages = 70 - 20 = 50 members
Both statement together are SUFFICIENT.

$$answer\ is\ OptionC$$
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