Of the 200 members of a certain association, each member who speaks German also speaks English, and 70 of the members

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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 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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BTGmoderatorDC wrote:
Sun Jun 06, 2021 4:25 pm
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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Source: GMAT Prep
Number who speak exactly two of three languages \(= (\)Total - Those who speak none - Those who speak exactly 1 language - Those who speak all 3 languages\()\)

(1) Not sufficient since it does not tell us how many don't speak any language \(\Large{\color{red}\chi}\)
(2) Not sufficient since we cannot conclude from this how many speak just one language (we know about English but not Spanish) \(\Large{\color{red}\chi}\)

\((1) \& (2)\) combined, sufficient \(\Large{\color{green}\checkmark}\)

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 \(= 50\)