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Of the 430 travelers on a plane, 220 travelers are fluent in

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by swerve » Sun Nov 03, 2019 12:00 pm
Of the 430 travelers on a plane, 220 travelers are fluent in the French language. How many of the travelers are fluent in the German language?

1) The number of travelers who are fluent in both French and German languages is twice the number of travelers who are fluent in neither French nor German language.
2) 25 travelers are not fluent in either German or French language.

The OA is C

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Source: — Data Sufficiency |
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by joao_cardoso123 » Sun Nov 10, 2019 9:16 am
430 travelers can be divided in 4 groups:
F (fluent only in French)
G (fluent only in German)
FG (fluent in both)
N (fluent in none)
we know that F+FG=220
we want to know G+FG

(1) tells us that FG=2*N but this is not enough to find a solution because we have 4 unknowns and 3 equations
430=F+G+FG+N
F+FG=220
FG=2*N

(2) tells us that N=25; this is not enought because again we have 4 unknowns and 3 equations
430=F+G+FG+N
F+FG=220
N=25

(1) and (2) is enough because we have 4 equations to find out 4 unknowns
430=F+G+FG+N
F+FG=220
FG=2*N
N=25
we can rewritte 430=F+G+FG+N as 430 =220+G+25, which gives us G=85
from FG=2*N and N=25 we know that FG=50
then we know that G+FG=135
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