LalaB wrote:Many of the students at the International School speak French or German or both. Among the students who
speak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speak
German do speak French. What fraction of the students speak German?
(1) Exactly 60 students speak French and German.
(2) Exactly 75 students speak neither French nor German.
Things which are given to us.
Let X= People who speak only French i.e. they do not speak German
Y = People who speak only German i.e. they do not speak French
Z = People who speak both
N = People who do not speak any language. [remember the question says 'Many of the students'
Also, we know that Z = 4X
And, we also know that 1/6th People who do not speak German do speak French(this includes X and N)
This means X = 1/6 (X+N) or 5x = N or X = N/5
Statement 1 -- From this statement we can only find the number of student who speak both languages. Nothing can be deduced about the people who don't speak any of the two. Also, we cannot deduce anything about the student who speak only 1 language.
Insufficient
Statement 2-- From this statement we know N= 75
From this we can find X, which is 1/5 of N i.e. 15. We also know that Z = 4X or = 4*15 = 60
Again, we cannot deduce anything about people who speak ONLY GERMAN from this statement
Combine the two statement
we know the value of X, Z, N but still nothing about Y can be deduced.
IMO
E
