At least 100 students at a certain high school study Japanese. If 4 percent of the students who study French also study Japanese, do more students at the school study French than Japanese?
1). 16 students at the school study both French and Japanese.
2). 10 percent of the students at the school who study Japanese also study French.
Japanese and French
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IMO C
Suppose F students study French.. and J students study Japanese
Then, 4F/100 study both, Japanese and French
Stmt 1  16 students study French and Japanese
So, 4F/100 = 16 => F = 400 students study French. However, Q does not say anything else so NOT SUFF
Stmt 2  10J/100 study both French and Japanese... We cannot determine anything about French Students so NOT SUFF
Together, 10J/100 = 4F/100 = 16
Solve to get J = 160 which is less than 400 SUFF
OA??
Suppose F students study French.. and J students study Japanese
Then, 4F/100 study both, Japanese and French
Stmt 1  16 students study French and Japanese
So, 4F/100 = 16 => F = 400 students study French. However, Q does not say anything else so NOT SUFF
Stmt 2  10J/100 study both French and Japanese... We cannot determine anything about French Students so NOT SUFF
Together, 10J/100 = 4F/100 = 16
Solve to get J = 160 which is less than 400 SUFF
OA??
For (2):
If # Students taking Japanese = 100 then the number of students taking Japanese and French = 10. # Students taking French = 4/100x = 10 = 250
250 > 100
If # Students taking Japanese = 200 then the number of students taking Japanese and French = 20. # Students taking French = 4/100x = 20 = 500
500 > 200
Answer is B.
***Alternatively***
(10/100)*J = (4/100)*F
10J = 4F
J/F = 2/5
If # Students taking Japanese = 100 then the number of students taking Japanese and French = 10. # Students taking French = 4/100x = 10 = 250
250 > 100
If # Students taking Japanese = 200 then the number of students taking Japanese and French = 20. # Students taking French = 4/100x = 20 = 500
500 > 200
Answer is B.
***Alternatively***
(10/100)*J = (4/100)*F
10J = 4F
J/F = 2/5

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luvaduva wrote:For (2):
If # Students taking Japanese = 100 then the number of students taking Japanese and French = 10. # Students taking French = 4/100x = 10 = 250
250 > 100
If # Students taking Japanese = 200 then the number of students taking Japanese and French = 20. # Students taking French = 4/100x = 20 = 500
500 > 200
Answer is B.
***Alternatively***
(10/100)*J = (4/100)*F
10J = 4F
J/F = 2/5
Small corrections to the above: 4/100x should be read as (4/100) *x
or 4x/100
rgds
Vittal