Data Sufficiency

Hi,

Couldn't find a good explanation in the forum for this one. Answer is B

134) At least 100 students study Japanese. If 4% of students who study French also study Japanese, do more students study French than Japanese?

a. 16 students study both French and Japanese
b. 10% of students at school who study Japanese also study French

Let no of Japanese be 'J'
Let no of French be 'F'

Information Given:

1) J > 100.
2) 4% of students who study French also study Japanese.
Means 4/100 (F) study both French and Japanese

Question can be paraphrased as: Is F-J > 0? or if F > J

stmt a) No of students who study both French and Japanese = 16
=> 4/100 (F) = 16
From the above we can find F. But stmt a) does not tell us anything about Japanese. Hence NOT SUFFICIENT.

stmt b) 10% of students who study Japanese also study French.
=> 4/100(F) = 10/100 (J) = students who study both French and Japanese.
Thus, solving above, we get F = (25/10) * J = 2.5 * J. Thus number of students who study French are 2.5 times
number of Japanese. Thus, it answers the question "Do more students French than Japanse" as "Yes". Hence SUFFICIENT.

Thus the answer is "B".

Thanks!