Please help me solve this DS from GMATPrep

beatthegmat wrote:

ramkarpa wrote:Atleast 100 students in a school study Japanese. 4% of students who study French also study Japanese.Do more students study French than Japanese ?

(1) 16 students study both French and Japanese
(2) 10% of students at school who study Japanese also study French.

The answer is B.

Any explanations ? Thanks

>=100 students study Japanese
4% of French students also study Japanese

(A) is not sufficient by itself because...
4/100 = 16/X
4X = 1600
X = 400

This is not sufficient because we still don't know the exact number of students studying Japanese (at LEAST 100)

(B) is sufficient because...
Let's say that 100 students study japanese. 10% of these students also study French, so that would be 10 students

The question prompt states that 4% of french students also study Japanese. We know that the number of students who study both are 10.

So, 4/100 = 10/X
4X = 1000
X=250

Thus, 250>100

(B) is the correct answer

ramkarpa wrote:Atleast 100 students in a school study Japanese. 4% of students who study French also study Japanese.Do more students study French than Japanese ?

(1) 16 students study both French and Japanese
(2) 10% of students at school who study Japanese also study French.

The answer is B.

Any explanations ? Thanks