Sets

[Deepthi Subbu]

At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school 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.

[Anurag@Gurome]

At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school 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.

Say, number of students studying Japanese = J and number of students studying French = F. Now, J ≥ 100 and 4% of F study both Japanese and French.

Statement 1: 16 students at the school study both French and Japanese.
Therefore, 4% of F = 16
=> F = (16/0.04) = 400
As we don't have any concrete idea about the value of J, we cannot say whether F is greater than J or not.

Not sufficient

Statement 2: 10 percent of the students at the school who study Japanese also study French.
Therefore, 4% of F = 10% of J
=> F = J*(0.10)/(0.04) = (2.5)*J
=> F > J

Sufficient

The correct answer is B.

[cypherskull]

Hey Anurag...Thanks for your response..! but what's confusing me in this problem is the following wordings:

"4% of F study both Japanese and French." ---- (1)
"10 percent of the students at the school who study Japanese also study French." ----- (2)

Are both 1 and 2 equivalent to the number of students who study both Jap and French?

My understanding of the problem was that (1) + (2) = number of students who study both Jap and French.

[Anurag@Gurome]

"4% of F study both Japanese and French." ---- (1)
"10 percent of the students at the school who study Japanese also study French." ----- (2)

Are both 1 and 2 equivalent to the number of students who study both Jap and French?

Yes, they are same.
The former is with respect to the number of students who study French while the later is eith respect to the number of students who study Japanese.