Set Theory Question

[ronnie1985]

At least 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

Please provide the venn diagram for each case.

[Anurag@Gurome]

At least 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

Please provide the venn diagram for each case.

Let F students study French, J study Japanese and X study both French and Japanese.

(1) 16 students at the school study both French and Japanese = 4% of F, which implies 0.04F = 16 or F = 400. So, 400 students study French. But this number does not give us the number of Japanese students.
So, (1) is NOT SUFFICIENT.

(2) X = 10% of J = 4% of F.
So, 5J = 2F or J = (2/5)F, which implies F > J. So, more students study French than Japanese.
Hence, (2) is SUFFICIENT.

The correct answer is B.

[[email protected]]

The common link was 'Students who study both Japanese and French.' These people comprised of 16 people.

So 10% of J = 4% of F.

Hence F>J.

This was a very important question...

[GMATGuruNY]

At least 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

Please provide the venn diagram for each case.

Let F = the total number of students who study French, J = the total number of students who study Japanese, and B = the total number of students who study both languages.
Since 4% of the students who study French study both languages, B = .04F.

Statement 1: 16 students study both French and Japanese
Thus:
.04F = 16
F = 400.
No information about J.
INSUFFICIENT.

Statement 2: 10% of students at school who study Japanese also study French
Thus, B = .1J.
Since it is also true that B = .4F, we get:
.04F = .1J
F/J = 10/4 = 5/2.
Thus, F>J.
SUFFICIENT.

The correct answer is B.