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French and Japanese_Data sufficiency

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by GMATGuruNY » Thu Apr 09, 2015 6:26 am
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.
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.
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by Brent@GMATPrepNow » Thu Apr 09, 2015 6:30 am
Here's a solution that uses the Double Matrix method: https://www.beatthegmat.com/at-least-100 ... 74669.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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