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Japanese and French students

by lukaswelker » Tue Apr 08, 2014 10:07 am
Here is the question

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

(1) is sufficient but why is (2) also?

Any suggestions
Many thanks
Lukas
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Source: — Data Sufficiency |
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by sanju09 » Sat Apr 19, 2014 12:44 am
lukaswelker wrote:Here is the question

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

(1) is sufficient but why is (2) also?

Any suggestions
Many thanks
Lukas
I don't think that statement (1) is sufficient.

Translating things to math, J ≥ 100 and both J & F = 0.04 F.

Target Question: Is F > J?

We may require the group formula for two groups J & F in which

Total = J + F - Both + Neither

Or we have

Total = (J ≥ 100) + F - 0.04 F + Neither

Total = (J ≥ 100) + 0.96F + Neither.

(1) So, 0.04 F = 16, or F = 400, and J ≥ 100, if J = 100, answer to the target question is YES, but if J ≥ 400, we've a NO, hence [spoiler]insufficient[/spoiler].

(2) It means that both J & F = 0.1 J = 0.04 F, or [spoiler]clearly F > J, hence YES, sufficient.



I choose B[/spoiler]
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by GMATGuruNY » Sat Apr 19, 2014 2:39 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
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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