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
Japanese and French students
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I don't think that statement (1) is sufficient.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
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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Let: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.
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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