At least 100 students at a certain school study Japanese. if 4 % of the students at school who study French also study Japanese, do more students at school study French than Japanese ?

A. 16 students at school study both French and Japanese

B. 10 % of students at school who study Japanese also study French.


DS: B is sufficient.

i swear i've answered this exact problem on this forum before, but i can't find the thread, so, here goes.

let FJ stand for the number of students who study both french and japanese. let F stand for the number who study french (regardless of whether they study japanese), and let J stand for the number who study japanese (regardless of whether they study french).

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the prompt states that FJ is 4% of F (not that J is 4% of F; make sure that you know this). this can be restated in a couple of ways: FJ = 0.04(F), or F = 25(FJ).

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statement (1):
this says that FJ = 16.
therefore, F = 25(FJ) = 400.
we don't know anything about J other than that J > 100 (as stated in the prompt), and that's insufficient to determine whether F = 400 is greater than J.
insufficient

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statement (2):
this states that FJ is 10% of J (again, not that F is 10% of J).
equivalently, FJ = 0.1(J), or J = 10(FJ).
since J = 10(FJ) and F = 25(FJ), it follows that F > J.
sufficient

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answer = b

Thanks Ron !!

you're welcome.