DS question - doubt - percents

[praveen_gmat]

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.

[selango]

J>=100

0.04F study both.

F>J?

stmt1,

0.04F=16

F=400.

We don't know any info abt J.

Insuff

stmt2,

0.1J study both

-->0.1J=0.04F

100J=4F

F/J=25 or F=25J

Suff

Pick B

[praveen_gmat]

Thanks Selango .. I think my mind is not working .. its such an easy problem.

[selango]

The trick used here s 4 percent of the students at the school who study French also study Japanese is equal to 10 percent of the students at the school who study Japanese also study French.

Cool..Once u started doing more problems you can improve your accuracy..

[lunarpower]

here's how to do it with a "double set matrix":

(note that these forums don't allow the use of the tab key, so the matrix is going to come out really funky... but i'll try)

the matrix will be organized like this (including the information in the prompt):
--------------- / JAPANESE / NO JAPANESE / TOTAL
FRENCH ---------- 0.04F ------------------------ F
NO FRENCH
TOTAL

--

statement (1)

---------------- / JAPANESE / NO JAPANESE / TOTAL
FRENCH ---------- 0.04F=16 ------------------------ F
NO FRENCH
TOTAL

this is enough to figure out that F = 400, but you still have absolutely no idea how many students are taking japanese.
insufficient.

--

statement (2)

--------------- / JAPANESE / NO JAPANESE / TOTAL
FRENCH ----- 0.04F=0.10J ----------------------- F
NO FRENCH
TOTAL ------------ J

we have 0.04F = 0.10J
multiply by 100 --> 4F = 10J
that's enough to realize that F > J. if you don't see why, then divide by 4 (giving F = 2.5J) or by 10 (giving J = 0.4F); either of these should help you make that realization.

[lunarpower]

if you just like words:

take it one statement at a time, and see what you can do with the facts.
(1)
taking this statement in combination with the 4% statistic cited in the prompt, we have that 16 = 4% of the total number of students studying french. this means that 400 students are studying french.
all we know is that 'at least 100' are studying japanese; that figure could be greater than, equal to, or less than 400, so, insufficient.

(2)
let 'Q' stand for the number of students who study BOTH french and japanese.
we have no idea of the size of 'Q', BUT:
-- Q is 4% of the number of students studying french (as stated in the prompt)
-- Q is 10% of the number of students studying japanese
these two facts together imply that the number of students studying french MUST be larger, because the same quantity Q is a smaller percentage of that number. (if you're interested, the number of students taking french must be exactly 10/4 times the number of students taking japanese for these equations to hold simultaneously.)
sufficient

answer = b

[selango]

Great explanations Ron..Thanks.