From GMAT Prep 1...Q#26

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.

Highlight for OA: B

Having a hard to even starting this problem. Any ideas?

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

Thanks for the great explanation Ron.

One of my weak points is Venn diagram, so thats what made the problem intimidating for me. After going through your explanation, the problem seems pretty straightforward!

do you have our word translations strategy guide?

venn diagrams are a BAD idea for problems that only deal with 2 sets. for such problems, you should use our 'double-set matrix' (or some similar device). this is a 3x3 grid, with yes/no/total for one set on the rows and yes/no/total for the other set on the columns.

the venn diagram is bad because certain totals - like the TOTAL number of students taking japanese - don't go anywhere in the diagram (that number would be split between students taking japanese and french, and students taking japanese but not french).

the venn diagram is sine qua non for problems with 3 sets, though.

hi ron, i still don't understand the second statement and also your explanation for the second statement. First of all, how i interpreted the second statement is 10 % of students study both japanese and french. in the question, it states 4% of students study french and japanese. Why is the percentage changing? I'm really confused...

statement 2 says: (emphasis mine)
10 percent of the students at the school who study Japanese also study French.

think about this like a sentence correction problem: that's an essential modifier. it serves as an adjective, and it can't be left out of consideration. it's 10 percent of the students who study japanese, not ten percent of all students.

From Ron...Q = 4% of F and Q = 10% of J [F = French speakers, J = Japanese speakers]

or

Q = 4% of F (can be derived from the sentence given in the question)
Q = 10% of J (from B)

Now 4F/100 = 10J/100
=> F/5 = J/2

hence F would be more as compared to J....hence the answer would be B.

Hi Ron,
Sorry to dig up such an old post but I was confused about to idea to use a "double-set matrix" here. Could you show how you would solve this question using such a matrix?

Thanks.

sure.

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.

Recently encounter this question as well. it is not as difficult as it appears. the explanation is great!

we appreciate the compliments on our posts, but please refrain from posting comments implying that problems are "easy" or "not as difficult as they appear". such comments serve no purpose, and can be demoralizing to other forum posters who actually do find these problems difficult.
thanks.

Dear instrc.
RE; stat. 2. the prompt explicitly states that Jap. student are at least 100, should not this value bu used when setting up proportion, rather than assigning an uknown variable as menyioned above (Q or so ).
Thank you.

how are you going to plug "at least 100" into an expression? that's not a value.

think of all the trouble you'll get into if you extend this argument. for instance, positive numbers are all "greater than 0", so, according to this line of thinking, you should never need a variable to represent a positive number.
do you see how this is a problem?

in general, if a quantity is unknown, it's a good idea to use a variable to represent that quantity. (note that a quantity is still “unknown” if you don't have finite set of hard values for it -- even if you can nail it down to some range, such as “at least 100”.)

Thanks for reply,
Since, the question stem gives us "this "value( atleast 100), I assumed it mast be used in some way. What is the point telling us that there were at least 100 students.
Thanks.

go ahead and use a variable, then double check at the end that what you come up with is consistent with the fact that the "at least 100" condition is satisfied. you may need to tweak other values to make sure you get at least 100. you are going to use the information somehow, just don't plug it in as you suggest..

_________________
Tim Sanders
Manhattan GMAT Instructor