GPREP DS#26

[hardikrs]

At least 100 students at a certain high school study Japanese. If 4% 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 % of the students at the school who study Japanese also study French.

Please explain your answer.

Thanks.

[nverma]

IMO B

[clock60]

i think B
x-number of students who study french
y-number of students who study japan and y>100
0,04x-study both
is x>y???
(1)0,04x=16, x=400 as we do not know the exact value of y it can be less or more than 400 insufficient
(2) 0,01y=0,04x, y=0,4x- the number who study japan
x>0,4x (french>japan) sufficient

[Fiver]

Agree with Clock. B it is.

[socker121314]

IMO E

Clock60- i understand your logic because initially i made that mistake but in this case i don't think 0.01y=0.04x....at least i don't think

OA????

[abhasjha]

IMO- B

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).


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).


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

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