A Word Problem

[billzhao]

At least 100 students at a certain high school study Japanese. If 4 percent of the students at the shcool 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


Can someone help to explain?

Thanks!

[mrsmarthi]

It is given that No of students who learn J >= 100.

4% of the students who learn French also study Japanese.

ie. F and U = 4/100 F.

From stmt 1, it is given F and U is 16

4/100 F = 16 ==> F = 400.

From stmt1, we know there are 400 students who learn French but no information abount Japanese.

From Stmt 2, it is given 10 of students who learn J also learn F. Considering this stmt alone, we don't know how many study both Japense and French. Hence Insufficient.

From Combine both the clues, 16 students study both F and J and 10% J study F and U

==> 10 /100 J = 16 ==> Solving we get J = 160.

From clue 1, we get F, and from both the clues we get J. Now we can answer the relation between F and J.

Hence my ans will be C.

[cramya]

Refer here:

https://www.beatthegmat.com/japanese-and ... 25888.html

Its a C trap question(to note: We just need to find if more students study French than Japanese). The official answer is B

[mrsmarthi]

Fell into the trap.....

[naaga]

Any one clear explanation please......I didn't understand why it's B...

[welcome]

By Question ..
.04F = also sudy J.

II - .01J = also sudy F.

means .01J = .04F
=> 10J = 4F
=> J<F. Ans

Ans : B.

[BuckeyeT]

Set up:
J(s) = Students at the school who study Japanese
F(s) = Students at the school who study French
S(jf) = Students at the school who study both Japanese and French

Original Statement:
J(s) >= 100
.04 F(s) = S(jf)

(1) 16 students at the school study both French and Japanese.

Don't be tricked here! It's tempting to dismiss this as insufficient (because we're not told about J(s) directly). But, we can determine F(s) from this statement. And if F(s) is < 100, the statement would be sufficient. I only mention this because some DS questions pray on those who overlook this.

.04 F(s) = S(jf)
.04 F(s) = 16
F(s) = 350
Since, J(s) >= 100, we don't know for sure if it is higher or lower than 350. Insufficient.

(2) 10 percent of the students at the school who study Japanese also study French.
.1 J(s) = S(jf)

Since we know .04 F(s) = S(jf) from the original question, we can set our two values equal to each other:
.04 F(s) = .1 J(s)
F(s) = 2.5 J(s)

This tells us there are 2.5 times as many French speaking students at the school than Japanese speakers. This is Sufficient.

Answer: B.