In a class of 30 students, 17 students study Chinese, and r

Question

In a class of 30 students, 17 students study Chinese, and r students study Japanese. Every student studies either Chinese, Japanese, or both. How many students study both Chinese and Japanese?

(1) r = 14
(2) Thirteen students take only Japanese.

shaselai · Answer

1.so we have C=17 and r=14. so we can see the overlap here. SUFF
2. so we know 13 take only japanese so we have 17 students left who study chinese BUT we dont know the dual language students so INSUFF

Bunuel · Answer

{Total} = {Chinese} + {Japanese} - {Both} --> 30=17+{Japanese} - {Both} --> {Japanese} - {Both}=13.

Question: {Both}=?

(1) {Japanese}=14 --> 14-{Both}=13 --> {Both}=1. Sufficient.

(2) {Japanese} - {Both}=13 --> the same info as in stem. Not sufficient.

Answer: A.

jlgdr · Answer

Just to illustrate

C No C Total
J r-13 13 r

No J 30-r 0 30-r

Total 17 13 30

Statement 1

Gives r=14 then, 14-13=1 study both

Sufficient

Statement 2

We already know this!

Insufficient

Answer: A

Nunuboy1994 · Answer

In order to solve this question we need to know the total, A and B. If we know, for example, what A only is and B only is then we can only solve the problem.

Statement (1) tells us that 14 students take Japanese; if we imagine a Venn Diagram then we know that the sum of C ( the circle that overlaps A and B) and B is 14. We also are given A and thus can calculate the answer using a set theory formula. Sufficient.
Total= A + B - Both. 
30= 17 + 14 - Both

Statement (2) tells us that thirteen students ONLY take Japanese; therefore, we cannot use either formula to calculate the answer. Insufficient.

bumpbot · Answer

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In a class of 30 students, 17 students study Chinese, and r

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