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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
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rxs0005
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.

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.
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