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

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In a class of 30 students, 17 students study Chinese, and r [#permalink] New post   09 Sep 2010, 07:52
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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.
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Re: Overlap Sets [#permalink] New post   09 Sep 2010, 09:21
rxs0005 wrote:
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.


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
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Re: Overlap Sets [#permalink] New post   09 Sep 2010, 09:55
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rxs0005 wrote:
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.


{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.
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Re: In a class of 30 students, 17 students study Chinese, and r [#permalink] New post   25 May 2014, 08:24
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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Re: In a class of 30 students, 17 students study Chinese, and r [#permalink] New post   24 Mar 2017, 21:35
rxs0005 wrote:
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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Re: In a class of 30 students, 17 students study Chinese, and r [#permalink] New post   14 Mar 2023, 10:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a class of 30 students, 17 students study Chinese, and r [#permalink]
14 Mar 2023, 10:59
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