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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, 06:52
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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.
[Reveal] Spoiler: OA

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Re: Overlap Sets [#permalink] New post 09 Sep 2010, 08:21
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, 08:55
Expert's post
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 14 Feb 2014, 04:48
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Re: In a class of 30 students, 17 students study Chinese, and r [#permalink] New post 25 May 2014, 07:24
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
Re: In a class of 30 students, 17 students study Chinese, and r   [#permalink] 25 May 2014, 07:24
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