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

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Director
Joined: 07 Jun 2004
Posts: 610

Kudos [?]: 952 [1], given: 22

Location: PA
In a class of 30 students, 17 students study Chinese, and r [#permalink]

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09 Sep 2010, 07:52
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Question Stats:

57% (01:09) correct 43% (01:10) wrong based on 178 sessions

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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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If the Q jogged your mind do Kudos me : )

Kudos [?]: 952 [1], given: 22

Current Student
Joined: 12 Jun 2009
Posts: 1836

Kudos [?]: 277 [0], given: 52

Location: United States (NC)
Concentration: Strategy, Finance
Schools: UNC (Kenan-Flagler) - Class of 2013
GMAT 1: 720 Q49 V39
WE: Programming (Computer Software)

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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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Kudos [?]: 277 [0], given: 52

Math Expert
Joined: 02 Sep 2009
Posts: 42302

Kudos [?]: 133015 [0], given: 12402

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09 Sep 2010, 09:55
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.

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Kudos [?]: 133015 [0], given: 12402

Current Student
Joined: 06 Sep 2013
Posts: 1970

Kudos [?]: 743 [0], given: 355

Concentration: Finance
Re: In a class of 30 students, 17 students study Chinese, and r [#permalink]

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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

Insufficient

Kudos [?]: 743 [0], given: 355

Director
Joined: 12 Nov 2016
Posts: 794

Kudos [?]: 36 [0], given: 165

Re: In a class of 30 students, 17 students study Chinese, and r [#permalink]

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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.

Kudos [?]: 36 [0], given: 165

Re: In a class of 30 students, 17 students study Chinese, and r   [#permalink] 24 Mar 2017, 21:35
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