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

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Manager
Joined: 11 Nov 2007
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In a class of 30 students, 17 students study Chinese, and r [#permalink]

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18 Nov 2007, 22:13
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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. 13 students take only Japanese

Why is the answer 1 only? I think 2 is okay well because:
we know from opening statement that, 30=17+r-both
Statement two tells us that 30=17+13-both. In this case, both equals 0

What am I missing? THANKS!
CEO
Joined: 17 Nov 2007
Posts: 3586
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 572

Kudos [?]: 3966 [0], given: 360

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18 Nov 2007, 22:27
VP
Joined: 10 Jun 2007
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19 Nov 2007, 12:42
aliensoybean 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. 13 students take only Japanese

Why is the answer 1 only? I think 2 is okay well because:
we know from opening statement that, 30=17+r-both
Statement two tells us that 30=17+13-both. In this case, both equals 0

What am I missing? THANKS!

You are looking at #2 wrong.
For #2, ONLY Japaneses means this:
r-both = 13

r is defined as ALL Japaneses students, not ONLY Japanese students
VP
Joined: 08 Jun 2005
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19 Nov 2007, 13:52
Total = Set1 + Set2 + Neither - Both

30 = 17 + r + 0 - Both

statement 1

r = 14

30 = 17 + 14 + 0 - Both

Both = 1

sufficient

statement 2

insufficient

Both = r - 13 ?

CEO
Joined: 17 Nov 2007
Posts: 3586
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 572

Kudos [?]: 3966 [0], given: 360

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19 Nov 2007, 14:06
I cry
#2 insufficient means a few cases. It is clearly for me that 13+17 is good and is single case.....
Manager
Joined: 25 Jul 2007
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19 Nov 2007, 21:47
The second statement basically gives you this equation.

Only Chinese + (both chinese and japanese) = 17.

Therefore, statement 2 is insufficient.
Director
Joined: 09 Aug 2006
Posts: 757
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19 Nov 2007, 22:42
aliensoybean 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. 13 students take only Japanese

Why is the answer 1 only? I think 2 is okay well because:
we know from opening statement that, 30=17+r-both
Statement two tells us that 30=17+13-both. In this case, both equals 0

What am I missing? THANKS!

Both does not equal 0. Neither equals 0. Both = r-13.
Manager
Joined: 11 Nov 2007
Posts: 60
Followers: 1

Kudos [?]: 7 [0], given: 0

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20 Nov 2007, 22:37
makes sense, thanks a lot guys!
CEO
Joined: 17 Nov 2007
Posts: 3586
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 572

Kudos [?]: 3966 [0], given: 360

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22 Nov 2007, 05:54
thanks!
22 Nov 2007, 05:54
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