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

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Manager
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In a class of 30 students, 17 students study Chinese, and r [#permalink] New post 18 Nov 2007, 21:13
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!
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 [#permalink] New post 18 Nov 2007, 21:27
Expert's post
:?
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Re: Sets [#permalink] New post 19 Nov 2007, 11:42
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
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 [#permalink] New post 19 Nov 2007, 12:52
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 ?

the answer is (A)
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 [#permalink] New post 19 Nov 2007, 13:06
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I cry :cry:
#2 insufficient means a few cases. It is clearly for me that 13+17 is good and is single case..... :(
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 [#permalink] New post 19 Nov 2007, 20:47
The second statement basically gives you this equation.

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

Therefore, statement 2 is insufficient.
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Re: Sets [#permalink] New post 19 Nov 2007, 21:42
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.
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 [#permalink] New post 20 Nov 2007, 21:37
makes sense, thanks a lot guys!
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 [#permalink] New post 22 Nov 2007, 04:54
Expert's post
:roll: thanks!
  [#permalink] 22 Nov 2007, 04:54
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