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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 28 Oct 2007, 13:39
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A
B
C
D
E

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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.


Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT SUFFICIENT
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 [#permalink] New post 28 Oct 2007, 14:04
I also chose D, but the OA is A.

I think it should be D as Statement 2 is also sufficient as #of Jap Speaking 13, #Chineses speaking 17 and # speaking both is zero

Can you explain.
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 [#permalink] New post 28 Oct 2007, 14:34
The reason 2 is insufficient is that you cannot determine how many students studied both languages. Look at the equation below.

Example: x = both languages
30 = 13 + x + 17 - x

x cancels out and we cannot determine x = both.
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 [#permalink] New post 29 Oct 2007, 07:45
You can solve this easily by Venn Diagram.
x= Chinese
a=both
y=Japanese

so x+a=17 and x+a+y=30 (*) ->y=13

(2) y=13. This can be concluded from (*) so this statement is redundant and insuff

(1) Y+a=14, -> a could be found (a=1)

so A.
  [#permalink] 29 Oct 2007, 07:45
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