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sets

by Woozler » Mon Dec 13, 2010 9:45 am
Sets A, B, and C have some elements in common. If 16 elements are in both A and B, 17 elements are in both A and C, and 18 elements are in both B and C, how many elements do all three sets A, B and C have in common?

(1) Of the 16 elements that are in both A and B, 9 elements are also in C
(2) A has 25 elements, B has 30 elements, and C has 35 elements
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Source: — Data Sufficiency |
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by kvcpk » Mon Dec 13, 2010 11:39 pm
Woozler wrote:Sets A, B, and C have some elements in common. If 16 elements are in both A and B, 17 elements are in both A and C, and 18 elements are in both B and C, how many elements do all three sets A, B and C have in common?

(1) Of the 16 elements that are in both A and B, 9 elements are also in C
(2) A has 25 elements, B has 30 elements, and C has 35 elements
Assume K elements are in all 3 sets.

only in A and B, But not in C = 16 - K
similarly others..

(1) Of the 16 elements that are in both A and B, 9 elements are also in C
this means that there are 9 elements common to all 3 sets. hence K = 9
SUFF

(2) A has 25 elements, B has 30 elements, and C has 35 elements
We need the count of the number of total elements in A, B and C combined to proceed further.
hence INSUFF

pick A.
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