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Another confusing question....please explain

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Another confusing question....please explain

by ankit1383 » Wed Oct 01, 2008 8:27 am
Sets A,B and C have some common elements in common.If 6 elements are both in A and B ,17 elements are both in A and C and 18 elements in both B and C,how many elements do all three of the sets A,B and C have in common?

1 Of the 16 elements that are both in A and B ,9 are in C

2 A has 25 elements B has 30 elements and C has 35 elements

Ans A
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Source: — Data Sufficiency |
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by jeffxujian » Wed Oct 01, 2008 1:27 pm
I got the right answer, but i am not sure if my method is correct.

condition 1, A AND B HAVE 16 elements in common, and C shares 9 of them. This condition should have given you sufficient information to conclude that A, B and C shared 9 elements in common.

condition 2, remember the equation A+B+C-Both-2*ALL=total# of people? From condition 2, we know A, B, C for certain, but we dunt know about ALL and total# of people, therefore, the condition is insufficient.

I hope that I have given you the correct explanation.
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