Sets A, B, and C have some elements in common : DS Archive
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# Sets A, B, and C have some elements in common

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Sets A, B, and C have some elements in common [#permalink]

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06 Dec 2006, 03:08
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Searched, but couldn't find this one. Venn type questions are the beans for my brain farts. Any lessons on approaching this with a Venn diagram would be helpful.

Sets A, B, and C have some elements in common. If 16 elements are in both A and B, 17 elements in both A and C, and 18 elements are 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 i 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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06 Dec 2006, 03:31
Sets A, B, and C have some elements in common. If 16 elements are in both A and B, 17 elements in both A and C, and 18 elements are 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 i both A and B, 9 elements are also in C.
2) A has 25 elements, B has 30 elements, and C has 35 elements.

= 9

EDITED

Last edited by yezz on 06 Dec 2006, 04:16, edited 1 time in total.
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06 Dec 2006, 04:11
A

Got this question in Gmatprep.

II) does not seems to provide enough info.
We got 3 equation from the question stem, another 3 from II). 6 total.
But we got 7 unknown, which is number of:
a, b, c, ab, ac, bc and abc .
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06 Dec 2006, 15:35
I'm getting A

1) Basically tells us that there are 9 elements in all 3

2) Doesn't give us enough information to construct a Venn diagram.
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06 Dec 2006, 16:20
Option A ,Stat1 clearly shows that 9 is the no of elements common to all the three
sets.
Stat2 by itself is not Sufficient to answer.
06 Dec 2006, 16:20
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