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# Set A, B, C have some elements in common. If 16 elements are

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VP
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Set A, B, C have some elements in common. If 16 elements are [#permalink]

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11 Mar 2008, 12:30
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Set A, B, 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 of the 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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11 Mar 2008, 18:16
A union B union C = A + B + C - A inte B - A inter C - B inter C + A inter B inter C, where inter is intersection
Also A union B = A + B - A inter B
Given Originally
A union B = 16, A union C = 17, B Union C = 18

Statement 1:
Gives us A inter B inter C = 9
So question cannot be answered alone with this statement.

Statement 2:
Gives us A, B, & C.
This alone cannot answer the question. However with the help of A, B & C and A union B = 16, A union C = 17, B Union C = 18, we can obtain A inte B, A inter C, and B inter C using formula mentioned in line 2 above.

Combining both statments:
We have all the things needs for calculation of A union B union C.

VP
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19 Mar 2008, 02:12
abhijit_sen wrote:
A union B union C = A + B + C - A inte B - A inter C - B inter C + A inter B inter C, where inter is intersection
Also A union B = A + B - A inter B
Given Originally
A union B = 16, A union C = 17, B Union C = 18

Statement 1:
Gives us A inter B inter C = 9
So question cannot be answered alone with this statement.

Statement 2:
Gives us A, B, & C.
This alone cannot answer the question. However with the help of A, B & C and A union B = 16, A union C = 17, B Union C = 18, we can obtain A inte B, A inter C, and B inter C using formula mentioned in line 2 above.

Combining both statments:
We have all the things needs for calculation of A union B union C.

actually OA is A. you yourself tell that from 1 we know abc.
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19 Mar 2008, 08:41
Sorry, I did it wrongly. Question does ask for A inter B inter C and that is what given in A, so A is the answer.
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19 Mar 2008, 08:43
A it is

1 - it pretty much tells the answer that 9 is common across all

2- in addition need to know the total numberof elements across all sets (i.e n(AUBUC) ) to calculate the number of common elements.
Re: gmatprep sets   [#permalink] 19 Mar 2008, 08:43
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