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

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

by BTGmoderatorLU » Mon Jul 09, 2018 6:12 pm

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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.

The OA is A.

I need help to solve this DS question. Please, can someone assist me? Thanks in advance!
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Source: — Data Sufficiency |
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by Shahrukh@mbabreakspace » Tue Jul 10, 2018 4:12 am

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Elements common in A&B have 2 parts, first are those which are just in A& B and not in C, others are those which are common in all 3.
Statement 1: It directly gives us the part which is common in all 3, So, it is sufficient
Statement 2: It is Insufficient because we need total number elements as well to solve it.
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by deloitte247 » Wed Jul 11, 2018 4:39 am

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Question: How many element do all 3 sets have in common?
Statement 1 : Of the 16 elements that are in bot A and B, 9 elements are common between A, B, and C.
Statement 1 is sufficient

Statement 2: A has 25 elements, B has 30 and C has 35 elements.
We need to find the total number of elements.
Total = A + B + C - AB - BC - CA - 2ABC
We don't have specific information on total and ABC.
Statement 2 is not sufficient because we cannot calculate ABC without knowing the total
Final Answer = A because statement 1 alone is sufficient and statement 2 alone is insufficient.
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