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aroon7: Master | Next Rank: 500 Posts; Posts: 160; Joined: Sat Dec 20, 2008 9:12 pm; Thanked: 11 times

Sets

by aroon7 » Sun Jan 25, 2009 4:36 pm

Sets 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 the 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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Source: Beat The GMAT — Data Sufficiency | Sun Jan 25, 2009 4:36 pm

Zipper: Master | Next Rank: 500 Posts; Posts: 119; Joined: Sun Nov 30, 2008 2:47 am; Thanked: 11 times

by Zipper » Sun Jan 25, 2009 7:49 pm

Correct me if I am wrong but isn't 1 your answer?

1) sufficient I guess since it gives you what you are looking for. (???)

2) Your formula would be Tottal(?)=A(25)+B(30)+C(35)-none(0)-AB(16)-AC(17)-BC(18)-2ABC(what you are looking for,?)
since you don't know the total and the same elements in A B C (two unknowns) we can't solve. //insuff

hence, A?

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gaggleofgirls: Master | Next Rank: 500 Posts; Posts: 138; Joined: Thu Jan 15, 2009 7:52 am; Location: Steamboat Springs, CO; Thanked: 15 times

by gaggleofgirls » Sun Jan 25, 2009 8:07 pm

1) is sufficient, it gives us the union of A, B and C, which is what the ? is asking for.

2) is insufficient. It gives us the total amount in A, B and C ans we know the overlaps for each set, but we still don't know enough to solve.

Answer = A

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