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Set A, B, C have some elements in common. If 16 elements are [#permalink]
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07 Apr 2011, 12:50
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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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Re: Overlapping sets DS [#permalink]
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07 Apr 2011, 13:03
S1 is restating the answer. Hence sufficient. S2 Very insufficient information. We still need the total number of elements. Hence A. gmatpapa wrote: Set A, B, C have some elements in common. If 16 elements are in both A and B, 17 elements are in both Aand 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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Re: Overlapping sets DS [#permalink]
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07 Apr 2011, 19:30
i agree, A looks sufficient. In B you will not be able to figure out the common elements.



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Re: Overlapping sets DS [#permalink]
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07 Apr 2011, 22:17
The answer is indeed A. You can see this for getting a proper visual idea of why (2) is insufficient. http://www.manhattangmat.com/forums/set ... t1921.html
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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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17 Jul 2012, 17:16
I do not agree at all that A is right ans....
Even if u consider 9 are common among A, B and C
still we dont have any clue that
whether
elements which are common b/w B and C also common with A also.... ?
and
whether
elements which are common b/w C and A also common with B too... ?
without these inf... nothing can be said....



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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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17 Jul 2012, 21:08
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smartmanav wrote: I do not agree at all that A is right ans....
Even if u consider 9 are common among A, B and C
still we dont have any clue that
whether
elements which are common b/w B and C also common with A also.... ?
and
whether
elements which are common b/w C and A also common with B too... ?
without these inf... nothing can be said.... Hiya  the statement reads that "of the 16 elements that are in both A and B, 9 elements are also in C". The first half of this means that there are 16 elements (let's say, 1 to 16) that are in A, and are also in B. The second half of the statement would indicate that of the numbers 116, 19 are also in C. This allows you to answer the question  there are 9 elements in A, B and C. Did that clear it up a little?



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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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17 Jul 2012, 21:38
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Thnx man , it was a word trap , with 2 weeks left to my exam I will have to b cautious.



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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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29 Jun 2013, 06:36
Just curious about the interpretation of question when it says If 16 elements are in both A and B if we draw a venn diagram it means the intersection of all 3 sections and a,b ( hope I made sense) PS: it isn't the best diagram...
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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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11 Jul 2013, 08:07
1. Statement 1 is sufficient because we know that A and B have 16 elements in common. Among these 16 elements, 9 are also in C. 2. Not sufficient since we still don't know if there's any element that's not belong to any of the 3 groups: A, B and C. The answer is A.



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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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11 Jul 2013, 09:06
fozzzy wrote: 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.
Just curious about the interpretation of question when it says
If 16 elements are in both A and B
if we draw a venn diagram it means the intersection of all 3 sections and a,b ( hope I made sense)
PS: it isn't the best diagram... 16 elements are in both A and B means sections d and g below: Hope it helps.
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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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14 Jul 2013, 03:10
Using statement 1 as statement 2 is insufficient The answer for the question common elements in all 3 (a,b and c) Statement 1 would be 25 Since C,B =9 A = 7 Correct?
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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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14 Jul 2013, 03:17
fozzzy wrote: Using statement 1 as statement 2 is insufficient
The answer for the question common elements in all 3 (a,b and c) Statement 1 would be 25
Since C,B =9 A = 7
Correct? (1) says: of the 16 elements that are in both A and B, 9 elements are also in C > sets A, B, and C have in 9 elements in common. Your answer does not make sense: if A and B have 16 elements in common, how can A, B, and C have more elements in common than only A and B?
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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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02 Oct 2013, 10:33
gmatpapa wrote: 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. fozzzy wrote: Hi, Could you please explain this particular question? Thanks in Advance! Dear Fozzzy, I got your p.m. and I am happy to help. First, the prompt. 16 elements are in both A and B  this 16 includes elements that are just in A & B as well as elements in A & B & C. 17 elements are in both A and C  this 17 includes elements that are just in A & C as well as elements in A & B & C. 18 elements are in both B and C  this 18 includes elements that are just in B & C as well as elements in A & B & C. To understand this, think about real world categories (these categories will include more elements than 18). Suppose A = set of males B = set of people who hold public office in the United States of America C = set of people who are AfricanAmerican. Some people are just in one of these categories. I'm a member of A, but not B or C. My senators Dianne Feinstein & Barbara Boxer are members of B, but not A or C. Oprah Winfrey & Alice Walker are members of C but not A or B. The US Secretary of State, John Kerry, is a member of sets A & B but not C. By contrast, the US President, Barack Obama, is a member of all three sets. If I say: list people who are members of A & B, then it would be perfectly acceptable to list both Kerry and Obama  all males who hold public office would be listed, irrespective of their race. The set of people in A & B, male office holders, would include some members who were part of C (such as Obama) and some members who were not part of C (such as Kerry). Now, the statements. (1) Of the 16 elements that are in both A and B, 9 elements are also in CWell, the members of the intersection set A & B includes some elements that are part of C and some elements that are not part of C. The 9 elements of (A & B) who are also included in C are the the nine elements common to all three sets. The remaining 7 would be those elements that, like John Kerry, are members of A & B but not C. Thus, this statement gives us enough information to answer the question, so it is sufficient. Did you have a question about the second statement as well? Mike
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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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21 Jan 2016, 05:07
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gmatpapa wrote: 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. Hi dear math experts, I'm just trying to refresh my skills for 3WayVennDiagram, would appreciate some comments on my solution. Thanks. (1) This gives us straight the solution. A,b,c have 9 elements in common. Sufficient (2) Clearly not sufficient, as we have no info about the TOTAL and the elements in group NEITHER (see formula: Total=a+b+cSum of 2Group overlaps+All 3+Neither) Answer A
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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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21 Jan 2016, 10:42
BrainLab wrote: gmatpapa wrote: 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. Hi dear math experts, I'm just trying to refresh my skills for 3WayVennDiagram, would appreciate some comments on my solution. Thanks. (1) This gives us straight the solution. A,b,c have 9 elements in common. Sufficient (2) Clearly not sufficient, as we have no info about the TOTAL and the elements in group NEITHER (see formula: Total=a+b+cSum of 2Group overlaps+All 3+Neither) Answer A Dear BrainLab, I'm happy to respond. My friend, you seem to understand quite well. If you would like more info on 2way and 3way Venn Diagrams, see this post: http://magoosh.com/gmat/2012/gmatsetsvenndiagrams/Best of luck! Mike
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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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02 Aug 2016, 16:12
if elements are a member of a and b, there are two possibilities. Either they can be in a, b, AND c. or they can be in ONLY a and b. It is very easy to see with a venn diagram. So let x = belongs to A,B, and C. Let y be ONLY belongs to A and B. Then x+y=16. Y is given as 9 from the first statement. That is what we want. So the number of elements belonging to A, B, AND C is 9.
We can attempt a formula for statement two. 25+35+30(16+17+18)+x+neither=? We have two many unknowns.



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Set A, B, C have some elements in common. If 16 elements are [#permalink]
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02 Aug 2016, 16:12
if elements are a member of a and b, there are two possibilities. Either they can be in a, b, AND c. or they can be in ONLY a and b. It is very easy to see with a venn diagram. So let x = belongs to A,B, and C. Let y be ONLY belongs to A and B. Then x+y=16. x is given as 9 from the first statement. That is what we want. So the number of elements belonging to A, B, AND C is 9.
We can attempt a formula for statement two. 25+35+30(16+17+18)+x+neither=? We have too many unknowns.



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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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05 Feb 2017, 01:14
option(1) => n(A u B) = 16 out of which 9 are also there in C, thus these 9 elements are common to all A,B & C, hence the answer and therefore this is sufficient to answer. option(2) => N(A) = 25 N(B) = 30 N(C) = 35 Missing Total and Neither category. Insufficient. Hence A.
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Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
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23 Mar 2017, 16:20
gmatpapa wrote: 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. I suppose that B is the trap answer in this question B seems like an appealing answer if you draw a Venn Diagram but I don't think you can calculate the total with the information given? A doesn't seem to give much information we cannot calculate the total; however, we can calculate the answer on a Venn diagram because the intersection of A and B only plus the intersection of A B C must equal 16. Therefore, Statement (1) is sufficient.




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