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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 [#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.
[Reveal] Spoiler: OA

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07 Apr 2011, 13:03
S1 is re-stating 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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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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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 1-16, 1-9 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.

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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
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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,

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 African-American.

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 C
Well, 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 3-Way-Venn-Diagram, 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+c-Sum of 2-Group overlaps+All 3+Neither)

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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 3-Way-Venn-Diagram, 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+c-Sum of 2-Group overlaps+All 3+Neither)

Dear BrainLab,
I'm happy to respond. My friend, you seem to understand quite well.

If you would like more info on 2-way and 3-way Venn Diagrams, see this post:
http://magoosh.com/gmat/2012/gmat-sets-venn-diagrams/

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.

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Re: Set A, B, C have some elements in common. If 16 elements are   [#permalink] 23 Mar 2017, 16:20
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