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Set A, B, C have some elements in common. If 16 elements are [#permalink]
07 Apr 2011, 11:50

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

55% (02:07) correct
45% (01:17) wrong based on 239 sessions

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.

Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
17 Jul 2012, 20:08

1

This post received KUDOS

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? _________________

Hi, I'm DonQuixote, a former GMAT Pill student who scored 780. I'm very grateful for this score and have now joined their staff My account of my GMAT experience can be found here.

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.

Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
11 Jul 2013, 07:07

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.

Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
11 Jul 2013, 08:06

Expert's post

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:

Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
14 Jul 2013, 02:17

Expert's post

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? _________________

Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
02 Oct 2013, 09:33

Expert's post

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 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?

Re: Set A, B, C have some elements in common. If 16 elements are [#permalink]
03 Jan 2015, 09:31

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