Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 29 May 2017, 09:20

# Today:

Memorial Day - GMAT Club Tests are Open without Subscription

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Current Student
Status: Up again.
Joined: 31 Oct 2010
Posts: 534
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Followers: 22

Kudos [?]: 465 [0], given: 75

Set A, B, C have some elements in common. If 16 elements are [#permalink]

### Show Tags

07 Apr 2011, 12:50
7
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

59% (02:05) correct 41% (01:24) wrong based on 449 sessions

### HideShow timer Statistics

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

_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 903
Followers: 14

Kudos [?]: 359 [0], given: 123

Re: Overlapping sets DS [#permalink]

### Show Tags

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.
Manager
Joined: 05 Jul 2010
Posts: 195
Followers: 1

Kudos [?]: 19 [0], given: 18

Re: Overlapping sets DS [#permalink]

### Show Tags

07 Apr 2011, 19:30
i agree, A looks sufficient. In B you will not be able to figure out the common elements.
SVP
Joined: 16 Nov 2010
Posts: 1666
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 34

Kudos [?]: 533 [0], given: 36

Re: Overlapping sets DS [#permalink]

### Show Tags

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
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 18 Jun 2012
Posts: 39
Followers: 1

Kudos [?]: 7 [0], given: 15

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

### Show Tags

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....
Manager
Joined: 25 Jun 2012
Posts: 56
Followers: 14

Kudos [?]: 22 [1] , given: 2

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

### Show Tags

17 Jul 2012, 21:08
1
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?
Intern
Joined: 18 Jun 2012
Posts: 39
Followers: 1

Kudos [?]: 7 [0], given: 15

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

### Show Tags

17 Jul 2012, 21:38
1
This post was
BOOKMARKED
Thnx man , it was a word trap , with 2 weeks left to my exam I will have to b cautious.
Director
Joined: 29 Nov 2012
Posts: 885
Followers: 15

Kudos [?]: 1194 [0], given: 543

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

### Show Tags

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...
Attachments

template.jpg [ 13.12 KiB | Viewed 11647 times ]

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Intern
Joined: 16 Jun 2010
Posts: 20
Followers: 0

Kudos [?]: 13 [0], given: 75

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

### Show Tags

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.
Math Expert
Joined: 02 Sep 2009
Posts: 39051
Followers: 7755

Kudos [?]: 106551 [0], given: 11628

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

### Show Tags

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.
_________________
Director
Joined: 29 Nov 2012
Posts: 885
Followers: 15

Kudos [?]: 1194 [0], given: 543

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

### Show Tags

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?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 39051
Followers: 7755

Kudos [?]: 106551 [0], given: 11628

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

### Show Tags

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?
_________________
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4044
Followers: 1421

Kudos [?]: 6801 [0], given: 84

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

### Show Tags

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 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
_________________

Mike McGarry
Magoosh Test Prep

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15518
Followers: 651

Kudos [?]: 210 [0], given: 0

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

### Show Tags

03 Jan 2015, 10:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Director
Joined: 10 Mar 2013
Posts: 597
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 17

Kudos [?]: 357 [2] , given: 200

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

### Show Tags

21 Jan 2016, 05:07
2
KUDOS
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)

_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4044
Followers: 1421

Kudos [?]: 6801 [0], given: 84

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

### Show Tags

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
_________________

Mike McGarry
Magoosh Test Prep

Intern
Joined: 17 Jul 2016
Posts: 9
Followers: 0

Kudos [?]: 3 [0], given: 1

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

### Show Tags

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.
Intern
Joined: 17 Jul 2016
Posts: 9
Followers: 0

Kudos [?]: 3 [0], given: 1

Set A, B, C have some elements in common. If 16 elements are [#permalink]

### Show Tags

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.
Senior Manager
Joined: 26 Oct 2016
Posts: 460
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Followers: 25

Kudos [?]: 64 [0], given: 823

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

### Show Tags

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.
_________________

Thanks & Regards,
Anaira Mitch

Manager
Joined: 12 Nov 2016
Posts: 196
Followers: 0

Kudos [?]: 7 [0], given: 135

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

### Show Tags

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   [#permalink] 23 Mar 2017, 16:20
Similar topics Replies Last post
Similar
Topics:
1 Both a set S and a set P have the same number of elements. Is a standa 5 02 Apr 2017, 05:09
1 Two sets, A and B, have the same number of elements 3 03 May 2013, 17:06
5 Is the probability of an element in Set B also being an elem 4 17 Jul 2014, 08:58
1 If set B is a subset of Set A, how many elements are in set 11 26 Jan 2013, 00:41
14 Is the product of all of the elements in Set S negative? 14 21 Apr 2016, 00:23
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.