GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 22 Feb 2020, 02:37

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 30 Mar 2010
Posts: 71
Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to  [#permalink]

Show Tags

New post Updated on: 31 Aug 2017, 10:07
3
10
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

67% (01:33) correct 33% (01:38) wrong based on 379 sessions

HideShow timer Statistics

Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to Z. If 2 belong to all three organizations and 3 belong to exactly 2 organizations, how many belong to none of these organizations?

A) 4
B) 6
C) 8
D) 10
E) 12

Originally posted by pardeepattri on 18 May 2010, 15:52.
Last edited by abhimahna on 31 Aug 2017, 10:07, edited 1 time in total.
Added Options
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 61385
Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to  [#permalink]

Show Tags

New post 24 May 2010, 03:00
10
8
pardeepattri wrote:
Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to Z. If 2 belong to all three organizations and 3 belong to exactly 2 organizations, how many belong to none of these organizations?

Sorry I don't have OA.


Above solution is not right.

The formula would be:

ALL = 20 = X+Y+Z - {Members of Exactly 2} - 2*{Members of All 3} + None --> 20=5+7+9-3-2*2+N --> N=6.

We subtract {Members of Exactly 2} once as when we add X+Y+Z, this intersection (exactly 2 - segments 1, 2 and 3 on the diagram below) is counted twice thus one should be subtracted.

We subtract {Members of All 3} twice as when we add X+Y+Z, this intersection (all 3 - segment 4 in the diagram below) is counted thrice, thus two should be subtracted.
Attachment:
Union_3sets.gif
Union_3sets.gif [ 11.63 KiB | Viewed 14462 times ]


For more check ADVANCED OVERLAPPING SETS PROBLEMS
_________________
General Discussion
Intern
Intern
avatar
Joined: 16 Oct 2009
Posts: 10
Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to  [#permalink]

Show Tags

New post 23 May 2010, 11:36
1
The answer should be 10. This is how I got to it,

Total - 20
Group X - 5
Group Y - 7
Group Z - 9

Common Between 2 Groups - 3 (Lets take this as X+Y)
Common Between 3 Groups - 2 (Lets take this as X+Y+Z)
Neither - N

Total - N = (X+Y+Z) - 2(common b/w 2 groups) - 2(common b/w 3 groups)
20 - N = 20 - (4 + 6)
20 - N = 10 & N = 10

Though you might want to check on the figures because 5,7 & 9 add upto 21 not 20. So if the total is 20 then 10 are part of neither.


Roy
Intern
Intern
avatar
Joined: 16 Oct 2009
Posts: 10
Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to  [#permalink]

Show Tags

New post 24 May 2010, 06:00
Sorry pradeep I stand corrected.

my quant is bit rusty and venn diagrams is something i really want to improve at, thank Quant Forum Moderator

Kudos to you!

Roy
Intern
Intern
avatar
Joined: 11 Jun 2010
Posts: 40
Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to  [#permalink]

Show Tags

New post 26 Jul 2010, 04:12
thanks for sharing this question
Manager
Manager
avatar
Joined: 20 Dec 2010
Posts: 155
Schools: UNC Duke Kellogg
Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to  [#permalink]

Show Tags

New post 25 Jun 2011, 09:15
Total = (Neither) + x + y + z - (Exactly 2) - 2*(All 3)

20 = (N) + 21 - (3) - (4)

20 = 14 + N

Neither = 6

Good question this -- helps if one knows the formula.
Director
Director
avatar
Joined: 01 Feb 2011
Posts: 522
Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to  [#permalink]

Show Tags

New post 25 Jun 2011, 17:20
total = X+Y+Z-2(all three) -(sum of two overlaps) + neither

20 = 5+ 7+9 - 2(2)-3+neither
=>neither = 6
Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 416
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to  [#permalink]

Show Tags

New post 29 Sep 2017, 07:44
Ans is B

20-None = 5+7+9-3-2x2
20-N=14
N=6
Intern
Intern
User avatar
B
Status: No Progress without Struggle
Joined: 04 Aug 2017
Posts: 42
Location: Armenia
GPA: 3.4
Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to  [#permalink]

Show Tags

New post 16 Jul 2018, 02:56
3
1
Here is the Venn Diagram Method, which is more applicable than using the formula with no understanding.
Attachments

ITEMSABC.PNG
ITEMSABC.PNG [ 69.56 KiB | Viewed 3693 times ]


_________________
Seryozha Sargsyan 21

Contact: sargsyanseryozha@gmail.com

What you think, you become,
What you feel, you attract,
What you imagine, you create.
GMAT Club Bot
Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to   [#permalink] 16 Jul 2018, 02:56
Display posts from previous: Sort by

Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne