December 09, 2018 December 09, 2018 07:00 AM PST 09:00 AM PST Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT. December 10, 2018 December 10, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 30 Mar 2010
Posts: 75

Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to
[#permalink]
Show Tags
Updated on: 31 Aug 2017, 10:07
Question Stats:
63% (01:35) correct 37% (01:35) wrong based on 275 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Click on kudos, if you like my post!
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




Math Expert
Joined: 02 Sep 2009
Posts: 51035

Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to
[#permalink]
Show Tags
24 May 2010, 03:00
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+932*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 [ 11.63 KiB  Viewed 12053 times ]
For more check ADVANCED OVERLAPPING SETS PROBLEMS
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Intern
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
23 May 2010, 11:36
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
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
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
Joined: 11 Jun 2010
Posts: 41

Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to
[#permalink]
Show Tags
26 Jul 2010, 04:12
thanks for sharing this question



Manager
Joined: 20 Dec 2010
Posts: 195
Schools: UNC Duke Kellogg

Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to
[#permalink]
Show Tags
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
Joined: 01 Feb 2011
Posts: 660

Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to
[#permalink]
Show Tags
25 Jun 2011, 17:20
total = X+Y+Z2(all three) (sum of two overlaps) + neither
20 = 5+ 7+9  2(2)3+neither =>neither = 6



Senior Manager
Joined: 29 Jun 2017
Posts: 467
GPA: 4
WE: Engineering (Transportation)

Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to
[#permalink]
Show Tags
29 Sep 2017, 07:44
Ans is B 20None = 5+7+932x2 20N=14 N=6
_________________
Give Kudos for correct answer and/or if you like the solution.



Intern
Status: No Progress without Struggle
Joined: 04 Aug 2017
Posts: 43
Location: Armenia
GPA: 3.4

Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to
[#permalink]
Show Tags
16 Jul 2018, 02:56
Here is the Venn Diagram Method, which is more applicable than using the formula with no understanding.
Attachments
ITEMSABC.PNG [ 69.56 KiB  Viewed 1295 times ]
_________________
Seryozha Sargsyan 21
Contact: sargsyanseryozha@gmail.com
What you think, you become, What you feel, you attract, What you imagine, you create.




Re: Of 20 Adults, 5 belong to X, 7 belong to Y, and 9 belong to &nbs
[#permalink]
16 Jul 2018, 02:56






