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Posts: 68
Updated on: 31 Aug 2017, 10:07
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.
Last edited by abhimahna on 31 Aug 2017, 10:07, edited 1 time in total.
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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
A) 4
B) 6
C) 8
D) 10
E) 12
pardeepattri
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 [ 11.63 KiB | Viewed 32248 times ]
For more check ADVANCED OVERLAPPING SETS PROBLEMS
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Here is the Venn Diagram Method, which is more applicable than using the formula with no understanding.
Attachments
ITEMSABC.PNG [ 69.56 KiB | Viewed 20695 times ]
General Discussion
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
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
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
my quant is bit rusty and venn diagrams is something i really want to improve at, thank Quant Forum Moderator
Kudos to you!
Roy
Posts: 39
thanks for sharing this question
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.
20 = (N) + 21 - (3) - (4)
20 = 14 + N
Neither = 6
Good question this -- helps if one knows the formula.
total = X+Y+Z-2(all three) -(sum of two overlaps) + neither
20 = 5+ 7+9 - 2(2)-3+neither
=>neither = 6
20 = 5+ 7+9 - 2(2)-3+neither
=>neither = 6
sahilvijay
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Ans is B
20-None = 5+7+9-3-2x2
20-N=14
N=6
20-None = 5+7+9-3-2x2
20-N=14
N=6
pardeepattri
The Formula:
Total=X+Y+Z-EXACTLY 2-2*ALL THREE +NEITHER (N)
20=5+7+9-3-2*2+N
N=6
The answer is B.
GMATNinja : Hope all is well
Can you please show how to solve these sort of problems using your method, showed here at 10:45 https://www.youtube.com/watch?v=OsKI-5z3Kg4&t=1039s ?
Thank you and looking forward to your reply
Can you please show how to solve these sort of problems using your method, showed here at 10:45 https://www.youtube.com/watch?v=OsKI-5z3Kg4&t=1039s ?
Thank you and looking forward to your reply
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