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# In a group of 20 people, 5 of them belong to the golf club, 7 to the

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
In a group of 20 people, 5 of them belong to the golf club, 7 to the  [#permalink]

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03 May 2017, 03:43
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25% (medium)

Question Stats:

75% (01:35) correct 25% (02:00) wrong based on 314 sessions

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In a group of 20 people, 5 of them belong to the golf club, 7 to the swim club, and 9 to the tennis club. If 2 of the people belong to all three clubs and 3 belong to exactly two of the three clubs, then how many of 20 people belong to neither of the three clubs?

A. 1
B. 2
C. 4
D. 6
E. 11

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Joined: 29 Apr 2017
Posts: 16
Re: In a group of 20 people, 5 of them belong to the golf club, 7 to the  [#permalink]

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03 May 2017, 05:08
IMO B
20 + 3 - 5 - 7 - 9 = 2

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Manager
Joined: 08 Sep 2016
Posts: 102
Re: In a group of 20 people, 5 of them belong to the golf club, 7 to the  [#permalink]

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03 May 2017, 06:09
IMO (D)
20 = 5+7+9-3-(2*2)+x
x=6
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Joined: 05 Mar 2015
Posts: 1015
Re: In a group of 20 people, 5 of them belong to the golf club, 7 to the  [#permalink]

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03 May 2017, 11:55
Bunuel wrote:
In a group of 20 people, 5 of them belong to the golf club, 7 to the swim club, and 9 to the tennis club. If 2 of the people belong to all three clubs and 3 belong to exactly two of the three clubs, then how many of 20 people belong to neither of the three clubs?

A. 1
B. 2
C. 4
D. 6
E. 11

direct formulae

20= 5+7+9-3-2*2+neither
neither =6

Ans D
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Re: In a group of 20 people, 5 of them belong to the golf club, 7 to the  [#permalink]

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06 May 2017, 17:33
Bunuel wrote:
In a group of 20 people, 5 of them belong to the golf club, 7 to the swim club, and 9 to the tennis club. If 2 of the people belong to all three clubs and 3 belong to exactly two of the three clubs, then how many of 20 people belong to neither of the three clubs?

A. 1
B. 2
C. 4
D. 6
E. 11

We can create the following equation:

Total # people = # who belong to golf + # who belong to tennis + # who belong to swim - (# who belong to 2 clubs) - 2(# who belong to all 3 clubs) + # who belong to neither

20 = 5 + 9 + 7 - 3 - 2(2) + N

20 = 14 + N

6 = N

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Re: In a group of 20 people, 5 of them belong to the golf club, 7 to the  [#permalink]

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05 Aug 2018, 03:07
ScottTargetTestPrep wrote:
Bunuel wrote:
In a group of 20 people, 5 of them belong to the golf club, 7 to the swim club, and 9 to the tennis club. If 2 of the people belong to all three clubs and 3 belong to exactly two of the three clubs, then how many of 20 people belong to neither of the three clubs?

A. 1
B. 2
C. 4
D. 6
E. 11

We can create the following equation:

Total # people = # who belong to golf + # who belong to tennis + # who belong to swim - (# who belong to 2 clubs) - 2(# who belong to all 3 clubs) + # who belong to neither

20 = 5 + 9 + 7 - 3 - 2(2) + N

20 = 14 + N

6 = N

Dear ScottTargetTestPrep
Why do you multiple by 2(#of members in all three groups)?
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Joined: 22 Feb 2018
Posts: 420
Re: In a group of 20 people, 5 of them belong to the golf club, 7 to the  [#permalink]

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05 Aug 2018, 03:38
1
nigina93 wrote:
ScottTargetTestPrep wrote:
Bunuel wrote:
In a group of 20 people, 5 of them belong to the golf club, 7 to the swim club, and 9 to the tennis club. If 2 of the people belong to all three clubs and 3 belong to exactly two of the three clubs, then how many of 20 people belong to neither of the three clubs?

A. 1
B. 2
C. 4
D. 6
E. 11

We can create the following equation:

Total # people = # who belong to golf + # who belong to tennis + # who belong to swim - (# who belong to 2 clubs) - 2(# who belong to all 3 clubs) + # who belong to neither

20 = 5 + 9 + 7 - 3 - 2(2) + N

20 = 14 + N

6 = N

Dear ScottTargetTestPrep
Why do you multiple by 2(#of members in all three groups)?

nigina93
Check out this link for overlapping set formulas
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Re: In a group of 20 people, 5 of them belong to the golf club, 7 to the  [#permalink]

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26 Aug 2018, 04:12
Can someone explain how we decide which formula to use in 3 or more overlapping sets problems. As I understand there are two formulas:
Formula 1:
Total= Golf + Swim + Tennis - (GnS) - (GnT) - (TnS) - (TnG) + (GnTnS)

Formula 2:
Total = Golf + Swim + Tennis - (sum of those in two groups) - 2*those in three groups

I'm getting different answers with the two formulas
Math Expert
Joined: 02 Sep 2009
Posts: 58320
Re: In a group of 20 people, 5 of them belong to the golf club, 7 to the  [#permalink]

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26 Aug 2018, 04:27
ayeshaahmed89 wrote:
Can someone explain how we decide which formula to use in 3 or more overlapping sets problems. As I understand there are two formulas:
Formula 1:
Total= Golf + Swim + Tennis - (GnS) - (GnT) - (TnS) - (TnG) + (GnTnS)

Formula 2:
Total = Golf + Swim + Tennis - (sum of those in two groups) - 2*those in three groups

I'm getting different answers with the two formulas

Explained here: ADVANCED OVERLAPPING SETS PROBLEMS

19. Overlapping Sets

For more:
ALL YOU NEED FOR QUANT ! ! !
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Re: In a group of 20 people, 5 of them belong to the golf club, 7 to the  [#permalink]

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27 Nov 2018, 22:51
Hi All,

3-Group Overlapping Sets questions are relatively rare on the Official GMAT (you likely will NOT see this version of Overlapping Sets on Test Day). However, there is a formula that you can use to solve it.

Total = (Those in none of the groups) + (1st group) + (2nd group) + (3rd group) - (1st and 2nd) - (1st and 3rd) - (2nd and 3rd) - 2(all 3 groups).

In overlapping sets questions, any person who appears in more than one group has been counted more than once. When dealing with groups of people, you're not supposed to count any individual more than once, so the formula 'subtracts' all of the 'extra' times that a person is counted.

For example, someone who is in BOTH the 1st group and the 2nd group will be counted twice....that's why we SUBTRACT that person later on [in the (1st and 2nd) group].

In this prompt, we're given the Total, a number for each of the 3 individual groups, the number of people in two of the groups and the number of people who appear in all 3 groups. The equation would look like this (note: the [ ] includes all three of the 2-group groups)...

20 = (None) + 5 + 7 + 9 - [3] - 2(2)

20 = (None) + 21 - 7

20 = (None) + 14

6 = (None)

The number of people who are in none of the three groups is 6.

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Re: In a group of 20 people, 5 of them belong to the golf club, 7 to the   [#permalink] 27 Nov 2018, 22:51
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