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# GMAT Club World Cup 2022 (DAY 1): A poll conducted in a football club

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Re: GMAT Club World Cup 2022 (DAY 1): A poll conducted in a football club [#permalink]
2
Kudos
I--- Only P+ Only A + Only F
II--- P&F together but not A + P&A together but not F + A&F together but not P
III--- all P, F, A together
O--- None of the P,F&A

II=120
I+2II+3III=450
I+3III=210

Total Football Fanclub members, T=O+I+II+III

S(1) Equal number of members root for Portugal only and for Argentina only.
Only P= Only A
does not help us to identify T

S(2) For every 2 members of the club who root for none of the three teams, there is 1 member who roots for all three of the teams.

If III=x, O will be 2x

T= I+II+x+2x
T=I+II+3x or I+II+3III

T=120+I+3III=120+210=330

S2 is sufficient
Therefore, B
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Re: GMAT Club World Cup 2022 (DAY 1): A poll conducted in a football club [#permalink]
1
Kudos
Bunuel wrote:
A poll conducted among the members of a football fan club, revealed that 100 of them root for Portugal, 150 of them root for France, and 200 of them root for Argentina. Also, 120 of them root for exactly two of the three teams. How many members does the fan club have ?

(1) Equal number of members root for Portugal only and for Argentina only.
(2) For every 2 members of the club who root for none of the three teams, there is 1 member who roots for all three of the teams.

 This question was provided by GMAT Club for the GMAT Club World Cup Competition Compete, Get Better, Win prizes and more

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Re: GMAT Club World Cup 2022 (DAY 1): A poll conducted in a football club [#permalink]
3
Kudos
Portugal (P) - 100
France (F) - 150
Argentina (A) - 200
PF - ?
FA - ?
PA - ?
PFA - ?
P only - ?
F only - ?
A only - ?
None - ?

PF+FA+PA = 120

Important question to keep in mind -

Total number of members = P + F + A - (PF+FA+PA) - 2 (PFA) + None

Statement 1 -
P only = A only

Insufficient as it doesn't give us information that can lead us to answer.

Statement 2-
None = 2 (PFA)

Total = 100+150+200-(120)-2(PFA)+None

Now , replacing the value of None = 2(PFA)

Total = 330 - 2PFA + 2PFA
Total = 330

Hence, statement 2 is sufficient.

B is the correct choice.
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Re: GMAT Club World Cup 2022 (DAY 1): A poll conducted in a football club [#permalink]
Hello from the GMAT Club BumpBot!

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Re: GMAT Club World Cup 2022 (DAY 1): A poll conducted in a football club [#permalink]
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