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If both club A and club B have more than 10 members each, are there so

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DS Forum Moderator
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If both club A and club B have more than 10 members each, are there so  [#permalink]

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New post 28 Jun 2018, 23:06
2
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

34% (00:57) correct 66% (01:06) wrong based on 36 sessions

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If both club A and club B have more than 10 members each, are there some people who are members of both club A and club B?

(1) All those who are not members of club A, are also not members of club B.

(2) All those who are members of club B, are also members of club A.
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Re: If both club A and club B have more than 10 members each, are there so  [#permalink]

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New post 29 Jun 2018, 08:57
Hi,

I'll give it a try.
(can you please comment on my method as well?)

Rephrased question = "Is (A and B) non void?"

(1) equivalent to: "Non A" included in "Non B"
(2) equivalent to "B included in A"

-------

(1) In logic, is a ==> b, then non-b ==> non-a. In this case, (1) means "B included in A".
By extension: "A and B" is non void: SUFFICIENT

(2) Obviously SUFFICIENT (let x in B, then x in A, so x in A and B)

Answer: D

Any better method?
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Re: If both club A and club B have more than 10 members each, are there so  [#permalink]

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New post 29 Jun 2018, 11:12
Answer - D
We can solve this using venn diagram..
A and B are greater than 10
1) All those who are not members of club A, are also not members of club B. that means that there are no individuals who are just B’s members but since members of B are greater than 10 that only leaves us with a possibiltiy that those more than 10 members are both the members of A and B - Sufficient

2) All those who are members of club B, are also members of club A

Its directly given in this option that all those who are members of B are ALSO members of A i.e. they are the members of BOTH A and B.. So Sufficient.

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Re: If both club A and club B have more than 10 members each, are there so &nbs [#permalink] 29 Jun 2018, 11:12
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