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# Of the 330 people living on the island of Lesbos, two thirds of them

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Math Expert
Joined: 02 Sep 2009
Posts: 56257
Of the 330 people living on the island of Lesbos, two thirds of them  [#permalink]

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28 Mar 2017, 04:56
2
7
00:00

Difficulty:

65% (hard)

Question Stats:

65% (03:15) correct 35% (03:21) wrong based on 116 sessions

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Of the 330 people living on the island of Lesbos, two thirds of them are members of various nature groups. 46 people are only members of both the Bucolic Society and the Animal Awareness Group, while 18 people are in neither the Crusaders for Nature Society nor the Bucolic Society. If 33 people are only members of both Animal Awareness and Crusaders, and the charters of both the Crusaders Society and Bucolic Society do not allow members to join the other group, how many people living on the island of Lesbos are solely members of the Crusaders Society or solely members of the Bucolic Society?

A. 233
B. 202
C. 169
D. 123
E. 86

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Joined: 19 Apr 2017
Posts: 2
Of the 330 people living on the island of Lesbos, two thirds of them  [#permalink]

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22 Apr 2017, 23:15
1
1
Bunuel wrote:
Of the 330 people living on the island of Lesbos, two thirds of them are members of various nature groups. 46 people are only members of both the Bucolic Society and the Animal Awareness Group, while 18 people are in neither the Crusaders for Nature Society nor the Bucolic Society. If 33 people are only members of both Animal Awareness and Crusaders, and the charters of both the Crusaders Society and Bucolic Society do not allow members to join the other group, how many people living on the island of Lesbos are solely members of the Crusaders Society or solely members of the Bucolic Society?

A. 233
B. 202
C. 169
D. 123
E. 86

Well, since no one has answered, I'll take a stab at it. First time posting in GMATclub so pardon any issues. This problem is easiest to be visualized with a venn diagram.

So (2/3)*330 = 220 is the total amount of people that are part of some group. We know that people in A + B = 46, A + C = 33, and A alone = 18. There is 0 people in B + C. The key thing here is that people from group B and group C CANNOT be in both groups, so we know that there is no one in all three groups.

So then we just sum 46 + 33 + 18 = 97 [this is group A]. Now 220 - group A = 220 - 97 = 123 so D is the answer.

Hope this helps! Let me know if there are any mistakes.
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Joined: 24 Jun 2008
Posts: 14
Re: Of the 330 people living on the island of Lesbos, two thirds of them  [#permalink]

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28 Apr 2017, 15:26
1
Bunuel wrote:
Of the 330 people living on the island of Lesbos, two thirds of them are members of various nature groups. 46 people are only members of both the Bucolic Society and the Animal Awareness Group, while 18 people are in neither the Crusaders for Nature Society nor the Bucolic Society. If 33 people are only members of both Animal Awareness and Crusaders, and the charters of both the Crusaders Society and Bucolic Society do not allow members to join the other group, how many people living on the island of Lesbos are solely members of the Crusaders Society or solely members of the Bucolic Society?

A. 233
B. 202
C. 169
D. 123
E. 86

Bunuel,

It took me alomst 4 min to solve this question. I could not understand Crusaders for Nature Society and Crusader Society is same and hang up there for a while.
What is the best way to solve these questions - I was confused whether I start drawing overlapping sets or just work of the equations.
Intern
Joined: 05 Aug 2018
Posts: 7
Re: Of the 330 people living on the island of Lesbos, two thirds of them  [#permalink]

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09 Aug 2018, 02:04
the ke'y sentence：【the charters of both the Crusaders Society and Bucolic Society do not allow members to join the other group】

thanks for N00b‘s explanation!
There is 0 people in B + C. The key thing here is that people from group B and group C CANNOT be in both groups, so we know that there is no one in all three groups.
Senior SC Moderator
Joined: 22 May 2016
Posts: 3077
Of the 330 people living on the island of Lesbos, two thirds of them  [#permalink]

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10 Aug 2018, 20:29
1
Bunuel wrote:
Of the 330 people living on the island of Lesbos, two thirds of them are members of various nature groups. 46 people are only members of both the Bucolic Society and the Animal Awareness Group, while 18 people are in neither the Crusaders for Nature Society nor the Bucolic Society. If 33 people are only members of both Animal Awareness and Crusaders, and the charters of both the Crusaders Society and Bucolic Society do not allow members to join the other group, how many people living on the island of Lesbos are solely members of the Crusaders Society or solely members of the Bucolic Society?

A. 233
B. 202
C. 169
D. 123
E. 86

Attachment:

venn 2018.8.10.jpg [ 74.47 KiB | Viewed 562 times ]

This question can be solved very quickly with a Venn diagram.
The numbers in blue indicate the order in which I entered the information.

There are three groups, call them A, B, and C, to which $$(\frac{2}{3}*330)=220$$ belong
After drawing three overlapping circles, A, B, and C, we have

(5) A = 18
Logically: if 18 persons ARE in a group, but are in neither B nor C, they must be in group A

B = ?
C = ?

(1) A and B = 46 (pink)

(2) A and C = 33 (yellow)

(3) B and C = 0 (green)
-- B and C cannot overlap anywhere; the charters of B and C do not allow their members to join the other group

(4) All three = 0 (gray)
In order to belong to all 3, a person would have to be in B and C. Not allowed.

(5) 18 people are in neither B nor C. Those 18 must be in A only. (orange)

(6) Add up all the numbers:
(18 + 33 + 46) = 97

The blank spaces (both purple) are only B and only C -- exactly what the question asks for.
"Only C" = solely members of the Crusaders Society and "Only B" = solely members of the Bucolic Society

(7) C only and B only? Subtract 97 from 220
(220 - 97) = 123 who are solely members of C or solely members of B

Whoever wrote this question . . . great question +1,
made even better by highbrow cultural literacy with a sardonic twist on the Green Panthers.
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Of the 330 people living on the island of Lesbos, two thirds of them   [#permalink] 10 Aug 2018, 20:29
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