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# There are 125 members in the winter sports club. Of those, 20 do not

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Math Expert
Joined: 02 Sep 2009
Posts: 56271
There are 125 members in the winter sports club. Of those, 20 do not  [#permalink]

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15 Apr 2018, 09:53
2
7
00:00

Difficulty:

55% (hard)

Question Stats:

60% (02:34) correct 40% (02:56) wrong based on 88 sessions

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There are 125 members in the winter sports club. Of those, 20 do not ski or snowboard. If 1/3 of the people who ski also snowboard, and if the number of people who only snowboard is equal to 1/2 of the number of people who ski and snowboard, how many people only snowboard?

A. 15
B. 20
C. 30
D. 45
E. 60

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Joined: 08 Apr 2018
Posts: 6
Re: There are 125 members in the winter sports club. Of those, 20 do not  [#permalink]

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15 Apr 2018, 10:06
Bunuel wrote:
There are 125 members in the winter sports club. Of those, 20 do not ski or snowboard. If 1/3 of the people who ski also snowboard, and if the number of people who only snowboard is equal to 1/2 of the number of people who ski and snowboard, how many people only snowboard?

A. 15
B. 20
C. 30
D. 45
E. 60
Let 3x people ski. So 2x people only ski and x people ski and snowboard. Now x/2 people only snowboard.
Out of 125 people, 20 do not participate. So only 105 remain.
So, 2x+x+x/2=105
So, x=30
But we need x/2 which is equal to 15.

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Posts: 167
Location: Viet Nam
There are 125 members in the winter sports club. Of those, 20 do not  [#permalink]

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02 Mar 2019, 04:21
1
Bunuel wrote:
There are 125 members in the winter sports club. Of those, 20 do not ski or snowboard. If 1/3 of the people who ski also snowboard, and if the number of people who only snowboard is equal to 1/2 of the number of people who ski and snowboard, how many people only snowboard?

A. 15
B. 20
C. 30
D. 45
E. 60

Call total Ski members = a => No Ski member = 1-a => People who ski & snowboard = a/3
Who only snowboard = 1/2 * people who ski & snowboard = 1/2 * a/3 = a/6
People do not ski or snowboard = 20 = 20/125 = 4/25
Total No ski members = People who only snowboard + People do not ski or snowboard => 1- a= a/6 + 4/25 => a = 90.
Hence, peple who only snowboard = a/60 = 90/6 = 15. Answer A
It is easier to solve by table but I dont know how to attach image so I write down this..
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Re: There are 125 members in the winter sports club. Of those, 20 do not  [#permalink]

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02 Mar 2019, 09:19
Bunuel wrote:
There are 125 members in the winter sports club. Of those, 20 do not ski or snowboard. If 1/3 of the people who ski also snowboard, and if the number of people who only snowboard is equal to 1/2 of the number of people who ski and snowboard, how many people only snowboard?

A. 15
B. 20
C. 30
D. 45
E. 60

Using Venn diagram
Attachments

image.jpg [ 1.88 MiB | Viewed 709 times ]

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Re: There are 125 members in the winter sports club. Of those, 20 do not   [#permalink] 02 Mar 2019, 09:19
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