In a group of 800 people, 1/5 play at least one instrument.. : GMAT Problem Solving (PS)
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# In a group of 800 people, 1/5 play at least one instrument..

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Intern
Joined: 30 Jun 2012
Posts: 8
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Kudos [?]: 23 [0], given: 1

In a group of 800 people, 1/5 play at least one instrument.. [#permalink]

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05 Aug 2012, 07:00
00:00

Difficulty:

25% (medium)

Question Stats:

80% (02:25) correct 20% (01:43) wrong based on 128 sessions

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In a group of 800 people, 1/5 play at least one instrument, 96 play two or more. What is the probability that one student play exactly one instrument?

A) 2/125
B) 3/125
C)2/25
D) 3/25
E) 1/5
[Reveal] Spoiler: OA

Last edited by ferrarih on 05 Aug 2012, 15:58, edited 2 times in total.
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Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96439 [1] , given: 10751

Re: In a group with 800 people... [#permalink]

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05 Aug 2012, 07:08
1
KUDOS
Expert's post
ferrarih wrote:
In a grouup of 800 people, 1/5 play at least one instrument, 96 play two or more. Whats it is e probability that one student play exactly one instrument?

A) 2/125
B) 3/125
C)2/25
D) 3/25
E) 1/5

Given that 1/5*800=160 students play 1 or more instrument and 96 play 2 or more, so 160-96=64 students play exactly 1 instrument.

Therefore the probability that a randomly chosen student plays exactly one instrument is 64/800=2/25.

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Director
Joined: 22 Mar 2011
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WE: Science (Education)
Followers: 101

Kudos [?]: 910 [0], given: 43

Re: In a group with 800 people... [#permalink]

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05 Aug 2012, 07:14
ferrarih wrote:
In a grouup of 800 people, 1/5 play at least one instrument, 96 play two or more. Whats it is e probability that one student play exactly one instrument?

A) 2/125
B) 3/125
C)2/25
D) 3/25
E) 1/5

P(playing 2 or more instruments) = 96/800 = 3/25.
Then, the probability of playing exactly one instrument is given by:
P(playing 1 or more instruments) - P(playing 2 or more instruments) = 1/5 - 3/25 = 2/25.

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PhD in Applied Mathematics
Love GMAT Quant questions and running.

Math Expert
Joined: 02 Sep 2009
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Kudos [?]: 96439 [0], given: 10751

Re: In a group of 800 people, 1/5 play at least one instrument.. [#permalink]

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13 Jul 2013, 23:11
Bumping for review and further discussion.
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Re: In a group of 800 people, 1/5 play at least one instrument..   [#permalink] 13 Jul 2013, 23:11
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