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Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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21 Apr 2006, 03:44
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Of a group of people, 10 play piano, 11 play guitar, 14 play violin, 3 play all the instruments, 20 play only one instrument. How many play 2 instruments?
A. 3
B. 6
C. 9
D. 12
E. 15



Director
Joined: 06 Feb 2006
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I would also need a clear instructions on this puzzle



Director
Joined: 24 Oct 2005
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Location: London

I get the ans as 12.
10 play piano,
11 play guitar,
14 play violin.
Out of this 3 people play all 3. Remaining = 32
20 play only 1.
So, those playing 2 out of 3 games is 3220=12



Manager
Joined: 23 Jan 2006
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is it 2?
Added & subtracted many eqs. will explain if right...



Senior Manager
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If those 3 guys who play all instruments and those 20 who play only one instrument are not from group of people stated earlier on (viz. 10 piano players, 11 guitar players and 14 violin players) and if these are the only players i.e. total no of players is 58 then answer is 12.



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gmatacer wrote: If those 3 guys who play all instruments and those 20 who play only one instrument are not from group of people stated earlier on (viz. 10 piano players, 11 guitar players and 14 violin players) and if these are the only players i.e. total no of players is 58 then answer is 12.
yeah. tricky wording. I thoght that they wera all inclusive, for a total of 35 people...
PS  I meant "3" in my original answer. Faulty arithmetic :/



Director
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Hallo,
think it is C
20=35people with 2 instruments6



Senior Manager
Joined: 05 Jan 2006
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couldn's solve but one thing is sure number of people is not 35! i will solve it tonight at home.



Senior Manager
Joined: 05 Jan 2006
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I am getting answer of 3 if it's correct I will explain...



Senior Manager
Joined: 09 Mar 2006
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2
This post received KUDOS
I think the answer is 3.
Total counted: 35 ( 10 + 11 + 14 )
however those who play all the instr. are counted 3 times , and those
who play 2 intstr. are counted 2 times hence the equation :
35 = 3 *3 + 2 *x + 20
x=3
Last edited by deowl on 21 Apr 2006, 15:27, edited 1 time in total.



VP
Joined: 21 Sep 2003
Posts: 1057
Location: USA

It the Q is interpreted as "exactly 2": then it is 3
If the Q is interpreted as "atleast 2": then it is 6
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Director
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ON a second thought agree with 3



Senior Manager
Joined: 08 Jun 2004
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Location: Europe

Vote for 6 people, so the answer is 'B'.
10 play piano, 11 play guitar, 14 play violin,
3 play all the instruments,
20 play only one instrument.
Solved with Vienne diagram.
103+113+143 = 26,
2620= 6 people.



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Re: Group of people [#permalink]
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21 Apr 2006, 13:34
getzgetzu wrote: Of a group of people, 10 play piano, 11 play guitar, 14 play violin, 3 play all the instruments, 20 play only one instrument. How many play 2 instruments?
A. 3 B. 6 C. 9 D. 12 E. 15
Consider the following venn diagram:
build the following equations:
10 people play piano:
a+x+y+3=10
11 play guitar:
b+y+z+3=11
14 play violin:
c+x+z+3=14
20 play only 1 instrument:
a+b+c=20
How many play 2 instruments:
x+y+z = ?
add the first 3 eqs together:
a+b+c+2x+2y+2z+9=35
we know a+b+c=20
so
20+2x+2y+2z+9=35
2x+2y+2z=6
x+y+z=3



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Re: Group of people [#permalink]
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22 Apr 2006, 03:34
kook44 wrote: getzgetzu wrote: Of a group of people, 10 play piano, 11 play guitar, 14 play violin, 3 play all the instruments, 20 play only one instrument. How many play 2 instruments?
A. 3 B. 6 C. 9 D. 12 E. 15 Consider the following venn diagram: build the following equations: 10 people play piano: a+x+y+3=10 11 play guitar: b+y+z+3=11 14 play violin: c+x+z+3=14 20 play only 1 instrument: a+b+c=20 How many play 2 instruments: x+y+z = ? add the first 3 eqs together: a+b+c+2x+2y+2z+9=35 we know a+b+c=20 so 20+2x+2y+2z+9=35 2x+2y+2z=6 x+y+z=3
Thanks for the detailed explaination. I somehow always make mistakes with the venn diagrams.



Director
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Re: Group of people [#permalink]
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22 Apr 2006, 04:04
kook44 wrote: getzgetzu wrote: Of a group of people, 10 play piano, 11 play guitar, 14 play violin, 3 play all the instruments, 20 play only one instrument. How many play 2 instruments?
A. 3 B. 6 C. 9 D. 12 E. 15 Consider the following venn diagram: build the following equations: 10 people play piano: a+x+y+3=10 11 play guitar: b+y+z+3=11 14 play violin: c+x+z+3=14 20 play only 1 instrument: a+b+c=20 How many play 2 instruments: x+y+z = ? add the first 3 eqs together: a+b+c+2x+2y+2z+9=35 we know a+b+c=20 so 20+2x+2y+2z+9=35 2x+2y+2z=6 x+y+z=3
Very nice explanation...



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It is the fastest method indeed!
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Senior Manager
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the question says how many people play 2 instruments....does this mean atleast 2 instruments or only two instruments ?
depending on this the answer would be 3 or 6 ?



Senior Manager
Joined: 08 Jun 2004
Posts: 495
Location: Europe

1. Need the Prof's explanation. Professor where are you?
2. Need the OA.



GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

M8 wrote: 1. Need the Prof's explanation. Professor where are you? 2. Need the OA.
Kook's method is the way I did it. I'm surprised we even picked the same algerbraic expressions A,B,C, x,y,z!!
x = 3 should be the answer.







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