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Senior Manager
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Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
 21 Apr 2006, 03:44
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
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Director
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I would also need a clear instructions on this puzzle 
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Director
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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 32-20=12
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Manager
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is it 2?
Added & subtracted many eqs. will explain if right...
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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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Manager
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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 :-/
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Director
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Hallo,
think it is C
20=35-people with 2 instruments-6
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Senior Manager
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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.
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Senior Manager
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I am getting answer of 3 if it's correct I will explain...
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Senior Manager
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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.
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VP
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It the Q is interpreted as "exactly 2": then it is 3
If the Q is interpreted as "atleast 2": then it is 6
_________________
"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."
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Director
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ON a second thought agree with 3
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Director
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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.
10-3+11-3+14-3 = 26,
26-20= 6 people.
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Manager
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Re: Group of people [#permalink]
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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Manager
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Re: Group of people [#permalink]
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.
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Director
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Re: Group of people [#permalink]
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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Manager
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It is the fastest method indeed!
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Thanks,
Zooroopa
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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 ?
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Director
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1. Need the Prof's explanation. Professor where are you? 
2. Need the OA.
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GMAT Club Legend
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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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close
