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Of a group of people, 10 play piano, 11 play guitar, 14 play

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Senior Manager
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Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink] New post 21 Apr 2006, 02:44
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
Director
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 [#permalink] New post 21 Apr 2006, 03:24
I would also need a clear instructions on this puzzle :)
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 [#permalink] New post 21 Apr 2006, 05:06
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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 [#permalink] New post 21 Apr 2006, 05:44
is it 2?
Added & subtracted many eqs. will explain if right...
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 [#permalink] New post 21 Apr 2006, 05:54
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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 [#permalink] New post 21 Apr 2006, 05:56
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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 [#permalink] New post 21 Apr 2006, 07:00
Hallo,
think it is C
20=35-people with 2 instruments-6
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 [#permalink] New post 21 Apr 2006, 07:30
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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 [#permalink] New post 21 Apr 2006, 08:05
I am getting answer of 3 if it's correct I will explain...
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 [#permalink] New post 21 Apr 2006, 09:23
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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, 14:27, edited 1 time in total.
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 [#permalink] New post 21 Apr 2006, 09:27
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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 [#permalink] New post 21 Apr 2006, 09:35
ON a second thought agree with 3
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 [#permalink] New post 21 Apr 2006, 11:07
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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Re: Group of people [#permalink] New post 21 Apr 2006, 12:34
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:
Image
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] New post 22 Apr 2006, 02:34
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:
Image
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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Re: Group of people [#permalink] New post 22 Apr 2006, 03:04
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:
Image
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...
Manager
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 [#permalink] New post 23 Apr 2006, 20:13
It is the fastest method indeed!
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Thanks,
Zooroopa

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 [#permalink] New post 23 Apr 2006, 20:59
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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 [#permalink] New post 24 Apr 2006, 02:33
1. Need the Prof's explanation. Professor where are you? :wink:
2. Need the OA.
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 [#permalink] New post 28 Apr 2006, 07:19
M8 wrote:
1. Need the Prof's explanation. Professor where are you? :wink:
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!! :lol:

x = 3 should be the answer.
  [#permalink] 28 Apr 2006, 07:19
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