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

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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
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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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21 Apr 2006, 04:24
I would also need a clear instructions on this puzzle
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21 Apr 2006, 06:06
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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21 Apr 2006, 06:44
is it 2?
Added & subtracted many eqs. will explain if right...
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21 Apr 2006, 06:54
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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21 Apr 2006, 06:56
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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21 Apr 2006, 08:00
Hallo,
think it is C
20=35-people with 2 instruments-6
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21 Apr 2006, 08:30
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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21 Apr 2006, 09:05
I am getting answer of 3 if it's correct I will explain...
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21 Apr 2006, 10:23
2
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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21 Apr 2006, 10:27
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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21 Apr 2006, 10:35
ON a second thought agree with 3
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21 Apr 2006, 12:07
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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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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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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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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23 Apr 2006, 21:13
It is the fastest method indeed!
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Thanks,
Zooroopa

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23 Apr 2006, 21:59
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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24 Apr 2006, 03:33
1. Need the Prof's explanation. Professor where are you?
2. Need the OA.
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28 Apr 2006, 08:19
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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