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Of a group of people, 10 play piano, 11 play guitar, 14 play [#permalink]
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?

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.

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 :-/

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.

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."

Re: Group of people [#permalink]
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:

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

Re: Group of people [#permalink]
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:

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.

Re: Group of people [#permalink]
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:

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