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Of the students in a certain class 10 can play piano,11 can

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Senior Manager
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Of the students in a certain class 10 can play piano,11 can [#permalink] New post 12 Jun 2008, 23:05
Of the students in a certain class 10 can play piano,11 can play guitar , 14 can play violon
if 3 students can play all three instruments and 20 can play one of the instruments , how many students can play exactly 2 of the instruments

3
6
9
12
15

what is the most optimal way of solving these kind of questions

Mnay thanks
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Last edited by vd on 13 Jun 2008, 00:11, edited 1 time in total.
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Re: of the students in a certain class [#permalink] New post 13 Jun 2008, 00:09
vdhawan1 wrote:
Of the students in a certain class 10 can play piano,11 can play guitar , 10 can play violon
if 3 students can play all the instruments and 20 can play one of the instruments , how many students can play exactly 2 of the instruments

3
6
9
12
15

what is the most optimal way of solving these kind of questions

Mnay thanks


Are you sure there is no typo in the problem?
Senior Manager
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Posts: 283
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Re: of the students in a certain class [#permalink] New post 13 Jun 2008, 00:12
alpha_plus_gamma wrote:
vdhawan1 wrote:
Of the students in a certain class 10 can play piano,11 can play guitar , 10 can play violon
if 3 students can play all the instruments and 20 can play one of the instruments , how many students can play exactly 2 of the instruments

3
6
9
12
15

what is the most optimal way of solving these kind of questions

Mnay thanks


Are you sure there is no typo in the problem?


ya i m sorry there was a typo

i have corrected it now
can u please attempt the problem now

Thanks
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Re: of the students in a certain class [#permalink] New post 13 Jun 2008, 00:28
I suppose It must be A
If 20 students play only 1 instrument than Only three students can play 2 instruments... there are no other ways :-D
However it took me 4 minutes to conclude that the best way to solve this particular task is - just to pick answer choices

What is AO?

Last edited by quantum on 13 Jun 2008, 00:33, edited 1 time in total.
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Re: of the students in a certain class [#permalink] New post 13 Jun 2008, 00:30
answer is 3,

14-3 + 11 -3 + 10 -3 = 20 + 3 + x (x is students who can play 2 instruments)
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Re: of the students in a certain class [#permalink] New post 13 Jun 2008, 23:41
friends, can someone explain it with the standard formula " : A + B +C –both – 2* All 3" ? ... maybe i´m just too tired...

cheers
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Re: of the students in a certain class [#permalink] New post 18 Jun 2008, 05:20
Yep here it is with the standard formula if u wish
might not be the shortest

let X be who play guitar and violin and NOT piano
Let Y be who play violin and piano and NOT guitar
Let Z be who play guitar and piano and NOT violin

so ( 11 - x - z - 3 (who play all 3) ) will be ppl who play only guitar
similarly ( 11-x-z) who play only violin
and ( 7-y-z) who play only piano

add all the 3 above which should equal to 20

solve for (x + y + z ) which is equal to 3
Re: of the students in a certain class   [#permalink] 18 Jun 2008, 05:20
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