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Sets problem (piano and flute)

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by anujan007 » Thu Jul 05, 2012 4:39 pm
1/3 of the students in the class play the flute and 2/3 of those students play the piano. How many students play neither the flute or the piano if 20% of the 270 students play both instruments and 50% play only 1?

A) 30
B) 45
C) 60
D) 75
E) 105

OA : D
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by anujan007 » Thu Jul 05, 2012 4:43 pm
I encountered this question on one of the sites with sample questions. Once again not sure if this is a correct question at all in the first place. The thing that particularly stumped me is the occurrence of 270 in the question stem.

I ended up going for B. My approach was using the Sets Table (Flute vs Piano). I tried solving it again a while ago and still not arriving at the OA. I will post my approach post a few feedback comments are received.
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by Anurag@Gurome » Thu Jul 05, 2012 7:50 pm
anujan007 wrote:1/3 of the students in the class play the flute and 2/3 of those students play the piano. How many students play neither the flute or the piano if 20% of the 270 students play both instruments and 50% play only 1?
We can write the situation using any of the following,
  • Total = Only flute + Only piano + Both + None ............ (A)
    Total = Flute + Piano - Both + None .......................... (B)
Now, Total = 270
(Only flute + Only piano) = 50% of 270
Both = 20% of 270

Hence, none = (100 - 50 - 20)% = 30% of 270 = 81
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by theCEO » Thu Jul 05, 2012 11:28 pm
Anurag@Gurome wrote:
anujan007 wrote:1/3 of the students in the class play the flute and 2/3 of those students play the piano. How many students play neither the flute or the piano if 20% of the 270 students play both instruments and 50% play only 1?
We can write the situation using any of the following,
  • Total = Only flute + Only piano + Both + None ............ (A)
    Total = Flute + Piano - Both + None .......................... (B)
Now, Total = 270
(Only flute + Only piano) = 50% of 270
Both = 20% of 270

Hence, none = (100 - 50 - 20)% = 30% of 270 = 81
Hi Anurag,

What would you say the values of only piano and only flutes are?
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by anujan007 » Sun Jul 08, 2012 3:17 pm
Anurag@Gurome wrote:
anujan007 wrote:1/3 of the students in the class play the flute and 2/3 of those students play the piano. How many students play neither the flute or the piano if 20% of the 270 students play both instruments and 50% play only 1?
We can write the situation using any of the following,
  • Total = Only flute + Only piano + Both + None ............ (A)
    Total = Flute + Piano - Both + None .......................... (B)
Now, Total = 270
(Only flute + Only piano) = 50% of 270
Both = 20% of 270

Hence, none = (100 - 50 - 20)% = 30% of 270 = 81
I followed the same approach (using sets table) and reached the answer of 81 myself. However this answer is not present in the choices. This led to my statement in my 2nd comment that I am not sure if this question is even correct as such. :(
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by theCEO » Sun Jul 08, 2012 8:13 pm
I am having problems with this question as well. I tried one approach got one answer; worked my ways backwards and got a different answer :(
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by Anurag@Gurome » Sun Jul 08, 2012 10:24 pm
anujan007 wrote:I followed the same approach (using sets table) and reached the answer of 81 myself. However this answer is not present in the choices. This led to my statement in my 2nd comment that I am not sure if this question is even correct as such. :(
The question is not properly constructed.
There are conflicting information which leads to different scenarios.

If we consider "20% of the 270 students play both instruments", then number of students who plays both = 20% of 270 = 54

However, if we consider "1/3 of the students in the class play the flute and 2/3 of those students play the piano", then number of students who plays both = 2/3 of 1/3 of 270 = (2/3)*(1/3)*(270) = 60
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by theCEO » Mon Jul 09, 2012 1:44 am
Perfect. I thought I was the only one who had a problem with this question.
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