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[#permalink]
I'll check out your recommendation on probability.
By the way, I got such a question:

In a music class, there are 10 students playing violin, 15 students playing piano, and 7 students playing trumpets. 3 students play all 3, and 20 students play two instruments. How many play only 1 instrument?
(I'm trying to remember the best I can, so if this doesn't make sense, apologies in advance). How do you solve this?

Thanks.
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sn157 wrote:
I'll check out your recommendation on probability.
By the way, I got such a question:

In a music class, there are 10 students playing violin, 15 students playing piano, and 7 students playing trumpets. 3 students play all 3, and 20 students play two instruments. How many play only 1 instrument?
(I'm trying to remember the best I can, so if this doesn't make sense, apologies in advance). How do you solve this?

Thanks.


don't worry. keep the spirit high and start working on the weak areas.
good luck..!

anyways..ans to your ques:

see the attachment herewith..
X=3
P+V+T+X+(PT+VT+VP) = total
P+V+T+3+20 = 10+15+7
GIVES 9.
Attachments

untitled.JPG
untitled.JPG [ 41.36 KiB | Viewed 2325 times ]

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When did you take it?
In December?
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The question you asked is pretty easy. It sounds like you just got beat by the jitters.
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I took it in December btw.

Also, I'm still pondering about this question. Shouldn't it be:
Total = 3(# of people playing all three) + 2(# of people playing only 2) +
# of people playing only 1 ?
& Total = people playing violin + people playing trumpet + people playing piano. In the example I gave previously, the math doesn't add up - maybe I remembered the numbers wrong.

Say if:
# of people playing all 3 instruments is 3
# of people playing 2 instruments is 10


Piano: 15

A B C
D E F G H I J K L M
N O

Trumpet: 15

A B C
D E F G H I J K L M
P Q

Violin: 7
A B C
R S T U

So total = 15+15+ 7 = 37
= 3(3) + 2(10) + 8 = 37
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Why did you use the number of instruments played as a quantitative factor? The number of instruments played should be used ONLY as a qualitative qualifier and thus should have no bearing on the final answer.
I think the best explanation to this is given by DJ with the Venn diagram. Otherwise, the formula should be:

# of students playing 1 instrument = sum of the # of students playing either instruments - # of students playing 2 instruments - # of students playing all 3 instruments.

And according to the second set of numbers given in your other question:

# of students playing 1 instrument = (15+15+7) - (10) - (3) = 24
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IMO the numbers provided are not correct. Refering to the VENN diagram posted above, the solution should be

P+V+T = TotalPiano + TotalViolin + TotalTrumpet - 2VP - 2PT -2VT -3X
= 10+15+7 - 2*(VP+PT+VT) - 3X
= 32 - 2*20 - 3*3
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