In a certain orchestra, each musician plays exactly one instrument. If

Hi TTP,

Please correct my approach :

total musicians = n
brass musi = 1/5(n) = n/5
wild musi = 2/3(n) + brass musi = 2n/3 + n/5 = 13n/15

brass + wild = 16n/15
total musi = Brass + Wild + neither
n = 16n/15 + x
x= n/15
x/n = (n/15) / n = 1/15

i am not sure where i messed it up!! i tried to understand your method but the above highlighted part is bit confusing!! Please shed some light

Kudos in advance

Let total no of musicians be 15
So, Total no of brass instruments players is 3
And, Total no of wind instruments players is 5
And, Total no of musicians not playing wind instuments and brass instruments is 7
Thus, fraction of the musicians in the orchestra play neither brass nor wind instruments is 7/15, Answer must be (C)

Can you please help me understand the 5/3 number, how is that arrived? I am stuck at that 5/3 number, the question says 2/3 greater that Brass brass is 1/5 of total. Please explain.

The 5/3 number is got through the following way:
If the number of brass players be X
Then number of wind players will be 2/3X + X =5/3 X
As wind players are 2/3 greater than that of brass players .

Now X which is number of brass players is 1/5 of the total number of musicians .
So 5/3X =5/3*1/5*total number of musicians
which is equal to 1/3 of total number of musicians.

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The mistake in your calculation is interpreting the sentence "the number of musicians playing wind instruments is 2/3 greater than the number of musicians playing brass instruments" as "the number of musicians playing wind instruments is 2/3 of the total number of musicians plus the number of musicians playing brass instruments". In this context, "2/3 greater than" should be interpreted as "5/3 times as much" (since 1 + 2/3 = 5/3). For such questions, it is really helpful to think in terms of percentages. 2/3 is roughly 66.66 percent; so we can actually rephrase the sentence as "the number of musicians playing wind instruments is 66.66% greater than the number of musicians playing brass instruments", which means that the number of musicians playing wind instruments is 166.66% of the number of musicians playing brass instruments.

Also, in your solution, the line following the equation "n = 16n/15 + x" is incorrect; if we solve this equation for x, we obtain -n/15, not n/15.

The highlighted part in my solution first calculates the fraction of musicians playing wind instruments. As I mentioned above, "2/3 greater than" means "5/3 times as much"; so the number of musicians playing wind instruments is 1/5 * 5/3 = 1/3 of the total number of musicians. Now, since each musician plays exactly one instrument, we have the following equality:

1 = fraction playing brass + fraction playing wind + fraction playing neither

fraction playing neither = 1 - fraction playing brass - fraction playing wind

fraction playing neither = 1 - 1/5 - 1/3 = 15/3 - 3/15 - 5/15 = 7/15

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