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

Question

In a certain orchestra, each musician plays exactly one instrument. If 1/5 of the musicians play brass instruments, and the number of musicians playing wind instruments is 2/3 greater than the number of musicians playing brass instruments, what fraction of the musicians in the orchestra play neither brass nor wind instruments?

A. 1/5
B. 2/5
C. 7/15
D. 8/15
E. 2/3

A. 1/5
B. 2/5
C. 7/15
D. 8/15
E. 2/3

Archit3110 · Answer

I solved it using 2x2 matrix; take total instruments as 15.. 
answer would be 7/15 option c

ScottTargetTestPrep · Answer

Solution:

Since 1/5 of the musicians play brass instruments and 1/5 x 5/3 = 1/3 of musicians play wind instruments, then 1 - 1/5 - 1/3 = 15/15 - 3/15 - 5/15 = 7/15 of the musicians in the orchestra play neither brass nor wind instruments.

Answer: C

SuryaNouliGMAT · Answer

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

Abhishek009 · Answer

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)

StarTrooper · Answer

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.

Mona2019 · Answer

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.

Posted from my mobile device

ScottTargetTestPrep · Answer

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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