2. In 6th grade class a, there are 24 students. Half of the students in this class play an instrument. Also, $\frac{5}{8}$ of the students in this class sing in the choir. If it is known that more than a third, but less than $\frac{5}{12}$ of the students in 6th grade class a both play an instrument and sing in the choir, how many students in this class neither play an instrument nor sing in the choir?
2. In 6th grade, there are 24 students. Half of the students in this class play an instrument. Also, $\frac{5}{8}$ of the students in this class sing in the choir. If it is known that more than a third, but less than $\frac{5}{12}$ of the students in 6th grade class 6a both play an instrument and sing in the choir, how many students in this class neither play an instrument nor sing in the choir?

## Solution.

The number of students who play an instrument is $24: 2=12$.

$1 \text{ POINT}$

In the choir, $\frac{5}{8} \cdot 24=15$ students sing.

$1 \text{ POINT}$

Since $24: 3=8, \frac{5}{12} \cdot 24=10$,

1 POINT

it follows that 9 students both play an instrument and sing in the choir.

$1 \text{ POINT}$

![](https://cdn.mathpix.com/cropped/2024_05_30_0b00c6f52e60bdba44a4g-13.jpg?height=408&width=1037&top_left_y=430&top_left_x=241)

The number of students who play an instrument, sing in the choir, or do both is

$(12-9)+9+(15-8)=18$.

1 POINT

$24-18=6$ students neither play an instrument nor sing in the choir.

1 POINT

Note: It is not necessary to draw a Venn diagram in the solution. A correct solution that includes all necessary calculations and conclusions is fully recognized even without a Venn diagram.