9.A

9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5?

Result

n =  14

Solution:

$3 \ ... \ prime number \ \\ 6=2 \cdot 3 \ \\ 9=3^2 \ \\ LCM(3, 6, 9)=2 \cdot 3^2=18 \ \\ \ \\ m=LCM(3,6,9)=18 \ \\ 20 <=t <=40 \ \\ t=2m \ \\ t=2 \cdot \ m=2 \cdot \ 18=36 \ \\ n=t \cdot \ (1-1/3-1/6-1/9)=36 \cdot \ (1-1/3-1/6-1/9)=14$

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