# 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:

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

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