I2.3 There are less than $4 Q$ students in a class. In a mathematics test, $\frac{1}{3}$ of the students got grade $A$, $\frac{1}{7}$ of the students got grade $B$, half of the students got grade $C$, and the rest failed. Given that $R$ students failed in the mathematics test, find the value of $R$.
$4 Q=56$, let the number of students be $x$, then $x$ is divisible by 2,3 and 7 .
i.e. $x$ is divisible by 42 , as $x<56$, so $x=42$
$R=$ number of students failed in mathematics $=42 \times\left(1-\frac{1}{3}-\frac{1}{7}-\frac{1}{2}\right)=1 ; R=1$