Let $x, y, z$ be the number of students in the categories of biology, physics, and chemistry, respectively. Then, according to the problem, we get the system of equations:

$$
\left\{\begin{array} { l } 
{ 5 x = 2 ( y + z ) , } \\
{ 7 z = 3 ( x + y ) . }
\end{array} \Rightarrow \left\{\begin{array} { l } 
{ 5 x - 2 y = 2 z , } \\
{ 3 x + 3 y = 7 z }
\end{array} \Rightarrow \left\{\begin{array}{l}
21 x=20 z \\
21 y=29 z
\end{array}\right.\right.\right.
$$

This means that the minimum values can only be: $x=20, y=29$, $z=21$.
Answer: 29. Answer to option: 4-2: 11.

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