The total number of students is 24 .
If the ratio of girls to boys is $g: b$, then we can write:

$$
\(g=k x, \quad b=k y, \quad g+b=k(x+y)=24\)
$$


So $\(k(x+y)\)$ must divide 24 evenly for the ratio $x: y$ to be possible with integer numbers of girls and boys.

Equivalently: $x+y$ must divide 24 because $\(k=\frac{24}{x+y}\)$ must be a positive integer.
Let's test each:
(A) $\(1: 2 \rightarrow x+y=1+2=3 \rightarrow 24 / 3=8\)$ integer $\(\rightarrow\)$ possible.
(B) $\(3: 5 \rightarrow 3+5=8 \rightarrow 24 / 8=3\)$ integer $\(\rightarrow\)$ possible.
(C) $\(1: 1 \rightarrow 1+1=2 \rightarrow 24 / 2=12\)$ integer → possible.
(D) $\(4: 3 \rightarrow 4+3=7 \rightarrow 24 / 7\)$ not integer → impossible.
(E) $\(7: 5 \rightarrow 7+5=12 \rightarrow 24 / 12=2\)$ integer → possible.

Thus, $\(\mathbf{D}\)$ is impossible.