If f is a function defined for every positive integer x in s

$${x^2} \cdot f\left( x \right) = {2^{8 - x}}\,\,\,\,\left( * \right)$$
$$? = 100 \cdot f\left( 5 \right)$$
$$x = 5\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,25 \cdot f\left( 5 \right) = {2^3}\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,4} \,\,\,\,? = 4 \cdot {2^3} = 32$$

The correct answer is (C).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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