With no calculators allowed in the PMDC MDCAT, physics questions are engineered to test proportional scaling, orders of magnitude, and unit analysis rather than tedious arithmetic.

The Proportional Scaling Rule

When a question asks "If the radius of a wire is halved, what happens to its resistance?", do not plug in $3.14159$ for $\pi$. Use proportionality:

$$R = \rho \frac{L}{A} = \rho \frac{L}{\pi r^2} \implies R \propto \frac{1}{r^2}$$

If $r \to r/2$, then $R \to \frac{1}{(1/2)^2} = 4R$. The resistance quadruples instantly.