Step 1: Read the question for the key word.
Two wires share the same material but differ in length (ratio $1:2$) and radius (ratio $1:2$). We are asked for the ratio of their specific resistances.
Step 2: Recall what specific resistance means.
Specific resistance is just another name for resistivity, written $\rho$. It is a built-in property of the material itself, like a fingerprint.
Step 3: Separate resistance from resistivity.
The total resistance is $R = \dfrac{\rho L}{A}$, and that surely changes with length $L$ and area $A$. But $\rho$ alone is not the same as $R$; it is the constant of proportionality that stays put.
Step 4: Ask what $\rho$ actually depends on.
Resistivity depends only on the kind of material and its temperature. It does not care about how long the wire is or how thick it is.
Step 5: Apply this to our two wires.
Both wires are made of the same material, so their resistivities are identical. The length and radius information is a deliberate distraction here. \[ \rho_1 = \rho_2 \]
Step 6: Write the ratio.
\[ \rho_1 : \rho_2 = 1 : 1 \] which is option (C).
\[ \boxed{\rho_1 : \rho_2 = 1 : 1} \]